Short Blocks

# Maths Year 5/6 Summer Number properties and Multiplication

Each unit has everything you need to teach a set of related skills and concepts.

## Number properties(suggested as 4 days)

### Planning and Activities

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.

### Short Mental Workouts

Day 1
Times table bingo

Day 2
Multiplication and division facts

Day 3
Halve 2-digit numbers

Day 4
Square numbers

### Worksheets

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.

### Mastery: Reasoning and Problem-Solving

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.

### Extra Support

Y5
Times Table Puzzler
Finding multiples and factors.

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