Medium Term Plan Level 2b Term 4 Class:

Problem Solving Strategy: Draw a Diagram or Make a Model

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Unit 1 : Number & Place Value

52bNN01 Understand, use and begin to read vocabulary related to place value and properties of number

2bNN02 Describe and extend number sequences: count on or back in steps of 1, 10 or 100 from any 2-digit number and 3-digit number

2bNN03 Identify the number that is 1, 10 or 100 more or less that any 2-digit or 3-digit number

2bNN04 Read and write whole numbers up to at least 1000

2bNN05 Count and represent collections of objects up to 1000 by grouping

2bNN06 Partition a 3-digit number into hundreds, tens and ones

2bNN08 Use knowledge of place value to order sets of whole numbers to at least 1000

2bNN09 Make estimates of numbers and measurements in a range of practical contexts e.g. estimate a group of

Count by grouping

Tom had 658 stickers in his collection. How could you check the number of stickers by counting?Discuss different ways of doing this.

Estimate, group and count a range of collections.

For example: lollies, sheets of stickers, beads in a jar, counters, paperclips in a box etc.

Can students count by grouping?

Can students use knowledge of place value to partition numbers?

Can students order a set of numbers?

Can students make an estimate?

Can students round numbers to the nearest hundred?

Cubes

Lollies, stickers etc.

Base Ten materials

Place value charts

Arrow cards

Number linesPartition numbers

In one step:make 478 into 978make 326 into 396change 263 to 203

Work through each question in turn. Make both numbers using practical materials e.g. MAB or paddle pop sticks. Identify the difference between each collection of objects. How does this relate to the digits? Write both digits in expanded form. Identify what we need to add or subtract to get from one number to the other.

Students model numbers in different ways to help answer similar questions

Write what each digit represents in numbers e.g. what is the 3 in 364 worth?

Complete statements with missing numbers: 364= + 60 + 4

Order sets of numbers

Think, Pair, Share:

Write a number on each blank card so that the five numbers are in order:

Compare answers and discuss why not everyone will have the same answer but can still be correct.

Order a range of numbers using different models to help.

base ten materialsplace value chartarrow cards

Solve problems which involve ordering numbers.E.g. 3 lengths of wood measure 456cm, 289cm and 701cm. Put them in order from shortest to longest.

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objects up to about 100

2bNN10 Round 2-digit and 3-digit numbers to the nearest ten or hundred

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

Make estimates

Think, Pair, Share: Make an estimate for where the arrow is positioned.

Ask students to share their estimates and discuss which estimates are appropriate.

Estimate the position of arrows on a range of different number lines.

e.g. 0-50, 40 -100 etc.

Estimate how many objects are in a container, lines on a piece of paper etc.

Compare and discuss estimates with a partner. Decide which is most reasonable and justify it.

Check by counting.

Round numbers to hundred

I open a book on page 271. Which page is it closer to: page 200 or page 300?

Draw a number line from 200 to 300. Which number would be in the middle? 250. Where would 271 be? Therefore it rounds up to 300.

Repeat by rounding several 3 digit numbers to the nearest 100. Draw a number line for each example.

Create an anchor chart with a number line diagram and statements clearly written: less than 50 are rounded down – the hundreds number stays the same, 50 or higher are rounded up.

Students may link this back to when rounding to the nearest 10.

Round to the nearest hundred: 433…..531….473….

Students draw a number line and place the number on. Use this to help round to the nearest 100.

2bNN02, 2bNN03 will be a focus during the mental starters.

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Unit 2: Addition & Subtraction

102bNA01 Use and begin to read vocabulary related to addition and subtraction

2bNA05 Recognise that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences

2bNA07 Recall addition doubles for all numbers up to at least 15; multiples of 5 up to 50; multiples of 10 up to 100

2bNA08 Use a range of mental strategies to solve addition and subtraction problems involving 1-digit and 2-digit numbers; use informal jottings to explain solutions orally

2bNA09 Use concrete materials and informal written methods to add 2-digit numbers

2bNA010 Use concrete materials and informal written methods to subtract 2-digit numbers2TM 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

Use mental strategies to solve addition problems

Focus: near doubles

There are 6 tree kangaroos and 7 wallabies at the nature park. How many animals are there altogether?

Model using double 6 and then adding 1 to find the answer.

Students solve a range of problems using near doubles.

e.g. Terry's house has 7 windows on one floor and 8 on the other. How many windows altogether?

Can students use near doubles?

Can students use known facts to add and subtract multiples of 100?

Can students use the compensation strategy to add and subtract 9 accurately?

Can students use the compensation strategy to add and subtract 19 accurately?

Can students use the compensation strategy to add and subtract 11 accurately?

Can students use the compensation strategy to add and subtract 21 accurately?

Can students use informal recordings to add 2 digit numbers?

Can students use informal recordings to subtract 2 digit numbers?

Can students select an appropriate method?

Can students identify

Near double dominoes

Near double games

Counters, cubes

Hundred squares

Number lines

Use mental strategies to solve addition and subtraction problems

Focus: known facts

When I visit the bank, I take out K600. I owe a friend K200. How much do I have left?

Link to known facts 6 - 2 = 4 so 600 - 200 = 400

Include addition examples too.

Add/subtract pairs of multiples of 100 without crossing 1000

e.g. 500 + 300, 800 - 200

Solve a mixture of addition and subtraction word problems using this strategy.

Use mental strategies to solve addition problems

Focus: adding a teens number to a 2 digit number

43 children and 14 adults are in the swimming pool. How many altogether?

Partitioning – Multiples of 10: add/subtract a teens number to/from a 2-digit number without crossing the tens boundary or 100 e.g. 45 + 13

Solve a mixture of addition and subtraction word problems using this strategy.

Use mental strategies to solve addition and subtraction problems

Problem: There are 28 prizes in the lucky dip. If 19 children have taken a prize how many are left?

Use the hundred square to help. students identify the patterns.

Students solve a range of problems adding and subtracting 9 and 19.

Use hundred boards and/or empty number lines.

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Focus: compensating (add or subtract 9 and 19)

Problem: There are 77 people in the queue at the bank. 19 more arrive. How many people are waiting now?

which operation is required?

Use mental strategies to solve addition and subtraction problems

Focus: compensating (adding and subtracting 11 and 21)

I use 11 packets of noodles from a carton containing 64. How many are left?

53 children are out at playtime. Another class with 21 students come out. How many students are outside now?

Model the strategy of compensating: adding/subtracting 11/21

. Use the hundred square to help students identify the patterns.

Students solve a range of problems adding and subtracting 11 and 21.

Use hundred boards and/or empty number lines.

Use written recordings to solve addition problems

46 people get on a plane at Port Moresby and a further 33 board at Lae before travelling to Rabaul. How many passengers arrive in Rabaul?

Model using partitioning and recording horizontally to record the calculation. Use MAB to reinforce what is happening.

e.g. 46 + 33

46 + 33 = 40 + 6 + 30 + 3

= 40 + 30 + 6 + 3

= 70 + 9

= 79

Solve a range of problems adding two 2 digit numbers.

Use MAB to help support calculations.

Some students may need to revisit the number line (Stage 1 Teaching Written Calculation: Guidance for Primary Teachers document)

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Referred to as Stage 2 in Teaching Written Calculation: Guidance for Primary Teachers document.

Use written recordings to solve addition problems

A trampoline has a safety sticker which says that it can only hold up to 80kg. Which of these friends can go together?

Jane 45kg

Sophie 32kg

Eddie 55kg

Timmy 26kg

James 31kg

Use the method to add a range of 2 digit numbers.

Could add the prices of items in a shop, lengths of string etc.

Pick a number from each circle. Add them together.

Use written recordings to solve subtraction problems

I have K45 in my purse and spend K23. How much money do I have left?

Record subtraction calculations based on partitioning

45 - 23

= 40 – 20 + 5 – 3

=20 + 2

= 22

Referred to as Stage 2 in Teaching Written Calculation: Guidance for Primary Teachers document

Solve a range of problems subtracting two 2 digit numbers.

Use written recordings to solve subtraction problems

I cut 35cm off a length of ribbon for a hair tie. The original piece was 86cm. How much was left?

Remind students of the need to put the larger number first: 86-35.

Model using partitioning to

Solve a range of problems subtracting two 2 digit numbers.

Students could generate their own subtractions by picking 2 digit number cards.

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calculate the difference. Do not use numbers which require decomposition.

Solve addition and subtraction problems

Present students with a range of calculations. In pairs discuss the methods which they would use to solve - include calculations which require a range of strategies - both mental and informal recording. Discuss with a partner how they would solve and review as a class.

Have a series of word problem cards. Students identify which operation and method to use.

Discuss in pairs as they solve the questions.

Review in small groups in the plenary.

2bNA05 and 2bNA07 will be a focus during the mental and oral starters.

Mental strategy of bridging through multiples of 10.

Unit 3: Money & Financial Mathematics

5 2bNMF01 Use, read and begin to write vocabulary related to money

2bNMF03 Read and write amounts up to K20/$20 in words and numerals; begin to use notation for money e.g. K, t, $, c

2bNA06 Recall addition and subtraction facts for each number to at least 20 and pairs of multiples of 10 with a total of 100

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

Investigate different ways to make K1/$1

Show students the different coins and remind them of their value.

Introduce them to the following problem:

The following children have K1. Which coins do they have?

Ask how we could solve this problem. As a class model using the coins to check different ways.

Have students work in pairs using play money and counting out the value. Emphasise that there should be a 100t in K1.

Students can then work in pairs to find other ways to make K1. For example: 3 of one coin, 4 of another coin. Swap their clues with another pair to check their answers. Extend by having 3 types of coin - for example 50t, 20t, 10t, 10t, 10t…

Can students find different ways to make K1?

Can students write amounts using notation?

Can students solve problems involving money?

Can students investigate combinations of prices they can afford?

Different coins

Price tags

Toy Money

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Use symbols to record amounts of money correctly

Activities over 2 days

Remind students that there are 100t in K1. Create a table to show how many toea are in K2, K3 etc and discuss the patterns

Show students two values for example 150t and K1.50 and ask them which is worth more. Let them discuss in pairs.

Model converting some different amounts from kina to toea and back.

Repeat with several examples on whiteboards.

Label prices of goods in the class shop. Some labels could be given in Kina, others in toea, students write the missing value.

Extend to using dollars and cents.

Students read labels and count out the money using coins. Can they find different ways to pay?

How many toea in K1.50? / How many cents in $1.50?

Solve problems involving money

Problem:

Problem:

Jack took $1.00 from his piggy bank and bought a truck that cost 20c and a car that cost 45c. How much did he spend altogether? How much change did he have?

Solve a range of problems involving money. For example:

Sally took K1.00 from her piggy bank and bought a lolly that cost 35t and an ice pop that cost 25t. How much did she spend altogether? How much change did she get?

Solve problems involving money

Explain to students that they have K10. Invite them to see which items in the shop they can buy. For example a ball for K3.00 and a doll for K4.50 but NOT a car for K7 and

Students investigate which items they can buy from the shop, how much change they would have. Record this using pictures and jottings.

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Focus: investigating combinations of items which could be purchased with a given amount

a doll for K4.50. Extend to using K20 and more complicated pricing or 3 items.

2bNA06 will be an explicit focus in mental starters and used throughout problem solving activities in this unit.

Unit 4: Shape

Three-dimensional

52bMS01 Use and begin to read vocabulary related to shape

2bMS03 Identify common three-dimensional objects in different positions and orientations; describe and classify objects referring to their properties

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

Name 3D objects

Matching 3D objects to their name: Collect examples of cubes, cuboids, cylinders, spheres, cone, and prisms and match them to name labels.

Create a model and add labels to show the different shapes used. Record the objects used e.g. my model was made with 7 cuboids, 10 cubes, 6 cylinders and 1 cone.

Can students name 3D objects?

Can students sort 3D objects according to different properties?

Can students describe 3D objects using mathematical vocabulary?

Cubes, cuboids, cylinders, spheres, cones, prisms

Labels for shapes

Construction kit/ straws

Mathematical vocab cards, create class dictionary during teaching

Sort three-dimensional objects according to their properties

Sort three-dimensional objects in different ways according to properties of their faces e.g. whether they have six faces; a triangular face; a rectangular face…

In pairs students sort shapes in different ways, take a photo and note down how it was sorted.How else could the shapes be sorted?Describe how another pair's shapes have been sorted.

Use mathematical vocabulary to describe shapes

Make a skeleton shape from a construction kit or straws, count the number of edges or corners.Check with a partner.

Describe three-dimensional objects using mathematical vocabulary

Who am I?I have has two flat surfaces, one curved surface and 2 curved edgesDiscuss with partner what shape has just been described.

In pairs students write a description for a shape. Swap with another pair, see if they can identify which shape it is.For example:It has five faces, nine edges and six vertices.

Describe three-

Hold a shape in a bag/behind a screen and explain that you will

Students play the game in pairs or small groups. Ask yes or no

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dimensional objects using mathematical vocabulary

only answer yes or not to questions. Students ask questions such as: Does it have a curved surface etc. Until someone guesses correctly. Emphasise the importance of checking properties before guessing shapes.

questions about a hidden shape in order to identify it e.g. Does it have a curved surface?

Match definition cards to shapes.

Unit 5: Multiplication & Division

102bNM01 Use and begin to read related vocabulary for multiplication and division to respond to oral questions phrased in a variety of ways

2bNM02 Count in multiples (skip count) of: 2, 4, 5, 10; recognise 2-digit and 3-digit multiples of 2, 5 and 10; count in multiples of 100 from zero to 1000

2bNM04 Derive quickly doubles of multiples of 5 up to 50 e.g. 35 x 2

2bNM05 Derive quickly doubles of all multiples of 10 up to 100; halves of multiples of 10 up to 100 e.g. half of 70

2bNM06 Recognise and represent multiplication as repeated addition, groups and arrays to solve simple problems

2bNM07 Recall multiplication facts: x2, x4, x5, x10

2bNM08 Multiply and divide by multiples of 10: Multiply a single digit by 1 or 10 e.g. 7 x 10; 3 x 1

Use repeated addition to solve problems

Focus x5, x10

Problem: Zara pays her boat fee using K10 notes. She hands over 7 notes. What is her fee?Have a child pay the boat fee while everyone joins in the counting.

Record on a number line, 7 jumps of 10.

Skip count and label the landing points 10,20,30,40,50,60,70.

Solve similar problems together.

Solve a range of word problems. For example:

Each day at school there are 5 lessons. How many in a week of school?

Work out how much money is in different purses containing K5 and K10.

See stage 1 repeated addition in Teaching Written Calculations: Guidance for Primary Teachers.

Can students model multiplication as repeated addition?

Can students record repeated addition using a number line?

Can students model division as repeated subtraction?

Can students record repeated subtraction using a number line?

Can students decide whether multiplication or division is needed?

Can students use arrays to model multiplication?

Can students use arrays to model division?

Can students use arrays to find the area of rectangles?

Can students write a story to describe an array?

Can students use various representations

Hundred squares

Dice

Counters/marbles/ cubes etc.

Number lines

Squared paper, cardboard rectangles

Use repeated addition to solve problems

Focus: x2, x4

Five people have four cakes each. How many cakes do they have altogether?Act out with children at the front and then record on a number line, 5 jumps of 4.

Skip count and label the landing points 4,8,12,16,20Solve similar problems together.

Solve a range of word problems. For example:

10 children are at a party. They each have 2 balloons. How many balloons in total?

There are 6 pairs of shoes in the cloakroom. How many shoes are there altogether?

Use repeated subtraction to solve problems

Focus: x5, x10

Problem: A box holds 5 coconuts. How many boxes are needed to hold 15 coconuts? Act out using cubes to represent the coconuts.

Record as repeated subtraction on the empty number line and as a number sentence.

A box holds 30 coconuts. How many people can have 5 coconuts each?

Use counters and share into groups of 5, 10

Record on a number line.

See stage 1 repeated subtraction in Teaching Written

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2bNM09 Represent division as grouping into equal sets (repeated subtraction) or sharing; solve simple problems using these representations

2bNM10 Begin to derive division facts from known multiplication facts: x2, x4, x5, x10

2bNM11 Divide a 2-digit multiple of 10 by 1 or 10 e.g. 20 ÷ 1, 80 ÷ 10

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

Calculations :Guidance for Primary Teachers

of multiplication and division to solve simple problems?

Use repeated subtraction to solve problems

Focus: x2, x4

Problem: How many sticks of 4 cubes can you make from a stick of 20 cubes?

Problem: There are 28 children here today. How many teams of four children can we make?

Act out the solutions to both problems, then record as repeated subtraction on the empty number line and as a number sentence.

Use concrete materials to model division as repeated subtraction e.g. If I have 12 marbles and each child is to get four, how many children will get marbles? 12 - 4 - 4 - 4 = 0

So 3 children will get 4 marbles each

Solve a range of word e.g.

How many 2cm lengths can you cut from 12cm of tape?

Solve problems using repeated addition and subtraction

Show students a range of word problems. In pairs, discuss how to solve - do they need repeated subtraction or repeated addition?

As a class, act out the problems, record using repeated addition/subtraction.

In pairs, solve a range of word problems, discussing whether to use repeated addition or subtraction. Ensure students have access to practical materials to help act out the problems.

Use arrays to solve simple problems

Focus: multiplication

Problem: On a sheet of stamps there are 4 rows with 5 stamps in each row. How many altogether.

Ask students to draw the sheet of stamps, find total by skip counting in 4s, then by check by skip counting in 5s.

Record both multiplication sums.

4 x 5 = 20 = 5 x 4

Solve a range of problems using counters to make array.s, calcuate via skip counting and record the number sentences.

For example: Josie takes a tray of biscuits out of the oven, there are 6 rows with 10 in each. How many biscuits altogether?

Use arrays to solve simple problems

Focus:

32 children sit in groups of 4 at tables. How many tables?

Ask students to draw on their whiteboard how they could solve

Solve a range of problems, by sharing out different numbers of counters into groups of 2,4, 5, and 10. Ensure they create an array.

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division this with an array - discuss in pairs if they would like to.

Reinforce the idea using cube towers with 4 in each row.

For example: A pizza is cut into 12 pieces. Joe, John and Josh share it equally. How many pieces each?

4 tanks are used to store 16 fish. How many fish are there in each tank?

Describe arrays using number sentences

Problem: What does this array show?

Students talk in pairs about what this array could show. Ask them to write their story on a post it note.

Sort the post it notes as a class to whether they have chosen x or ÷.

3 x 4= 12

3 groups of 4 children gives 12 altogether.

12 ÷ 3 = 4

12 children split into teams of 3.

Different arrays.Students write one multiplication and one division story for each.

Use an array to measure area

Problem: How many squares does this rectangle cover?

Show students a cardboard rectangle and ask them how many squares they think it will cover on squared paper.

Count how many rows and columns there are and use this to work out how many squares it will cover.

Students use a range of cardboard rectangles and place on squared paper. Work out the array and how many squares it would cover.

Could also draw rectangles by rolling dice to find each length.

.

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Compare to their estimates.Solve simple problems

Worded problems for multiplication & division – select a method – this could be number line or arrays. A range of contexts so that students have to consider the language which is used and decide whether to multiply or divide.

Students work to solve a range of worded problems using concrete materials.

Mixed multiplication and division.

2bNM02, 2bNM04, 2bNM05, 2bNM07, 2bNM08, 2bNM10, 2bNM11 focus for mental starters

Unit 6: Fractions

52bNF01 Understand, use and begin to read vocabulary related to fractions

2bNF02 Recognise, model, represent and describe halves, quarters and eighths of a whole or set of objects

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

Model fractions of a whole

Discuss: What fraction is the white part of this shape?

Give students a chance to chat in pairs. If none of the students realise, point out that the pieces aren't equal and so don't show a fraction. Emphasise the need for equal parts. Ask students to draw a circle on whiteboards and cut into 4 equal parts to show 1/4.

Are these shapes cut into equal pieces? Are they fractions? Students look at a range of pictures, identifying which shapes are cut into equal parts and what fraction one part would be. Some should be simply labelled as 'not equal parts.

Can students identify when a shape is cut into equal parts?

Can students shade a given fraction of a range of shapes?

Can students find fractions of quantities using practical materials?

Can students say what fraction of a shape is ringed or shaded?

Can students create a pattern following given criteria?

Shapes

Marbles

Counters

Fraction dominoes

Pattern blocks

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Model fractions of a whole

Show students a range of shapes, cut into equal parts.

Ask for volunteers to shade a range of fractions - 1/2, 1/4, 1/8.

Students shade a range of fractions in given shapes.

Play dominoes matching a fraction to a word to a picture.

Find a fraction of a set of objects

Problem: Box of 12 counters. Tell class that you want to give half the box to one student and half to another. Discuss and share methods. Check by counting two groups of counters. Emphasise that each student has 1 part out of 2 parts.

Students practise in groups of 3 – one student shares to the two others.

Find half and quarter of quantities using concrete materials.

Find a fraction of a sets of objects

What Fraction? - 6-11 year olds - TopmarksGreat interactive which lets you ask 'which fraction is shaded?'

Tracy wrapped 4 gifts. She put a bow on 1 gift. What fraction had bows?

2 out of 4 apples are red. 2 out of 4 apples are green. Draw a picture to show this.

What fraction of the set of buttons

is ringed?

Complete the shading on this diagram so that one half of it is shaded:

Luke made a flag with 4 equal parts. He made 2 parts of his flag yellow. Draw a picture to show his flag. Can you find more than one way?

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Find a fraction of a set of objects

Investigate:Use pattern blocks to create a pattern where ¼ is red.

Discuss with students what the statement means. Ask for suggestions of how this could be approached. Encourage a range of solutions from each child. Ask them how their pattern ensures that 1/4 are red. Discuss and explain their patterns to a friend.

Unit 7: Time 52bMM01 Use and begin to read vocabulary related to measurement

2bMM05 Tell time to the quarter-hour, using the language of past and to

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 quarter past the hour

Over 2 days - check assessment records from T2 to check what the focus should be

Remind students of the time for quarter past and quarter to model what position the hands are in. Students set the time for a range of times to the hour, quarter past and half past. Record also their digital equivalents. Reminds students that for quarter to, with the digital equivalent, the hour will be one less. i.e. quarter to 5 is 4.45

Use small clocks to show a range of times.

Match digital and analogue clocks which tell the same time.

(all hour, half past, quarter past , quarter to)

Can students tell the time to the hour and half past the hour?

Can students tell the time to quarter past the hour?

Can students tell the time to quarter to the hour?

Can students match digital and analogue clocks showing the same time?

Can students solve simple problems involving lengths of time?

Mini -clocks

Match analogue, digital and word times

Play snap: match the times written on cards in words, or in digital time, to the time shown on pictures of clock faces

Solve simple problems involving time

Range of problems over 2 days

Sue got on the bus at 9 o’clock. The journey took half an hour. What time did she get off the bus?Mary went into a shop at 10:30. She came out at 10:45. How long was she in the shop?James walked from 9:45 until 10:15. For how many minutes did he walk?Model using small clocks and or an empty number line, as appropriate, to explain the solution.

Solve a range of problems using clocks and a number line to help.

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