Maths Year 5 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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Mental multiplication/division problems (suggested as 3 days)

Objectives

Solve problems using mental multiplication and division
Unit 1: ID#5813

National Curriculum
Mult/Div (i) (iv) (v) (ix)

Hamilton Objectives
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
14. Use efficient mental methods to multiply two or three numbers.
15. Perform divisions mentally in range of tables.
21. Solve problems involving multiplication and division, using knowledge of factors and multiples.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 10 × 46 = 460. Use this to find 5 × 46, 15, × 46, 20 × 46, 21 × 46. How could we work out 19 × 46? Children multiply even 2-digit numbers by 10, then 5, 20 and 21. Children write answers to 20 × 6, 30 × 6, 20 × 7, 30 × 7, 20 × 8 and 30 × 8. Use these facts to help work out answers to division: 123 ÷ 6, 154 ÷ 7 and 244 ÷ 8, writing any remainders as fractions.
Group Activities
-- Multiply 3, 4 and 6 by 10, 20 and 30; use these facts to help work out divisions, writing remainders as fractions.
-- Multiply 6, 7 and 8 by 20, 30 and 40, then find divisions with answers in given ranges.

Day 2 Teaching
Display and read: A tea shop has 27 trays of shortbread. Each tray is divided so it holds 20 pieces of shortbread. How many pieces of shortbread are there? What do we need to do to the numbers in this problem to solve it? Can we work out this multiplication mentally? Solve and then repeat for: A coach party of 46 people has come to the tea shop. They all want scones. Scones come in packs of 4. How many packs are needed?
Group Activities
-- Collaborate to use mental strategies alongside written jottings to solve a series of multiplication and division word problems.

Day 3 Teaching
Display: A Boeing 747 can carry 416 passengers. How many passengers were carried on three such planes if a total of 27 seats were empty? Children read, discuss and agree what they need to do with the numbers in the problem. Take feedback. Agree that we first need to find how many passengers could fly on the 3 planes, then subtract the empty seats. Repeat with a different word problem.
Group Activities
Use the in-depth problem-solving investigation ‘One O Five’ from NRICH as today’s group activity.
Or, use these activities:
-- Solve single- and multi-step word problems using a strategy to lead step-wise through the problem.
-- Create and solve single- and multi-step word problems.1

You Will Need

  • Mini-whiteboards and pens
  • ‘Using known facts to help with divisions’ sheets 1 and 2 (see resources)
  • ‘Multiplication and division word problems’ sheets 1, 2 and 3 (see resources)
  • ‘Holiday word problems’ sheets 1 and 2 (see resources)

Mental/Oral Maths Starters

Day 1
7 times table (pre-requisite skills)

Day 2
8 times table (pre-requisite skills)

Suggested for Day 3
24-hour clock (simmering skills)

Procedural Fluency

Day 1
Multiply 6, 7 and 8 by 10, 20 and 30 or by 20, 30 and 40. Use these facts to help solve divisions, writing remainders as fractions.

Day 2
Work in pairs to read word problems, visualise or represent the context, agree the necessary calculation(s) then answer the problems.

Day 3
Work in pairs to solve ‘holiday’ word problems.

Mastery: Reasoning and Problem-Solving

  • Write the correct symbol (<, = or >) in each box to make the statements correct:
    15 × 10 ☐ 7 × 20
    120 ÷ 6 ☐ 180 ÷ 9
    70 × 30 ☐ 4 × 500
    440 ÷ 4 ☐ 720 ÷ 60
  • A box contains trays of oranges. There are 12 oranges in a tray. There are 5 trays in a box. A grocer sells 30 boxes of oranges. How many oranges does the grocer sell?
  • Write the missing number in each calculation:
    252 ÷ 6 = ☐
    ☐ ÷ 6 = 10 remainder 3
    102 ÷ ☐ = 12³/4

In-depth Investigation: One O Five
Explore the maths behind a ‘trick’ to work out the number someone else is thinking of, using division and remainders. One O Five from nrich.maths.org.

Extra Support

Epic Times Tables
Knowing the 6 and 8 times table and using the 6 and 8 times tables and place value to generate the 60 and 80 times tables

Unit 2 Problems with multiples, factors, scaling (suggested as 3 days)

Objectives

Problems involving multiples, factors, scaling.
Unit 2: ID #5821

National Curriculum
Mult/Div (i) (viii) (ix) (xi)

Hamilton Objectives
20. Recognise and use square and cube numbers and the matching notation.
17. Scale up or down by a factor of 2, 5 or 10; solve problems involving scaling up/down by simple fractions and problems involving simple rates.
14. Use efficient mental methods to multiply two or three numbers.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples, square and cube numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write: 12, 15, 24, 30, 13, 48, 36, 25, 28, 21, 27 and 33. Give a card (2 to 12) to each child. Circle 12. Children hold up their number if it is a factor of 12. So, 12 is common multiple of all the numbers you are holding up. Repeat for other numbers, including 13 (a prime number). Ring 12 and 24. Hold up your number if it is a factor of both numbers: a ‘common factor’. Repeat for 12 and 15, 36 and 48, 21 and 28.
Group Activities
-- Roll two 0–9 dice; find a common multiple. Find numbers on a multiplication square which have more than two common factors.
-- Interpret a word problem; find factors, common multiples and lowest common multiples.

Day 2 Teaching
Show children the scale model of Hogwarts castle on the internet. Every dimension is 1/24 of what would be real life-size. Explain that children will work in a group to design their ideal bedroom. They are going to make a scale model, and so will need to calculate the new dimensions for each length. Work out scale dimensions of a room, four-poster bed and trunk.
Group Activities
-- Collaborate to make a scale model of a bedroom at Hogwarts, choosing from a list of items, first calculating dimensions, then making the items from cm2 paper.

Day 3 Teaching
Children draw 3cm by 3cm square on cm² paper. What is the area? We can write 3 × 3 like this (write 3²) and read it as ‘three squared’. This means 3 multiplied by itself. It is like the little 2 we write after cm to show that each centimetre is squared. So 3 squared equals 9. Nine is a square number – can you remember any other square numbers? Children come up and ring any square numbers that they see on a multiplication square. Repeat for squares with sides 2, 4, 5 … 12cm. Make a 3 by 3 by 3 cube from cm³ cubes. Work out total number of cubes: 3 × 3 × 3 = 27. Write 3³ = 27. Together work out the first 5 cube numbers: 1³ = 1, 2³ = 8 … 5³ = 125.
Group Activities
Use the in-depth problem-solving investigation ‘What an odd thing!’ as today’s group activity.
Or, use these activities:
-- Represent square numbers with paper cut-outs. Play a game to practise recognising square numbers.
-- Work in pairs to make ‘follow-me’ cards for sets of square or cube numbers.

You Will Need

  • 2–12 cards
  • 0–9 dice
  • Multiplication square (see resources)
  • 1–6 dice
  • Hogwarts Castle scale model from www.telegraph.co.uk or Hogwarts scale model from www.wbstudiotour.co.uk
  • List of items for Hogwarts bedroom (see resources)
  • cm² paper and tape
  • cm³ cubes
  • 1–10 dice, plain card and scissors

Mental/Oral Maths Starters

Day 1
Times tables (pre-requisite skills)

Day 2
Times table bingo (pre-requisite skills)

Suggested for Day 3
Halve 2-digit numbers (simmering skills)

Procedural Fluency

Day 1
Practise finding common multiples and common factors.

Day 2
Calculate the dimensions of items in a scaled down bedroom.

Day 3
Ring square numbers. Find cube numbers from 2 to 5.
Mark and correct a piece of homework about square and cube numbers.

Mastery: Reasoning and Problem-Solving

  • Ring the numbers that are the common factors of 12 and 18:
    2 3 6 9 12
  • Write all the common multiples of 3 and 8 that are less than 50.
  • Using the digits 1, 5 and 6, make the following 2-digit numbers:
    - a prime number
    - a common multiple of 5 and 13
    - a common factor of 60 and 90
  • Put these values in order with the smallest first:
    5², 3², 3³, 2³

In-depth Investigation: What an Odd Thing!
Children create a triangle of odd numbers and identify patterns when rows are summed or their end numbers are averaged.

Extra Support

Times Table Puzzler
Finding multiples and factors

Unit 3 Division problems with short division (suggested as 3 days)

Objectives

Solve division problems with short division
Unit 3: ID #5827

National Curriculum
Mult/Div (vi) (x)
Add/Sub (iv)

Hamilton Objectives
18. Divide 2, 3, 4-digit numbers by 1-digit numbers above tables range; choose and use efficient methods; interpret remainders appropriately according to context.
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Model short division to find 2381 ÷ 3. Cover the digits 3, 8 and 1 with a sticky note. Make 2381 using base-10 equipment or use the ‘Short division 1’ presentation. Point out that we cannot make a group of three 1000s blocks from the two 1000s blocks available. Move the sticky note to reveal the 3. Change the two 1000 blocks for twenty 100 blocks. How many 3s in 23? Continue the division to give answer 793 r 2. Repeat with 1381 ÷ 6 and 1281 ÷ 5 using just the sticky notes.
Group Activities
-- Investigate short division of given 4-digit numbers. Explain a pattern in the remainders.

Day 2 Teaching
Use the ‘bus shelter’ short division layout to model calculating 5466 ÷ 4. Agree the remainder as 2. We can divide 2 by 4 to give 2/4. How can we simplify this? Agree the answer as 1366¹/2. Repeat for 5120 ÷ 6, agreeing an answer of 853¹/3. Write 5118 ÷ 6. What do you think will be the answer to this? Can you suggest other divisions by 6 that will not have a remainder? A division that will have 1/6 in the answer?
Group Activities
Use the in-depth problem-solving investigation ‘Remainder runners’ as today’s group activity.
Or, use these activities:
-- Make a 3-digit number; divide by a fourth number. Score the remainder.
-- Divide 4-digit numbers by single-digit numbers, investigating largest possible fraction remainders.

Day 3 Teaching
Write: 472 ÷ 4, 3958 ÷ 3, 2786 ÷ 4, 7975 ÷ 4. Children agree an estimate for each. Take feedback on how they did this. Model a calculation of 2786 ÷ 4 using base-10 equipment or use the presentation provided. Express the remainder as fraction and simplify to 696¹/2. Children calculate 2054 ÷ 3 on their whiteboards. Challenge children to write a division with an answer of more than 1000 and one with an answer of less than 1000.
Group Activities
-- Practise short division of 3- and 4-digit numbers, creating calculations with number cards.

You Will Need

  • ‘Short division 1’ presentation (see resources)
  • 1000s, 100s, 10s and 1s base-10 equipment
  • Sticky notes
  • ‘Short division 2’ presentation (see resources)
  • Mini-whiteboards and pens
  • ‘Short division 3’ presentation (see resources)
  • 0–9 digit cards

Mental/Oral Maths Starters

Day 1
Division facts for the 6 times table (pre-requisite skills)

Suggested for Day 2
Place value in 6-digit numbers (simmering skills)

Day 3
Division facts (pre-requisite skills)

Procedural Fluency

Day 1
Practise short division of 3-digit numbers with remainders.
Practise short division of 4-digit numbers with remainders.

Day 2
Calculate multiplications; use them to choose 3-digit numbers to divide by 3, 4 and 5 to give answers within given ranges.
Practise dividing 4-digit numbers, expressing remainders as fractions, simplifying where possible.

Day 3
Use short division to divide 3-digit and 4-digit numbers by 1-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Find:
    581 ÷ 7 = ☐
    3456 ÷ 5 = ☐
    5400 ÷ 9 = ☐
  • A farmer is packing eggs. Each box holds six eggs. The farmer has 890 eggs to pack. How many boxes will the farmer fill?
  • Fill the missing boxes to give an answer with fraction remainders as follows:
    187 ÷ ☐ = ____1/2
    331 ÷ ☐ = ____3/4
    ☐ ÷ 10 = ____2/5

In-depth Investigation: Remainder Runners
Children divide 1234, 2345, 3456 by 3, 4, 5 … 12 and look for patterns in the remainders.

Extra Support

Chunking Champs
Using chunking to divide, answers between 10 and 30, with remainders.

Unit 4 Grid, short and long multiplications (suggested as 5 days)

Objectives

Grid multiplication; short and long multiplication
Unit 4: ID #5843

National Curriculum
Mult/Div (iv)

Hamilton Objectives
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
16. Multiply 2, 3, 4-digit numbers by numbers ≤26 using long or short multiplication or grid method; multiply 2-digit by 2-digit numbers using grid method.
21. Solve problems involving multiplication and division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 6 × 4872. Ask children to estimate the answer. Discuss rounding to 6 × 5000 to give an estimate of 30,000. Remind children how to use both short multiplication and the grid method. Challenge children to work in pairs to come up with another multiplication with an answer within 1000 of 30,000. All digits in their multiplication must be different. Discuss answers.
Group Activities
-- Practise written methods for multiplication through a short investigative task.

Day 2 Teaching
Write 12 × 34. Agree that you could work out 10 lots of 34 and 2 lots of 34, and then add the 2 products. Draw a grid to show this. Write 23 × 34. How could we work this out? This time it would also be helpful to partition the 34. Model. Explain what is worked out on each row. Repeat for 57 × 24.
Group Activities
-- Multiply 34 by at least 5 numbers between 20 and 30.
-- Sketch fields with given dimensions, then use the grid method to find those with the least and greatest areas.

Day 3 Teaching
How many hours do you think might be in a year? Agree an estimate with your partner; write it down. Ask children how they came up with their estimates, e.g. using rounding. Show how to use the grid method to find the answer. Discuss what is calculated on each row. Repeat for 32 × 247 and 423 × 27.
Group Activities
-- Relate grid multiplication to tables facts and place value.
-- Consolidate use of the grid method to multiply 3-digit numbers by 2-digit numbers.
-- Extend use of the grid method to multiply 3-digit amounts of money by 2-digit numbers.

Day 4 Teaching
Children use the grid method to work out 48 × 16. Show the same calculation using long multiplication. Discuss what is worked out in each line and how this compares to the grid method. Use both methods for other multiplications: 13 × 87, 14 × 47.
Group Activities
-- Use grid and long multiplication side by side to multiply pairs of 2-digit numbers (both numbers <20).
-- Collaborate to multiply pairs of 2-digit numbers (one number <20).
-- Collaborate to multiply pairs of 2-digit numbers (one number <30).

Day 5 Teaching
A group of 14 people are walking 874 miles from Land’s End to John o’Groats for charity. Roughly how far will they have walked if you add the distances that each person has walked together? Discuss rounding 14 to 10 and 874 to 1000 to give an approximate answer of 10,000 miles. Children find the exact answer the using grid method. Model using long multiplication. Children calculate distance walked by 13 people. They then work out 11 × 248 and 15 × 248.
Group Activities
Use the in-depth problem-solving investigation ‘Reverse digits, same product’ as today’s group activity.
Or, use these activities:
-- Find how many hours per year a person is awake if they sleep for 8 hours per day. Repeat for 6, 11, 10, 9 and 7 hours sleep each night.
-- Use long multiplication to solve word problems, multiplying 3-digit numbers by 2-digit numbers, where the 2-digit number is less than 40.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pens
  • ‘Multiplying pairs of 2-digit numbers’ (see resources)
  • Squared paper or squared background on the Interactive Whiteboard
  • ‘Using the grid method to multiply 3-digit numbers by 2-digit numbers’ (see resources)
  • ‘Long multiplication’ (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Double and halve 3-digit numbers (simmering skills)

Day 2
Multiply multiples of 10 by single-digit numbers (pre-requisite skills)

Day 3
Multiply multiples of 10 by multiples of 100 (pre-requisite skills)

Day 4
Multiply by 20 (pre-requisite skills)

Suggested for Day 5
Roman numerals (simmering skills)

Procedural Fluency

Day 1
Calculate 3-digit by 1-digit multiplications using grid multiplication.
Use short multiplication to multiply 4-digit by 1-digit numbers.

Day 2
Use the grid method to multiply numbers between 20 and 30 by 2-digit numbers (grids are drawn for children initially).
Use the grid method to multiply pairs of 2-digit numbers.

Day 3
Use the grid method to multiply pairs of 2-digit numbers.
Use the grid method for 3-digit by 2-digit multiplications, including amounts of money.

Day 4
Use grid and long multiplication side by side to multiply pairs of 2-digit numbers (beginning with both numbers <20).
Multiply pairs of 2-digit numbers (beginning with one number <20) using long multiplication.
Multiply pairs of 2-digit numbers (one number <30) using long multiplication

Day 5
Multiply 3-digit numbers by 2-digit numbers, using long multiplication:
-- where the 2-digit number is <20
-- where the 2-digit number is <30
-- where the 2-digit number is <40, including some money amounts

Mastery: Reasoning and Problem-Solving

  • Choose a method to find:
    50 × 70 = ☐
    879 × 3 = ☐
    71 × 16 = ☐
    54 × 23 = ☐
    2307 × 4 = ☐
  • A crate contains 27 boxes of oranges. There are 24 oranges in a box. A supermarket orders 3 crates of oranges. How many oranges is this in total?
  • How many hours are there altogether in November and December?
  • Tom’s baby sister Katie has been alive for 3000 hours. How many days is this?

In-depth Investigation: Reverse Digits, Same Product
Children find the product of a pair of 2-digit numbers then reverse the digits of both numbers and find an identical product.

Extra Support

Multiplying Choices
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Digit Discovery
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Unit 5 Solve long multiplication problems (suggested as 3 days)

Objectives

Solve long multiplication problems
Unit 5: ID#5851

National Curriculum
Mult/Div (iv)

Hamilton Objectives
16. Multiply 2, 3, 4-digit numbers by numbers ≤26 using long or short multiplication.
21. Solve problems involving multiplication and division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Remind children how to use long multiplication to calculate 57 × 16. They then work out 14 × 38. Write 26 × 57. What is an efficient way to multiply by 20? (Double, then multiply by 10) Write this in the multiplication, work out the next row, then add to find the answer. Discuss multiplying by 30. Children then try using long multiplication to find 24 × 57 and 34 × 57. Children working towards ARE can use the grid method, comparing products with long multiplications scribed for them.
Group Activities
-- Continue to develop understanding of long multiplication for 2-digit by 2-digit multiplications.
-- Consolidate use of long multiplication for 2-digit by 2-digit multiplications.
-- Consolidate use of long multiplication for a sequence of 2-digit by 2-digit multiplications where one number is less than 40. Describe and explain patterns in answers.

Day 2 Teaching
Write 25 × 37 and 27 × 35. Do you think they will give the same answer? Children work in pairs to find the 2 answers. Agree that they do not give the same answer. Show children how to find the digital root of each number in the first multiplication and the answer. Children multiply the digital roots in each multiplication and find the digital root of the product. Compare with the digital root of the answer to find that it is the same. Children repeat for the second multiplication. What do they find?
Group Activities
-- Apply long multiplication in an investigative context. Explore digital roots and explain observations.

Day 3 Teaching
Write 18 × 324 and 13 × 368. Which do you think will have the bigger answer? Use rounding to make estimates. Ask children what is different about these calculations from those they did last time (there is a 100s digit in one of the numbers). Model using long multiplication to find 324 × 18. Compare with the grid method. Ask children to work in pairs to find 368 × 13. Model using long multiplication to find 28 × 324; ask children to calculate 23 × 368, estimating the answer first.
Group Activities
-- Create a Top Tips poster for using long multiplication. Use to scaffold calculation.
-- Multiply 3-digit numbers by numbers between 40 and 60.

You Will Need

  • Mini-whiteboards and pens
  • ‘Multiplying 2-digit numbers’ (see resources)
  • Flipchart and pens
  • ‘Multiplying 3-digit numbers by 2-digit numbers’ (see resources)

Mental/Oral Maths Starters

Day 1
Multiplication facts (pre-requisite skills)

Suggested for Day 2
Rockin’ remainders (simmering skills)

Day 3
Multiply multiples of 10 by multiples of 100 (pre-requisite skills)

Procedural Fluency

Day 1
Use long multiplication to multiply pairs of 2-digit numbers. Are the children fluent enough to finish the Multiplication Marathon?

Day 2
Choose pairs of 2-digit numbers to multiply together to give answers within given ranges.

Day 3
Use long multiplication to multiply 3-digit numbers by 2-digit numbers up to 30.
Use long multiplication to multiply 3-digit numbers by 2-digit numbers up to 60.

Mastery: Reasoning and Problem-Solving

  • Alan saves 50p coins. He has saved 93 of them. How much money has Alan saved?
  • Mel’s hotel swimming pool is 33 metres long and 12 metres wide. On every day of her 3-week holiday, she swam 15 lengths. How far did she swim in total? Each day, her brother Sammy swam 35 widths. Who swam farthest?
  • Write the missing digit:
    2☐3 × 7 = 1981
    46☐ × 13 = 6097

In-depth Investigation
Use the Whole class investigation on Day 2.

Extra Support

Root Revelation
Using the grid method to multiply 3-digit numbers by 1-digit numbers