Short Blocks

# Maths Year 5/6 Spring Multiplication and Division

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

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The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Division (suggested as 3 days)

### Objectives

Division
Unit 3: ID# 56540

Y5: Short division
Y6: Short and long division

National Curriculum
Y5: Mult/Div (vi)
Y6: Mult/Div (ii)

Y5 Hamilton Outcomes
18. Divide 2-, 3- and 4-digit numbers by 1-digit numbers above tables range; choose and use efficient methods; interpret remainders appropriately according to context.

Y6 Hamilton Outcomes
16. Divide numbers with up to 4 digits by a number up to 12 using short division and giving an appropriate answer.
17. Divide numbers with up to 4 digits by 2-digit numbers using a formal written method of long division and giving an appropriate answer.
19. Use estimation to check answers and determine an appropriate degree of accuracy.

### Planning and Activities

Day 1 Teaching
Say that Y5 are going to use a method of division called short division (sometimes nicknamed the ‘bus shelter’ or ‘bus stop’ method). Use a slide presentation or base-10 equipment to model this method of division for 678 ÷ 3. Solve similar divisions.
Group Activities: T with Y5
Y5 -- Solve short division calculations and investigate remainders. Some children use base-10 equipment to help.
Y6 -- Discuss which divisions have an answer more/less than 100 or 1000. Create short divisions with mixed number answers.

Day 2 Teaching
Use the slide presentation, alongside base-10 equipment, to demonstrate using short division to solve 281 ÷ 3. Repeat for 281 ÷ 6 and 281 ÷ 5.
Further Teaching with Y6
Write 632 ÷ 14. Write the multiples of 14 and then use these to solve 632 ÷ 14 using long division. Repeat this process with 532 ÷ 17.
Group Activities: T with Y6
Y5 -- Solve short division calculations and investigate remainders, including examples where the first digit is less than the divisor.
Y6 -- Use step-by-step ‘efficient chunking’ to perform long division. Practise long divisions and then create similar divisions using the same number and different divisors.

Day 3 Teaching
Y5 calculate 742 ÷ 4 and 742 ÷ 8, and compare the answers. Y6 calculate 348 ÷ 24 and 510 ÷ 24 and compare answers.
Group Activities: T with Y5 or Y6 according to assessment on Days 1 and 2
Use the in-depth problem-solving investigation ‘Dozen divisions’ as today’s group activity.
Or, use these activities:
Y5 -- Explore division, expressing remainders as fractions.
Y6 -- Divide by 16 using the step-by-step chunking process; write remainders as fractions and as equivalent decimals for halves/quarters. Explore patterns of answers ending in .25 or .75 when dividing by 16 and attempt to find dividends with answers ending in .5.

### You Will Need

• Base-10 equipment
• Slide presentation (see resources)
• 1–9 number cards

### Short Mental Workouts

Day 1
Times tables

Day 2
17 times table

Day 3
Equivalent fractions and decimals

### Worksheets

Day 1
Y5: Divide 3-digit by 1-digit numbers, including answers with remainders.
Y6: Divide 3-digit and 4-digit numbers by 1-digit numbers, writing answers as mixed numbers.

Day 2
Y5: Divide 3-digit by 1-digit numbers, including word problems.
Y6: Write multiples and use these to help with long division of 3-digit numbers by 2-digit numbers (answers with remainders).

Day 3
Y5: Divide 3-digit by 1-digit numbers; write remainders as fractions in their simplest form.
Y6: Write multiples and use these to help with long division of 3-digit numbers by 2-digit numbers, writing remainders as decimals and/ or fractions.

### Mastery: Reasoning and Problem-Solving

Y5

• Fill in the missing digits (see download) in this vertical chunking division calculation:
7 8 3 ÷ 9 = ☐
Complete the same calculation using short division.
Which method did you find easier? Explain why.
• (i) Is the answer to 1539 ÷ 3 treble the answer to 1539 ÷ 9?
(ii) Now use short division to find an answer to both calculations. Was your answer to (i) correct?

Y6

558 ÷ 9
308 ÷ 7
7302 ÷ 6
£93.52 ÷ 8
• Which of the following divisions give an answer which ends 1/4 or .25?
3750 ÷ 24
2223 ÷ 18
7300 ÷ 16
Write two more calculations in the form  ÷  that also give a remainder of 1/4.

In-depth investigation: Dozen divisions
Y5 Children use short division to divide 3-digit numbers with consecutive digits by 12. They reverse the digits in the 3-digit number and repeat, then find the difference between the two answers. Y6 As Year 5, but children use long division to divide 3-digit numbers by 2-digit numbers less than 30.

### Extra Support

Y5: Any Left?
Using chunking to divide, answers between 10 and 20, with remainders

Y6: Any left?
Using chunking to divide (answers less than 100)

## Unit 2 4-Digit multiplication and division (suggested as 4 days)

### Objectives

4-Digit multiplication and division
Unit 4: ID# 56556

Y5: Short multiplication and division
Y6: Short and long multiplication and division

National Curriculum
Y5 Mult/Div (iv) (vi)
Y6 Mult/Div (i) (ii) (iii) (ix)

Y5 Hamilton Outcomes
16. Multiply 2-, 3-, 4-digit numbers by numbers ≤ 26 using long or short multiplication or the grid method.
18. Divide 2-, 3- and 4-digit numbers by 1-digit numbers above tables range; choose and use efficient methods; interpret remainders appropriately according to context.

Y6 Hamilton Outcomes
12. Multiply numbers with up to 4 digits by 2-digit numbers using formal long multiplication.
16. Divide numbers with up to 4-digits by a number up to 12 using short division and giving an appropriate answer.
17. Divide numbers with up to 4 digits by 2-digit numbers using a formal written method of long division and giving an appropriate answer.

### Planning and Activities

Day 1 Teaching
Estimate and then solve 5783 × 7. Write 2341, 5372, 4278, 6143. Divide the class into 4 groups. A child from each group takes a 3–9 digit card. Each group decides which number to multiply by the card number, aiming for an answer close to 20,000.
Group Activities: T with Y5
Y5/Y6 -- Use given digits to create 4-digit by 1-digit multiplications with answers as near to a given target as possible.

Day 2 Teaching
Use both grid method and short multiplication to model finding the cost of 6 hoodies (6 × £25.79) and 7 pairs of jeans (7 × £34.45).
Further Teaching with Y6
A teacher travels 16 miles to and from school for 195 days a year. How far in a year? Estimate then show how to use long multiplication to work out 16 × 195. Check using the grid method. Repeat for 23 miles × 195 days.
Group Activities: T with Y6
Y5 -- Estimate products, then multiply 4-digit money amounts by 1-digit numbers.
Y6 -- Use the context of 24 hours in a day to multiply by 24 to find the number of hours in a year or other 3-digit numbers of days. Use long multiplication to calculate how many days, then hours, children have been alive.

Day 3 Teaching
Use short division to divide 4-digit numbers by 1-digit numbers, using base 10 equipment and/or slide presentation.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Division remainder patterns’ as today’s group activity.
Or, use these activities:
Y5 -- Explore division, expressing remainders as fractions. Some children will explore division, looking for answers in given ranges.
Y6 -- Use short division in a problem-solving context.

Day 4 Teaching
Discuss estimates and then divide 4-digit numbers of legs by 3 to find how many toy aliens can be made.
Further Teaching with Y6
List multiples of 32 to find how many 32-page comic books can be made using 3-digit then 4-digit numbers of pages.
Group Activities: T with Y6
Y5 -- Explore division, looking for answers in given ranges. Divide 4-digit money amounts by 1-digit numbers.
Y6 -- Choose 3-digit numbers to divide by 18. Estimate answers, then solve problems involving long division by 32, using efficient chunking.

### You Will Need

• 1–9 digit cards
• Large cards
• Calendars
• Slide presentation (see resources)
• Base-10 equipment
• ‘Short division’ sheet 1 (see resources)
• ‘Short division’ sheet 2 (see resources)

### Short Mental Workouts

Day 1
Times tables

Day 2
Factors and multiples

Day 3
Count in 1/4s and 1/8s

Day 4
Multiplication and division facts

### Worksheets

Day 1
Y5: Use given digits to make 4-digit by 1-digit multiplications with answers as close to given products as possible.
Y6: Use short multiplication to multiply amounts of money, aiming for answers close to £200.

Day 2
Y5: Estimating and solving multiplication problems with money.
Y6: Use the grid method to multiply 3-digit numbers by 2-digit numbers.
Use long multiplication to multiply 3- and 4-digit numbers by 2-digit numbers.

Day 3
Y5: Divide 4-digit by 1-digit numbers, including word problems.
Y6: Practise using short division then answer word problems requiring decisions about remainders.

Day 4
Y5: Match 4-digit ÷ 1-digit divisions with given answers. Use short division or multiplication to check answers.
Y6: Write multiples of given 2-digit numbers and use these to divide 3- and 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

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

Y6

• Complete each multiplication using a different method:
(i) 4530 × 23
(ii) 399 × 25
(iii) 476 × 6
• Multiply 531 by 32 using long multiplication or the grid method. Now double 531 five times to check if this gives the same answer.
• Tom multiplies his number by 9 and gets 7074. What was his starting number?
• If Sally multiplies a number by 12, she gets 9,432. What was her starting number?

In-depth investigation: Division remainder patterns
Children look at patterns of remainders in 4-digit numbers when dividing by numbers 3 to 6. Can they establish a rule?

### Extra Support

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

Y6: Monster Multiplications
Using known times tables and place value to multiply, e.g. 6 × 4, 6 × 40, 6 × 400

Aim for 2000
Using the grid method to multiply 3-digit numbers by 1-digit numbers