Maths Year 5/6 Summer Number properties and Multiplication

Day 1
Write: 12, 15, 24, 30, 13, 48, 36, 25, 28, 21, 27 and 33. Give a card (2–12) to each child. 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: T with Y5
Y5 Use the in-depth problem-solving investigation ‘What an odd thing!’ as today’s group activity.
Or, use these activities:
-- Find common multiples from dice rolls/ common factors of pairs of numbers on a multiplication square.
-- Interpret a word problem; find factors, common multiples and lowest common multiples.
Y6 -- Investigate patterns made by joining multiples around the circumference of a circle. Reason about observations.

Day 2
Children draw 3cm by 3cm square on cm² paper. What is the area? Show how we can write this as 3². 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 using cm³ cubes. Calculate total number of cubes. Write 3³ = 27. Together, calculate the first 5 cube numbers.
Further Teaching with Y6
Highlight the prime numbers on the ITP Number grid. Explain Goldbach’s conjecture.
Group Activities: T with Y5
Y5 -- Represent square numbers with paper cut-outs. Play a game to practise recognising square numbers.
-- In pairs, make ‘follow-me’ cards for sets of square or cube numbers.
Y6 -- Investigate Goldbach’s conjecture.

Day 3
Show children a scale model of Hogwarts castle on the internet. Every dimension is 1/24 of what would be real-life size. Explain that groups of children will design their ideal bedroom. They are going to make a scale model, and so will need to calculate the new dimensions for each length. Calculate scale dimensions of a room, four-poster bed and trunk.
Group Activities: T with Y5
Y5/Y6 -- 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 4
Children measure their heart rates in beats per minute. Use this to discuss the concept of ‘rate’ (an amount of something that happens in a given unit of time). Discuss other examples of rate, e.g. rate of growth, rate of pay, speed.
Further Teaching with Y6
Children run for 30 seconds then retake their pulse. Repeat after running for 1 minute, 2 minutes, and then 3 minutes. Show children how to draw a line graph of the results.
Group Activities: T with Y6
Y5 -- Calculate rates involved in World Record breaking achievements.
Y6 -- Construct and interpret line graphs to investigate the effect of different forms of exercise on heart rate.

• 2–12 cards
• 0–9 dice, 1–6 dice, 1–10 dice
• ‘Multiplication square’ (see resources)
• Rulers, plain card, scissors, tape
• ‘Times table patterns’ (see resources)
• cm2 paper
• ‘Multiplication square’ (see resources)
• cm cubes
• Flipchart and pens
• ITP Number grid
• ‘Goldbach’s Conjecture’ (see resources)
• Images of scale model of Hogwarts Castle, e.g. http://www.telegraph.co.uk/culture/harry-potter/9118856/Harry-Potter-studio-tour-detailed-Hogwarts-model-to-be-grand-finale.html or https://www.wbstudiotour.co.uk/explore-the-tour/art-department
• ‘Design your bedroom at Hogwarts castle’ (see resources)
• Guinness World Records book or online version
• Interactive whiteboard timer
• Stopwatches
• ‘Rates’ Sheet 1 and 2 (see resources)

Day 1
Times table bingo

Day 2
Multiplication and division facts

Day 3
Halve 2-digit numbers

Day 4
Square numbers

Day 1
Y5: Practise finding common multiples and common factors.
Y6: Investigate ‘Abundant’ numbers.

Day 2
Y5: Identify square and cube numbers. Mark and correct a piece of homework about square and cube numbers.
Y6: Investigate Goldbach’s conjecture.

Day 3
Y5/Y6: Calculate the dimensions of items in a scaled-down bedroom.

Day 4
Y5: Use multiplication and division to solve problems involving rate.
Y6: Calculate rates involved in World-Record breaking achievements.

Y5

• 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

Y6
This unit has no separate problem-solving activities for Y6.

Y5 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.

Y6 In-depth investigation: Complete Group Activity from either Day 1 or Day 2.

Y5
Times Table Puzzler
Finding multiples and factors.

Y6
This unit has no separate Extra Support activities for Y6.

Day 1
Write 6 × 4872. Discuss strategies for estimating the answer. Remind children how to use grid and short multiplication. Pairs of children come up with another multiplication with an answer within 1000 of 30,000.
Group Activities: T with Y5 or Y6
Y5 -- Practise written methods for multiplication through an investigative task (multiplications with consecutive digits).
Y6 -- Use multiplication by 1089 to generate a sequence of answers. Reason about patterns in the sequence.

Day 2
Show children a set of Napier’s rods and demonstrate how to use the method, e.g. for 3 × 524.
Further Teaching with Y5
Model use of partitioning in a grid, with jottings, to solve 12 × 34, 23 × 34 and 57 × 24.
Group Activities: T with Y5
Y5 -- Relate grid multiplication to tables facts and place value.
-- Introduce the grid method to multiply 3-digit numbers by 2-digit numbers.
Y6 -- Explore the use of Napier’s rods/bones for multiplication.

Day 3
Children use the grid method to calculate 48 × 16. Show the same calculation alongside completed with long multiplication. Discuss what is calculated in each line and how this compares to the grid method. Use both methods for other multiplications: 13 × 87, 14 × 47.
Group Activities: T with Y5
Y5 Use the in-depth problem-solving investigation ‘Reverse digits, Same product’ as today’s group activity.
Or, use these activities:
-- Use grid and long multiplication side by side to multiply pairs of 2-digit numbers (both numbers less than 20).
-- Collaborate to multiply pairs of 2-digit numbers (one number less than 20).
Y6 Collaborate to multiply pairs of 2-digit numbers (one number less than 30).

Day 4
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? Round to estimate an answer of 10,000 miles. Children find the exact answer using the grid method; then model use of long multiplication. Children calculate the distance walked by 13 people; then calculate 11 × 248 and 15 × 248.
Group Activities: T with Y5
Y5 -- Find how many hours per year a person is awake if they sleep for 8 hours per night. 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.
Y6 -- Investigate patterns in the answers to 21 × 123; 22 × 234; 23 × 345; 24 × 456; 25 × 567; 26 × 678; 27 × 789.
-- Multiply 3-digit numbers by numbers between 40 and 60.

Day 5
Remind children how to use long multiplication to calculate 57 × 16. They then calculate 14 × 38. Write 26 × 57. What is an efficient way to multiply by 20? Write this in the multiplication, calculate 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 (Y5); 24 × 357 and 34 × 357 (Y6).
Group Activities: T with Y5
Y5 -- Use long multiplication to find the answers to 12 × 21, 13 × 31, 14 × 41 … 19 × 91; look for pattern in the sequence of answers.
-- Apply long multiplication in an investigative context. Explore digital roots and explain observations.
Y6 -- Apply long multiplication in an investigative context. Explore digital roots and explain observations.

• ‘Amazing 1089’ (see resources)
• Mini-whiteboards and pens, scissors
• ‘Napier’s rods/bones’ (see resources)
• Flipchart and pens
• ‘Using the grid method to multiply 3-digit numbers by 2-digit numbers’ (see resources)
• ‘Long multiplication’ (see resources)
• ‘Multiplying 3-digit numbers by 2-digit numbers’ (see resources)

Day 1
Multiplication facts

Day 2
Multiply multiples of 10 by 1-digit numbers

Day 3
Multiply multiples of 10 by multiples of 100

Day 4
Multiply by 20

Day 5
Roman numerals

Day 1
Y5: Calculate 3-digit by 1-digit multiplications using grid multiplication.
Use short multiplication to multiply 4-digit by 1-digit numbers.
Y6: Use multiplication by 1089 to generate, then reason, about a sequence of answers.

Day 2
Y5: Use the grid method to multiply numbers between 20 and 30 by 2-digit numbers (grids are drawn).
Use the grid method to multiply pairs of 2-digit numbers.
Y6: Explore the use of Napier’s rods for multiplication.

Day 3
Y5: Practise using long multiplication to multiply 2-digit numbers (one less than 20).
Y6: Use long multiplication to multiply pairs of 2-digit numbers.

Y5

• 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 (30 days) and December (31 days)?
• Tom’s baby sister Katie has been alive for 3000 hours. How many days is this?

Y6
This unit has no separate problem-solving activities for Y6.

Y5 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.

Y6 Complete Group Activity from Day 2

Y5
Multiplying Choices
Using the grid method to multiply 3-digit numbers by 1-digit numbers.

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

Y6
This unit has no separate Extra Support activities for Y6.