Short Blocks

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

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 Properties of numbers, including primes (suggested as 3 days)

### Objectives

Properties of numbers, including prime numbers
Unit 3: ID# 56134

Y5: Find common multiples, factors and prime numbers.
Y6: Find common multiples, highest common factors and prime factors.

National Curriculum
Y5: Multi/Div (i) (ii) (iii)
Y6: Multi/Div (v)

Y5 Hamilton Objectives
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
13. Identify prime numbers up to 100 and know primes up to 19; understand the vocabulary of prime and composite numbers; identify prime factors.

Y6 Hamilton Objectives
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.

### Planning and Activities

Day 1 Teaching
Identify multiples of given numbers on a grid. Discuss divisibility tests. Identify common multiples of two numbers. Identify the lowest common multiple.
Group Activities
Y5 -- Explore common multiples, either using a Venn diagram for sorting, or by playing a 4-in-a-row dice game.
Y6 -- Explore common multiples, either by playing a 4-in-a-row dice game or a card game.

Day 2 Teaching
Find factors of 2-digit numbers. Play a game to help children understand that bigger numbers don’t necessarily have more factors.
Further Teaching with Y6
Find common factors; then the highest common factor.
Group Activities
Use the ‘Long as you like’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Investigation: Find the number less than 50 with the greatest number of factors; explore numbers which have an even or odd number of factors.
Y6 -- Play games finding common factors and then highest common factors.

Day 3 Teaching
Play a game which encourages children to think which numbers have fewest factors, introduce prime and composite numbers.
Group Activities
Y5 -- Investigation: Find all the prime numbers to at least 50.
Y6 -- Investigation: Find which numbers from 10 to 50 can be made by multiplying two prime numbers together.

### You Will Need

• ITP: Number Grid
• Whiteboards and pens
• IWB calculator
• Flipchart and pen
• Sticky notes
• 12 × 12 multiplication grid (see resources)
• 0–9 dice
• Coloured pencils
• Several sets of number cards 2–12
• Large number cards 1–10
• ‘Common factors’ grid (see resources, enlarge to A3)
• ‘Common factors’ grid (see resources)
• 1–6 dice

### Short Mental Workouts

Day 1
Divisibility

Day 2
Stand up – sit down squares

Day 3
Times tables

### Worksheets

Day 1
Y5: Place numbers into a Carroll diagram, depending on divisibility by 3 and 4.
Y6: Find common multiples.

Day 2
Y5: Find factors of 2-digit numbers.
Y6: Find common factors of 2-digit numbers.

Day 3
Y5: Identify prime numbers to 100.
Y6: List prime numbers in a given range. Identify numbers with a pair of prime factors. Reduce a composite number to a list of its prime factors.

### Mastery: Reasoning and Problem-Solving

Y5

• Are there more or fewer common multiples of 2 and 3 under 30 than of 3 and 5? Explain your answer.
• Write the common multiples of 2, 3 and 4 up to 50. Write the common multiples of 3, 4 and 5 up to 200. Which is the bigger group?
• True or false?
5 is a factor of 20 and a factor of 40.
3 is a factor of 7 numbers less than 20.
15 is a factor of 100.
• Prime numbers are often one more or less than a multiple of 6. Write two prime numbers for which this is not true.
• Write the following as the product of 2 or more prime numbers: 30, 35, 42, 56.

Y6

• Which pair of numbers under 20 have the largest number of common factors? What is the highest common factor of these numbers?
• 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.
• True or false?
The lowest common multiple of two prime numbers, a and b is always a × b.
The highest common factor of two multiples of 6 is always 6.

In-depth Investigation: Long as You Like
Children create chains of numbers by finding factors and multiples. Their aim is to create the longest chain possible.

### Extra Support

Y5: Array or Disarray
Making different arrays using a given number as an introduction to factors.

Y6: Factor Hunt
Finding factors of numbers within times tables.

## Unit 2 Written multiplication strategies (suggested as 5 days)

### Objectives

Written multiplication strategies
Unit 1: ID# 56262

Y5: Grid method and short multiplication.
Y6: Short multiplication: whole numbers and money.

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

Y5 Hamilton Objectives
16. Multiply 2, 3, 4-digit numbers by numbers ≤ 26 using long or short multiplication or grid method.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples.

Y6 Hamilton Objectives
11. Multiply 2-digit, 3-digit and 4-digit numbers by numbers up to 12 using short multiplication or another appropriate written method.

### Planning and Activities

Day 1 Teaching
Remind Y5 how to use the grid method to multiply 3-digit numbers by 1-digit numbers, and how to round to approximate answers.
Further Teaching with Y6
Write 5 × 2326, 4 × 3943, 6 × 2082 and ask children to estimate which will have the largest answer. Model estimating and also short multiplication; draw comparisons.
Group Activities: T with Y6
Y5 -- Whole year group investigation: work in groups to find the 3-digit × 1-digit multiplication with the biggest and smallest answers.
Y6 -- Move from using the grid method to short multiplication, using ‘friendly’ digits. Investigate arranging the digits in a multiplication to give the largest answer, then the smallest.

Day 2 Teaching
Teach Y5 short multiplication (3-digit × 1-digit), comparing with grid multiplication. Show Y6 examples, 4-digit by 1-digit. Tell Y5 this is the same method, just with more digits.
Group Activities: T with Y5
Y5 -- Multiply using short multiplication. Identify ranges of multiples of 100 for multiplications and say which multiple of 100 will be nearer.
Y6 -- Write multiplications with answers in given ranges. Estimate which multiplications will give the smallest and largest answers and use short multiplication to find exact answers.

Day 3 Teaching
Use short multiplication to estimate how many drinks and meals might be consumed in a year.
Further Teaching with Y6
Use short multiplication to find the cost of three presents (4-digit prices).
Group Activities: T with Y6
Use the in-depth problem-solving investigation for this unit ‘Excellent eights’ as today’s group activity.
Or, use these activities:
Y5 -- Use the grid method and short multiplication to multiply 3-digit by 1-digit numbers.
Y6 -- Estimate and calculate the exact cost of buying 3 items (3-digit prices). Some children will calculate target spends between £50 and £100.

Day 4 Teaching
Model using the grid method to multiply 2-digit numbers by teens numbers, then by numbers between 20 and 30, stressing what is being calculated on each row.
Group Activities: T with Y5
Y5 -- Partition rectangles to find areas, link to the grid method. Multiply 2-digit numbers by 24 using the grid method.
Y6 -- Multiplication investigation swapping 1s digits of 2-digit numbers.

Day 5 Teaching
Consolidate setting out the grid method to multiply pairs of 2-digit numbers. Discuss which will have largest/smallest answer.
Further Teaching with Y6
Discuss and show how to use the grid method to calculate 17 × 234 and 27 × 234. Children then find 43 × 345.
Group Activities: T with Y6
Y5 -- Create multiplications of 2-digit numbers with answers in given ranges.
Y6 -- Use the digits 3, 4 and 5 in any order to make a 3-digit number and multiply it by 16, then 26. Create multiplications with a target answer of 15,000.

### You Will Need

• Mini-whiteboards and pens
• Digit cards
• Flipchart and pens
• ‘Multiplying 3-digit numbers by 1-digit numbers’ (see resources)
• ‘Multiplying 4-digit by 1-digit numbers’ (see resources)
• ‘Oscar’s online gifts’ (see resources)
• ‘Written multiplication practice’ (see resources)
• ‘Greta’s online gifts’ (see resources)
• cm2 paper

### Short Mental Workouts

Day 1
6, 60, 7 and 70 times tables

Day 2
Times tables

Day 3
Find the time later using the 24-hour clock

Day 4
Multiply by 20

Day 5
Multiply pairs of multiples of 10, and 10s by 100s.

### Worksheets

Day 1
Y5: Multiply 3-digit numbers by 1-digit numbers (grid method).
Y6: Multiply 3-digit numbers then 4-digit by 1-digit numbers (short multiplication).

Day 2
Y5: Multiply 3-digit numbers by 1-digit numbers (short or grid multiplication).
Y6: Short multiplication.

Day 3
Y5: Multiply 3-digit numbers by 1-digit numbers (short multiplication).
Y6: Use short multiplication to multiply amounts of money.

Day 4
Y5: Multiply 2-digit numbers by numbers between 10 and 30 using the grid method.
Y6: Multiply pairs of 2-digit numbers together using the grid method.

Day 5
Y5: Multiply pairs of 2-digit numbers together using the grid method.
Y6: Multiply 3-digit numbers by 2-digit numbers using the grid method.

### Mastery: Reasoning and Problem-Solving

Y5

• Find the product of 274 and 6 using two different methods. Do your answers agree?
• Explain how you can calculate 235 × 4 mentally. Now check your answer using short multiplication.
• Fill in the missing digits:
 8 4 ☐ x ☐ ☐ ☐ 0 5
• Write a multiplication of one 3-digit number by 6 where the last two digits of the product are consecutive (e.g. 5, 6).

Y6

• Maya says that 2578 × 4 gives the same product as 8 × 1289. Is she correct? Demonstrate why/why not. Multiply 1386 by 9. Write the product. Add the same number (1386) to the product. What do you notice?Repeat with 2547 × 9, adding 2547 to the product. Explain what happens. Could you use this to make finding the product easier?
• Write the missing digits in this multiplication:
3 6 ☐ 2 × 8 = ☐ 9 ☐ 3 6

In-depth investigation: Excellent Eights
Children explore patterns when multiplying numbers with consecutive digits by 8.

### Extra Support

Y5: Grid Luck
Using the grid method to multiply 2-digit numbers by 1-digit numbers.

Y6: Greatest Grid Gurus
Using the grid method to multiply 3-digit numbers by 1-digit numbers.

## Unit 3 Mental division strategies (suggested as 2 days)

### Objectives

Mental division strategies
Unit 2: ID# 56270

Y5: Use tables facts for mental division, with and without remainders.
Y6: Use tables facts for mental division, with remainders.

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

Y5 Hamilton Objectives
15. Perform divisions mentally in range of tables; use remainders, fractions, decimal equivalences.

Y6 Hamilton Objectives
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
Perform divisions mentally within tables using fractions and decimal equivalences for remainders, then an example beyond tables.
Group Activities: T with Y5
Y5 – Play division game. Some children will create divisions having answers with given remainders.
Y6 -- Choose a number to divide by the number on a dice. Score points for each way the answer is expressed.

Day 2 Teaching
Use number facts and place value to answer 54 ÷ 6, 540 ÷ 6, 36 ÷ 9, 360 ÷ 9. Write and share 240 ÷ ? number sentences, e.g. 240 ÷ 8 = 30.
Further Teaching with Y6
Progress to write answers to divisions with remainders, e.g. 541 ÷ 6, 542 ÷ 6, 543 ÷ 6, 544 ÷ 6, 545 ÷ 6 and 546 ÷ 6.
Group Activities: T with Y6
Use the in-depth problem-solving investigation for this unit ‘Remainder rally as today’s group activity.
Or, use these activities:
Y5 -- Create divisions using given numbers, known multiplication
facts and place value.
Y6 -- Create divisions with remainders using given numbers, known multiplication facts and place value.

### You Will Need

• ‘1–100 grids’ (see resources)
• Mini-whiteboards and pens
• Flipchart and pens
• Blank dice and pen

### Short Mental Workouts

Day 1
Times tables

Day 2
Multiply 10s or 100s by 1-digit numbers

### Worksheets

Day 1
Y5: Calculate mental division, writing answers with remainders as mixed numbers, as decimals and as money.
Y6: Calculate mental division, writing answers with remainders as mixed numbers, as decimals and as money.

Day 2
Y5: Answer divisions using known multiplication facts and place value (no remainders).
Y6: Answer divisions using known multiplication facts and place value (with and without remainders).

### Mastery: Reasoning and Problem-Solving

Y5

• Correct Paola’s work. She has made the same mistake twice. Explain what the mistake is. Show the correct calculations (see download).
• Look at the remainders in each of these divisions. Compare the remainder with the divisor.
a) 56 ÷ 3
b) 75 ÷ 4
c) 94 ÷ 5
• Can you write a division where you divide by 6 and the remainder is 5?
• Find the missing numbers:
420 ÷  = 70
80 = ÷ 7
490 ÷ 7 = 

Y6