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Wiltshire 27 - Early Years Foundation Stage

Objective Always/Sometimes/Never Thinking questions Add, Remove Replace

Say and use number names in order in familiar contexts.

A six follows a five. Have two sets of numbers from 0 – 10 with different ones missing. Order the two sets of numbers. What’s the same and what’s different? What if we had another set of numbers with some missing?

Have a selection of hankies in a basket e.g. one red one, two blue ones, three yellow ones, five green ones, eight white ones. Sort them on a washing line. What do you notice? What if we had these other hankies?

Count reliably up to ten everyday objects. When I count a pile of bricks there are 10.

When I count objects 6 comes before 7.

Show several groups of nine objects.

What’s the same and what’s different?Why?

What if we put some more in each group? How do you know?

Take a pile of cubes and count them.Remove some and count the pile again.What’s happened? Put the cubes back.What do you notice?What if I started with a different pile of cubes?

Recognise numerals 1 to 9. Where there is a ‘5’ there are five ‘things’. Why do we need the digit 8? Where can I find the digit 8? What’s the same and what’s different? Why?

What about a different digit?

Given the numbers 1-5, order them.What if I give you the number 8? Where will it go? What if you now have the number 6? What do you notice?What about other numbers?

Use developing mathematical ideas and methods to solve practical problems.

The missing number is a 6. Show lego towers/walls made from 10 bricks each. What’s the same and what’s different? What if we took some bricks away? Why?

Given 6 teddies, 5 chairs, 8 knives, 4 forks and 2 spoons: How do we lay the table? What do you notice? What if there was another teddy?

In practical activities and discussion, begin to use the vocabulary involved in adding and subtracting.

When I add two numbers the answer is five.

When I take some away I have 3 left.

Model making a total of 7 out of two different coloured bricks, in different ways. What’s the same and what’s different?Why? What if I had 6 dinosaurs?

Have 5 frogs on each of two lily pads. What if I move 2 frogs from this pad to that pad? What do you notice? What if I move…?

1


Use language such as ‘more’ or ‘less’ to compare two numbers.

When I add 2 I have more than when I add 1.

Show two piles of cars. What’s the same and what’s different? What if I move this car from this pile to that pile? Why?

Show 2 shelves of books, 7 on one and 9 on the other. What do you notice? What if we take 2 books off this shelf? Why?

Find one more or one less than a number from one to ten.

When I remove an object from a pile there are less than I started with.

Have 8 different coloured bricks. Take away the red one. What happens?

Put it back. Take away the yellow one.What happens? Etc.

What’s the same and what’s different?Why?

What if I started with 9 bricks?

I have some apples in my bag. I take 1 out. How many might I have left?What if I put 1 in?Why?

Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’.

There are three different ways to make 5. Show some piles of sticks e.g. 7, 3, 10. What’s the same and what’s different?What if I want 4 sticks in each pile?What do I need to do? Why? What if I wanted 5 in each pile? Why?

I need 8 volunteers. If I’ve got some boys how many girls do I need to make 8? How many ways can I do this? What do you notice?What if I needed 9?

N.B. Although most of these ideas are context free, it would be preferable for them to link to learning themes and role play areas where possible.

2

Wiltshire 27 – Year 1


Count reliably at least 20 objects, recognising that when rearranged the number of objects stays the same; estimate a number of objects that can be checked by counting.

If I take a handful of cubes and then count them I get more than 10. When you estimate a number of objects and then count them, the answer is the same.

I’m thinking of a number. When I add 2, I get 12.What was my number?What if I add 3, 4?What’s the same, what’s different?Why?What if the number I get is 11?13p, 13, 13 toys etc. What’s the same?What’s different?

Count a group of objects. Remove a handful and count them again. Put the handful back and count again. What do you notice?

Compare and order numbers, using the related vocabulary; use the equals (=) sign.

On a number line to 20, a number with a digit 2 comes before a number with a digit 3.

14, 17, 13, 19, 9, 4, 2.Order the numbers.What’s the same, what’s different? Why?What if we have another number?

□ + □ = 5

5 = □ + □□ + □ = □ + □Using an arm balance or cubes what numbers can you put in here to make the sentences true?

Read and write numerals from 0 to 20, then beyond; use knowledge of place value to position these numbers on a number track and number line.

Numbers between 10 and 15 are nearer to 10 than 15.

Find the numbers on either side of 4 and 14.What’s the same, what’s different? Why?What about 7 and 17?What if we look at other pairs of numbers?

5 is between □ and □

How many ways can you complete this?

Say the number that is 1 more or less than any given number, and 10 more or less for multiples of 10.

If I add one cube to a handful of cubes, there will be more than 10.

9 + 1 = 1010 – 1 = 9What’s the same, what’s different? Why?What if it was 8 + 1?

□ is 1 more than □□ is 10 less than □How many ways can you complete this?What do you notice?Why?

3


Use the vocabulary of halves and quarters in context.

A half of an object is bigger than a quarter. Fold a piece of paper in half. Now fold it in half a different way.What’s the same, what’s different?Why?What about folding a different piece of paper?

Half of is □ is □How many ways can you complete this?What do you notice?Why?

Derive and recall all pairs of numbers with a total of 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts.

When you roll 2 dice and add the numbers there are more than 9 spots.

A number less than 5 plus a number less than 5 is a number less than 5.

Find all the number facts of 5.What’s the same, what’s different? Why?What if we look at the pairs that make 10?

10 - □ = □How many different ways can you make this true?

Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10 to the tenth multiple.

When you count on in fives you land on odd numbers.

How many ways can I count in equal steps to 20?What’s the same, what’s different? Why?What if I count to 30?

□, □, □, 0What numbers can I count back in to make this sequence true?

Recall the doubles of all numbers to at least 10.

When you double a number you add 2. Double 6 is 12.Half of 12 is 6.What’s the same, what’s different?Why?What if I use different numbers?

Double □ = □How many ways can you complete this?

Relate addition to counting on; recognise that addition can be done in any order; use practical and informal written methods to support the addition of a one-digit number or a multiple of 10 to a one-digit or two-digit number.

1 □ + □ = a number less than 20.

The only way to add is to count on your fingers.

□ + 10 = □How many ways can you make this true?What’s the same and what’s different?Why?What if it was 10 + □□?

□ count on 2 is □How many ways can you complete this?What’s the same, what’s different? Why?What if you count on 3?Why?

4


Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one digit or two-digit number and a multiple of 10 from a two-digit number.

If I subtract 2 the answer is more than 5. How many ways can you show me a difference of 2.(e.g. with different resources)What’s the same, what’s different? Why?What if you show me a difference of 1?

Find 10 different ways to complete this.□ - □ = 5What do you notice?□ count back 5 is □How many ways can you complete this?What’s the same, what’s different?Why?What if you count back 3?Why?

Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentences.

When I add I get more than 10. 3 + 2 = 55 = 2 + 35 – 2 = 32 = 5 – 3What’s the same, what’s different? Why?How many other number sentences can you write?What if you have different numbers?

□ add 2 = □□ minus □ = 5

How many ways can you complete this?What’s the same, what’s different?Why?

Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal groups.

Bags of fruit can be sorted into equal sets of 2s or 5s.

If you give children 2 toys each how many might you have had?What’s the same, what’s different?Why?What if you give them 5 toys each?If I only have 10p coins in my purse, how much might I have?

I have □ coins in my money box.They are all 10 pence coins.How much could I have?

N.B: Although all these ideas are context free, it would be preferable to make links with topic work and other areas of mathematics such as measures and money.

5



Estimate a number of objects; round two-digit numbers to the nearest 10.

When I estimate a number of objects the answer is the same when I count them.When I round a number to the nearest ten I reach a larger number.

Given a set of 2 digit numbers, plot them on a blank number line.What’s the same, what’s different?Round (slide) the numbers to the nearest 10.What’s the same, what’s different? Why?What if we tried some other numbers?

□ rounds to 20.How many different numbers can you use to make this true?What’s the same, what’s different?What about numbers that round off to 40?

Count up to 100 objects by grouping them and counting in tens, fives and two; explain what each digit in a number represents, including numbers where 0 is a place holder; partition two-digit numbers in different ways, including into multiples of 10 and 1.

A 2 digit number can be partitioned in more than 3 ways.When you count a number of objects you get more than 50.

When I count on in tens I only land on numbers that end in 0.

6, 36, 630, 63, 306, 603.What’s the same, what’s different? What about the value of digits?Why? What if the 3 was a 4?

Count a large group of objects in twos, fives or tens. Remove a handful and count them again. Put the handful back and count again.What do you notice?What happens if you do it again?Why?

Read and write two digit and three digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers.

When I count on in 5s from 0 the numbers I land on are even.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.Sort numbers into odd or even.What’s the same, what’s different? Why?What about other numbers?How can you use this to tell if another number is odd or even?

0, 2, 7.Given 3 digits how many different numbers can you make?Are they all 3-digit numbers?Why not?What if you had a 4 instead of 0?

Order two-digit numbers and position them on a number line; use the greater than (>) and less than (<) signs.

A number which contains the digit 2 is smaller than a number which contains the digit 3.

23, 37, 53, 79, 93.What’s the same, what’s different?What do you look for when you order numbers?Why?

□ > 12 > □How many ways can you complete this number sentence?What do you notice?What if you change the 12?

6


Find one half, one quarter and three quarters of shapes and sets of objects.

Three quarters of a shape is bigger than a half.

Find a quarter of circles of different sizes.What’s the same, what’s different?How could you find ¼ of a piece of string?What about ¼ of 2 pieces of string?

¼ of □ is □so ¾ of □ is □How many ways can you make this rue using objects?What do you notice?Why?

Derive and recall all addition and subtraction facts for each number to at least 10, all pairs of multiples of 10 with totals up to 100.

When you roll 3 dice there are less than 15 spots.

List all the pairs that make 10.What is the same, what’s different?Why?What if you rearrange the numbers into the corresponding subtraction sentence?Does this work for all the number pairs?How many subtraction sentences can you make from each tens pair?What about multiples of 10?Why?

□ + 3 = □ – 3How many different ways can you make this true?Change the 3 for something else. What’s the same, what’s different?Why?100 = □ + □Which numbers could you use that are multiples of 10 to make this true?Have you found all the possibilities?How do you know?

Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves.

Halving a number less than 20 gives an answer less than 10.

5 + 5 = 10 10 = 5 x 26 + 6 = 12 12 = 6 x 2What is the same, what’s different?Why?What about other pairs of statements?

Double □ = □Half of □ = □How many pairs of statements can you make?What do you notice?Why?

Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10.

All the multiples in the 5 times table end in 5.

□ x 5 = □How many different answers can you make?What’s the same and what’s different?Why?What if you multiply by 10?

□□ ÷ 2 = □How many ways can you make this true?What if it was□□ ÷ 2 = □ remainder 1.

Objective Always/Sometimes/Never Thinking questions Add, Remove Replace7

Use knowledge of number facts and operations to estimate and check answers to calculations.

If you add 7 then take 7 away you get back to where you started.

13 + 8 = □□21 = 13 + □13 = □□ – 8

21 - □□ = 8Complete the number sentences. What’s the same, different? Why?What if the 8 was a 9 …?

I think of a number and add 5.What could my number be?How do you know?What if I add 6?

Add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers.

The best way to count on or back is to use your fingers.

To subtract 10 you count back 10 on a number line.

List pairs of number where one is ten more than the other.What’s the same, what’s different? Why?What if one was ten less than the other?Why?I’m thinking of a number, when I subtract 8, I get 57.What was my number?What if I subtract 7, 9, 10?What’s the same, what’s different?Why?

1□ + 1 □ = 33How many ways can you make this true?How do you know?Are they are other pairs of numbers that add up to 33?What’s the same, what’s different? Why?What if the total was 34?

Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences.

Any addition number sentence can be rearranged into a subtraction number sentence.

How many ways can you show me a difference of 9 (e.g. with different resources).How could you record it?What about a difference of 11?You know 7 + 8 = 15.Can you rearrange this into any other number sentences?What’s the same, what’s different? Why?

74 - □ = 61Write more number sentences using these numbers.How do you know whether they are correct?What’s the same, what’s different? Why?What if you change one of the numbers?

8


Use the symbols +, -, x, ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a umber sentence,(e.g. □ ÷ □ = 6, 30 - □ = 24).

If I divide by 2 the answer is odd. 3 □ – 9 = 2 □Complete this in different ways.What’s the same, what’s different? Why?What if you subtract 8?

How many numbers from 1 – 30 can you make using 2, 5 and 10 and any of the symbols + , -, x, ÷ and =

Represent repeated addition and arrays as multiplication; and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders.

Multiples of 2 are also multiples of 5.

If I start at 0 and make 3 jumps the same size, the biggest number I can land on is 15.

Divide some numbers by 5.Which numbers have a remainder?What’s the same, what’s different?Why?What if I divide by 10?

□ = 24 ÷ □Using 24 cubes how many ways can you divide 24 into equal groups?How did you work this out?

What if you had □ cubes?

N.B. Although all these ideas are context free, you may be able to link them to topic work and other areas of mathematics such as measure and money.

9



Read, write and order who numbers to at least 1000 and position them on a number line; count on from and back to zero in single-digit steps or multiples of 10.

A number with 5 tens is bigger than a number with 3 tens.

Starting with a single digit number count in multiples of 10.What do you notice about the numbers you say?What’s the same and what’s different?Why?What if you start at a different number?

Using the digits 3, 4, 5 and 6 how many different 3 digit numbers can you make? Order them on a number line.What’s the same and what’s different?What if you used 4, 5, 6 and 7?

Partition three-digit numbers into multiples of 100, 10 and 1 in different ways.

All 3 digit numbers can be portioned in more than 5 ways.

How many ways can 287 be partitioned using multiples of 100, 10 and 1?What’s the same and what’s different?Why?How can you be sure you have found them all?

342 + 655Can you replace a single digit so that only one digit changes in your answer?(2 digits, 3 digits?)

Round two-digit or three digit numbers to the nearest 10 or 100 and give estimates for their sums and differences.

If I add together 2 two digit numbers that each round to 100 the answer will round to 200.

I round a number to the nearest 10 and the answer is 70.What number could it be?What’s the same and what’s different about the numbers?What if it rounded to 60?

□ rounds to 30.How many ways can this be true?

Read and write proper fractions (e.g. 3/7, 9/10), interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents.

The numerator and the denominator are the same.

⅔ of a shape is bigger than ⅓ of a shape.

When is the numerator smaller than or equal to the denominator?Draw some of these.What do you notice?

□ + □ < 1

□ □When could this be true?What if the denominator is different?

10


Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100.

A number less than ten added to a number less than ten = a number less than ten.

List all the subtractions pairs of 10 and then the subtraction pairs of 20.What’s the same and what’s different?Why?What if we looked at pairs of multiples of 10 to 100?Why?

3 + □ = □ – 7

How many ways can this be true using numbers less than 20?What’s the same and what’s different.

Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000.

If I add 3 consecutive numbers the answer is divisible by 3.

Multiples of 10 are only divisible by 2, 5 and 10.

□ 5 + 8 = □How many ways can you make this true?Is there a pattern?

□ ÷ □ 4 = □How many ways can you make this statement true? (using numbers less than…)What do you notice?Why?What if it were □ ÷ 4 = □ remainder 1.

1 □ x □Using the digits 3, 4, 5, how many different totals can you make?How do you make the biggest total?What if the digits were …?

Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations.

Halving a number gives me an odd answer. Choose an even number, take away 2 and halve it. Starting from the same even number halve it, then take away 2.Do this lots of times.What do you notice?What’s the same and what’s different?How do I get back to the starting number?

Double □ + double □ = ?If you increase/decrease one or both of your starting numbers, what happens to the total?Why?

11


Add or subtract mentally combinations of one-digit and two-digit numbers.

If I add two 2 digit numbers the answer has 3 digits.

Find some pairs of numbers with a difference of 19.What’s the same and what’s different?Why?What if the difference was 21?

□ 5 – 8 = □ How many ways can you make this true? Is there a pattern? Why?What if you subtract 9?

Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers.

A number line is the best way to find the difference between 2 numbers.

Counting on is the best way to do subtractions.

Add 99 to some 3 digit numbers.What do you notice?Why?What if you subtract 99?

1□□ - □ 9 < 100.Using the digits 4, 5 and 6 how many ways can you make this true?

Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect.

When I multiply a number by 10 the answer is divisible by 5.

Why is 3 x 100 = 30 x 10?What other examples can you find?What’s the same and what’s different?What if the 3 was a 4?

□ 0 x 10 = □ x 100Complete this number sentence in lots of different ways.What’s the same and what’s different.Why?

Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 x 3, 50 ÷ 4); round remainders up or down, depending on the context.

A teens number times a single digit number gives an answer between 40 and 80.

Dividing an even number by 6 gives a remainder of 3.

1□ x □Using the digits 3, 4 and 5 how many different totals can you make?How do you make the largest total?What if the digits were …?You can pack your 72 cubes into boxes. Of 2x, 3s, 4s, 5s or 6s.How many boxes would you fill?What’s the same and what’s different?Why?

What if you had □ cubes?

□ ÷ 5 = □ r 1

How many ways can you make this true?What do you notice?Why?What if it were remainder 2?

12


Understand that division is the inverse of multiplication and vice versa;use this to derive and record related multiplication and division number sentences.

I can rearrange any multiplication sentence into a division sentence.

Using the digits 2, 3, 4 and 5 write as many multiplication statements as you can and their corresponding division sentences.What’s the same and what’s different?Why?What if we made them 10 times bigger?

□ ÷ 3 = □How many ways can you make this true?What multiplication sentences can you write?What’s the same and what’s different?Why?

Find unit fractions of numbers and quantities (e.g. ½, ⅓, ¼ and of 12 litres).

Half of one number is smaller than ¼ of another.

Find half of lots of numbers.What’s the same and what’s different?

⅓ of □ is □How many ways can you make this true? What do you notice?

13



Recognise and continue numbersequences formed by counting on orback in steps of constant size

Counting on in 6s only uses evenNumbers.When you count in 4s you land on multiples of ten.

Given a mixture of multiples of 4 and6 askWhat's the same, what’s different?What if you double them?Why?What if you double them again?

……..27……..What sequence could this number be part of?How many different sequences can you make that also have the number □ in them?

Partition, round and order four-digitwhole numbers; use positive andnegative numbers in context andposition them on a number line; stateinequalities using the symbols < and >e.g. -3 > -5, - 1 < +1

A number with 5 hundreds is bigger than a number with 3 hundreds.

3475, 3574. 4537, 3754, etc.What's the same, what's different?Order them.What if you change the 4 to an 8?Which numbers change position?Why?

□ □ < □ □Using the digits 3, 5, 6, 8, how manyways can you make the sentence true?What's the same, what's different?What if we use different digits?Why?

Use decimal notation for tenths andhundredths and partition decimals;relate the notation to money andmeasurement; position one-place andtwo-place decimals on a number line

A number with one decimal place is smaller than a whole number.

4.9, 4.90, 4, 5.1, 5, 5.01What's the same, what's different?What if you order them?What if you write them as money?Why?What if you try plotting a number between each one in the list?

□ □ < □ □Using the digits 3, 4, 6, 9, how many ways can you make the sentence true?What's the same, what's different?What if we use different digits?Why?

Recognise the equivalence betweendecimal and fraction forms of one half, quarters, tenths and hundredths.

If the numerator is half the denominator then the fraction is equivalent to 0.5.

Show a selection of fractions equivalentto 0.25What's the same, what's different?What if you doubled numerator, denominator, both?Why?

0.4 = □ □How many ways can you make thisTrue?

14


Use diagrams to identify equivalent fractions [e.g. 6/8 and 3/4, or 70/100 and 7/10); interpret mixed numbers and position them on a number line e.g. 3 1/2.

A fraction with 6 as the numerator is more than 1.

Show a selection of fractions with some equivalent fractions. What's the same, what's different? Change a number. Can you change another number to maintain the equivalence?

□□ Using the digits 4, 2, 5, make as many different fractions as you can (including vulgar fractions to be written as mixed fractions). Plot them on a number line. What if you had another digit?

Use the vocabulary of ratio and proportion to describe the relationship between two quantities (e.g. There are 2 red beads to every 3 blue beads, or 2 beads in every 5 beads are red); estimate a proportion (e.g. About one quarter of the apples in the box are green).

If there are 2 red beads to every 3 blue beads the total number of beads is a multiple of 10.

Show some bead patterns of different ratios (include some equivalent ones). What's the same, what's different? Why? What if you add one bead to each pattern?

Using 5 beads of 2 different colours what might the ratio of one colour to the other be? What if you had □ beads?

Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000.

A multiple of 100 plus a multiple of 100 makes a multiple of 1000.

List all the pairs of multiples of 10/100/1000 that make □What's the same, what's different? Why? What if you made a different total?

9000 = □□ 00 - □00How many ways can you make this true? What if it was 8000?

Identify the doubles of two-digit numbers; use these lo calculate doubles of multiples of 10 and 100 and derive the corresponding halves.

Half of a multiple of 10 has a five in the unit column.

Show some multiples of 10 and 100, e.g. 50, 500, 70, 700, 80, 800 and derive their halves. What's the same, what's different? Why? What about other multiples of 10 and 100? Which were easier to find?

Double □ 7List some possible pairs. What do you notice? What if it was □8? Try halving □4 What do you notice?

15


Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple.

Multiples of 4 are also multiples of 8. List the multiples of 6. What's the same, what's different? Why does the pattern in the units column occur? What if you look at multiples of 4?

72 ÷ □ = □36 ÷ □ = □How many ways can you make these statements true? What's the same, what's different? Why? What if you divided 18..? 48..?

Use knowledge of rounding, number operations and inverses to estimate and check calculations.

You use multiplication to find a missing number in a division calculation.

List a family of calculations e.g. 6 x 7 = 42 42 ÷ 7 = 6 7 = 42 ÷ 6 42 = 6 x 7 What's the same, what's different? Why? Can you extend the family?

□ x 4 = □□ ÷ 4 = □

How many pairs of calculations can you find? What's the same, what's different?

Identify pairs of fractions that total 1. A fraction less than 1 plus a fraction less than 1 equals a total less than 1.

Show some pairs of fractions, some that total less than 1, some 1 exactly and some more than 1. What's the same, what's different? How do you know?

□ □ + = 110 10

How may ways can you make this true? What's the same, what's different? Why? What if the denominator was different?

Add or subtract mentally pairs of two-digit whole numbers: e.g. 47 + 58, 9l - 35

2 digit number + 2 digit number makes 3 digit number.

35 + 67, 27 + 45, 15 + 37, 47 + 25 What's the same, what's different? What if we change the 5 to 6? Why?

□ 1 - □ 7 = □□ How many ways can you make this true? What's the same/different? Why? What if you change the 7...?

Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £p.

If you use 3 digits and make the biggest and smallest 3 digit numbers you can and then add them the answer is palindromic.

Show a subtraction calculation as decomposition, counting on to find the difference on a number line and counting back on a number line. What's the same, what's different? Which method is best? Why?

4 □□ – 1 □ 9Using the digits 2, 5 and 8 how many different answers can you get?

16


Multiply and divide numbers to 1000 by 10 and then 100 (whole-number answers), understanding the effect; relate to scaling up or down.

When you multiply a number by 10 the answer is divisible by 20.

26, 260, 2600, 2060, 206, 37, 370, 3700. What's the same, what's different? What if you change the 6 to a different digit? What if you double them all? Why?

□ ÷ 10 = □ ÷ 100 Complete this number sentence in lots of different ways. What's the same, different? Why? What if you multiplied?

Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders, e.g. 15 x 9, 98 ÷ 6

If you divide a multiple of 5 by 6 there is a remainder.

Display 46 x 3 in three different ways, partitioning, grid method and compact vertical method. What's the same, what's different about these methods? What if you changed one of the digits? What else changes? Why?

□□ ÷ □Using the digits 3,4,5,6 how many calculations can you do where the answer is greater than 10? What if you change the digits?

Find fractions of numbers, quantities or shapes (e.g. 1/5 of 30 plums, 3/8 of a 6 by 4 rectangle).

When finding quarters of even numbers there are no remainders.

Find ⅓ of lots of numbers. What's the same, what's different?Why? What if 1 found fifths? When is it easy, when is it not?

2/5 of □ = □How many ways can you make this statement true? What's the same, what's different? Why? What if I found ⅔ of some numbers?

Use a calculator to carry out one-step and two-step calculations involving all four operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money.

When you divide by 8 the answer has 2 decimal places.

Divide some numbers by 11. What's the same, what's different? What if you divide by 9?

Given the digits 2, 4, 6, 7, 9 and X what's the biggest number you can make?

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Count from any given number in whole-number and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line.

If a is greater than b, then -a is greater than -b.

If you count in steps of 0.4, when do you land on whole numbers? Why? How do you know? What if you start on a different number? What's the same, what's different? Why?

1, 2, □, □, □? How could you continue this sequence (apart from 3, 4, 5!)? What is your rule?

Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers.

A number with two decimal places is bigger than a number with one decimal place.

What's the same, what's different about these numbers? 1.4, 1.04, 1.40. 4.10, 4.1, 4.01 Order them.How do you decide how to order the numbers? What if you add 0.5 to them all? Why?

Order the decimals 3.3, 1.3, 1.33, 331, 1.31 3.33. Write some more numbers with 3 tenths and put them in order. What numbers could go in between each one? Why?

Express a smaller whole number as a fraction of a larger one (e.g. recognise that 5 out of 8 is 5/8); find equivalent fractions (e.g. 7/10 =14/20, or 19/10 = 1 9/10); relate fractions to their decimal representations.

A fraction where the denominator is 10 is bigger than a half.

If the numerator is more than 1 the fraction is more than ½.

What's the same, what's different? 1/3, 2/6, 4/12, 2/3, 4/6, 8/12. How do you know? What if you double the numerator? Why?

0.25 = □ □How many ways can you complete this? What's the same, what's different? Why? What about 0.75? 1 = 2□ □ What fractions can this be? What's the same, what's different? Why? What if the numerator was 3?

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Understand percentage as the number of parts in every 100 and express tenths and hundredths as percentages.

25% is the same as a quarter.

50% of a number is bigger than 10% of a number.

Display a range of fractions, percentages and decimals, e.g. 5%; 0.2; 20% 1/10; 0.05; 50%; 2/5; 3/5; 80% What's the same, what's different? Which are larger than a half, have the sum of 1, etc?

10% of □ = □? How many ways can you complete this? What's the same, what's different? Why? What if it was 5%? □% of 200 = □?

Use sequences to scale numbers up or down; solve problems involving proportions of quantities (e.g. decrease quantities in a recipe designed to feed six people).

With a pattern of beads of two reds to every four green the fifth bead is green.

Find 5/6 of several numbers.Look at the answers, e.g. 10 out of 12, 20 out of 24.What's the same, what's different Why?

Show two recipes for the same dish, one for four people and the other for two people with some of the measures missing. What are the missing measures? What if it was just one person?

Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences and doubles and halves of decimals (e.g. 6.5 + 2.7, half of 5.6, double 0.34).

When I add two decimal numbers the answer is a whole number. When I find the difference between two decimal numbers the answer is a whole number. Doubling a number makes it bigger.

24+47, 204+307, 6.4+5.7, 2304+2407 Work out the answers. What's the same, what's different? Why? What if the 7was an 8? Order a group of decimals by how close they are to 3.5, 5.7 or 10.2.What's the same, what's different? Why?

4.7 - 2.□ = □.□How many different ways can you make this true? What's the same, what's different? Why? What if you changed the 7 to a 6? □.4 + □.7 = □.1Half of □.6=?

Double 4.□ =?

Recall quickly multiplication facts up to 10 x 10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts.

If I multiply a number by 6 the answer is a multiple of 3.If you add three consecutive integers, the answer is a multiple of 6.

6 x 80 = 480 6 x 8 = 48 .6 x 0.8 = 4.8 What's the same, what's different? Why? How many division statements can you write using the same numbers?

□ ÷ 40 = □ ? What do you notice? What if it was ÷ 400? ÷ 0.4? Why? How may different ways can you make this true? □ x □0 = □□0

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Identify pairs of factors of two-digit whole numbers and find common multiples (e.g. for 6 and 9).

Numbers between 10 and 30 do not have more than five factors.

What are the factors for 6, 12 and 18? What's the same, what's different? Why? What other numbers have the same common factors? Why?

Find the common multiples of 12 and 16. What other numbers less than 20 have the same multiples? Why?

Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations.

The best way to check an answer is to do the inverse operation.

4 x 4.6 = □18.4 ÷ □ = 4

18.4 = □ x 4

18.4 ÷ 4.6 = □What's the same, what's different about these statements? Why? If one of them is ten times bigger, what happens to the others? Why?

□ x □ = □□ ÷ □ = □What 3 numbers could you use to make these inverse operations correct? Try some different sets or 3 numbers. What if one of them was ten times smaller? What happens to the others? Why?

Extend mental-methods for whole-number calculations, for example to multiply a two-digit by a one-digit number.(e.g. 12 x 9), to multiply by 25 (e.g. 16 x 25), to subtract one near-multiple of 1000 from another (e.g. 6070 – 4097).

The best way to find a difference between two 4 digit numbers is by counting on.

Multiply some multiples of 4 by 25 (on a calculator).What's the same, what's different? Why? What if you multiply some multiples of 4 by 50? What if it was 16 x 50? How could you work out the answer mentally?

□ x 100 ÷ 4 = □How many ways can you make this true? What do you notice? Why?

Use efficient written methods to add and subtract whole numbers and decimals with up to two places.

□.□□ + □.□□ = a number greater than 10.

Show 462 - 158 using different methods Which is easier? Why? What about 6002-5979?

Use 6 digits and one decimal point to make two numbers. What's the biggest difference you can make?

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Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000.

If I multiply a number by 10 the answer ends in a 0.

When you multiply by 100 the answer has two zeros.

Why is 4.6 x 10 equal to 0.46 x 100.What other examples like this can you make?

Choose some numbers and divide them by 10.Which ones give decimal answers?Why?

Refine and use efficient written methods to multiply and divide HTU x U, TU x TU, U.t x U and HTU ÷ U

When I multiply two 2-digit numbers the product is a three digit number.

Show 146 ÷ 6 using a number line and chunking method.What’s the same, what’s different?

□□□ ÷ 8

Use the digits 3, 4, 8, 9 to make as many calculations as you can.Which ones have remainders?Why?

Find fractions using division (e.g. 1/100 of 5 kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of £80).

The bigger the denominator of a fraction, the smaller the portion of pizza.

20% is the same as a fifth.

Is 10% of a number bigger than 5% of a number?Why?How do you know?

□ of 72 = ?

□Using 1, 2, 3, 4, 6 and 12, how many answers can you get?

Use a calculator to solve problems, including those involving decimals or fractions (e.g. find ¾ of 150g); interpret the display correctly in the context of measurement.

Using a calculator,1.□ x 0.□ gives an answer less than one.

If I multiply a number by 3 and divide by 4, what fraction of the number have I found?How else could I find ¾ of a number using a calculator.

The calculator is broken, only the following keys work: 2, 5, 6, 8, ÷ and = - +Can you make every number from 1-25?

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Find the difference between a positive and a negative integer, or two negative integers in context.

When you subtract one number from another the answer is smaller than the first number.

3 + 4 = 7-3 + 4 = 1-3 -4 = -73 – 4 = -1What’s the same, what’s different? Why is this? What if you had 2 and 5?

5 – 8 = -3What happens if the first number gets smaller/bigger?What happens if the second number gets smaller/bigger?What if both numbers change?

Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line.

A number with 3 decimal places is bigger than a number with 2 decimal places.

What’s the same and what’s different about these numbers?1.707, 1.007, 1.7, 1.77, 1.077Place the numbers in order.What if you added 0.04 to every number?Would this change the order?Why?

0. □□ < 0. □□How many ways can you make this statement true, using the digits 3 5 7 9?What’s the same, what’s different? Why?What if you changed the digits?

Express a lager whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents 8/5 or 1 pizzas); simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator.

When you order a set of fractions you have to multiply the denominators to find out the common denominator first.

Given a set of fractions (include ones which are more/less than one, half, some have same denominator, some equivalent fractions).What’s the same, what’s different? What if we added 1/5 to them all?What if we wanted to order them?What strategies could we use?Why?

2 < 3 < 4□ 7 □How many different ways can you make this true?What do you notice?

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Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000); find equivalent percentages, decimals and fractions.

5% of a number is the same as 1/5 of a number.

Display a selection of “fractions” (decimals, percentages, fractions) some which are equivalent and some of which are not.What’s the same, what’s different? What if we doubled everything?What if we changed them all to decimals/percentages/fractions?What do you notice?Why.

4 – 8□ □How many different ways can you make this true? What do you notice?50 = □% of □?

□ = 40% of □?How many ways can you make these statements true?

Solve simple problems involving direct proportion by scaling quantities up or down.

If you want to make larger quantities of a recipe you just double all the ingredients.

Show 2 recipes of the same food, one serves 2, one serves 6.What’s the same, what’s different about these 2 recipes?What if we wanted to make enough for 4 or 9 people?What would we change? Why?

Show 3 different recipes for the same dish. For 2, 4 and 5 people with some of the measures missing from each one.How could we work out the missing measures?

Use knowledge of place value and multiplication facts to 10 x 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 x 7, 4.8 ÷ 6).

Multiplication makes numbers bigger. Show a set of calculations e.g. 8 x 7 = 56, 8 x 0.7 = 5.6, 0.8 x 7 = 5.6, 0.7 x 0.8 = 0.56, 80 x 7 = 560, 70 x 8 = 560.What’s the same and what’s different?What if we wanted to create a similar set using division?Why?

0. □ x □ = 4. □How many ways can you make this true?

Use knowledge of multiplication facts to derive quickly squares of numbers to 12 x 12 and the corresponding squares of multiples of 10.

If you multiply a number by ten and then square it you get the same answer as squaring then multiplying by ten.

Display a range of square numbers and squares of multiples of ten e.g. 4 x 4 = 16, 40 x 40 = 1600.What’s the same and what’s different?Why?Do you notice any patterns?

□ x □ = 36

□ x □ = 49Find as many pairs of factors as you can for the square numbers.What do you notice?Why? Try other square numbers.

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Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit numbers.

Factors come in pairs.

Prime numbers are next to a multiple of 6.

Use 3 and 5 or 2 and 3 as factors to make some numbers.What do you notice about these numbers?What if you used some other prime factors?Why?

□ x □ = 36

□ x □ x □ = 36

□ x □ x □ x □ = 36(without using 1) How many ways can you complete these?What’s the same, what’s different? What about other multiples of 9? Why?

Use approximations, inverse operations and tests of divisibility to estimate and check results.

When you divide an even multiple of 3 by 6 you get a remainder.

Write several calculations that would round off to 60 + 40, (or 6 + 4) e.g. 61 + 37, 55 + 42 (6.4 + 4.4).Which answers are more than/less than 100?Why?

If the approximation is 27 ÷ 10, what could the question have been?

Calculate mentally with integers and decimals: U.t U.t, TU x U, TU U, U.tU, U.t U

When you add two decimals numbers you get an answer less than 10.

Display a range of additions where two numbers appear in the same position, e.g. 170 + 350, 27 + 55, 4.7 + 6.5 and 3.07 + 14.05.What’s the same and what’s different?Why?What if you change the 5 to a 6?

□.4 + □.8 = □.□?How many different ways can you make this true?What do you notice?

Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer.

When you divide a 3 digit number by a single digit the quotient is a single digit.

Show 23.2 ÷ 4 using number line, chunking and compact method.What’s the same and what’s different?What if you changed one of the digits.What changes and why?

□□.□ ÷ □ > 10How many ways can you make this true using the following digits 2, 3, 5, 7?What if you chose four different digits?

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Relate fractions to multiplication and division (e.g. 6 ÷ 2 = ½ of 6 = 6 x ½): express a quotient as a fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 13); find fractions and percentages of whole-number quantities (e.g. 5/8 of 96, 65% of £260).

When dividing by 6, the remainders are sixths.

Divide some numbers by 5, writing remainders as fractions. Now do the same calculations on a calculator. What’s the same, what’s different?Why?What if you divided by 8?

□ of □2 = □?4.Investigate how many different ways you could use this to create a whole number answer.Do you notice any patterns?

Use a calculator to solve problems involving multi-step calculations.

I can use addition then division to get from one number to another.

Choose a starting number, ÷ 4, + 3, x 5.Try doing these in different orders.What’s the same, what’s different?Why?

Using only 4s and any operations, can you make all the numbers from 1 – 20?

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