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. '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 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.

Teaching and Group Activities for Understanding

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

Procedural Fluency

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.

Teaching and Group Activities for Understanding

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.

Procedural Fluency

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:
84
x
05
  • 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.

Teaching and Group Activities for Understanding

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

Procedural Fluency

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

  • Write four division word problems leading to these answers:
    17 r3
    17.75m
    173/4
    €17.75

In-depth investigation: Remainder Rally
Children explore patterns of remainders when dividing by numbers 3 to 6.