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Short Blocks

Maths Year 4 Summer Multiplication and Division

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Factors, multiples, mental multiplication (suggested as 2 days)

Objectives

Factors, multiples and mental multiplication
Unit 1: ID# 4877

National Curriculum
Mult/Div (i) (ii) (iii)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and multiply and divide by 1.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children list the pairs of factors of 20. Write 20 × 36 on the board. Agree that we can solve this by multiplying 36 by 2, then by 10 (or vice versa). Explain that when we do this we are using the factors of 20. Encourage children to reflect on their preferences: Which way did you find quicker or made more sense? Children list the pairs of factors for 14, then use factors to work out 14 × 52. Repeat for 24 × 45.
Group Activities
Use the ‘Race to 200’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Children multiply 23 by 8, 12, 14, 16 and 18 by listing factors and using a chosen pair to aid multiplication.
-- Use a ‘broken’ calculator to multiply 379 by 6, 8, 12, 18 and 24 by listing factors and using a chosen pair to aid multiplication.

Day 2 Teaching
Write 2 + 7 + 8 and ask children how they would work this out. Draw out changing the order to add the pair to 10, then add 7. Say that multiplication can also be done in any order. Write 4 × 7 × 5. How could we change the order of this multiplication that might simplify the calculation? Model reordering as 4 × 5 × 7, i.e. working out 20 × 7. Repeat with 7 × 2 × 8.
Group Activities
-- Children multiply three numbers 2-9, recognising where reordering can simplify the calculation. Record the multiplication in order in books; write a sentence to explain choice.
-- Children multiply three numbers, recognising where factors and reordering can simplify the calculation. Record the multiplication in order in books; write a sentence to explain choice.

You Will Need

• Calculators
• Mini-whiteboards and pens
• Number cards 2–9
• Flipchart and pens

Mental/Oral Maths Starters

Day 1
7 times table (pre-requisite skills)

Day 2
11 times table (pre-requisite skills)

Procedural Fluency

Day 1
List factors, then choose a pair to help work out multiplications.

Day 2
Choose a number from each star. Decide the easiest order to multiply them together.

Mastery: Reasoning and Problem-Solving

• Find three different multiplication facts that you can multiply by 10 to give an answer of 400.
• Use doubling to help you solve:
23 x 4 18 x 8 141 x 4
• How could you use the factors of 12 to help multiply a number by 12?
Try this to find:
16 x 12 23 x 12 34 x 12
• Use and explain a mental method to find:
8 x 13 7 x 16 12 x 13

In-depth Investigation: Race to 200
Children apply knowledge of factors within the 2, 3, 4, 5, 9 and 10x tables.

Extra Support

Creepy Crawlies
Learning the 6 times table

Sleeping Spiders
Learning the 8 times tables.

Unit 2 Scaling and correspondence problems (suggested as 3 days)

Objectives

Solve mental problems, including those involving scaling and correspondence
Unit 2: ID# 4889

National Curriculum
Mult/Div (ii) (v)

Hamilton Objectives
18. Use known facts, place value, factors and commutativity to multiply and divide mentally
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division
22. Solve scaling & harder correspondence problems: n objects are connected to m objects.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 35 ÷ 7, 350 ÷ 7, 3500 ÷ 7. Children discuss the answers to each in pairs. Take feedback, recognising that we can often use times tables and place value to divide really big multiples of 10! Children list all the factors of 24. Use these to write lots of divisions beginning with 240, e.g. 240 ÷ 4 = 60, 240 ÷ 6 = 40, 240 ÷ 8 = 30… Repeat for 2400. Present some missing number divisions, e.g. 210 ÷ 7 = 30, 7 ÷ 9 = 600.
Group Activities
-- Whole class activity: Children list the factors of a 2-digit ‘tables answer’, e.g. 36, 20, 32, 18, 45, 28, 42 etc, then write divisions beginning with 10x that number. Repeat for other numbers on the list. (See variations for children working towards ARE/at greater depth)

Day 2 Teaching
A stage designer - working on a production of Jack and the Beanstalk - is calculating the dimensions for the giant's furniture! Children measure length, width and height of a table to nearest cm, multiply dimensions by 4 and write answers in metres. Discuss use of scale drawings or models in real life.
Group Activities
-- Whole class activity: Calculate the scaled-up dimensions for a giant’s furniture, converting cm to metres. Most children multiply by 4; some multiply by 5.

Day 3 Teaching
Together create a two-course menu, with 4 main courses and 3 desserts. We’re going to find out how many different possible meals you could have at our café! Write the first main meal and first dessert. Repeat for 1st main with 2nd, then 3rd desserts. Can you suggest an estimate for how many different combinations there might be?
Group Activities
-- Whole class investigation: How many different combinations of two-scoop ice creams are there from a choice of four flavours?

You Will Need

• Mini-whiteboards and pens
• Tape measures
• Rulers
• Chairs
• Bowls, spoons and mugs

Mental/Oral Maths Starters

Day 1
Multiply single-digit numbers by multiples of 10 and 100, e.g. 4 × 60, 7 × 400 (pre-requisite skills)

Day 2
Double and halve 2-digit numbers (pre-requisite skills)

Suggested for Day 3
12 times table (simmering skills)

Procedural Fluency

Day 1
Choose pairs of numbers to divide using times tables and place value.

Day 2
Work out real and scale model dimensions, converting from cm to m and vice versa.

Day 3
Work out possible combinations of ice cream flavours and toppings.

Mastery: Reasoning and Problem-Solving

• Write lots of divisions beginning with 3600, e.g. 3600 ÷ 4 = 900.
• Mr Jones’ rectangular garden measures 5m by 8m. His neighbour – Mr Payne – says, ‘My garden is twice as wide and double the length of your garden, so yours is half the size of mine.’ Do you agree with Mr Payne?
• The top-seller at Giovanni’s café is the ‘Quad-Choc-Challenge’ – a dessert with 4 different flavours of chocolatey ice cream in a long thin dish! Here is one arrangement of flavours (see download). How many others are there?

In-depth Investigation
Use the Group activity on either of Days 1 or 2.

Extra Support

Revisit the group activity from Day 1, creating Factor Bugs for a wide range of 2-digit numbers.

Unit 3 Efficient chunking with remainders (suggested as 2 days)

Objectives

Divide using efficient chunking, including remainders
Unit 3: ID# 4909

National Curriculum
Mult /Div (ii)

Hamilton Objectives
20. Know how to use ‘efficient chunking’ for division above the range of the tables facts, e.g. 84 ÷ 6 = ? Begin to extend this to 3-digit numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 48 ÷ 3; sketch an empty number line from 0 to 48 on the board. Can you estimate how many 3s there are in 48? More than ten? Fewer than 10? More than 20? Model chunking on the empty number line, then using the ‘bus shelter’ layout as modelled on the ‘Teaching and Group Activities’ download. Children choose empty number line or ‘bus shelter’ to find 72 ÷ 3, then 96 ÷ 4.

Group Activities
-- Calculate 10x, 20x and 30x 3, 4, 5, 6, 7 and 8. Use to estimate answers when dividing 2-digit numbers by 1-digit numbers, with answers less than 20, then 30.
-- Divide 2-digit numbers by 1-digit numbers, with answers between 30 and 40. Make up divisions with answers in given ranges.

Day 2 Teaching
Write 85 ÷ 3, 85 ÷ 4, 85 ÷ 5. Children talk to partners about which they think might have the biggest answer/smallest answer, then write in order on whiteboards. Take feedback. Model finding 85 ÷ 4 using the ‘bus shelter’ layout, pointing out that this time there is a remainder. Children work in pairs, one to work out 85 ÷ 3 and the other 85 ÷ 5. Repeat with 134 ÷ 5, 134 ÷ 6 and 134 ÷ 7. Answer some division problems that require rounding up or rounding down.
Group Activities
Use the in-depth problem-solving investigation ‘Arranging the tables’ from NRICH as today’s group activity.
Or, use these activities:
-- Play a game to discover 2-digit by 1-digit divisions that have answers between 10 and 20.
-- Play a game to discover 2-digit by 1-digit divisions that have answers between 20 and 30, or between 30 and 40.

You Will Need

• Mini-whiteboards and pens
• ‘Division practice’ (see resources)
• Flipchart and pens

Mental/Oral Maths Starters

Day 1
Division facts for the 8 times table (pre-requisite skills)

Day 2
Division facts for the 7 times table (pre-requisite skills)

Procedural Fluency

Day 1
Practise using the ‘bus shelter’ layout to record the steps in division (no remainders).

Day 2
Division with remainders, including a few word problems.

Mastery: Reasoning and Problem-Solving

• Write the missing number in each calculation.
26 ÷ ☐ = 3 remainder 5
55 ÷ ☐ = 18 remainder 1
• Fill in the missing numbers on the number lines (see download).
• Charlie has 95 pound coins. She makes six equal piles of coins as high as she can. Does she have any left over? If so, how many?
• Taking a taxi home from the cinema, 5 friends equally shared the cost of £12. How much did each passenger pay?
• True or False?
An odd number divided by an odd number always gives an odd answer.
An even number divided by an odd number always leaves a remainder.

In-depth Investigation: Arranging the Tables
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places. Arranging the Tables from nrich.maths.org.

Extra Support

Remainders Rule
Using ‘chunking’ to divide numbers just beyond the times tables, including with remainders.

Unit 4 Multiplication problems, formal methods (suggested as 3 days)

Objectives

Solve multiplication problems using formal methods; word problems
Unit 4: ID# 4919

National Curriculum
Mult /Div (iv) (v)

Hamilton Objectives
18. Use known facts, place value, factors and commutativity to multiply and divide mentally
19. Multiply 1-digit numbers by 2-digit or 'friendly' 3-digit numbers mentally or using grid method (i.e. using the distributive law).
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/ division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children use the grid method to work out 4 × 786. When they have finished, write the ladder layout on the board (see Teaching & Group Activities download). Talk through each stage. Discuss pros and cons of each method. Children choose either grid method or ladder method to work out 7 × 876.
Group Activities
-- Whole class investigation: Children work in pairs to solve 3-digit by 1-digit multiplication challenges. Most children use the ladder method.

Day 2 Teaching
Write: 4 × 782; 618 × 6; 5 × 579. Children discuss in pairs which they think will have the biggest answer and why. Model using rounding to estimate products. 1/3 of class work out exact answers for each. Repeat for 3 × £6.27, 6 × £3.89 and 5 × £4.78.
Group Activities
-- Use a written method for 3-digit by 1-digit multiplications, finding answers in a several given ranges.
-- Multiply 3-digit numbers, including amounts of money, by 1-digit numbers. Begin to investigate large multiplications which can be worked out mentally.

Day 3 Teaching
Display: Zak is 8 years old. He eats three meals a day. How many meals will he eat in a year? and If Zak eats three meals a day, how many days will it take him to eat 132 meals? Discuss what to do to the numbers in each, noticing superfluous and missing numbers. Children write and solve the actual calculations needed. Stress trying to imagine a word problem before trying to answer it. Now they know the answers, can they turn each problem around so the first becomes a division and the second a multiplication?
Group Activities
-- Sort problems into those needing x/÷, discuss as a group, then answer.
-- Solve multi-step problems that include multiplication or division and another operation.

You Will Need

• Mini-whiteboards and pens
• Place value cards: hundreds, tens and ones (optional)
• Written multiplication practice (see resources)
• Multiplication and division word problems sheets 1 and 2 (see resources)
• Scissors
• Solving multi-step word problems (see resources)

Mental/Oral Maths Starters

Day 1
90 times table (pre-requisite skills)

Day 2
Quickly round 3-digit numbers to nearest 100 (pre-requisite skills)

Day 3
Times table bingo (pre-requisite skills)

Procedural Fluency

Day 1
Choose a number from each of two sets to multiply together. Write at least three multiplications with answers < 2000, and three multiplications > 2000.

Day 2
Practise using the ladder method for 3-digit by 1-digit multiplications, including some amounts of money.

Day 3
Solve multiplication and division word problems.

Mastery: Reasoning and Problem-Solving

• Calculate:
154 x 7 6 x 289
4 x 5 x 9 x 3
• This calculation has the same number missing from each box. Write the missing number in the boxes.
☐ x ☐ - ☐ = 72
• A shop sells some boxes of ‘Posh-Chocs’ that cost £3.58 each, and makes £32.22. How many boxes did they sell?

In-depth Investigation
Use the whole-class activity on Day 1.

Extra Support

Multiplication Mix
Using the grid method to multiply 2-digit numbers by 1-digit numbers

Unit 5 Revise problems: all four operations (suggested as 2 days)

Objectives

Revise and solve problems involving all four operations
Unit 5: ID# 4931

National Curriculum
Mult/Div (ii) (iv) (v)

Hamilton Objectives
11. Use column addition to add 3-digit & 4-digit numbers: first expanded, then compact method.
14. Use column subtraction to subtract 3-digit & 4-digit numbers: first expanded, then compact method.
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display the list of calculations on resource sheet 1. Children work in pairs to find an addition they would choose to solve mentally; then another to solve using a written method. Discuss. Repeat for each operation. Challenge children to write a further BIG addition, subtraction, multiplication or division that they can do mentally. Share and discuss.
Group Activities
-- Choose a mental or written method to solve given calculations; justify choices.
-- Create calculations that might best be solved using a mental or written method; justify choices.

Day 2 Teaching
Give each pair three word problems (see resource). They read the first together and discuss what they need to do with the numbers in the problem to solve it, then write the calculation on the problem. Discuss -do we need a mental or written strategy? Find the answer to the calculation as a class, then check that the answer makes sense in the problem’s context. Repeat with the other two problems.
Group Activities
Use the ‘Set square’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities
-- Solve word problems, choosing which operation to use.
-- Solve multi-step word problems, choosing which operation(s) to use.
-- Rewrite given word problems so that different operations are necessary to solve them.

You Will Need

• ‘Choosing how to do calculations’ sheet 1 (see resources)
• ‘Choosing how to do calculations’ sheet 2 (see resources)
• A3 paper, sticky notes, flipchart and pens
• ‘Word problems’ (see resources)
• ‘Holiday word problems’ sheet 1 (see resources)
• Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Round 4-digit numbers to nearest 10, 100 and 1000 (pre-requisite skills)

Day 2
Add/subtract pairs of 2-digit numbers (pre-requisite skills)

Procedural Fluency

Day 1
Practise choosing how to solve a range of calculations, then complete as many calculations as possible.

Day 2
Solve word problems using all four operations. Recognise calculations that may be done mentally.

Mastery: Reasoning and Problem-Solving

• Choose to use a mental or written strategy for each of these. Say why you chose that method.
17 x 11
298 x 3
25 x 19
• Write > = or < in each box to make the statements correct:
15 x 10 ☐ 11 x 14
90 ÷ 30 ☐ 60 ÷ 20
120 ÷ 4 ☐ 160 ÷ 8
30 x 8 ☐ 100 x 10
• A shop sells some boxes of ‘Posh-Chocs’ that cost £3.69 each, and makes £59.04. How many boxes did they sell?
• In July, Ali collects 2, 3 or 4 eggs each day from her hens. In the first 20 days, she collects 57 eggs altogether. What is the greatest number of eggs Ali can collect in July?

In-depth Investigation: Set Square
Use digits 1-9 once only to complete a calculation grid with given answers for each row and column.

Extra Support

A Day Out
Deciding what calculation is necessary to solve a word problem (multiplication or division)