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Medium Term Plan Level 2a Term 4 Class:

Problem Solving Strategy: Draw A Diagram or Make a Model

Unit Days Outcomes Overview of Key Learning Activities Assessment ResourcesL.I.We are learning to…

INTERACTIVE TEACHING STUDENT ACTIVITIES

Unit 1: Number & Place Value

52aNN01 Understand and use vocabulary related to place value and properties of number, initially in practical contexts

2aNN02 Describe and extend number sequences: count on or back in steps of 1 or 10 from any given 2-digit number

2aNN04 Read and write whole numbers up to at least 100

2aNN05 Count collections to 100 by grouping

2aNN06 Partition a 2-digit number into tens and ones

2aNN08 Use knowledge of place value to order sets of whole numbers to at least 100

2aNN10 Round 2-digit numbers to the nearest ten

2TM 01 Describe mathematical situations and methods using everyday language and some mathematical language, actions, concrete materials, diagrams and symbols; present solutions in an organised way

Count by grouping in tens

Count by grouping: use Paddle Pop sticks

Context: Pencils are sold in packs of ten. We need one pencil per person for next year. How many bundles do we need?

Model counting using tallies and tens frames – get the same answer.

Problem Solving: use stick bundles to work out how many bundles of pencils if every student is given one.

Can you count these 65 things by grouping them in tens?

Can students count by grouping in tens?

Can students partition a 2- digit number into tens and ones?

Can students use place value to compare and order numbers?

Can students round a 2-digit number to the nearest ten?

Paddle Pop sticks

Ten frames

Arrow cards

Place value charts

Number cards with 2 digit numbers on

Larger collections of objects.

Partition numbers into tens and ones

Problem: I'm thinking of a number. It has 6 tens and 3 ones. What is the number?

Model making the number with 6 bundles of tens and 3 ones. Write into the place value chart and show using arrow cards.

Problem: I'm thinking of a 2-digit number. It has 9 ones. What could it be?

Discuss how this problem is different and ask students what it might be. How many different answers could there be?

In one step:make 6 into 16make 5 into 75make 14 into 4change 49 to 9

Solve a range of riddles.

Partition numbers into a place value chart, using the Paddle Pop sticks. Record as the number of tens and number of ones, record in digits and words.

Use

arrow cards to show numbers, records as 50 + 3 etc.

(select activities after referring to assessment records from Term 3)

Order a set of numbers

Jack 63Natalie 52Wendy 81Tom 47

Put these in order, largest/smallest first: 27, 16, 85, 72, 52

Position 2-digit numbers on a 100

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14 = + 412 = 10 + 64 = + 453 = 50 +



Problem: Jack, Natalie, Wendy and Tom play a game. Their points are recorded in the table. Order them from the highest score to the lowest score.

Model thinking about each number using bundles or arrow cards. Which has the most bundles? If we write the numbers in a place value chart, which has the most tens?

square.

This is a 0 to 100 line marked in tens.

Position these numbers on the line: 20, 60, 90…

Round 2-digit numbers to the nearest ten

Use a counting stick (metre rule with ten equal equal divisions). Position numbers on the counting stick e.g. If 30 is the starting number, and 40 is the end, where would 37 be positioned? Is it closer to 30 or 40?

Repeat with a range of other numbers.

Include some numbers with 5 in the ones column. Discuss that it is right in the middle but that we round up.

Estimate to the nearest ten, the number of objects in a collection and check by counting e.g. estimate the number of children in the room to the nearest ten. Check by counting and using a number line.

Pick a card, label a number line with 10 marks, place the multiple of 10 at the beginning and end. Decide which number it rounds to.

Round 2-digit numbers to the nearest ten

Remind students of rounding yesterday. Perform a few examples. As a class write an anchor chart to remind them of the rules.

33 is closer to 30 than 40; the nearest ten to 33 is 30

37 is closer to 40 than to 30; the nearest ten to 37 is 40

35 is halfway between 30 and 40; the nearest ten to 35 is 40 because we round up when the number is half way between two tens

When finding information in a book, is page 34 closer to page 30 or closer to page 40? Why?

Round a range of numbershttp://www.co.uk/Flash.aspx?f=DartboardRoundingv2

http://www.topmarks.co.uk/Flash.aspx?f=ThinkingOfANumberv3

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http://www.co.uk/Flash.aspx?f=DartboardRoundingv2

http://www.co.uk/Flash.aspx?f=DartboardRoundingv2



NB: 2aNN02 will be a focus during mental starters.

Unit 2: Addition & Subtraction

10 2aNA01 Understand and use the vocabulary for addition and subtraction, initially in practical contexts

2aNA04 Recognise that addition can be done in any order (commutative law)

2aNA06 Recall addition and related subtraction facts for all numbers up to 10, including addition doubles

2aNA07 Begin to use a range of mental strategies to solve simple addition and subtraction problems involving 1-digit and 2-digit numbers; use informal jottings to explain solutions orally

2aNA08 Use concrete materials and informal recordings to support the addition of a 1-digit number, or a multiple of 10, to a 1-digit or 2-digit number

2aNA09 Use concrete materials and informal recordings to support the subtraction of a 1-digit number from a 1-digit or 2-digit number, and a multiple of 10 from a 2-digit number

2TM 02 Use concrete materials, actions, diagrams and technology to model and explore mathematical problems involving one and two steps;

Use partitioning to add two numbers mentally

(Introduction to the mental strategy)

Range of activities over 2 days

Problem: There are 12 boys and 14 girls in a classroom. How many children altogether?Strategy: begin to add a pair of teens numbers without crossing the tens boundary e.g. 12 + 14

Model making the numbers with lolly pop bundles and then joining the two collections together. Make jottings to show what is happening.

Partition numbers and add.

Use practical materials to make numbers and then add as needed.

Use arrow cards to help support students.

Can students partition into tens and ones to add 2 teens numbers?

Can students add 9 by adding 10 and subtracting 1?

Can students add a 1-digit number to a 1-digit or2-digit number?

Can students subtract a 1-digit number from a 1-digit or 2-digit number?

Can students select the correct operation and strategy when solving problems?

Lolly pop bundles

Hundred Square

Number lines

Solve addition problems using written recordings

(Informal recordings)

Focus: adding a 1-digit number to a 1 or 2 digit number

There are 28 students in the swimming pool and another 5 jump in. How many altogether?

Model using a number line, bridging through the tens boundary and then adding on 3 more. It is more efficient to do this than to count on in ones.28 + 5 = 33

Solve problems in a range of contexts using a number line

Record using symbols + and =

Solve subtraction problems using written recordings

Focus: subtract a 1-digit number from a 1 or 2

Wendy had K36 in her wallet and spent K8. How much money did she have left?

Model using a number line to help solve the problem. Show that it is more efficient to land at 30 and then go back to 28 than use single jumps.

Record using 36 – 8 = 28


Record using symbols - and =

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begin to check the reasonableness of solutions

digit number

Solve addition problems using written recordings


Focus: adding a multiple of 10 to a 1 or 2 digit number

Range of activities over 2 days

I have K24 and a friend gives me K20 they owe me. How much is in my purse?

Model using a number line to help solve this, counting on in jumps of 10. Place 24 on the number line, land on 34, then 44.

It is more efficient to jump on in tens than ones.


Record using symbols + and =

Solve subtraction problems using written recordings

Focus: subtract a multiple of 10 from a 1 or 2 digit number


Anna made K65 from her market stall and then spent K30 in the store. How much does she have left?

Model using a number line to help solve this, counting back in jumps of 10. Place 65 on the number line, land on 55, 45 then 35.

It is more efficient to jump on in tens than ones.


Record using symbols - and =

Use mental strategies to solve addition problems

Focus: Compensation

Sarah has been on holiday for 5 days. She has 9 more days to go. How long is her holiday altogether?

Strategy: Compensating: add 9 to single digit numbers by adding 10 and subtracting 1

Add 9 by jumping forwards 10 and back 1. Use an empty number line to record.

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– adding 9 to single digit numbers

Add 9 by using a number line - Jump on 10 but then move back one.

Use mental strategies to solve addition problems

Focus: adding 9 to single digit numbers

(Introduction to the mental strategy)

Add 9 using the hundred square, circling the number and answer e.g. 5, 14. Ask them to look for a pattern as you count on 9 from different numbers. What have we done? Add 10, subtract 1.

Race a partner - both students have a number square. Roll a dice and race to add 9 - one student counts on in ones, one student adds 10 and then subtracts one. Swap over.

Use a number square to help add 9 by adding 10 then taking away 1.

Solve problems using addition and subtraction

Show students a range of questions and discuss in pairs which method they would use.

Create an anchor chart to remind them of the different strategies available. Include strategies from previous terms as well.

E.g. re-order numbers, use bridging, use a number line, add 9, partition.

Solve a range of questions, working with a partner, discussing the appropriate method to use.

2aNA06 will be a focus during the mental starters.

Unit 3: Money & Financial Mathematics

52aNMF01 Use in context and begin to read vocabulary related to money

2aNMF02 Recognise, describe, sort and order coins and notes according to their value

2aNMF03 Count the value of small collections of coins and notes

Count collections of coins and notes

Problem: Whose wallet would you rather have?

Show students two collections of notes. Which has more in?

Count collections of notes (to K20)

Count collections of coins (to 50t)

Investigate how many ways to pay different amounts. List the different ways with a partner.

Can students identify the value of coins and notes?

Can students use different coins to pay for an item?

Can students find different ways to pay for an item?

Can students use different

Coins, notes

Pictures/ examples of coins and notes from Australia and other countries if possible

Count collections of coins and

Show students a class shop. Have a mixture of prices, some in K and some in toea.

Read prices of items in the class shop.

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2TM 02 Use concrete materials, actions, diagrams and technology to model and explore mathematical problems involving one and two steps; begin to check the reasonableness of solutions

notes Ask a child to pick an item and explain how they could pay for it.

Find the amount of money needed to pay for it.

Select two or more items and pay the total.

notes and coins to pay for an item?

Can students work out the cost of two or more items?

Count collections of coins and notes

Problem: This ball costs K4. How many different ways can you pay for it?

Recap the value of different notes and coins.

Investigate different ways of paying for an amount with similar problems.

Sort money coins and notes into spaces in a shop till.

Solve problems involving money

Teach over 2 days

Problem: A can of Coca-Cola costs K3.

Describe the different ways you could make this amount of money?

Problem: Can you order these items from cheapest to most expensive?

$5 30c 10c $2

Students solve different word problems, working out the cost of items, and how to pay for them in notes and coins.

Unit 4: Shape

Three-dimensional

5 2aMS01 Understand and use vocabulary related to shape

2aMS03 Identify and classify common three-dimensional objects using their features

2TM 03 Recognise and describe patterns and relationships involving numbers or shapes; make and test predictions (conjectures)

Identify three-dimensional objects

Give each group of children a collection of everyday objects which includes: cubes, cuboids, cones, spheres and cylinders,

Call out the name of a shape and ask each group to find an example of it.

Talk about how the shapes are similar/different, for example whether there are flat surfaces or curved surfaces.

Make models using everyday materials (containers, packets), malleable materials such as clay or play dough; describe the model e.g. the top of this tree is a sphere and its trunk is a cylinder

Can students name 3D objects?

Can students identify features of 3D shapes?

Can students select a shape when the properties are described?

Can students sort a collection of objects according to a property?

Can students describe a 3D shape using mathematical vocab?

Collections of cubes, cuboids, cones, spheres, cylinders

Everyday objects, construction kits, play dough

Labels for shapes

Word banks showing properties

Describe features of 3D objects

Show students a cylinder and a cuboid. How are they different how are they the same?

Identify the different shapes on the surface, edges, flat surfaces, curved surfaces.

Make models using three-dimensional objects such as construction kits e.g. Lego everyday materials (containers, packets), malleable materials such as clay or play dough

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As they make models, describe the properties to a partner.

Can students find an object given a description?

Identify and describe 3D objects

Have a collection of 3D objects on the carpet - these should include maths shapes and everyday objects. Call out a property. Allow students time to talk about which object it is and then choose someone to find it.

Clues could include :

Find a three-dimensional object with six square faces.

Find me a shape which has… students select shapes from a collection which has flat surfaces, some curved surfaces, some flat surfaces etc

Students label the different features of 3D shapes

Sort 3D objects according to their features

How could we sort these objects into 2 groups? Encourage students to sort according to mathematical properties of 3D shapes rather than size or colour. Could record by placing objects in a simple table marked out on the carpet. For example:

Curved Surfaces

No curved surfaces

Give students a collection of 3D objects and ask them to sort them in different ways. Record how they have sorted the shapes using photos.

Prompts could include: square faces, circular faces, curved edges, only straight edges etc.

Describe a 3D object

Select a shape and describe as a class, using a word bank to help use mathematical vocabulary

For example: this object has five faces, four are triangles and one is square.

Choose a three-dimensional object from a collection and describe it to a partner. Partner keeps track and scores points for the mathematical vocab used. Partner has to find the object from the group of objects.

e.g. This object has six faces and each face is a rectangle

Unit 5: Multiplicati

10 2aNM01 Understand and use the vocabulary for multiplication and division,

Double and halve numbers

Show students a range of problems which need doubling and halving. In pairs students discuss which strategy is required for each.

Various games to practise doubling and halving Spin a spinner, double the number

shown

Can students find doubles of numbers to 10?

Can students find halves of

Counters

Cubes

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on & Division

initially in practical contexts

2aNM02 Count on or back in multiples (skip count) of : 2, 5 , 10 starting from zero to the tenth multiple

2aNM03 Recall doubles of all numbers to 10, and corresponding halves

2aNM04 Use equal grouping of objects as a strategy for solving practical multiplication problems

2aNM05 Recall multiplication facts: x2, x10; begin to know multiplication facts: x 5

2aNM06 Solve practical division problems that involve sharing into equal groups and grouping into equal sets


For example:12 children are lined up in 2 equal lines. How many in each?8 pairs of shoes have been left at the door. How many shoes are there altogether?

Throw a dice, make a double jump on a number line

Count the number of K2 notes and double to find the amount of money. Fold a piece of string in half – how

long is it now? Share the counters between 2 Matching cards ‘half of 18’ and 9

etc.

even numbers to 20?

Can students count groups of objects in 2s, 5s and 10s?

Can students make arrays and count the rows to find out how many are in them?

Can students describe arrays?

Can students make an array to match a story?

Can students share objects into equal groups?

Can students group objects?

Can students describe the number of groups and the number of left overs?

Can students decide whether to make an array or share objects?

Cards to match for doubles/halves

Count by grouping

Show students the tally chart and ask how they can work out how many for each category.

Model counting in 5s and recording the answer to complete the tally chart.

Students count different collections by counting in 2s, 5s and 10s

For example: How much money are these 10t coins worth?

How many fingers on 6 hands?

How many socks in 7 pairs?

Values on different tally charts - can be made easily at the link below.http://www.softschools.com/math/data_analysis/tally_chart/tally_chart_maker/

Use arrays to count in groups

Show half the class an array. Ask for volunteers to describe it.

For example: It has 5 rows and 3 columns.

The rest of the class draw it on their whiteboards.

Use skip counting to work out how many dots altogether.

Swap over.

Arrange students in pairs. Ask the students to take turns to make an array which is hidden from their partner’s view. The student then describes the array to the partner by stating the number of counters in each row and the number of rows. The partner then attempts to make the array. He or she then determines the total number of counters in the array.

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http://www.softschools.com/math/data_analysis/tally_chart/tally_chart_maker/%20%20





Use arrays to count

Show students objects in arrays. They write down how many rows and how many in each row, then skip count to find how many altogether.

3 rows of 5 = 15

Students take a card from a pile which describes an array. For example 8 rows of 2. Use stamps, shape prints, thumb prints etc to create the array.Students show their print to a partner who has to describe the array. Check it matches the original card.

Use arrays to solve problems

Problem: 7 children have 2 pencils each. How many pencils are there altogether?

Create an array using pencils on the carpet, then skip count to find out how many altogether.

Make an array for different stories, find the total.Make up stories for different arrays.

Solve division problems by sharing

There are 5 teams in each class. 20 children in class 4 are split into the teams. How many will be in each team?

Solve a range of problems by sharing, using counters or other small objects to help model.

Solve division problems by sharing

25 lollies are shared between 4 children. How many each?

Use concrete materials to calculate. Discuss that each child will get 6 lollies and there will be one left over.

Share objects to solve a range of situations. E.g. biscuits for teddy bears, toy cars for children etc.

Include examples where there are left overs.

Solve division problems by grouping

Problem: 23 children are put into groups of 5.Use concrete materials to form equal groups and calculate the answer. Identify that there will be 4 groups and 3 children in a 5th group.

Group objects to solve a range of problems.How many sticks of 4 cubes can you make from 16 cubes? Etc.Include examples where there are left overs.

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Solve division problems

Mixture of grouping and sharing problems – identify what to do in each situation and model practically.

Solve a range of division questionsInclude examples where there are left over objects.

Solve division and multiplication problems

40 apples in a box. How many bags of 10 apples can be filled?

8 tables of 5 children. How many children?

24 sweets shared between 4 children. How many each?

Select whether to share or make an array – act out the problem and solve using counters or cubes.

Work in pairs to solve a range of problems, making arrays, making groups or sharing.

2aNM02, 2aNM03, 2aNM05 are a focus during mental starters.

Unit 6: Fractions

5 2aNF01 Understand and use the vocabulary related to fractions, initially in practical contexts

2aNF02 Recognise and describe one half as one of two equal parts of a whole or set of objects

2aNF03 Recognise and describe a quarter as one of four equal parts of a whole or set of objects


Identify one quarter of a whole

Use a strip of paper to model half and quarter of a whole object by halving e.g. Fold this piece of paper in half. How many parts are there? Now fold the same piece of paper in half again. How many parts are there now? These are called quarters.

Fold another piece of paper into 4 parts which are not equal. Explain that these are not quarters because they are not equal. Introduce notation for 1/4.

Investigate which shapes can be folded into 4 equal parts. Draw the folds onto the paper shape.

Make sure some of the shapes can't be folded in quarters.

Can the shapes which can't be folded in quarters be folded in half?

Can students fold different shapes in quarters? i.e. Do students recognise that a quarter means four equal parts?

Can students use appropriate vocabulary/symbols to describe the shaded part of a shape or container?

Can students share a collection of items into halves?

Can students share a collection of items into quarters?

Can students shade a shape in a range of ways

Paper shapes

Sheet with grids on

Collections of items to split into halves and quarters

Counters

Cubes

Identify which fraction is shaded

What fraction of these shapes is shaded?

Shade a given fraction of different shapes.

Identify whether a shaded part of a shape is a fraction or if the parts are unequal - is the shaded part more or less than a half? More or less than a quarter?

Find half of a set of objects

Problem: Steve and Susie share 14 lollies. How many do they each

Find halves of numbers to 20.Circle half of different collections.

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have?Share the lollies into two equal piles, with half in each.Relate this to division and sharing into two equal groups.

Find a quarter of a set of objects

Teach over 2 days

4 teddy bears share a packet of biscuits. There are 12 biscuits. How many each?Share the biscuits into 4 equal piles, reminding students of the link to division and that there are 4 equal piles.

Use concrete materials to model a quarter of a collection and describe equal parts of a collection of objects.

e.g. I have quarters because the four parts have the same number of counters.

Find one quarter of 12 biscuits, of 8 pencils….

Unit 7: Time 5 2aMM01 Understand and use the vocabulary of measurement, initially in practical contexts

2aMM04 Tell time to the half-hour using digital and analogue clocks

2TM 01 Describe mathematical situations and methods using everyday language and some mathematical language, actions, concrete materials, diagrams and symbols; present solutions in an organised way

Tell the time to the hour and half-hour

Use mini clocks, model how to move the hands to show various times on the hour and half hour.

Students play snap. Match times written in words to pictures on clock faces.Listen to a story with different times in. As each time is said the group of students must make the time on their mini clocks. For example: Jimmy work up at half past five. He washed at 6 o clock and had breakfast at 6:30

Can students tell the time to the half hour using an analogue clock?

Can students tell the time to the half hour using a digital clock?

Can students calculate how long an event lasts for?

Mini Clocks (students could make their own using card and split pins if these are not available as a commercially produced resource.)

Tell the time to the hour and half-hour using digital clocks.

Teach over 2 days

Model using digital clocks to go with analogue clocks for on the hours and half hour.

Match times written in words to clock faces and digital clocks.Draw clock hands on to show a digital/written timeRead a range of digital times and make them using mini clocks.

Solve simple time problems

Teach over 2

Problem: It is now 10:30. Maths is another hour. What time till it finish?

Problem: Junior practises the piano for half an hour every day after school. What time might he start and

Solve a range of simple problems, for example:How long is it from 2 o’clock to 6 o’clock?It is now half past seven. What time was it 2 hours ago?

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days finish practising?

Model solving these problems using clocks to help work out the solutions.

It is 5 o’clock. What time will it be 4 hours from now?What time was it 3 hours ago?If you had lunch at 12 o’clock, how long ago was that?If you go to bed at 8 o’clock, how many hours until bed time?

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