Year 4 Multiplication and Divisionschools.oxfordshire.gov.uk/.../Primary_Mathematics_Acti… ·...

Primary Mathematics Activiti es

Every Child Counts

April 2015

Tom Filmer – St Joseph’s Catholic Primary School, Oxford

Rebecca Clare, John Blandy Primary School, Abingdon

Stephanie Cottriall, St Amand’s Catholic Primary School, Wantage

Contents

Multiplication and Division

Number Facts

Odd and Even numbers

Addition and Subtraction

Place Value

NCETM Activities

Year 1

Number and Place Value



Measurement

Year 2




Measurement

Year 3




Fractions

Measurement

Year 4




Fractions

Measurement

Year 5




Fractions

Measurement

Year 6




Fractions

Ratio and Proportion

Measurement


Numicon multiplication and division

Use piles of ten 5-shapes, 3-shapes, 4-shapes and 10-shapes and x/÷ dice/spinner.

Children take some shapes from one of the piles and spread them on the table. Children then spin a multiplication or division sign and write down the multiplication or division fact they can see from the shapes.

Click for illustration

Using array for multiplication (Fill the board)

Roll 2 dice (6 sided or 10-sided) and multiply together to get the calculation. Use Cuisenaire to make array and draw around it. Write calculation inside to own the square.

To play it as a game, count the total number of squares filled in on a completed board.


Real world arrays

Find examples of arrays used in the real world eg egg boxes, chocolate boxes.


Handful of points – using and understanding the vocabulary of multiplication and division

Select a handful of points and arrange them in arrays. Score points for factors, prime numbers and square numbers.


Coin counting – linking multiplication to counting

Practise counting piles of 1p, 2p, 5p and 10p coins. Link totals to the relevant number sentence.

Repeated addition on a number line

Using a number line, place same length Cuisnaire rods to replicate repeated addition. Link the physical representation to the relevant number sentence.

Number Facts

Numicon balance scales

Develop number bonds knowledge by using Numicon on balance scales.


Number detectives

Guess the secret number based on number facts. Children asked questions to solve the mystery eg Odd or even, greater/smaller than, multiple of. Use a number square to cross off numbers that are ruled out.

Number bonds using bead strings (Beads to 10)

Thread a number of beads onto a string to develop recall of number bonds. Split a number of the beads off and calculate how many beads will be left.


Function machine robot

Make a function machine robot with an input hole and output hole. Use to work on three types of answer:

Give an input and a function and name the output Give an output and a function and name the input using an inverse

operation Give an input and an output and name the function

Linking number sentences to word problems

Use the ECC connections sheet to link number sentences, word problems and illustrations.

Shut the box

Roll two dice (6 or 10 sided) and multiply, add or subtract the numbers together to get a score. Fold down the digits in your answer. The winner is the 1st to close down all their digits.


Odd and Even numbers

Odd and even stories

Click on the link below to find a story and illustration to develop knowledge of odd and even.

http://www.counton.org/magnet/minus/bugs/bugs2.html

The children could make their own bugs using plasticine and write their own story.

Odd and even rhymes

Help recall of odd and even numbers by using rhymes:

1,3,5,7,9, I love odd numbers all the time

0,2,4,6,8, even numbers they are great.

Deliver the post

Make a street with even numbered houses on one side and odd numbered houses on the other. Get the children to deliver letters to the correct houses. Question the children whether the letter has an even or odd numbered address.

Odd and even collection challenge

A two player game – spread a selection of numbered cards out. One child collects odd numbers and the other collects even numbers. The children have a limited amount of time to collect as many of their type of number as possible. Look at the collection – score +1 point for each correct number, -1 point for each incorrect number. The child with the most points wins.

http://www.counton.org/magnet/minus/bugs/bugs2.html

Odd and even grab bag

Choose an odd or even Numicon number out of a grab bag by using the sense of touch. Explain why the number is odd or even. Can the child name which number they have chosen?

Odd and even with coins

Choose a number of 10p pieces and 1p pieces. Can the children work out whether the total is odd or even? This focuses the importance of the number of ones as the key to odd or even.


I’m putting them together (Game for two children)

Children choose two pieces of Numicon e.g. 3 and 4.

One posts them through and makes the addition sum – “I’m putting together 3 and 4 and it equals 7”

The other posts it back making the subtraction – “I have 7, I take away 4 and I am left with 3”

Counting with stuff

Totalling multiple pieces of Numicon and linking them to a 100 square


Next 10

Take pieces of Numicon from a feely bag and recognise the two-digit number that has been made. Work out which number to add to make the number bond to the next 10 and record as a number sentence


What’s left

One player chooses a piece of Numicon and hides it behind their back. They then ask a subtraction question – eg “I have 9 and I take away 1. What’s left?” The other players choose the piece of Numicon which answers the question. The children all compare their answers.

Bridging through 10 (using a 10 egg box)

With an egg box which resembles a Numicon 10, children complete addition questions which bridge over 10 by filling the box and seeing what is left.


Chase game

Set out a number line from 0 to 100. One player starts on 50, the other on 0. The chasing player rolls a dice, doubles the number and counts on along the number. The chased player rolls the dice and just counts on the number rolled.

The game allows different questioning possibilities such as asking where they will finish when counting on, how many more steps they need to catch up as well as practising doubling.

Place Value

Highest wins

Ordering game using cards to 100 where players try to win the most tricks by playing their hand of 5 cards.


Nasty game

Children to have a blank TU or HTU frame. Children decide if the highest or lowest number wins. They choose from a pile of 0-9 digit cards alternately and then decide which column to place their digit card in. When the place value frames are full, compare the numbers made and see who has won.

Greater than/less than – Heads and Toes

From a pack of 0-100 cards, children choose a card which becomes the target number. They then choose a further card. If the number is greater than the target number, the children put their hands on their head. If the number is less than the target number, they touch their toes.

Double dice

Doubling game with dice that involves placing digits in a TU frame to try and get nearest to a target number.


Numicon multiplication and division

©Numicon 2006

Fill the board

Arrays

Handful of Points

Numicon balances

©Numicon 2006

Beads to 10

©Jon Kurta – Scholastic 1997

Shut the box

Double dice

© Fizz Buss LDA

Highest wins

©Numicon 2006

Counting with stuff

©Numicon 2006

Next 10

©Numicon 2006

Bridging through 10 (using a 10 egg box)

Year 1 Number and Place Value

Programme of Study statements

Activities

A B C D E F G

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

given a number, identify one more and one less

identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

read and write numbers from 1 to 20 in numerals and words

Activity A - Skipping: Counting and timing actions

See how many skips, catches, goals, circuits you can do without stopping. Can you beat yesterday’s score? How many seconds does it take you to get dressed/undressed, do a circuit, 20 skips? Can you do it quicker than last time? Time with a timer and record on a number line.

Activity B - Constant function

On a calculator one child keys in 80 + 1, then keeps pressing =. (or press -1===). Their friend has to predict the next number before = is pressed. Use this function to find how to write numbers crossing tens boundaries or to go over 100. Write numbers on an empty number line or fill in a 100 to 200 number square. Press + 2 = = to count in 2s.

Activity C - Fingers and hands

Count fingers on lots of hands by counting in 5s or 10s. Can the children challenge themselves to find out the number of fingers and/or hands on each alien?

Activity D - Incy Wincy (pdf)

Playing number games, including board games like Snakes and Ladders, has been proven by research to increase children’s understanding of relative number size as well as counting. This ‘Incy Wincy’ document from Nrich is full of ideas and questions for the classroom.

Activity E1 - Tidying (pdf)

Children count resources indoors and outdoors to check none have got lost. They can make labels for containers to show how many there should be, using numerals and words.

Activity E2 - Collecting (pdf)

Children can make collections of everyday objects, count them in different ways, sort them and label them

Activity F - Number Rhymes (pdf)

Number rhymes encourage children to predict the result of taking one away, or more unusually of adding one, as with 10 currant buns. In year 1, number rhymes can be linked to staircase images and number lines to help children to see the ‘successor function’ (one more / less than) pattern.

Activity G - Pounds in the pig

Put 8 coins in a piggy bank so they cannot be seen –check the child knows how many there are, then take one out and ask how many there are. Children can play this in pairs. (You can obviously use plastic coins or any objects and any container, box, cloth or screen.) This activity allows you to see if children can apply their knowledge of one more or less to a practical problem.

Year 1 Addition and Subtraction

Programme of study statements

Activities

A B C D

read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs

represent and use number bonds and related subtraction facts within 20

add and subtract one-digit and two-digit numbers to 20, including zero

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as7 = ? – 9

Activity set A

It is really important that the children understand the equals sign as a sign of equivalence, that what is on one side of it has the same value as what is on the other. Many children develop the misconception that the answer to a calculation is on the right-hand side of the equals sign. To ensure that they don’t develop this misconception you could give them a set of balance scales and some interlocking cubes. They can then explore adding different numbers of cubes on each side of the balance to find out what happens. For example, if they put 5 cubes on one side and 10 on the other, the scales won’t balance. They can then find out how many they need to add to the side with 5 cubes so that they balance. They could record this in a number sentence such as, 5 + 5 = 10 or 10 = 5 + 5.

They could explore subtraction in the same way, for example, they put 20 cubes on one side and 12 on the other. They then find out how many they should take away from the 20 cubes so that the scales balance with 12 cubes on each side. Again they could record this in a number sentence such as, 20 – 8 = 12

You could give the children missing number sentences and ask them to find the solutions using the scales, for example:

? + 3 = 12 (put 12 cubes on one side of the balance and 3 on the other, add cubes to the 3 until they balance)

8 + ? = 15 (put 15 cubes on one side of the balance and 8 on the other, add cubes to the 8 until they balance)

20 - ? = 13 (put 20 cubes on one side of the balance and 13 on the other, take cubes from the 20 until they balance)

? – 4 = 7 (put 7 cubes on one side of the balance and another amount on the other, they explore how many they need so that when they take 4 away the scales will balance)

When the children are confident at doing this, they could then use the bar model and draw the problem, for example:

? 3

12

8 ?

15

20

? 13

?

4 7

Activity set B

The children need to learn number bonds or number pairs for all numbers to 20 not simply those that make 10 and 20.

You could give them counters or cubes for the number you wish to focus on and ask the children to put them into two groups. How many different groups can they make. They would need to keep track of their work by writing number sentences, for example:

Making 7

1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7, 4 + 3 = 7 and so on…

You might be interested in using ‘Number pair Love Hearts’ from the "What makes a good resource?" section of the NCETM website. The instructions and downloadable resources are available. You could adapt this for any numbers to 20.

Activity set C

Give the children calculations to solve that involve adding and subtracting numbers to 20. They should use manipulatives, such as bead strings, cubes or counters, so that their experiences are concrete. Alongside these encourage them to write the appropriate number sentences. You could also encourage them to draw number lines to show what they have done.

You could ask them to write the age they are on a piece of paper. They then try to make their age using as many different additions and subtractions as they can. Here is an example:

Activity set D

You could give the children problems such as these to solve:

Harry had 6 marbles. His friend gave him 12 more. How many marbles does Harry have now?

They could solve these using the bar model as described for the first requirement, for example:

6 + 12

6 12

?

The children could place the correct number of objects in the two numbered sections of the bar and then count them all to find the missing number.

Holly 13 biscuits. She ate 5. How many does she have left

13-5

13

5 ?

You could ask them ‘What number am I thinking of?’ type questions, for example:

I am thinking of a number .When I add 3, I get 8. What number am I thinking of? I am thinking of a number. When I take away 4, I get 7. What number am I thinking of?

You could use straws, dice and elastic bands and play a game that will introduce the children to the concept of exchange:

Throw a dice. Collect that number of straws. When you have 10 make a bundle using an elastic band. The winner is the first player to make more than 20.

This can also be done for subtraction:

Take two bundles of straws. Throw the dice. Take that number of straws away. (The children will need to ‘unbundle’ one

bundle) The winner is the first player to lose all their straws.

Year 1 Multiplication and Division

Programmes of Study statements

Activities

A B C D

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of a teacher.

Actvity A - Noah’s Ark

Give the children the opportunity to count in twos, finding the total number of animals on board the Ark. As the children gain fluency counting in twos, start at different numbers and perhaps changing from using concrete objects, to jumping in twos along a number line. Further uses could be to find the number of groups of two on the ark, again initially using tangible objects, then moving on to using a number line and demonstrating repeated subtraction.

Activity B - Arrays powerpoint

This resource is based in ‘PowerPoint’. The teacher can set simple multiplication word problems for the children to solve. It is also useful for modelling arrays and how to write a multiplication sentence.

Activity C - Whole class counting sessions

For this activity the children themselves are the objects to count. You can count in twos to find the number of shoes in a group, count fingers on hands in fives and number of toes in tens. To extend the children you can ask them to model how to write down this calculation or alter it to practise their division facts from the 2, 5 and 10 times tables.

Activity D - NRICH Share Bears:

A lovely investigation involving the children in division by sharing, and early introduction to the concept of remainders.

Year 1 Measurement


Activities

A B C D

compare, describe and solve practical problems for:

lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half)

mass or weight (e.g. heavy/light, heavier than, lighter than) capacity/volume (full/empty, more than, less than, quarter) time (quicker, slower, earlier, later)

measure and begin to record the following:

lengths and heights mass/weight capacity and volume time (hours, minutes, seconds)

recognise and know the value of different denominations of coins and notes

sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening

recognise and use language relating to dates, including days of the week, weeks, months and years

tell the time to the hour and half past the hour and draw the hands on a clock face to show these times

Activity set A

You could ask groups of four children to collect five items from around the classroom and order them according to criteria of their own. They could share their ideas and then order according to a different criterion and then another. Encourage them to think about ordering according to, for example, length or height and weight.

Again, working within a group of four, you could give each child a piece of plasticine and ask them to roll it to make the longest worm that they can in a minute. They then order their ‘worms’ from shortest to longest. The shortest worm could become a (non-standard) unit and children can estimate and measure how many worms long different things are. They could then measure the shortest to the nearest centimetre and use this to estimate the lengths of the others. Once they have estimated the ’worms’ they measure them to see how close their estimates were.

You could give the children a selection of containers, measuring jugs for one or two litres and access to water. They could then find out each container’s capacity to the nearest litre.

You could play a ‘Just a minute’ type game so that the children become familiar with the vocabulary related to measurement. Write a selection of words on pieces of card and then say the meaning for each one. The children need to work out the word you are describing. Time them to see how quickly they guess all the words. Do they get quicker the more they practise?

Activity set B

To help the children recognise different coins and their values, you could give them a random number of up to 100 pennies. Ask them to count these into piles of 10 and when they have exchange each pile for a 10 pence coin. For any coins left over they exchange these for two pence and/or five pence coins.

You could focus on exchanging pennies for two and five piece coins and also 10 pence coins for 20 pence, 50 pence and one pound coins.

You might be interested in giving the children 15 pennies and the task ‘Money Bags’ from Nrich

Activity set C

You could ask the children to draw a picture to show something that they do in the morning, then in the afternoon and evening. They cut these out and give them to a friend to put in the right order.

You could display a weekly time table of activities that the children do and ask questions from it, for example:

What do we do on Wednesday morning? What day comes two days after Monday? What day comes before Thursday

You could display a calendar and ask the children to write their name in that month in which their birthday occurs. Again, ask questions from this, such as:

Who has a birthday between June and September? Which month is two months after ‘Julie’s’ birthday?

You could play the ‘Just a minute’ type game as described in Activity set A but purely related to the vocabulary of time, for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening, o’clock, half past, hands, day, week, month, year.

Activity set D

Give each child a paper plate and let them use it to make their own clock with moving hands. Firstly, they write the hour numbers around the outside. Cut out hands of the right lengths so that the minute hand will touch the outside of the ‘clock face’ and the hour hand will touch the hour numbers. Help the children to attach these using a paper fastener. Call out different o’clock and half past times for the children to find on their clocks.

You could attach some of the clocks that they children made to a board which is at an appropriate height. Write times on post it notes and position one beside each clock. The children can then work with a partner to move the hands on the clocks into the correct positions for the times.



Activities

A B C D

count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward

recognise the place value of each digit in a two-digit number (tens, ones)

identify, represent and estimate numbers using different representations, including the number line

compare and order numbers from 0 up to 100; use <, > and = signs

read and write numbers to at least 100 in numerals and in words

use place value and number facts to solve problems

Activity set A

(i) You could use a counting stick to practice counting in steps of 2, 3, 5 and 10. You could also use these facts and adapt them to practice counting in steps of 20, 30, 50 and 100 and 200, 300, 500 and 1000 etc. You could ask questions as if the counting stick was a number line, for example:

What would go on this division? What would go half way between these divisions?

(ii) You could give each child a paper clip and a strip of paper that has been divided into ten sections as below:

Tell them that at one end is zero and at the other is 30. Ask them to tell you what they need to count in to get from zero to 30. Next ask them to show you where different multiples of three would go, for example 27, 18, 9. The children put their paper clip on the line that shows where the number you call out will go.

(iii) You could draw a Venn diagram on the board with two interlocking circles. Start writing multiples of 3 in one circle and five in the other until the children can tell you what the numbers in each circle have in common. They could then suggest numbers that go in each circle, in the middle and outside the circles.

(iv) You could set number problems, for example, give a series of clues that involve counting in steps of different sizes. The children try to identify your ‘mystery’ number from the clues you give, for example:

If you count in 5s you will reach my number It is an odd number It is larger than 20 but smaller than 30

You could ask the children to make up some of their own for a partner to solve.

Activity set B

The children need to develop their concept of place value. Many teachers think that if children can partition numbers into tens and ones then they understand this concept. This is not necessarily the case. There are four aspects of number value that children need to understand. These are:

Tens Ones

10 1

2 7

Positional: The digit 2 is in the tens position and the digit 7 is in the ones Multiplicative: The digit 2 is two tens (10 x 2) which is 20, the digit 7 is seven ones (1 x 7) which is

7 Additional: combine the two numbers to make the whole by addition 20 + 7 = 27 Base10: the value of the digits increase or decrease by the power of 10 as they get bigger or

smaller

You could make simple grids like this for the children to use in class and work through the ’big ideas’ of place value (in simple terms) as they make numbers to explore using digit cards. It would be a good idea to include a 100s column in your grids. Encourage the children to write the additional number sentence in figures and then the total in words. You could ask them to think of reasons why writing the number in words can help their understanding of place value.

The children should explore partitioning numbers in different ways, for example, 58 as 50+ 8, 40 + 18, 30 + 28, 20 + 28, 10 + 38.

Activity set C

It is really important that the children are given plenty of opportunities to identify and represent numbers using different representations. You could ask the children to show you, for example, 46 using:

Bead strings (4 groups of 10 and 6 singles) Base 10 apparatus (4 tens sticks and 6 cubes) Straws (4 bundles of 10 and singles) Money (four 10 pence and seven 1 pence coins) Two different coloured counters, one representing 10s and the other ones

Once they have done this practically ask them to show how to make the number on a number line: jump of 40 and then 6.

You could ask the children to make a selection of numbers using the representations above. Once they have ask them to order them onto a number line and compare pairs using < and >. You could also ask them to choose pairs of their numbers and make number sentences using = where they need to work out a missing number to make the number sentence correct, for example: 46 = 13 + ?

Activity set D

You could give the children problems such as these to solve:

Harry had 6 bundles of10 straws and 7 single straws. How many straws did he have altogether? Hamish had five 10p coins and 3 pennies. How much money did he have altogether? Sandy had 37 pennies. He wanted to change them into other coins. What are the fewest coins that

he could use? Suzie made some cakes. She put them on plates in groups of 10. She had 8 full plates and 7

cakes left over. How many cakes did she have altogether?



Activities

A B C D

solve problems with addition and subtraction:

using concrete objects and pictorial representations, including those involving numbers, quantities and measures

applying their increasing knowledge of mental and written methods

recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

a two-digit number and ones a two-digit number and tens two two-digit numbers adding three one-digit numbers

show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.

Activity set A

Use of concrete models and apparatus and helpful visual images are vital aspects of children’s mathematical activity – for all ages and all attainer groups. Knowing and using mental calculation strategies remain important in the National Curriculum. Use of manipulatives and mental strategies are practised and developed through a variety of short activities, for example:

bridging through ten adding near multiples of 10 and adjusting

Give each child a 100 square. Ask them to put a finger on the number 3 and then give a series of instructions that involve the strategies above, for example: add 9 (add 10, subtract 1), add 13 (add 8 to get to 20 and then 5), take away 11 (subtract 10 and then another one). Activities similar to this, carried out regularly, will ensure that most children will remember and use them when appropriate.

You could also write four or five addition or subtraction calculations on the board for the children to represent in concrete, pictorial an abstract ways, for example:

Addition

35 + 36 (e.g. near doubles: double 35 and add 1) 36 + 49 (e.g. adding near multiples of 10: 36 + 50 – 1) 75 + 8 (e.g. bridging through 10: 75 + 5 + 3) 38 + 27 (e.g. partitioning: 30 + 20 = 50, 8 + 7 = 15, 50 + 15 = 65 or sequencing 38 + 20 + 7)

Subtraction

54 – 5 (e.g. bridging through 10: 54 – 4 – 1) 46 – 19 (e.g. subtracting near multiples of 10: 46 – 20 + 1) 50 – 25 (e.g. doubles: know two 25s make 50) 53 – 22 (e.g. sequencing: 53 – 20 – 2)

** Strategies given are examples, others can be used as efficiently.

You could give the children problems that they can answer using the strategy they think is best, which might include using practical apparatus, a number line, the bar model or a mental calculation strategy.

For example:

Nathan had a collection of 46 coins. His friend gave him another 29. How many coins does he have now?

Fran baked 97 cakes for the school cake sale. She sold 73. How many were left unsold? Ben had 25 football stickers. Bobby has 36. How many do they have in total? How many more

stickers does Bobby have?

Activity set B

The children need to be able to recall and use addition and subtraction facts for all numbers to 20. They need to have plenty of practice in order to become fluent. Here are some examples of activities that can help:

Write the number you wish the children to find facts for on the board, for example 18. Give the children a minute to write down as many facts as they can for addition and then another minute for subtraction facts. Encourage them to be systematic in their recording.

Use a pendulum (three interlocking cubes on a piece of string), as it swings one way you call out a number to, say, 15 and as it swings the other way they call out the number pair that goes with it to make 15.

Use a set of number cards to 20. Hold up one at a time. For each card you hold up the children write down the number that goes with it to make 20.

You can adapt these for any facts you wish to practice, including multiples of 5 and 10 to 100.

For practising number facts for 10, encourage the children to use their fingers. For example, ask them to show you the number of fingers needed to add to 8 to make 10, ask them to show you the number of fingers you need to take away from 10 to give four.

Activity set C

The children need to develop the understanding that addition is commutative (whichever way you add numbers the answers will always be the same). Provide plenty of practical experiences to show this:

Give the children two different colours of counters and a simple addition to explore. Ask them to count out the correct number of coloured counters for one of those in the calculation and then the correct number of a different colour for the other number. Ask them to add one of the coloured counters to the other and then vice versa. What do they notice? The total is the same!

You could then repeat the above with bead strings and base 10 apparatus. You could demonstrate this idea with the bar model:

13 12

25

12 13

25

The children could then explore this using a number line, for example:

The children need to develop the understanding that subtraction is not commutative. However, it is important that children don’t develop the misconception that they cannot take a larger number from a smaller one. This is only the case when dealing with concrete apparatus. Provide opportunities for the children to explore taking small numbers away on a number line. Give or show them a number line that begins with -10 and ends with 10. Ask them to put their finger on, for example, 4 and take away 8.

Some children develop the misconception that our number system begins with zero because this is how our number system is presented on many number lines. Most young children are aware of negative numbers in real life, for example winter temperatures. We need to capitalise on this from an early age to demonstrate that our numbers are replicated on the other side of zero with equivalent negative numbers.

Activity set D

In order to develop the understanding of the inverse relationship between addition and subtraction, the children initially need practical experiences. You could provide counters or similar apparatus. Ask the children to add two small quantities, for example 12 and 15. Once they have 27, ask them what they think they will have left if they take 15 away from the 27. Then ask them to check by taking 15 counters away leaving the other quantity.

Inversion loops and the bar model are useful visual representations of inverse:

Inversion loops

The bar model

12 15

27

27

15 ?

You could give the children problems such as these to solve and then check using the inverse operation:

Nafisat had 23 marbles. Her friend gave her 18 more. How many does she have now? The children add 23 and 18 to give 41. They then check by taking away 18 from 41 to give the original number.

Adnaan had 36 sweets. He gave 21 to his friend. How many did he have left?

The children take 21 from 36 to give 15 and then check by adding 15 to 21 to give the original number



Activity

A B C D

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.

Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals(=) signs

Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.

Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Activity Set A

Multiplication tables - pelmanism style matching cards. Find the pairs of cards showing the product and multiplication fact in a timed activity.

Counting stick: using a metre stick with ten divisions use sticky notes to mark multiples of 2, 5 or 10. Practise counting on and back from different numbers. As the children become more fluent, remove more sticky notes and see how they can recall multiples starting at different points counting on and back.

BBC KS1 Bitesize: Camel Times Tables and Division Mine. These two games are a super resource for the children to practise their recall of multiplication and division facts independently

Activity Set B

BBC KS1 Starship Number Jumbler game, a simple animation where children choose the missing operation sign in the calculation.

Write the calculation: give the children different pictures of groups of items or arrays. They then have to write the multiplication sentence to match the picture. 2p, 5p and 10p coins could be used

for this activity. The children can write down how many of each coin they have and the total amount. Using coins, the children could also write division calculations to match the images.

Activity Set C

Triangle of numbers: a good activity to use as a starter or plenary, demonstrating the commutativity of multiplication. It can be used to demonstrate one number fact and the children can suggest the others.

Function box: reinforcing the relationship of division being the inverse of multiplication. To build up to this online activity, a function box could be made and used as a visual resource in class. For example, model how a number goes in and doubles, but put the number back through the machine it will halve. There are lots of different ways to use the function box in class to deepen the understanding of the relationship between multiplication and division.

Class number sentence: using digit cards and x and ÷ and = cards. Get the children to show how we can take one known fact and find others using those numbers. As the children move the digits around, they will demonstrate their understanding of using and applying their tables knowledge. What numbers can we move around in a division sentence? Can they spot the relationship between multiplication and division? Ensure they really understand the concept behind this activity, by encouraging them to show you with practical apparatus.

Activity Set D

TES word problems with differentiated questions: resources submitted by a Year 2 teacher, focusing on problem solving using multiplication.

BBC Class Clips: problem solving - how many chairs? Use multiplication facts to help the Chuckle Brothers organise their tables ready for their guests’ arrival.

Give the children a multiplication or division fact. Can they write a word problem to match it? Now swap calculations with a partner and talk about how you would solve the problem.

Year 2 Measurement


Activities

A B C D

choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

compare and order lengths, mass, volume/capacity and record the results using >, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

find different combinations of coins that equal the same amounts of money

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

compare and sequence intervals of time

tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times

know the number of minutes in an hour and the number of hours in a day

Activity Set A

Sally and Josh measured the hall using their feet but they couldn't agree how many feet long the hall was. Why do you think that happened? What else could they use to measure the hall? Will that be better? Why?

Other questions to use as starting points;

o What could you use to find out how much water this container holds?o Would it be better to use multilink cubes or peas to balance the weight of this shoe? Why?o Would you measure the length of a book in centimetres or metres? Why?o What units would you use to measure the width of the classroom?o How about the weight of your teacher?o Look at a mug. Which of these amounts would you choose to say how much water the

mug holds? 1 metre, 1 litre, 1 centimetre, ¼ kilogram, ¼ litre

Possible contexts include:

o Estimating measures, e.g. give children a 1kg weight to hold. Then give them a range of everyday items and ask them to say whether they weigh more, less or about the same as 1kg.

o Estimate and then check how far you can jump from this line.o Units used to measure everyday objects, e.g. look at food labels and find a big packet of

food that weighs less than a small packet of food.o Comparing objects using appropriate measurements, e.g. working with two or more

objects to find the shortest, longest, heaviest, smallest capacity, etc. and explain how this was done and what units of measurement were used.

Ruler

(NB The following three resources were produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resources have the potential to complement teaching in line with the new 2014 mathematics curriculum)

This Interactive Teaching Programme displays an on-screen ruler you can use to measure lines and the sides of shapes. There is a choice of rulers and five screens to use to demonstrate measuring length. You can draw your own lines and shapes or select those that are available on the ITP. The ITP can be used to demonstrate how to use measure using different rulers. The ITP can be used to compare lengths and the perimeters of shapes and to support children's understanding of scale. You can develop their ability to estimate length against a given scale and use the ruler to check the accuracy and demonstrate what to the nearest half and whole unit means.

Measuring scales

This ITP allows you to add different masses to or from a scale pan. You can add masses of 1, 2, 5, 10, 50, 100 and 500 units. The pointer or hand shows the total mass. This can be hidden to promote children’s prediction skills. The maximum value of the circular scale can be changed together with the size of the interval. A digital readout can also be hidden or displayed. A red marker can be used to keep a track of previous values and to set target quantitiesp

Measuring cylinder

This ITP allows you to control two taps that pour a liquid in and out of a measuring cylinder. You can set the scale on the cylinder to a maximum of 50, 100, 200, 500 or 1000 units and the scale interval to 1, 2, 5 or 10 units. You can simply turn the taps on and off and ask questions that involve prediction, addition and subtraction.

Activity Set B

Order Order! In Order

Both of these activities require the children to order various quantities from smallest to largest. A good activity to assess estimation skills and knowledge of units of measurement.

Activity Set C

Fair Exchange

In your bank, you have three types of coins. The number of spots shows how much they are worth. Match your coin values to those shown.

Coin matching computer activity.

This activity from Nationwide Bank Education has three levels of difficulty, requiring children to share coins equally.

Christmas Shopping

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Change White Elephant is an activity about giving change.

Activity Set D

Tell The Time ITP

(NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to complement teaching in line with the new 2014 mathematics curriculum)

This ITP can be used to show analogue time, digital time or synchronised analogue and digital clocks. The program allows you to add or subtract a selected time interval.

Counting stick

Use a counting stick to practise counting in 5-minute, quarter-hour or half-hour intervals.

1 pm 2 pm 3 pm

1/2 past

Since counting sticks usually have 10 intervals, you may wish to make a stick with 12 divisions.

What Is the

Time? o Routine activities

Provide plenty of opportunities to tell the time during the routine of the day. Put children in charge of letting everyone know when it is 10 minutes before assembly/lunch/break.Check that children can tell you how many minutes are in an hour and how many hours in a day. Have a detailed timetable for children to refer to, with times displayed as analogue clock faces as well as written times.

Matching times to everyday events, e.g. match some pictures of daily events to some given clock faces showing their typical times.

Comparing times, e.g. sort some given times into a sequence from earliest to latest and draw hands onto corresponding clock faces.

Problems involving the duration of time, e.g. School starts at 9 o'clock; show this time on your clock. Now show what time it would be if you were half an hour late.

I went out for a walk at half past 3 and walked for quarter of an hour. Show me on these two clock faces what time I started and what time I would then have finished.


Programme of Study statement

Activity

A B C D E

Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

Compare and order numbers up to 1000

Identify, represent and estimate numbers using different representations

Read and write numbers up to 1000 in numerals and words

Solve number problems and practical problems involving these ideas

Activity A – Ordering 2 digit numbers; creating 2-digit numbers from 3 or 4 digits

Year 3 Lessons 66 – 70 from Centre for Innovation in Mathematics Teaching: MEP scheme of work

These resources comprise lesson plans. Scroll through the pdf to find Lesson 66. Thecorresponding pupil worksheet can be found on Page 66. There are further resources that can be projected onto an interactive whiteboard or other screen.

Again scroll through until you find a sheet with LP 66/2 in the bottom right hand corner – the ‘2’ refers to task 2 on the lesson plan. Further lessons 67 – 70 are on the same topic. Use practical apparatus such as Dienes’ blocks to support the children’s reasoning. These resources are quite demanding mathematically and arranged to be taught through whole class teaching which is a different approach from differentiating by task. The idea is that every child in the class is exposed to each of a number of short tasks and sees the correct answers which are shared at frequent intervals even though they may not all manage to complete everything.

The scheme of work to help you find more resources like this can be found here in the centre of the page.

Activity B – Which Scripts?

This rich activity encourages children to think deeply about place value and the nature of numbers. It requires children to sort out the information and to work out what they know in order to solve the problem. Suggestions about how to structure a lesson around using it are included in the notes.

Activity C – Which is quicker?

This activity explores what happens when you count in jumps of different steps. How many steps will you need to make to reach your target number? Which will be quicker counting in 3s or 30s to reach 1000? Why? Plenty of scope for extension and exploring the meaning of the children’s findings as well as opportunities to practice counting in jumps in a meaningful context.

Activity D – The Deca Tree

An exploration of the ways in which our place value system works by exploring a fantasy problem. Detailed suggestions of approaches, extension and support are offered and there are, as usual from NRICH, some real examples of children’s response to the task which help to see where it might lead.

Activity E – Exploring Place Value or the Value of Place

Take 3 digit cards and see how many different numbers you can make. Write them in words and symbols. Order them from smallest to largest. Order them from largest to smallest. How many do you think you can make? How do you know that you have got them all? These ideas are explored further by Mike Ollerton in his task Exploring Place Value which you can find on hiswebsite.



Activity

A B C D E F G H

add and subtract numbers mentally, including:

a three-digit number and ones a three-digit number and tens a three-digit number and hundreds

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction

estimate the answer to a calculation and use inverse operations to check answersy

solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

Activity A – Reach 100

The challenge is to find four different digits that give four two-digit numbers, which add to a total of 100. A good way to practise a particular method of written addition.

Activity B – Consecutive numbers

An investigation looking at consecutive numbers, adding and subtracting them and looking for patterns. A great context for gaining a deeper understanding of our number system. It offers opportunities to work together by sharing results and making decisions.

Activity C – Five Coins

An open-ended activity to practise addition and subtraction in the context of money.

Activity D – Super Shapes

A good starter activity that provides an opportunity for pupils to practise using addition and subtraction, and it reinforces their inverse relationship. It also helps them become familiar with the idea of a symbol (in this case a shape) representing a number.

Activity E – Triangular cards

An interactive resource, which is useful for demonstrating inverse operations. You can select different number bonds including decimals or input your own numbers. Useful for mental maths starters and plenaries. Children could also make their own cards and play hide and reveal as a group activity.

Activity F – Addition of three digit numbers

A good visual aid to show regrouping.

Activity G – The missing digit trick!

A great magical activity for rehearsing addition and subtraction.

Activity H – Conductor counting

Split the whole class into three ability groups. Tell each group how they will be counting, i.e. one group could count in threes forwards, another group could count in threes backwards and another group could count in tens forwards etc. Teacher stands at the front of the class as the conductor and points to each group at different times.

This is a great way of differentiating whole class counting. It keeps the children on their toes, as they need to keep looking and listening, so that they know at which point they will need to be continue the count. You could stop at different intervals and ask what the calculation would be to get from one number to the next.



Activity

A B C D E

recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

Activity A – Always, Sometimes, Never

A wonderful, generic resource that can be adapted to suit learners of different abilities as well as different aspects of the curriculum. Versatile resource to use to spark discussion and gain a deep insight into pupils’ understanding of a concept. This set is specifically for division and multiplication.

Activity B – Using pendulum to count in equal steps

Children choose their individual target table and count in steps of their chosen multiple silently in their head in time to pendulum / counting stick etc. Teacher stops and children give the number they have reached and times table facts for that multiple.

Activity C – Arrays for TU x U

Interactive website that gives the array model for the calculation and children input the missing numbers. Also provides an empty numberline representation of the calculation to support children’s developing mental strategies. Arrays can be printed / matched to word problems or children can write their own word problems for the arrays/ calculations.

Activity D – Multiplication involving multiples of 10 and 100, describing effects and moving onto modelling multiplication of 2 digit numbers

Year 3 lessons 131 – 140 from the Centre for Innovation in Mathematics Teaching: MEP

Lesson plans Workbooks with pupil exercises Copymasters

These activities are quite challenging and are based around whole class interactive teaching with pupils having regular opportunity to explain, self correct and reason. There are a number of shorter tasks in each lesson, giving the children chance to engage with a concept in different ways.

Activity E – Andy’s Marbles

A challenging problem that requires children to link multiplication, division and fractions to find the number of marbles Andy started with. A perfect example for the use of the Bar Model.

Year 3 Fractions


Activity

A B C D E F G

count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

recognise and show, using diagrams, equivalent fractions with small denominators

add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

compare and order unit fractions, and fractions with the same denominators

solve problems that involve all of the above

Activity A – visualising fractions along a line

Use counting sticks and bead strings to help children visualise fractions.

If the bead string represents one whole, then each set of ten coloured beads could represent one tenth and each individual bead could represent one hundredth.

1. Label the two ends of the bead string as 0 and 1. Give students tags to place each tenth on the bead string. You could use a 1-10 bead string instead of a 1-100 bead string.

2. Join several bead strings together to create fraction lines that extend over one. For example, five bead strings allow fractional numbers from 0 to 5. Label simultaneously in mixed numbers (2 ½) and improper fractions (5/2).

3. Ask the pupils to represent each tenth with a variety of manipulatives, for example, Numicon, Dienes (Big Base) and coins.

4. Extend pupils’ understanding to include the equivalence of fractions, decimals and percentages. For example, ½ = 0.5 = 50% or 2 2/10 = 2.2 = 220%

Activity B

Fractional Triangles

This practical activity develops an understanding of the part and the whole,

Understanding unit fractions: A Hungarian Approach

A series of lessons on finding fractions of amounts from Lesson 11, page 9 onwards based on an alternative, Hungarian approach, to teaching maths. There are linked resources and activities, although the site is slightly tricky to navigate.

Activity C

Trains

An activity from New Zealand that involves using number rods to develop children’s understanding that fractions can extend beyond 1.

Children can make number lines for display around the classroom, that demonstrate counting in different fractional steps. For example counting in steps of ½ an apple, 1/4s of pizza, 1/10 of a £1 (steps of 10p)

Daily practice of counting forwards and backwards in 1/2s, 1/4s, 1/10s and 1/3s, including extending to below zero

Activity D – equivalent fractions

Fractional Walls

An activity based on Cuisenaire / number rods.

Matching Fractions

A ‘pelmanism’ style matching activity based on fractions.

Use equivalence circles, for example pizza or cake slices in a variety of activities for pupils to explore equivalence.

Activity E – adding fractions

Addition, subtraction and equivalent fractions

A series of activities based on deepening students’ understanding of adding and subtracting fractions with the same denominator.

Use a variety of representations, for example, number rods, paper strips and equivalence circles to model what happens when you add or subtract fractions with the same denominator. This will help children understand why the denominator doesn’t change.

Activity F

Fractions interactive teaching programme

NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to complement teaching in line with the new 2014 mathematics curriculum)

This ITP allows you to divide a green strip into a number of equal parts and colour the individual parts in yellow, clearly showing any comparison.

Smartie Fractions

Use mini packets of smarties for children to find the fraction of each colour in a packet. This is useful for comparing fractions with the same denominator and for adding and subtracting fractions

More wonderful ‘Maths and Smarties’ ideas.

Activity G – solving problems

Use the Bar Model to solve problems

Use the ‘Thinking blocks on the maths playground’ website to model word problems involving fractions and to model adding and subtracting unit fractions. There are video demonstrations, guided problems and the ability to use the blocks to solve your own problems.

Fair Feast

Assess and develop children’s understanding of equal sharing with this picnic problem.

Year 3 Measurement


Activity

A B C D

measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/m)

measure the perimeter of simple 2-D shapes

add and subtract amounts of money to give change, using both £ and p in practical contexts

tell and write the time from an analogue clock, including Roman numerals from I to XII, and 12-hour and 24-hour clocks

estimate and read time with increasing accuracy to the nearest minute, record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight

know the number of seconds in a minute and the number of days in each month, year and leap year

compare durations of events [for example to calculate the time taken by particular events or tasks].

Activity set A

This is a simple but effective way to practise estimating, measuring and comparing lengths: give each learner a small piece of plasticine or modelling clay. They work in groups of about four. Give them 30 seconds to roll the longest worm that they can. As a group, they order the worms from shortest to longest. They then estimate the length of the shortest worm and once they have, they measure it. They use this knowledge to estimate the length of the next worm and then measure it. They continue to do this for all the worms. They can then find the differences in length between their worms and also add pairs of their lengths together.

Resources required: plasticine or modelling clay

You could adapt this mass investigation from Nrich. You could set this up for the learners to work on practically with balance scales.

Resources required: balance scales

This Nrich investigation involves capacity:

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Activity B - Perimeter

Give the children a piece of squared paper and ask them to draw a variety of shapes by shading sets of 5 squares. They then find their perimeters.

Resources required: centimetre squared paper

This Smaller and smaller investigation from Nrich asks the learners to predict, without drawing, the perimeters of shapes in a pattern.

Activity C – Add and subtract amounts of money

Set problems that involve finding totals and change. For example: Mike spent 76p on a bar of chocolate and £1.35 on a packet of biscuits. How could he have paid for them using the least number of coins? If he had a £5 note, how much change will he need?

Resources required: coins

Make a collection of take-away menus and store catalogues (particularly those that include toys). The children can use these to make up meals, wish lists for birthdays and so on to practice finding totals and amounts left from a given budget.

Resources required: take-away menus, store catalogues

Activity D – Time

Give learners sets of digit cards. They pick three and make up as many times as they can using their cards. They then draw their times on analogue clock faces and label them with the 12-hour and 24-hour times.

Resources required: digit cards, pre-prepared analogue clock faces without hands

The ‘Two Clocks’ investigation from Nrich asks the learners to find the times on a clock with no minute hand and to solve problems involving a clock with no hour hand!

‘Just a minute’ type activities for practising the vocabulary of time (or any other concept) are fun and the learners really enjoy playing them. Write the words that you wish to practice on pieces of paper or card. Pile the words together and then, taking one at a time, give the meaning of each (without saying the word) How many do the learners successfully guess in one minute. Repeat this a few times. Ensure you begin with the words they guessed correctly – to build on their success. Do they improve their score? You could also do this in mixed ability groups with the most confident learner taking the first turn.

Resources required: vocabulary cards for the words you wish the learners to focus on

Give the children practice sessions where they use their mental calculation skills of, for example, addition, subtraction, multiplication, doubling and halving to deduce new information:

You could repeat this for days in different numbers of weeks, months in different numbers of years and so on.

You could adapt this investigation from Nrich which asks:

During the third hour after midnight the hands on a clock pointed in the same direction (so one hand was over the top of the other). At what time, to the nearest second, did this happen?

For Roman Numerals this interactive clock can be set to display Roman numerals for a variety of ‘Time’ activities.



Activity

A B C D E F G H I J

Count in multiples of 6, 7, 9, 25 and 1000.

Find 1000 more or less than a given number.

Count backwards through zero to include negative numbers.

Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

Order and compare numbers beyond 1000.

Identify, represent and estimate numbers using different representations.

Round any number to the nearest 10, 100 or 1000.

Solve number and practical problems that involve all of the above and with increasingly large positive numbers.

Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

Activity A – Some games that may be nice or nasty

This a variety of activities that can be teacher led as a whole class or used in pairs or groups. Use dice or spinners to generate single digits to be placed on a place value grid to create four-digit numbers. Whoever has the larger four-digit number wins etc. Take the opportunity to randomly ask, “What is 1000 more?” or “What is 1000 less?”

Activity B - The Thousands Game

Children pull digits out of a bag to create 4 digit numbers and compete and compare. Take the opportunity to randomly ask, “What is 1000 more?” or “What is 1000 less?”

Activity C - Place Value KS2 KS3

Children should be given a copy of one of the grids within the document and asked to place their digits in various positions. This activity can be made as simple or as complicated as required. Teachers can take the opportunity to randomly ask, “What is 1000 more?” or “What is 1000 less?”

Activity D - Clapping Times

This activity is similar to the traditional game Fizz Buzz and can be played as a whole class. In pairs or more, children take turns to count and clap in ones, clapping loudly on their chosen/assigned multiple, therefore practicing counting in selected multiples. This activity can be easily adapted for multiples of 6, 7 and 9.

Activity E - Music to My Ears

This activity can be teacher led or played in pairs or more. Clap and click a rhythm (or use musical instruments) using the selected multiples. Ask questions regarding what will come next, what will happen on the 100th beat? In pairs or more use different multiples and predict when there will be a clap at the same time etc.

Activity F - Count from a Random Number

This is a quick activity. Count forwards and backwards as a whole class e.g. “6, 12, 18, 24,

30, 36, now back again 30, 24, 18, 12, 6.”

Generate a random number by asking a child or rolling a dice. Now count forwards and backwards. E.g. a child chooses 23 as the starting number and you all count in multiples of 6 so “23, 29, 35, now back again, 29, 23, 17, 11, 5, -1, -7”

Or you count in thousands so “ 23, 1023, 2023, 3023, 4023, 5023 now back again 4023, 3023, 2023” etc.

Roll a dice, get 3, then say “ 3, 4, 5 now back again, 4, 3, 2, 1 , 0, -1, -2, -3, -4, -5” Try to do it reasonably fast.

Activity G - Sea Level

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

Activity H - Money Bags

An investigation involving money that begins: Ram divided 15 pennies among four small bags. This activity can be extended.

Activity I - Rounding Quiz

A motivational activity to practise rounding skills with multiple choice answers, which spell out a joke and punch line.

Activity J - Roman Numerals

A fun interactive activity to learn and use Roman numerals.



Activity

A B C D E F G

Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

Estimate and use inverse operations to check answers to a calculation

Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Pupils should be taught to:

Activity A - Interactive Base Ten Blocks

This software shows a clear, interactive version of the use of base ten blocks for addition of two 3-digit numbers. It clearly demonstrates regrouping, and has a useful focus sheet for pupils to guide their work.

Activity B – Twenty divided into Six

This task from Nrich requires children to arrange a pack of 20 cards numbered 1-20 into 6 unequal piles of the same total. A good activity for consolidating mental addition skills and encouraging children to discuss their approaches and ideas. Could it be extended to larger numbers?

Activity C - Images of addition and subtraction

This activity comes from the NCETM Secondary Magazine, and looks at the range of models and images used for addition and subtraction. Challenge the children to sort the cards and think about all the skills they are using.

Activity D – Models and Images

‘Slidey- box’ cards, number trios and the function blocks Interactive Teaching Programme (ITP) can all be used to support children in understanding the concept of inverse operations for addition and subtraction.

Activity E - Reach 100

This activity from Nrich requires children to use their knowledge of addition and subtraction to add several two digit numbers to reach a target total.

Activity F – Estimating differences

In pairs, children take turns to circle two numbers from a grid such as this:

They agree a time period in which to estimate the difference between the two numbers and check the range in which the estimate falls on the chart below. Play continues until all of the numbers are used, and the player with the most points wins.

Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Activity G – Bar Models

This resource provides a useful introduction to the bar model approach for calculating, with lots of ideas for problems to use in the classroom. Additional resources can be found at the‘Thinking Blocks’ website



Activity

A B C D

Recall multiplication and division facts for multiplication tables up to 12 × 12.

Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers .

Recognise and use factor pairs and commutativity in mental calculations.

Multiply two-digit and three-digit numbers by a one-digit number using formal written layout.

Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

Activity Group A

Year 4 Statutory requirement: Recall multiplication and division facts for multiplication tables up to 12 × 12

Last Digit Patterns – A ‘Teachers’ TV’ activity

Generating and using last digit patterns to explore and create patterns in a ‘clock face’. Fantastic activity for practising times tables facts, predicting and reasoning as to why some times tables share the same patterns on the ‘clock’.

http://www.tes.co.uk/teaching-resource/Teachers-TV-Primary-Maths-Numbers-6044819/

12 x 12 Grid Patterns – Exploring arrays, multiples and factors

Resources required: Blank 12 x 12 (half or a whole sheet of A4) grid and write in numbers 1-12 along the horizontal and vertical to create a multiplication grid.

Start with a number such as 12 and use cubes to create all of the possible arrays (e.g. 1 x 12, 12 x 1, 2 x 6, 6 x 2 etc) Place these cube arrays in the multiplication grid to show that 2 x 6 = 12 because we have a 2 by 6 array and therefore 12 cubes. Children can see that the 2 x 6 array could be 2 across and 6 down or 6 across and 2 down etc.

Now we should be able to place a cube everywhere 12 would be on the 12 x 12 grid. How many 12’s will there be and why? Do you notice anything about where the cubes are when you’ve finished? Can you explain why this is? (Commutative Law)

Repeat this with other numbers and focus upon predicting where the cubes will be placed and reasoning why e.g. How many times will ‘7’ appear on this grid and why? Will it be more or less times than 12?

Explore larger numbers such as 24 where two of the factors will not appear on this particular grid (1 x 24 and 24 x 1) ask the children to discuss which factors won’t appear and why and how they can use the factors of numbers like 20 to determine the factors of 40 and 80 etc.

Linking Division and Multiplication Facts Quiz

Children work in pairs.

Ask children to choose a times table to practice e.g. 7. One child writes down a vertical list of multiples of this number (up to and beyond 12 x 12 to apply partitioning skills when appropriate)

Version 1: Child passes this list to partner and asks them to say how many 7’s are in this particular multiple. Their partner must explain how they are working it out (if it is not a known fact) and emphasis is placed upon efficient use of known facts to generate derived facts e.g. ‘Well I know that 5 x 7 is 35 so 6 x 7 will be 7 more so that’s 42’.

Version 2: Child passes paper over and partner works against the clock. Jottings are allowed (and encouraged) whilst working with more challenging multiples.

Multiplication Square Jigsaw

Complete the multiplication grid using cut out interactive ‘jigsaw’ pieces

http://nrich.maths.org/5573

Activity Group B

Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

Multiplying and Dividing with Straws

Resources required: Straws in bundles (see below)

Give children straws which have been halved and ask them to bundle them into single colour groups of 10. Then bundle 10 groups of 10 to form hundreds. Create sets of hundreds, tens and units straws for pairs of children to use. (These are an excellent resource for teaching columnar calculation methods and other aspects of place value and fractions too, so well worth making).

Look at a series of calculations such as 6 x 3, 60 x 3 and 600 x 3. Ask children to talk about what this calculation means and model it using their bundles of straws. Discuss in pairs and small groups what they have found out and reason why the patterns they are seeing exist.

Ask children to create their own series of calculations and model them using straws.

Ask children to generalise the rules regarding multiplying by 1, 10 and 100 and apply this to other calculations of their own creation. If ‘add a zero’ comes up in discussion explore what would happen if the zero/s were not there and help children see zero as a ‘place holder.’

Use straws to repeat activity but using division by 1, 10 and 100.

Use straws to explore multiplying and dividing by 0 and discuss what happens and why.

What’s in the Box?

What has the large box multiplied the numbers by to get the numbers which come out at the end? (And just to get us really thinking….we don’t know what the numbers were that went in at the beginning: only those that came out after they’d been multiplied!)

Activity Group C

Year 4 Programme of Study: Recognise and use factor pairs and commutativity in mental calculations

Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Factors and Multiples Game

A game which helps children derive, practise and use their knowledge of factors and multiples. Can you block your opponent?

Sports Practice

Work in pairs and use cubes or counters to explore and build mathematical models and support conjecture.




Your teacher is running an after school club. Some weeks the number of children who turn up make it really easy to divide everyone up into equal groups for all different kinds of games. Some weeks the number of children who turn up makes it almost impossible!

Explore which totals would make life easier and which would cause problems. Explain why some numbers are ‘better’ than others in this context. Explore models which show all of the possible solutions and link this to arrays, commutability, square numbers, prime numbers and factor pairs. Explore which totals have an odd number of factors and explain why. Use explorations to predict which larger numbers could be divided in many ways and which would cause problems.

Activity Group D

Year 4 Statutory requirement: Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects."

Resources required: Interlocking cubes or straw bundles (see activity group A)

Build 14 x 4 using cubes (14 multiplied 4 times)

Ask children how they would calculate this total. Most likely response is 10 x 4 = 40, and 4 x 4 = 16. Then 40 + 16 = 56

Record this model as a grid to link children’s method and use of distributive law to multiply 2 -digit by 2-digit numbers.

Use straw bundles to make 124 x 3. Record model as a grid to show use of distributive law to multiply 3- digit by 2-digit.

Repeat these activities and similar activities using place value counters (see video below) instead of cubes/dienes and straw bundles.

Using grid method as a formal written method Lower Key Stage 2 NCETM video: Using manipulatives (place value counters)

Real-life Connections: Regularly link these calculations to real life, meaningful problems relating to familiar situations such as shopping and cooking. For example:

My brother is working part time in the supermarket in the evening stacking shelves. He needs to stack the boxes 7 high and 15 across. How many boxes will he need?

The people in the stadium are sitting in rows of 36 and there are 9 rows in each sections. What is the capacity of each section? If there are 40 sections in the stadium what is the total capacity? (Using multiplication by 10 as well as grid method).

(See also upper Key Stage 2 video moving from grid method to formal written method – 2- digit by 2-digit long multiplication)

Upper Key Stage 2 NCETM video example discussing grid method and its relationship with long multiplication

Exploring Wild and Wonderful Patterns!

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Exploring Number Patterns You Make

The Amazing Splitting Plant

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Scaling Recipes

Find the recipe proportions needed by scaling up the ingredients.

http://www.iboard.co.uk/activity/Recipe-Proportions-Scale-Up-361




https://www.ncetm.org.uk/resources/40530




Harry Potter’s Portions (Ratio and direct proportion)

Can you work out how to scale the recipe to make ‘Snape Sponge’ for everyone?

Lengthy Journeys

Use the data to describe the journeys as proportions of each other e.g. Norwich to Cambridge is 105 km and Norwich to Oxford is 272 km so we could say that the first journey is just over a third of the second and the second is approximately two and half times further.

Use a mapping website to research distances which have greater meaning to the children and make similar comparisons using appropriate written methods to justify answers.

(Also use this activity for other areas of maths such as difference)

Sports Mega-Facts

Research the capacity of sports stadia around the world and link to geography to locate on a world map. Collect as data and make comparisons as above in terms of fractions and scaling.

Once Upon a Time

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?



http://www.tes.co.uk/teaching-resource/Harry-Potter-and-39-s-Potions-A-Ratio-lesson-Powerpoint-6012867/

Year 4 Fractions


Activity

A B C D E F G

Recognise and show, using diagrams, families of common equivalent fractions.

Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten.

Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

Add and subtract fractions with the same denominator.

Recognise and write decimal equivalents of any number of tenths or hundredths.

Recognise and write decimal equivalents to ¼; ½; ¾.

Round decimals with one decimal place to the nearest whole number.

Compare numbers with the same number of decimal places up to two decimal places.

A range of web based interactive programmes, aimed at providing practice and consolidation for pupils exploring equivalent fractions.

Of course, concrete materials and activities are the best way to teach children about fractions and enable them to build strong concepts.

Activity A – interactive programmes

1. Game matching pictures and equivalent fractions

Activity B – Tenths and Hundredths

1. A resource pack of materials including an interactive place value grid to teach tenths and hundredths, activities on key vocabulary and terms, reference material and animations and three differentiated worksheets on tenths and hundredths

2. A series of activities to introduce and use hundredths3. Make a hundred square of pennies in the classroom and talk about one hundredth of a pound and

a tenth of a pound. Consider how, for example, 23p is written as a decimal. How would we write four pound and eighty-two pence? What would it look like in our coins?

4. Interactive matching of decimal notation to a shaded 10x10 grid representation

Activity C – fractions to calculate quantities

1. Game for one or two players required to match the answer to the unit fraction of amount requested

Activity D – adding and subtracting fractions

1. Game practising adding two or more fractions with the same denominator2. Online adding and subtracting fractions activities written as word problems. Some useful

ideas.

Activity E – decimal equivalents

1. Excellent ‘splat’ game accessible at several different levels, requiring children to match the fraction (in tenths or hundredths) to the decimal representation

2. ‘The Decifractor’. A flexible resource demonstrating equivalences between fractions and decimals.

3. Pelmanism-style game , matching fractions to decimals.4. Arcade type game, where ‘Fraction Man’ has to defeat the decimals (by matching

them). Note – this does get challenging! find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths

Activity F – dividing by 10 and 100

1. Interactive Teaching Program – ‘Moving Digits’. A good modelling program to show how digits move when multiplied or divided by 10 or 100.

2. Interactive game where children are required to find the calculation that matches the answer given… to help them cross the river.

Activity G – rounding and comparing decimals

1. Rounding decimals activity – uses one and two decimal places.2. Practise rounding numbers to one decimal place.3. Spreadsheets ‘Rounding’ and ‘Rounding Decimals’4. Ordering numbers with up to two decimal places.5. Arrange the decimals in order from lowest to highest.6. Order the decimal number cards (select number of decimal places) from lowest to highest.

Activity H – solve problems involving fractions and decimals

1. Pelmanism-style game. Match the coin pictures to the correct fraction of amount.2. BBC skillswise activity focusing on money amounts as fractions.3. Fractions of amounts interactive word problems.

Year 4 Measurement


Activities

A B C D

convert between different units of measure (e.g. kilometre to metre; hour to minute)

measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

find the area of rectilinear shapes by counting squares

estimate, compare and calculate different measures, including money in pounds and pence

read, write and convert time between analogue and digital 12 and 24-hour clocks

solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days

Activity set A

(i) You could copy these units onto card and cut them out to give to the children to match:

1kg 750g 1l 224ml 1km 500m 2550g 1245cm 10050l

1m 10cm 25mm 6kg 75g 1.75kg 1.224l 12m 45cm

103mm 1500m 2.65l 2l 650ml 2cm 5mm 1750g

2.55kg 6.075kg 10l 50ml 6075g 12l 450ml 2l 650ml

12450ml 10.05l 12.45m 1.45l 1.5km 1.10cm

2.5cm 10.3cm 1.1m 1224ml 2kg 500g 10cm 3mm

(ii) You could ask the children to work in groups of 4 or 5. Each child will need a piece of modelling clay or plasticine. Time them for 30 seconds while they roll their plasticine into the longest ‘worm’ that they can. After 30 seconds, they place their ‘worms’ in order from shortest to longest. They estimate the shortest worm and write their estimate down in both centimetres and millimetres, e.g. 54mm, 5.4cm. Then they measure it, write that down in centimetres and millimetres and then work out the difference between their estimate and the actual measurement. They use this measurement to estimate the length of the next worm. Then measure it and so on for all the ‘worms’.

Activity set B

You could give the children problems similar to these:

Sophie would like to build a rectangular patio in her garden. She wants the area of her patio to be 24m2.

What to do:

o Think about the possible sizes that Sophie’s patio could be. Write these down.o Draw some designs using these sizes.o Draw these to a scale of 1cm = 1m.o Use another piece of paper if you need more room.o Measure accurately using your ruler. Label the measurementso Once you have drawn your rectangles, check to make sure the areas are correct.o Work out the perimeters of each shape using the formula 2(a x b).

Sam has been given a large area of land. He would like to build a stable for his horse on part of it. He wants it to be rectangular with a perimeter of 50m.

What to do:

o On paper work out some of the possible areas for Sam’s stable. Write them down.o On a piece of squared paper, sketch some designs using these sizes.o Use the scale of 1cm = 1m. Remember to label them.o Once you have drawn your rectangles, check to make sure the perimeters are correct.o Work out the areas of each shape in the most efficient way you can.

You might like to give the children the ‘Area and Perimeter’ problem from Nrich which asks them to create shapes with different areas and perimeters.

Or this one: ‘Numerically Equal’ which asks the children to draw a square with the same numerical values for its perimeter and its area

Activity set C

(Firstly, ensure that you, yourself, are very clear about the difference between volume and capacity. It is important that you are able to explain clearly and model use of the language correctly.)

You could ask the children to work in groups of four and carry out this activity

Collect 4 different containers from around the classroom. They all need to look different. As a group estimate the capacity of one of your containers. Write your estimate on paper in litres and also millilitres. Measure the amount you estimated into a measuring jug and see if it fills the container. If your estimate was not correct. Find out how the actual capacity of the container. Add this

information to the table. Repeat this for the other 3 containers.

You could give groups of children some sand, weighing scales, a book and some plastic bags and ask them to try out this activity:

Sara says: I can make three different masses using bags of sand. These will help me estimate the mass of a dictionary.

What do you think? How are you going to find out? Do you agree with Sara?

You could ask the children problems within the context of money. Ask them to estimate their answers first by rounding the money to the nearest pound. For example:

Leona saved £50. She wants to buy a music player for £23.48. She also wants to download music from the internet. This will cost £9.67. Does she have enough money left to buy some headphones at £8.96?

Paul and Lisa were making a list of food they would like to buy for their party. This is their list so far with the prices for the amounts they need:

Food Price

French Sticks £4.45

Doughnuts £9.99

Tubs of ice cream £15.25

Pizzas £42.80

Samosas £4.50

Cheese sticks £10.75

They have £75. How much more money do they need to buy everything on this list?

Billy had 10 coins. They totalled £4.50. What coins could they be? How many possibilities can you find?

Activity set D

You could give the children problems similar to these and ask them to solve them using a number line:

Cherri went strawberry picking. She began at 10:20 and was picking strawberries for 2 hours 45 minutes. When did she finish?

Adnan spent 1 hour 55 minutes at the gym. She left at 16:30. When did she get there? The twins went to the beach. They arrived at 11:50 and left at 17:15. How long were they at the

beach for? Zeina and Mona left for school at 07:15. They spent the day working hard. They got home at

17:05. How long were they away from home? Brent and Chris were gardening. They started at 13:25. Brent finished at 15:55. Chris carried on

for another hour and ten minutes. For how long was Chris gardening?

Next, ask the children to make up and solve some problems of their own.

You could give the children opportunities use their mental calculation skills of, for example, addition, subtraction, multiplication, doubling and halving to deduce new information about units of time:

You could repeat this for days in different numbers of weeks, months in different numbers of years and so on.



Activities

A B C D E F

read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

interpret negative numbers in context count forwards and backwards with positive and negative whole numbers including through

round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

solve number problems and practical problems that involve all of the above

read Roman numerals to 1000 (M) and recognise years written in Roman numerals

Activity set A

It is important that the children understand the place value of different digits. Conceptually, place value is complex and difficult for children to learn. Sometimes we assume children understand this concept if they can partition, say, 1345 into 1000 + 300 + 40 + 5. This isn’t necessarily so. Place value needs to be understood in four important ways: ‘positional’ ‘multiplicative’ additive’ and ‘base 10’.

Display a grid similar to this on the board:

1 000 000 100 000 10 000 1000 100 10 1 . 1⁄101⁄100

1⁄1000

6 8 2 4 2 5 7 . 9 3 5

Ask the children to explain what each digit is. For example the 2 is in the 10 000 column (positional) to find the number it represents we multiply it by 10 000 to give 20 000 (multiplicative). The 7 is in the ones column (positional); to find what the number 7 represents we multiply by one to give 7 (multiplicative). The 3 is in the hundredths column (positional) to find the number it represents we multiply it by one hundredth to give 3/100 (multiplicative). When we put the digits together to give the total value we must add the values represented in each of the columns together to know the total value represented 6 824 157 . 935 (additive). Each digit represents a number that is either 10 times larger or 10 times smaller than the values in adjacent columns (base 10).

You could give the children a set of digit cards and ask them to make and read large numbers following instructions that you call out such as these: make 34 now 234 now 2348, 23 487, 123 487, 9 123 487. Show the cards that show how many hundreds, tens, millions, thousands etc. there are .

They could then swap different digits and say whether the number is now bigger or smaller and by roughly how much- for example, 9 123 487 swap the 2 and 8: the number is bigger by roughly 60 thousand.

They could select four, five or six digit cards and make the highest and lowest number and the one closest to 5000.

The children could do a similar activity on their whiteboards. This has the added bonus of writing the numbers as well.

You could give the children problems such as:

Freddy scored 28 456 points on the computer game. His friend Hugh scored 5000 points more than Freddy. How many points did Hugh score?

There were 85 356 people at the Liverpool match. There were 40 000 fewer people at the Manchester United match. How many people were at the Man U match?

A London post office delivered 1 750 000 Christmas cards on the Monday before Christmas and 300 000 more on the Tuesday. How many did the post office deliver on the Tuesday?

You could explore place value with a calculator. Ask the children to key in a six digit number for example 234 568. Next give them instructions such as ‘change the 4 into a 9’, ‘change the 2 into a 7’. Each time. ask them to explain what they did (take 4000 and add 9000 or add 5000 take 200 000 away and add 700 000 or add 500 000)

Activity set B

The children could write numbers on their whiteboards and then make them 10, 100, 1000 times larger.

You could use a pendulum (easily made from three multilink cubes and a (long) piece of string) to mark time while children practise counting on or back in steps of different 10, 100, 1000 and 1million from and to a given number e.g. from 75 to 175/1075/10 075 etc. You could also do this for tenths, hundredths and thousandths.

You could use a counting stick and count forwards and backwards in steps of thousandths, hundredths, tenths 10 100 1000 etc. You could start by telling them that zero is at one end and for example 10 000 at the other. The children then need to work out what equal steps they need to count in to get from one end to the other. Be sure to jump around the counting stick to keep the children on their toes!

You could ask questions as if the counting stick was a number line; for example, what would go on this division what about half way between each end?

You could give the children this Nrich activity The Thousands Game

Activity set C

You could show the ITP (Interactive Teaching Programme from National Strategies) Thermometer. Set the maximum temperature at 500, the minimum at -300 and the interval at 2. You could then ask volunteers to show different temperatures. The children could work out differences between: two negative temperatures; a negative and a positive temperature; and two positive temperatures.

Discuss in which countries or regions of the world negative temperatures are found and how cold it can get in these places. You can find some information on this in a feature on Polar Regions in the Primary Magazine.

Activity D

Ask the children to draw different number lines that would enable them to identify a number that would be rounded to 10 100 1000 10 000 or 100 000. For example:

Round 1346 to the nearest 10

1346 is closest to 1350.





Activity set E

You could ask the children problems which involve approximate answers that can be found by rounding, for example:

Becky wanted to buy some clothes. The jeans she wanted cost £48.75, the sweat shirt cost £29.99, the trainers cost £59.80. She has saved up £150. Does she have enough money to buy the clothes?

Sam was taking a survey of the number of cars being driven down the High Street over a four hour period. These were his results: 1st hour 219 cars 2nd hour 498 cars 3rd hour 314 cars 4th hour 189 cars. To the nearest hundred how many cars did he record?

You could ask the children problems involving positive and negative numbers for example:

The temperature in Reykjavik at 6am was -120C. During the day the temperature rose by 18 degrees. What was the new, higher temperature?

The average annual temperature in the Antarctica is -570C. The average annual temperature in the Maldives is 270C. What is the difference between these two averages?

Activity set F

You could give the children a table showing the basic Roman numerals follow a pattern:

Units I II III IV V VI VII VIII IX

Tens X XX XXX XL L LX LXX LXXX XC

Hundreds C CC CCC CD D DC DCC DCCC CM

Thousands M MM MMM IV V VII VII VIII IX

Ask the children to use the table to make up different 4 digit Roman numbers for example 2365 or the year they were born or the year we are in now.

You could write some of these on the board and ask the children to convert them to ‘our’ numbers for example MCDLXIV.

A Little Bit of History in issue 2 of the Primary Magazine gives details of how to write Roman Numerals.



Activities

A B C D E

Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

Add and subtract numbers mentally with increasingly large numbers

Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Activity A – Two and Two

Challenging activity which requires finding the numbers which each letter stands for in an alphanumeric question

Activity B- Reach 100

A challenging activity from Nrich requiring the children to place digits in a 2x2 grid so that the four 2-digit numbers made, total 100. Can they extend it to a 3x3 grid? What might their total be? What about a 4x4 grid? Can their reach a total that is a multiple of 1000?

Activity C- Rounding Spreadsheets

‘Rounding’ and ‘Rounding Decimals’ are two spreadsheets from this wider set, produced by the National Strategies, and now hosted in the STEM Centre E-library. They allow a number of a given size to be

generated and a level or accuract for the number to be rounded to. The rounded number can then be revealed. Teachers’ notes are also included.

Activity D- Ordering the Problems

Children could be provided with a variety of one and two-step problems. They can be asked to estimate the answers to each, then order the problems according to their estimates.

Activity E-CIMT Problems (pdf)

Pages 70 – 75 of this workbook contain a variety of multi-step problems

Write the Problems

Children could be given written calculations such as 23 456 + 46 019. They could be asked to write an imaginative problem that would require this calculation. Can they extend their problem to make it a multi-step problem?

As a variation of this, give children a selection of cards. Some should contain word problems and others should contain the corresponding calculations. Children should match the problems to the appropriate calculation.

Other problem solving opportunities

Wherever possible, try to link problems to cross-curricular topics, so that children get used to solving problems with a real-life context.

Display a ‘problem of the week’ in the classroom, with an opportunity for pupils to respond, perhaps by posting their answer into a box or container.



Activities

A B C D E F G H

identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers

know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

establish whether a number up to 100 is prime and recall prime numbers up to 19

multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

multiply and divide numbers mentally, drawing upon known facts

divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000

recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes

solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Activity set A

You could write a number on the board, such as, 6 and ask the children to write down as many multiples of six as they can in one or two minutes. Encourage them to think of multiples that come in the multiplication table for 6 and others, for example, 720, 360, 1440. Once they have done this ask them to look at what they wrote and to identify other numbers that these are multiples of so finding common multiples.

You could do something similar for factors. Write a number, such as 144 on the board and give the children two minutes to find all the factors they can of 144. Once they have done this, ask them to look at the factors and to find another number that each is a factor of.

Take a look at the Nrich problem ‘Factors and multiples puzzle’. It is quite challenging as it stands but can be adapted to suit most attainment levels, for example, you might like to provide a list of numbers for children to put into the correct cells in the table:

80, 21, 1, 40, 6, 8, 30, 2, 3, 12, 36, 48, 25, 60, 18, 24

Multiple of 3 Factor of 24 Multiple of 5 Factor of 72

Even Number

Odd Number

Multiple of 8

Factor of 120

You could then ask the children to think of other numbers to add to each section.

Activity set B

Remind the children that a prime number is a number that can only be divided by one and itself. So a prime number has two factors. You could give the children a 100 square and ask them to shade the numbers from 1to10 that are not prime numbers (1, 4, 6, 8, 10). They then shade all the multiples of 2, 3, 4, 5, 6, 7, 8, 9 and 10. The numbers that are left unshaded are all primes. You could ask them what they notice about these (they are mostly either side of multiples of six).

You could write some single and 2-digit numbers on the board and ask the children to break these down as much as they can. What do they notice? If they have broken them down as far as possible they will end up with prime factors. Here is an example: 24 – factors include 2 and 12, 2 is a prime factor. Factors of 12 include 3 and 4, 3 is a prime. Factors of 4 include 2 and 2, both of which are prime factors. So, the prime factors of 24 are 2, 2, 2 and 3.

You could carry out similar activities for composite numbers.

Activity set C

You could display a variety of multiplication and division calculations on the board and ask the children to decide which strategy they would use to answer them. They could then discuss their thinking with a partner. Encourage them to look at the numbers and decide whether they can use a mental calculation strategy, jottings or a written method. Here are some examples of questions you could use and some possible appropriate strategies:

24 x 50 (x 100 and halve) 52 x 4 (double and double again) 12 x 15 (x 10, halve and total x10 and half x10) 136 x 9 (partitioning, x10 and take away 136 or column method) 245 x 1.6 (grid method or the column method or x1, x half, x tenth and add together) 123 x 3 (re-partition number into 120 and 3, 4 x 3 = 12 so 40 x 3 = 120 (so 120 ÷ 3 = 40), 3 ÷ 3 = 1,

answer 41) 165 x 10 (make number ten times smaller) 325 x 25 (use knowledge that there are four 25s in 100) 408 x 17 (grouping in 17s, 20 groups make 340, 4 groups make 68 so answer is 24) 623 x 9 (short method)

You could try ‘All the digits’ The multiplication given uses each of the digits 0 - 9 once and once only. Using the information given, the children need to replace the stars in the calculation with figures.

You could give the children a set of calculations which have been answered using column method and ask them to look at them and decide which are easy and which are difficult and why.

Activity set D

Give the children place value grids similar to the one below and a set of digit cards with some extra zeros:

1000 100 10 1 . 10th 100th

Ask them to make a three digit number, such as 34.8, and place it in the grid. They can then multiply the number by 10 and 100 using zeros as place holders and describe what is happening: the number is becoming 10/100 times bigger, the digits are moving to the left.

They could then divide their number by 10, 100 and 1000 and describe what is happening: the number is becoming 10/100/1000 times smaller, the digits are moving to the right.

Activity set E

You could give the children centimetre squared paper and ask them to explore square numbers by drawing squares 1 x 1, 2 x 2, 3 x 3 etc. Ask them what they notice. Encourage them to notice that a square is made with sides of equal lengths and that to find the area they multiply the length by the width so giving 12, 22, 32 and so on. These are known as square numbers. Can they work out the formula for the area of a square: n2. Give them a variety of numbers to represent ‘n’.

Ask the children to list as many square numbers as they can in ascending order in two minutes.

Give the children a centimetre cube. Ask them to work out the volume by multiplying the length, width and height. Next, ask them to build another cube with three dimensions of 2cm. They work out the volume of this and then explore other cubes. What do they notice? Encourage them to notice that each cube has

three dimensions of the same size. When multiplied they produce cubed numbers: 13 is 1 x 1 x 1 = 1, 23 is 2 x 2 x 2 = 8, 33 is 3 x 3 x 3 = 27 and so on.

Ask the children to list as many cubed numbers as they can in ascending order in two minutes.

Stand a container (tank or bowl or bucket) inside another container ( a larger bowl or a tray with sides at least a few centimeters high). Fill the container to the brim with water. Place the 1000 Dienes cube (or equivalent) into the container. Catch and measure the volume of water that overflows (is displaced). What do you notice?

Activity set F

You could ask the children to solve problems such as:

Sally was asked to find all the factors of 48. She found 8. These were, 1, 48, 2, 24, 3, 16, 4, 12. Did she find them all? How do you know?

Bobby was asked to find all the multiples of 12. He said that it was impossible because there were an infinite number. Was he correct? Explain your thinking.

Farmer Giles bought a plot of land. It was a square shape with a perimeter of 48m. What was its area? He paid £56 for each square metre. How much did he pay in total?

Fatima bought a microwave for her kitchen. It was cube shaped and had a length of 30cm. How much space did it take up?

Activity set G

Give the children algebraic type problems that involve balancing to help them understand the meaning of the equals sign. For example:

2n + 10 = 36 (take 10 from each side to give 2n = 26, divide each side by 2 to give n = 13 7 = 2x ÷ 6 (multiply each side by 6 to give 7 x 6 = 2x which is 42 = 2x, divide each side by 2 to give

21 = x

You could also give problems such as:

Sharon and Tim each had a collection of football stickers. Tim had 5 times as many as Sharon. He had 150. How many did they have altogether?

You could encourage the children to use the bar model to solve this:

Sharon

Tim

Tim has 150 stickers, so each square represents 30 stickers. Therefore Sharon has 30 and altogether they have 180.

Tina had a cupboard in her bedroom on which she kept her books. There were 15 books on each of 8 shelves. A friend gave her another 24 books which she put equally onto the 8 shelves. How many books were on each shelf?

Activity set H

You could show photographs of some famous buildings or the children to illustrate how objects or people are scaled down. Explain that, to describe how much something has been scaled down, we often use ratio or simple fractions.

You could set this problem: A tennis court is 7m wide and 24m long. A scale plan of it is drawn with a width of 3.5cm. What is its length? Agree that 7m has been divided by 100 to become centimetres and then halved. The same must therefore be done with 24m to give 12cm. You could repeat this type of problem with other similar scenarios.

The children could work in a small group to make 2D drawings of objects in the classroom. They measure heights and widths of their objects and then scale them down. They decide their own ratio for scaling down, for example, 1:2 (half the size) or 1:3 (one third of the size). Make the point that scaling down is the same as multiplying by a value less than 1.

Year 5 Fractions


Activities

A B C D E F

compare and order fractions whose denominators are all multiples of the same number

recognise mixed numbers and improper fractions and convert from one form to the other

add and subtract fractions with the same denominator and related fractions

multiply proper fractions and mixed numbers by whole numbers

read and write decimal numbers as fractions (e.g. 0.71 = 71/100)

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

read, write, order and compare numbers with up to three decimal places

Solve problems involving numbers with up to three decimal places

recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred” and write percentages as a fraction with denominator 100, and as a decimal

write percentages as a fraction with denominator 100, and as a decimal

Activity A - Fractions ITP

An interactive program that allows you to model part-whole relationships using a strip divided in to equal parts. Relationships can be shown as fractions, decimals (to three places) or percentages.

Activity B - Fractions Jigsaw

A jigsaw-based activity that requires children to add and subtract fractions with the same and different denominators. Pieces must be matched to an answer that may be expressed in equivalent forms. It also includes multiplying fractions by a whole number.

Activity C - Peaches today, Peaches tomorrow…

A problem solving activity that requires children to find fractions of whole numbers. It provides plenty of practice and has many extension opportunities.

Activity D - Metre sticks and metre strips

Use classroom metre sticks/rulers and I metre long strips of paper to model relationships between a whole, tenths, hundreds and thousandths. Children can explore the size of 1, 2 and 3 decimal places and how they link to units of measurement. Labelling points with decimal, fraction and percentage equivalents can help to reinforce links between all three.

Activity E - Matching fractions, decimals and percentages

A pelmanism-style activity matching pairs of equivalent fractions, decimals and percentages. Points are awarded for correct answers and deducted for turning over cards without success.

Activity F - Using blank hundred squares

Use blank hundred squares to model and explore percentages, tenths and hundredths. Decimals, fractions and percentages can be represented by colouring in blank hundred squares which children can use to support addition and subtraction.

Year 5 Measurement


Activities

A B C D E

convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

understand and use equivalences between metric units and common imperial units such as inches, pounds and pints

measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

calculate and compare the area of rectangles (including squares) and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

Activity A - If the world were a village

This activity involves ‘shrinking’ the world population to a group of just 100, and focusing on the different proportions that emerge and the ways in which the data can be presented

Watch a video about this activity

Activity B - Numerically equal

Find shapes that have a numerical equal area and perimeter.

Activity C-Area and Perimeter

Draw shapes according to the rules of area and perimeter.

Activity D - Converting between metric units

A useful jigsaw-style activity, where the children use their knowledge of conversion of different units of measure to match pieces together.

Activity E- Converting between metric and imperial

A worksheet.



Activities

A(i) A(ii) B C

read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

round any whole number to a required degree of accuracy

use negative numbers in context, and calculate intervals across zero

solve number and practical problems that involve all of the above.

Activity A(i)

Activities related to space will provide opportunities for children to work with large numbers, ordering and rounding. Try these:

model of the solar system alternative way to model the solar system

Activity A(ii)

Activities in the context of space and the solar system also provide excellent opportunities for working with positive and negative integers. There are a number of interactive and relevant activities.

Activity B - Tug Harder

This two player game from Nrich requires the children to use their knowledge of both positive and negative numbers, and the effect they have on each other. Some useful question prompts are included too – to really get them thinking!

It is important that children become familiar with both ordinal and cardinal aspects of number so although moving along a number line is the most common way to teach negative numbers, it is also important for them to see negative numbers as the absence of something – teachers oftendig (concretely or pictorially) holes to represent a negative value. You could have a lot of fun with moles and holes that will help children develop a robust concept of negative numbers. The‘cancellation’ effect of adding an integer with the opposite sign is something that children should explore and incorporate into their understanding of negative numbers.

Activity C - Sometimes we lose things

This intriguing activity introduced children to working in base 9, with a real focus on understanding our number system more deeply.



Activities

A B C

perform mental calculations, including with mixed operations and large numbers

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

solve problems involving addition and subtraction use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy

Activity A

Present the children with problems such as:

Taznim measured two lengths of material. One measured 3.45m and the other 2.65m. How much longer was the longest? What is the total length?

Discuss mental calculation strategies that can be used to answer these, for example complementary addition for the subtraction, number facts and partitioning for addition.

Louis poured 1998ml of water into one bucket and 2550ml into another. How much water did he have? How much more was in the second bucket?

Discuss suitable mental calculation strategies, for example, rounding and adjusting for both addition and subtraction.

Teachers could decide on the mental calculation that they wish the children to rehearse, practice and then make up problems for them to answer. Common mental calculation strategies for addition and subtraction include:

Partitioning and recombining Doubles and near doubles Use number pairs to 10 and 100 Adding near multiples of ten and adjusting Using patterns of similar calculations Using known number facts Bridging though ten, hundred, tenth Complementary addition

Activity B

Set problems such as this for the children to solve:

Sammy wanted to buy a DVD player for £326.98 and a DVD box set for £49.50. How much money will she need? How much more will the DVD player cost?

Encourage the children to use the method they think best to calculate with these numbers, e.g. the column method, rounding and adjusting (£326.98 + £50 – 50p), sequencing (326.98 + 40 + 9 + 50p).

Give the children a set of 0-9 digit cards. They pick five, make a five-digit number and write it down. They then use those five cards to make up another number. They find the total of the two numbers and then make up a problem using their numbers and calculation. They could do the same for subtraction.

This Nrich activity asks children to solve a subtraction calculation where the numbers are represented by letters.

Activity C

The children could be presented with problems such as:

Kieran was saving to buy a laptop for £465.98 and a printer for £126.78. How much money does he need to save?

Maddie saved £1987.50. She wanted to buy a new TV. It cost £1268.45. Has she enough money left to buy a games console costing £474.99?

The children could be given a selection of amounts of money, e.g. £852.79, £1089.50, £60.98, £284.99. They could pick two of the amounts and find their totals and differences. They could then make up problems to go with their calculations.

For each problem, ask the children to check their answer by rounding the amount to the nearest pound or £10. They could also use this method to estimate what the answer might be at the beginning.



Activities

A B C D E F G

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

perform mental calculations, including with mixed operations and large numbers

identify common factors, common multiples and prime numbers

solve problems involving multiplication and division use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy

Activity A

Teachers could ask the children to create their own numbers to multiply using digit cards and dice. Make the link between the grid method and the compact method, for example, asking the children what is the same and what is different about the two methods:

Activity B

Set problems such as:

Naomi had a stamp album; it had 135 pages. On each page there were 45 stamps. How many stamps did she have?

3000

500

60

7

20

60000

10000

1200

140

71340

4

12000

2000

240

28

14268

Total

85608

3567

x24

14268

71340

85608

This Nrich activity entitled ‘Long Multiplication’ requires children to solve a multiplication puzzle where all except one of the digits are missing. A wonderful challenge!

Activity C

Set problems such as:

Yukesh was given a box of 755 books to put on the shelves in the library. He put 24 books on each shelf. How many shelves did he fill? How many shelves did he need for all the books?

Courtney had a collection of 1256 coins. She put them into piles of 16. How many piles did she have? How many were left?

Activity D

Give the children a set of 0-9 digit cards. They choose four of the cards, make a four-digit number and write it down. They then use two of those cards to make the divisor. They calculate the answer and then make up a linked problem using their numbers.

Activity E

Provide the children with problems that involve using mental calculation strategies, such as:

x4 by doubling and doubling again, x5 by x10 and halving x20 by x10 and doubling x9 by multiplying by 10 and adjusting x6 by multiplying by 3 and doubling

Activity F‘Abundant Numbers’, an activity from Nrich requires children to explore factors of numbers.‘Factors and multiples’ is another Nrich game, perfect for practising skills.

Activity G

Provide problems such as:

Milly is saving £2.75 a week to buy a pair of jeans. The jeans cost £37. For how many weeks does she need to save?

In Sports 4 U, there are 18 larges boxes each containing 136 footballs. How many footballs are there altogether?

For each problem, ask the children to check their answer by rounding. They could also use this method to estimate what the answer might be before solving the problem.

Year 6 Fractions


Activities

A B C D E F G

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Compare and order fractions, including fractions >1

Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [ for example, 3⁄8 ]

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Multiply simple pairs of proper fractions, writing the answer in its simplest form [ for example, ¼ × ½ = 1⁄8 ]

Divide proper fractions by whole numbers [ for example, ⅓ ÷ 2 = 1⁄6 ]

Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places

Activity A : Factors and Multiples Game

This game from Nrich could replace standard practice exercises on finding factors and multiples. In order to play strategically, pupils must start to think of numbers in terms of their factors

Activity B(i) : Rod Fractions

Compare a series of coloured rods and the relationships between them with this clearly presented Nrich activity

Activity B(ii) : Laundry Line

This activity features a laundry line with ‘fraction washing.’ The aim is to hang the fractions on the line in the right order between 0 and 1. Once a game has been completed, you can raise the level of difficulty.

Activity B(iii) : Chocolate

Using chocolate bars to compare fractions – a context guaranteed to keep them focused!

Activity C : Fraction strips

The ‘Fractions’ Interactive Teaching Programme, allows the user to divide a strip into equal parts and colour them as needed. Strips can be labelled as a fraction, decimal or percentage. The ratio of parts can also be displayed. Multiple strips can be created to demonstrate equivalence.

Activity D(i) : Clock Faces

Give children the chance to explore clock faces as a way of representing time. Talk about 5 minute sectors of the clock being equivalent to twelfths, ten minute sectors to sixths, fifteen minute chunks to quarters etc…

Use this to support them in adding 20 minutes plus 15 minutes as 1/3 + 1/4

Activity D(ii) : Andy’s Marbles

This challenging activity from Nrich requires children to use their conceptual understanding of fractions, and their sums, to determine the answer to Andy’s marble problem

Activity D(iii) – Soccer Shoot Out

Score and save goals by correctly answering fraction based calculations. A range of difficulty levels makes this game easy to adapt.

Activity E(i) : Folding ribbons

Show the children a lengths of ribbon (or string) measuring 3/4 metre in length. Fold it into three parts. What fraction of the ribbon have we found? ( 1/3 ). Measure the folded piece together. How long is it? ( 1/4 m). So, 1/3 of 3/4 or 1/3 x 3/4 = 1/4.

Try this with other fractions and starting lengths.

Activity E(ii) – ratio tables

Ask children to use their multiplication tables to scale recipe quantities up and down to complete the table below. Consider their multiplication of simple fractions for quantities of vanilla extract and chocolate chips.

Ingredients 3cupcakes

6cupcakes

12cupcakes

18cupcakes

24cupcakes

Self- raising flour 130 gm 260 gm

Caster Sugar 100 gm

Butter 125 gm

Large Eggs 2

Vanilla extract ½ teaspoonful 1 teaspoonful

Chocolate chips ¾ cupful

Activity F(i) - Pizzas

This pizza themed fraction resource from the TES can be used in many different ways, and includes several suggestions from the author.

Activity F(ii) – Planetary Wars

Published by BEAM, and hosted within the National STEM Centre E-library, this two-player dice game requires children to find fractional quantities of numbers.

Activity G – Decimal Point Chair

When multiplying or dividing by powers of ten, the key issue to emphasise in many classrooms is that it is not the decimal point which moves, but the digits of the number. Prepare a range of cards to include several zeros, a decimal point and two whole numbers [e.g. 2 and 7]. Give a group of children one card each and ask the child with the decimal point to sit in the middle of a row of chairs, facing the class. Ask the 2 children with the cards with whole numbers to choose a chair to sit on, leaving no empty chairs between them and the decimal point. Explore ways to do this. Then introduce one zero in various places and talk about the numbers created. Add a second zero and do the same. Move on to asking the children to decide what happens to the number created if we multiply or divide by 10, then 100, then 1000 – emphasise that the decimal point must not move. Ask children to consider ways in which they might record this.

For a similar activity visit the National Stem Centre E-library, for the Interactive Teaching Programme ‘Moving Digits’

Please note that you will need to log in to this site in order to access the materials. This is free and simple to do.

Year 6 Ratio and Proportion


Activities

A B C D

solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

solve problems involving similar shapes where the scale factor is known or can be found

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Activity set A

You could give the children, for example, one green and three yellow counters, the children could identify, for example, the ratio of green to yellow, the proportion of green. They could then work out other numbers of counters that would give the same ratio, for example two green and six yellow, three green and nine yellow,. This would help them to understand that the numbers of counters might change but the ratio does not change, if the relationship between the different parts remains the same. You could ask them to explore what they need to do to find a formula for ‘g’ green and ‘y’ yellow so that they can work out any number of these counters that give the same ratio and proportion.

Give the children some blue and white interlocking cubes and ask them to show you different ratios and proportions, such as:

a 5:2 ratio of blue to white a 2:5 ratio of blue to white blue is 2/5 of white blue is 5/2 or 2½ of white the proportion of cards from a normal pack of 52 that is red the proportion of cards from a normal pack of 52 that are aces

You could give the children a selection of recipes from the internet and ask them to work out the ratio of, for example, flour:sugar:margarine in a sponge cake, or the proportion of a ready meal that should be eaten by 2 people if the meal is intended to serve 6 people. You could then ask them to rewrite a list of ingredients for a recipe, originally written for 4 so that it will serve 6 or 12 people.

You could give the children problems such as:

Tom and Nafisat win £750 between them. They agree to divide the money in the ratio 2:3. How much do they each receive?

A necklace is made using gold and silver beads in the ratio 3:5. If there are 80 beads in the necklace:

o How many are gold?o How many are silver?

To make a tasty chocolate milkshake James needs one part chocolate sauce to six parts milk. Each part is 150ml

o If he used 4 parts of chocolate sauce how much milk would he need?o If he had 420 ml milk, how much chocolate sauce?

Activity set B

The children could construct a pie chart and then make up and solve problems from it. You could set scenarios such as: the local health authority are surveying the eating habits of school children and want to know how many of the 360 children in a local school have school dinners, packed lunches or go home. If appropriate the children could find out this information or could make up the data. They could then construct a pie chart using a protractor with every degree representing one child. They could then find the numbers, fractions or percentages of children having each type of lunch.

Set problems such as this for the children to solve:

Tammy was saving for a laptop. The laptop she wanted cost £360. She has saved 60% of the amount. How much more money does she need?

Encourage the children to use effective methods to find 60%, such as find 50% by halving and then 10% by dividing £360 by ten and adding the two amounts together.

In the sale a coat has been reduced by 20%. It now costs £56. What was its original price?

The children could use the bar model to help them solve this:

Each section of the bar is worth £14 so the original cost of the coat must be £70.

You could give the children the Nrich activity ‘Rod Ratios’ or, as a challenge, ‘Weekly Problem 27’

Activity set C

Children could look at photographs of themselves or famous buildings and discuss why they are smaller than the actual children or buildings. Establish that they have been scaled down. Discuss where else they might see scaled down images, for example, maps, models, architects plans.

The children could measure the lengths/heights and widths of objects around the classroom, scale these measurements down by an amount they choose and then sketch the object to that size on paper. Other children could estimate by how much these have been scaled down.

The children could look at maps and work out distances from one place to another using the given scale.

You could discuss when objects might need to be scaled up – explain that this is called ‘enlarged’. A good example would be looking at very small objects under a magnifying glass or microscope. If you have any available the children could use the equipment to see what different objects, such as an apple pip or the head of a pin, would look like if scaled up by the magnification on the apparatus.

Activity set D

The children could look at paintings such as ‘Tiger in a storm’, by Henri Rousseau. They could explore mixing blue and yellow paints to get the colours that Rousseau has achieved. What ratios of blues and yellows have they made? What are these as proportions or fractions of the total paint mix? They could paint a jungle scene using their mixed paints.

See The Art of Mathematics for other ideas of how to link ratio and proportion to art

Year 6 Measurement


Activities

A B C D E

solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places

convert between miles and kilometres

recognise that shapes with the same areas can have different perimeters and vice versa

recognise when it is possible to use formulae for area and volume of shapes

calculate the area of parallelograms and triangles

calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³

Activity A : Numerically Equal

Challenge the children to see if they can draw a square in which the perimeter is numerically equal to the area. What about other shapes?

Activity B: Weekly Problem 20 – 2011

Can you find the perimeter of this unusual shaped polygon?

Activity C : Through the window

The local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Activity D : Making boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume? How do we know?

Activity E : A little bit of history - Marco Polo

Compare historical journeys and convert units of measure whilst learning all about the well-known traveler, Marco Polo.

©NCETM

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