Short Blocks

# Maths Year 5/6 Spring Multiplication

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

First time using Hamilton Maths?

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 Multiples, factors and mental strategies (suggested as 2 days)

### Objectives

Multiples, factors and mental strategies
Unit 1: ID# 56508

Y5: Multiples, factors and mental strategies
Y6: Multiples, factors and mental strategies

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

Y5 Hamilton Outcomes
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
14. Use efficient mental methods to multiply two or three numbers.

Y6 Hamilton Outcomes
9. Know all multiplication and division facts up to 12 × 12; identify common factors, common multiples, square numbers to 144 and prime numbers up to 20.
10. Multiply/divide whole numbers mentally, using facts to 12 × 12 and place value (e.g. 60 × 70); use facts to work with larger numbers.

### Planning and Activities

Day 1 Teaching
Use the ITP Number grid to highlight multiples, look for the lowest common multiple of 2 and 3, 3 and 4, 3 and 6, 6 and 9. Then find the highest common factor of 32, 16 and 24, then 12, 20 and 32.
Group Activities: T with Y6
Y5 -- Derive lowest common multiples and highest common factors. Investigate finding lowest common multiples.
Y6 -- Play games to practise finding common multiples and factors.

Day 2 Teaching
Use mental strategies to multiply 2-digit numbers by 1-digit numbers. Aim to reach given targets.
Further Teaching with Y6
Write the 0.4 times tables. Use this to multiply 2-digit numbers with 1 decimal place by 1-digit numbers. Check the place value of answers is reasonable.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘LCM Squares’ as today’s group activity.
Or, use these activities:
Y5 -- Investigation to practise mentally multiplying 2-digit numbers by 1-digit numbers.
Y6 -- Derive the 0.6, then 2.6 times table. Investigation to practise mentally multiplying numbers with 1 decimal place by 1-digit numbers.

### You Will Need

• ITP: Number grid
• Number cards 2–12
• Common multiples (see resources)
• Common factors activity sheet (see resources)

### Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Times table bingo

### Worksheets

Day 1
Y5: Find common multiples and factors of given numbers.
Y6: Find highest common factor and lowest common multiple of sets of numbers.

Day 2
Y5: Mentally multiply 2-digit numbers by 1-digit numbers. Explain strategies.
Y6: Derive the 0.3 times table then related facts.
Mentally multiply 2-digit numbers with 1 decimal place by 1-digit numbers.

### Mastery: Reasoning and Problem-Solving

Y5

• Is the lowest common multiple of 6 and 4 smaller than the highest common factor of 30 and 45?
Write common factors of 24 and 48.
Write common multiples of 3 and 5 up to 60.
Are any numbers in both sets?
• True or false?
There are exactly four 2-digit, common multiples of 3 and 7.
4 and 5 are common factors of all 2-digit multiples of 10.
15 is a factor of 100.
• If 350 ÷ 5 is 70, calculate 350 ÷ 10, 350 ÷ 20 and 350 ÷ 70.
Now try 350 ÷ 2.5.

Y6

• Which pair(s) of numbers under 20 have the largest number of common factors? What is the highest common factor?
Write common multiples of 4 and 6 up to 60. What is the lowest common multiple?
Use this information to find the lowest common multiple of 8 and 12.
• Write out the 0.7 times table up to 12 × 0.7. Use this to help you write the 2.7 times table.

Y5 In-depth investigation: LCM Squares
Children use trial and improvement to find the smallest possible total on a square of lowest common multiples.

Y6 In-depth investigation:
Use the Day 2 group activity for Working at ARE/Working at Greater Depth, supporting children working towards ARE.

### Extra Support

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

Y6: Factor Hunt
Finding factors of numbers within times tables

## Unit 2 Multiplication (suggested as 3 days)

### Objectives

Division
Unit 2: ID# 56524

Y5: Short multiplication
Y6: Long multiplication

National Curriculum
Y5: Mult/Div (iv)
Y6: Mult/Div (i)

Y5 Hamilton Outcomes
16. Multiply 2-, 3-, 4-digit numbers by numbers ≤ 26 using long or short multiplication or the grid method.

Y6 Hamilton Outcomes
12. Multiply numbers with up to 4 digits by 2-digit numbers using formal long multiplication.

### Planning and Activities

Day 1 Teaching
Model both the grid method and short multiplication to calculate 6 × £5.24. Children choose one of the two methods to calculate the cost of 8 items at £6.79.
Further Teaching with Y6
Children first use grid method to calculate 16 × 258. Then revise and model long multiplication to solve the same calculation.
Group Activities: T with Y6
Y5 -- Use the new method of short multiplication for multiplying amounts of money. Use the grid method for multiplying amounts of money.
Y6 -- Use the digits 1 to 6 to create 3-digit by 2-digit (teen) multiplications. Answer using the grid method, then long multiplication. Estimate and calculate 13, 15, 16, 17 and 18 × 485 using long multiplication.

Day 2 Teaching
Use long multiplication to calculate how many hours there are in a year and in a leap year.
Further Teaching with Y5
Work towards using short multiplication to multiply 3-digit, then 4-digit numbers by 1-digit numbers, discussing the extra column/digit to be multiplied.
Group Activities: T with Y5
Y5 -- Estimate products, then multiply 4-digit numbers by 1-digit numbers. Estimate products, then multiply 4-digit money amounts by 1-digit numbers.
Y6 -- Find how many hours are in a number of days (generated by dice) using long multiplication. Use long multiplication to multiply numbers greater than 20 and move on to numbers greater than 30.

Day 3 Teaching
Estimate before using short multiplication of 4-digit numbers by 1-digit numbers. Discuss top tips for the method.
Further Teaching with Y6
Teach children how to multiply by 30, then use long multiplication to multiply 3-digit numbers by numbers between 30 and 40. In pairs, children calculate a row each, then compare with estimates.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘Riveting reversals’ as today’s group activity.
Or, use these activities:
Y5 -- Investigation: find answers to given challenges, using short multiplication of 4-digit by 1-digit numbers.
Y6 -- Find a multiplication of the form □□× □□□ with an answer close to 20,000. Use the grid method. Multiply 33 by 3-digit numbers with identical digits using long multiplication.

### You Will Need

• ‘Find the cost’ (see resources)
• 0–9 dice

### Short Mental Workouts

Day 1
Times tables

Day 2
Factors and multiples

Day 3
Tables facts and powers of 10

### Worksheets

Day 1
Y5: Find the total cost of multiple numbers of items.
Y6: Use grid or long multiplication to multiply 3-digit numbers by numbers between 10 and 20.

Day 2
Y5: Multiply 1-digit by 4-digit numbers using the grid method or short multiplication.
Y6: Use long multiplication to multiply 3-digit numbers by numbers between 20 and 30.

Day 3
Y5: Estimate and solve multiplication calculations; create puzzles.
Y6: Use long multiplication to multiply 3-digit numbers by numbers greater than 30.

### Mastery: Reasoning and Problem-Solving

Y5

• Does 2340 × 8 give the same answer as 4320 × 4? Explain how you are certain that your answer is correct.
• Choose a strategy for each of these three multiplications. Explain why it is not sensible to use the same method for all three.
(i) 340 × 5 =
(ii) 421 × 7 =
(iii) 350 × 9 =
• ☐☐☐ × ☐
Using the digits 3, 5, 6 and 7, how close can you get to 2,000?

Y6

• Have a go at doing each of these 3 multiplications mentally.
Explain how you did each one.
280 × 25 =
143 × 21 =
210 × 15 =
Children could check each using long multiplication or the grid method.
• Multiply 531 by 16 using long multiplication or the grid method.
Now double 531 four times to check if this gives the same answer.
• True or false?
8 × 572 is the same as 286 × 16.
15 × 626 is the same as 6260 add 3130.
24 × 333 is half of 12 × 666.

Y5 In-depth investigation: Riveting reversals
Multiply 4-digit numbers with consecutive digits by a 1-digit number; reverse the 4-digit number and repeat. Find the difference between the two answers.

Y6 In-depth investigation:
Multiply 3-digit numbers with consecutive digits by a 2-digit number; reverse the 3-digit number and repeat. Find the difference between the two answers.

### Extra Support

Y5: Multiplication Splits
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Y6: Grid Triplets
Revising using the grid method to multiply 3-digit numbers by 1-digit numbers