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

Objectives

Mental mult/div; problem solving
Unit 3: ID# 56286

Y5: Mental multiplication and divisions. Solve scaling and rate problems.
Y6: Mental multiplication and divisions. Solve scaling and rate problems.

National Curriculum
Y5: Mult/Div (v) (ix) (xi)
Y6: Mult/Div (iv)

Y5 Hamilton Objectives
14. Use efficient mental methods to multiply two or three numbers.
15. Perform divisions mentally in range of tables.
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.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples.

Y6 Hamilton Objectives
10. Multiply/divide whole numbers mentally, using facts to 12 × 12 and place value; use facts to work with larger numbers.
13. Scale up or down by a factor of 2, 4, 5 or 10; solve scaling problems and those involving rates.
14. Perform divisions mentally within the range of tables facts; divide multiples of 10 and 100 (4500 ÷ 9) and use mental strategies such as halving (450 ÷20).

Teaching and Group Activities for Understanding

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

Procedural Fluency

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.

Unit 2 Written division strategies (suggested as 4 days)

Objectives

Written division strategies
Unit 4: ID# 56300

Y5: Division of big numbers using vertical layout.
Y6: Securing short division.

National Curriculum
Y5: Mult/Div (vi) (vii)
Y6: Mult/Div (iii)

Y5 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.

Y6 Hamilton Objectives
16. Divide numbers with up to 4-digits by a number up to 12 using short division and giving an appropriate answer.
15. Interpret remainders as whole number remainders, fractions, including decimal fractions where equivalents are known or by rounding up or down.

Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate how to use both chunking on the empty number line and vertical layout to calculate 196 ÷ 6. Repeat with 113 ÷ 3, asking children to make an estimate first.
Further Teaching with Y6
Model using short division (3-digit and 4-digit) giving fractional answers, simplifying where possible.
Group Activities: T with Y6
Y5 -- Estimate the answer for divisions between two multiples of 10. Use both empty number line and vertical layout for chunking.
Y6 -- Choose 3-digit numbers to divide by 4, 6 and 8, so as to give a mixed number answer. Some children will work with 4-digit numbers and divide by 5, 4, 6, 8 and 12.

Day 2 Teaching
Children first estimate answers to different divisions. Then write 148 ÷ 3, 148 ÷ 4, 148 ÷ 5, 246 ÷ 5, 246 ÷ 6, 246 ÷ 8. Which of these could you calculate mentally? How?
Further Teaching with Y6
Show how we can write fraction parts of answers, e.g. ½ or ¾, and as decimals, e.g. 23¾ as 23.75. Model with 4-digit numbers divided using short division.
Group Activities: T with Y6
Use the in-depth problem-solving investigation for this unit ‘Remainders rule!’ as today’s group activity.
Or, use these activities:
Y5 -- Spot divisions with the same answer, and write others with the same answer. Identify divisions that can be done mentally; explain how.
Y6 -- Choose amounts of money between £100 and £1000 (whole number of pounds) to divide by 4, to give answers which are not whole numbers of pounds. Some children will work with amounts between £1000 and £5000 and divide by 4 and 5.

Day 3 Teaching
Children discuss what calculation is needed to solve a given word problem. Model vertical layout and short division. Decide whether to round up or down. Repeat with a new problem.
Group Activities: T with Y5
Y5 -- Use sketching to help visualise contexts for short division; decide whether to round up or down to solve division problems.
Y6 -- Use base 10 equipment to support short division, and then decide where to round up or down to solve division problems. Use multiplication to check division.

Day 4 Teaching
Display some given word problems, one at a time. Agree the calculation for each, solve it; discuss whether the answer needs to be rounded up or down OR the answer needs to be exact with a fraction or decimal part.
Group Activities: T with Y5
Y5 -- Discuss whether problems will need the answer rounding up, rounding down or leaving as is.
Y6 -- Discuss whether problems will need the answer rounding up, rounding down or leaving as is. Some children will solve division problems, and then make up division word problems for given answers.

You Will Need

• Mini-whiteboards and pens
• Sticky notes
• PowerPoint resources 1 and 2 (see resources)
• Flipchart and pens
• ‘Division’ sheets 1 and 2 (see resources)
• Calculators
• ‘Rounding up and down’ Sheet 1 (see resources)
• ‘Rounding up or down’ Sheet 2 (see resources)
• Base 10 equipment
• ‘Division word problems’ sheets 1, 2 and 3 (see resources)

Short Mental Workouts

Day 1
Mental division

Day 2
Multiplication and division facts

Day 3
Elapsed time

Day 4
Place 5-digit numbers on a human number line

Procedural Fluency

Day 1
Y5: Division practice (vertical layout)
Y6: Use short division to divide 3- or 4-digit numbers by a single digit.

Day 2
Y5: Practise using the vertical layout to divide numbers, spotting the occasional division that can be worked out mentally.
Y6: Divide 3-digit or 4-digit numbers to give answers with fractions. Rewrite each as a decimal using equivalence.

Day 3
Y5/Y6: Divide, then round up or down to solve the problem

Day 4
Y5/Y6: Division word problems

Mastery: Reasoning and Problem-Solving

Y5

• Explain how each of these three divisions can be solved mentally:
250 ÷ 5 =
180 ÷ 6 =
210 ÷ 3 =
So, now explain how you would complete these three:
255 ÷ 5 =
186 ÷ 6 =
213 ÷ 3 =
• Divide 456 by 8 using just 2 hops along a number line. Show the same division using vertical layout.
• Use vertical layout to find the answer to 234 ÷ 6 and say why it is possibly less straightforward than 244 ÷ 6.
• Write a division of a 3-digit number by a 1-digit number where the remainder is 5.

Y6

• Divide 3666 by 3, 4, 5, 6 and 8 and write exact answers with a fraction part as necessary.
• Write the missing numbers in this division.
6 ☐ 0 7 ÷ 6 = 1 1 3 4 .
• Write a division of one 3-digit number by 6 where the answer contains the fraction 1/6. Write a similar division where the answer contains the fraction 5/6.

In-depth Investigation: Remainders Rule!
Children find numbers between 100 and 200 that will give a remainder when divided by numbers 2 to 9.

Extra Support

Y5
Chunking Challenge
Using chunking to divide, answers between 10 and 20, no remainders.

and

Leftovers
Using chunking to divide, answers between 10 and 20, with remainders.

Y6
Chunky Jumps
Using chunking to divide (answers less than 60).

and

Toffee Apples
Using chunking to divide (answers less than 60); round up or down to answer word problems.