Short Blocks

# Maths Year 5/6 Autumn Multiplication and Division (B)

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

## Mental mult/div; problem solving(suggested as 4 days)

### Planning and Activities

Day 1 Teaching
Write 23 × 10 and 23 × 5 and show how we can use the former to solve the latter. Repeat for 23 × 20 and 23 × 19. Model 23 × 6 as 23 × 3 doubled. Discuss strategies for 23 × 8 and 123 × 8 by repeated doubling.
Group Activities: T with Y5
Y5/Y6 -- Explore mental methods based on doubling and halving to multiply by 5, 20, 6, 4 and 8.

Day 2 Teaching
Use 240 ÷ 10 to find 240 ÷ 5 and 240 ÷ 20. Use 270 ÷ 3 to find 270 ÷ 6. Use repeated halving to divide by 4 and 8.
Group Activities: T with Y6
Use the in-depth problem-solving investigation for this unit ‘Get to the root’ as today’s group activity.
Or, use these activities:
Y5 -- Explore mental methods to divide by 5, 20 and 4. Some children will also divide by 6 and 8.
Y6 -- Explore mental methods to divide by 5, 20, 6, 4 and 8. Some children will divide 3-digit numbers by 5, 20 and 8 to give answers with decimal places.

Day 3 Teaching
Show a table of dimensions of scale models of dinosaurs. Each model is 1/20 of the actual height and length. Ask how we can calculate full size. Repeat for a shop that is selling toy dinosaurs where each measurement is 1/200 of the size of the real dinosaurs.
Group Activities: T with Y5
Y5 -- Calculate the heights of children and classroom furniture if heights are scaled up by a factor of 5. Some children will work with a factor of 8 and will scale widths by a factor of 4.
Y6 -- Scale down dimensions of dinosaurs by factors of 10 or 100 to sketch on paper. Look at relative sizes.

Day 4 Teaching
Describe how much a blue whale eats and the rates of growth of a calf. Define ‘rate’. Calculate the growth in one week.
Group Activities: T with Y6
Y5 -- Calculate how long different creatures take to eat their body weight in food. Calculate a rate for tasks, and how many of these tasks could be performed in a school day at the same rate.
Y6 -- Solve and create problems involving rates in the natural world.

### You Will Need

• Number cards 1–9
• Flipchart and pens
• ‘Scaling up’ (see resources)
• ‘Dimensions for dinosaur toys’ (see resources)
• A3 paper
• ‘Dinosaur measurements’ (see resources)
• Tape measure or trundle wheel to measure the length of the classroom
• Stopwatch
• Internet access
• Solve problems involving rate’ (see resources)

### Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Double and halve 3-digit numbers

Day 3
Multiplication and division facts

Day 4
Place value counting

### Worksheets

Day 1
Y5: Using mental strategies to multiply by 5, 20, 6, 4 and 8 (mostly 2-digit numbers).
Y6: Using mental strategies to multiply by 5, 20, 6, 4 and 8 (mostly 3-digit numbers).

Day 2
Y5/Y6: Using mental strategies to divide by 5, 20, 6, 4 and 8.

Day 3
Y5/Y6: Solve scaling problems about dinosaurs

Day 4
Y5/Y6: Solve problems involving rate

### Mastery: Reasoning and Problem-Solving

Y5

• 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?
• Alfie’s uncle drinks chocolate milk at a rate of 3 pints a day. How much milk does he drink in a week? In 5 weeks? In 20 weeks?

Y6

• Solve these calculations using mental strategies:
(i) 234 × 5
(ii) 450 × 20
(iii) 1270 ÷ 8
(iv) 253 × 6
(v) 732 ÷ 5
Explain which you found tricky and why.
• A doll's house is made so that all the furniture is 1/20 size of actual real furniture. Write the dimensions of these items in the doll's house:
-- Bed (actual size 2.4m by 1.2m)
-- Sofa (actual size 1.8m by 120cm)
-- Wardrobe (actual size 2.4m by 1.8m by 60cm)
• Alfie’s uncle drinks chocolate milk at a rate of 17 pints a week! How much milk does he drink in 5 weeks? In 20 weeks?

In-depth Investigation: Get to the Root
Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication.

### Extra Support

Y5: Mammoth Multiplication
Using known times tables and place value to multiply, e.g. 4 × 3, 4 × 30, 4 × 300.

Y6: Factors and Multiples Game
Use this game where players take turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player: Factors and Multiples Game from nrich.maths.org.