Maths Year 4 Spring Multiplication and Division

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Times tables: x/÷ facts (suggested as 3 days)

Objectives

Times tables: multiplication and division facts
Unit 1: ID# 4567

National Curriculum
Mult /Div (i) (ii) (iii)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and 1; divide by 1.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.

Teaching and Group Activities for Understanding

Day 1 Teaching
Count in 9s along a counting stick. Rehearse division facts, e.g. How many 9s are in 27? How many 9s are in 45? Demonstrate the ‘finger trick’ of showing 9 times tables facts. Point out that the digits of each multiple of 9 add to 9. This is the ‘digital root’ or ‘digit sum’ and is an important ‘test for divisibility’.
Group Activities
-- Explore all multiplication and division facts for the 9 times table.

Day 2 Teaching
Count in 7s along a counting stick. Rehearse division facts, e.g. How many 7s are in 21? How many 7s are in 42? Launch ITP ‘Number grid’. Use the toggle to highlight multiples of 7. Describe the pattern to partner. Discuss ways to remember facts from the 7 times table.
Group Activities
Use the in-depth problem-solving investigation ‘Table digital roots’ as today’s group activity.
Or, use these activities:
-- Explore all multiplication and division facts for the 7 times table.

Day 3 Teaching
Children write out the first seven multiples of the 11 times table, noticing the pattern. The 11 times table has a memorable pattern until we reach 10 × 11. How can we use 110 as a starting point to find 11 x 11 and 12 x 11? Write out the first few facts for the 12 times table. How will we find 8 × 12? Use partitioning to find 8 x 12.
Group Activities
-- Explore multiplication facts for the 11 and 12 times tables.

You Will Need

  • 1–12 dice
  • Picture of a dog
  • ITP ‘Number grid
  • 2-minute sand timer
  • 0–12 number cards
  • Cubes

Mental/Oral Maths Starters

Day 1
Division facts for the 6 times table (pre-requisite skills)

Day 2
Multiplication and division facts (pre-requisite skills)

Day 3
9 and 90 times tables (pre-requisite skills)

Procedural Fluency

Day 1
Solve multiplications and divisions with the 9 times table.

Day 2
Use the multiplication grid to solve calculations, applying the 7 times table.

Day 3
Solve multiplications and divisions with the 11 and 12 times tables.

Mastery: Reasoning and Problem-Solving

  • Which of these numbers are multiples of 9?
    28, 108, 126, 49, 153, 891 How do you know?
  • Which of these numbers are multiples of 7?
    84, 79, 32, 63, 56, 140, 133
    How do you know?
  • Complete this grid in under 1 minute.
x7912
5
7
8
  • Write a word problem to help practise the 11 times table. Your word problem must have one of these answers:
    88p, 132cm, £121, 154 minutes.

In-depth Investigation: Table Digital Roots
Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. They identify patterns and relate these to what they know of numbers.

Extra Support

Fantastic Facts
Knowing the 2, 3, 4, 5 and 10 times tables by heart

Unit 2 Times tables revision: factors & multiples (suggested as 3 days)

Objectives

Times tables revision: factors and multiples
Unit 2: ID# 4583

National Curriculum
Mult/Div (i) (iii)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and 1; divide by 1.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.

Teaching and Group Activities for Understanding

Day 1 Teaching
Launch ITP ‘Number dials’. Randomise the central number and multipliers. Click on an outside number. What times table do you think it might be? What else could it be? What can't it be? Why? Reveal another product. Carry on until children all agree. Repeat.
Group Activities
-- Complete a multiplication grid up to 12 × 12.
-- Explore the calculations on a 12 × 12 multiplication grid that children often find harder to remember.

Day 2 Teaching
Sketch 24 counters arranged in a 6 by 4 array. What other arrays are possible using 24 counters? Each child sketches a different way on their whiteboard. Share ideas. Say that 24 is a multiple of 1, 2, 3, 4, 6, 8, 12 and 24. Explain that these are its factors. Write factors of 21 then of 16.
Group Activities
-- Investigate the factors of numbers up to 40.

Day 3 Teaching
Show children an Interactive Whiteboard multiplication grid. Look at the number 16. Where does it appear on the grid? It is in the 2 times table and in the 8 times table. It is also in the 4 times table. Write its pairs of factors. Some numbers on the grid only have 2 factors, other than themselves and 1, e.g. 21 has 3 and 7. This is why it only occurs twice on the grid. It is only in two tables, the 3 times and the 7 times tables. Repeat for 44. Introduce into the whole class investigation.
Group Activities
Use the in-depth problem-solving investigation ‘Shape Times Shape’ from NRICH as today’s group activity.
Or, use this activity:
-- Explore the factors of numbers that occur multiple times on a multiplication grid.

You Will Need

  • ITP ‘Number dials
  • Flipchart, whiteboards and pens
  • ‘12 × 12 Multiplication grid’ (see resources)
  • ‘Partially completed multiplication grid’ (see resources)
  • Cubes, counters and 0 - 9 dice
  • Interactive Whiteboard multiplication grid
  • ‘Highlighted 12 × 12 multiplication grid’ (see resources)

Mental/Oral Maths Starters

Day 1
7 times table (pre-requisite skills)

Day 2
9 times table (pre-requisite skills)

Suggested for Day 3
Telling times to the next hour (simmering skills)

Procedural Fluency

Day 1
Identify missing numbers on a multiplication grid.

Day 2
Match numbers to lists of factors.

Day 3
Identify all the factors of given numbers.

Mastery: Reasoning and Problem-Solving

  • Selma says ‘The bigger a number, the more pairs of factors it has’. Do you agree with her? Explain your ideas.
  • What one number does the letter ‘a’ stand for in each of these number sentences?
    a × 6 = a + 40
    7 × a = 60 take away ½ of a.
  • Always true, sometimes true or never true?
    A number with only two factors is odd.
    A number with 4 factors is even.
    A number less than 100 with 6 factors is even.
    A number with 6 as one of its factors, also has 3 as a factor.
    An odd number can have 2 as a factor.

In-depth Investigation: Shape Times Shape
Eleven different shapes each stand for a different number. Children use the multiplication calculations to work out what they are. Shape Times Shape from nrich.maths.org.

Unit 3 Multiply multiples of 10 and 100 (suggested as 3 days)

Objectives

Using tables facts to multiply multiples of 10 and 100
Unit 3: ID# 4591

National Curriculum
Mult/Div (i) (ii) (v)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and 1; divide by 1.
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use ITP ‘Number Dials’, select 3 as the central number. Children count round in 3s. If we know the 3 times table, we can work out the 30 times table! Have 30 as the central number and repeat. These numbers are 10 times as big. Repeat for 6 and 60, then 8 and 80. Repeat for the 900 times table. Then repeat for 4, 40, 400; 7, 70, 700.
Group Activities
-- Multiply multiples of 10 and 100 by a range of 1-digit numbers.

Day 2 Teaching
Write 3 × 5, 3 × 50 and 3 × 500 on the Interactive Whiteboard. Children answer each in pairs. Show how 3 × 50 is the same as 3 × 5 × 10. Then show how 3 × 500 is the same as 3 × 5 × 100. Children then work in groups of 3 to work out 2 × 9, 2 × 90, 2 × 900. They repeat for 4 × 8, 4 × 80, 4 × 800 and 7 × 3, 7 × 30, 7 × 300.
Can I write an inverse division number sentence, based on knowing that 40 x 6 = 240? Explore grouping 240 in 40s and 6s.
Group Activities
-- Write multiplication and division facts for big numbers derived from multiplication tables.

Day 3 Teaching
Show four incomplete tables facts: 7 × 5 =, 3 × 8 =, 6 × 7 =, 4 × 9 =. Explain that these can help us to solve related multiplications and divisions, e.g. 7 × 50 = 350. Show how children can write related ‘mega-facts’, e.g. 350 ÷ 7 = 50.
Group Activities
Use the in-depth problem-solving investigation ‘Multiples Grid’ from NRICH as today’s group activity.
Or, use this activity:
-- Write ‘mega multiplications’, and associated divisions, based on a 12 × 12 tables-grid.

You Will Need

  • ITP ‘Number Dials
  • 1s–1000s place value grid (see resources)
  • 0–9 dice
  • ‘Ladder of 10s’ (see resources)
  • ‘Ladder of 100s’ (see resources)
  • ‘Target numbers’ (see resources)
  • ‘Multiplication grid’ (see resources)

Mental/Oral Maths Starters

Day 1
Count in steps of 40 (pre-requisite skills)

Day 2
Count on and back in multiples of 10 and 100 (pre-requisite skills)

Suggested for Day 3
Convert cm to mm (simmering skills)

Procedural Fluency

Day 1
Multiply 1-digit numbers by 10s and 100s.

Day 2
Apply tables knowledge to write multiplication facts for multiples of 10 and 100, e.g. 480, 2400, 2100, 540, etc.

Day 3
Multiply 10s and 100s by 1-digit numbers. Derive associated division facts.

Mastery: Reasoning and Problem-Solving

  • Write 360 ÷ ☐ = ☐ and then complete the sentence in at least four different ways.
  • Jimmy writes: 40 x 5 = 2000.
    Is he correct? What might he not understand yet?
  • Write three mega-facts to match 4 × 8 = 32. At least one must be a division fact.
  • Which four number sentences link these numbers: 5600, 8, 700?

In depth Investigation: Multiples Grid
What do the shaded numbers on a 100 square have in common? Children apply knowledge of tables facts and divisibility. Multiples Grid from nrich.maths.org.

Extra Support

Moving multiplications
Multiplying by 20, 30, 40 and 50 using times tables and place value

Unit 4 Grid multiplication: vertical layout (suggested as 3 days)

Objectives

Grid multiplication leading to vertical layout (ladder)
Unit 4: ID# 4603

National Curriculum
Mult/Div (ii) (iv)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and 1; divide by 1.
19. Multiply 1-digit numbers by 2-digit or 'friendly' 3-digit numbers mentally or using grid method (i.e. using the distributive law).

Teaching and Group Activities for Understanding

Day 1 Teaching
Children revise using grid method to work out 45 × 5, 3 × 76 and 58 × 6. Write 3 × 134 and discuss how the same partitioning strategy can be used for these 3-digit numbers. Model using grid method to solve this. Repeat with 145 × 5, 3 × 276, 158 × 6. Repeat for 5 × 345 and 576 × 3, discussing how the product is a 4-digit number.
Group Activities
-- Use partitioning to multiply 3-digit numbers by 1-digit numbers.
-- Use partitioning to multiply 3-digit numbers by 1-digit numbers. Troubleshoot ‘deliberate’ multiplication errors.

Day 2 Teaching
Ask children to use the grid method to work out 423 × 6. When they have all finished, write the ‘ladder’ layout on the board (see Teaching and Group Activities document). Discuss the similarities with grid method: the partial products that we find and add are exactly the same; we are just laying it out differently.
Group Activities
-- Explore grid and/or ladder multiplication to multiply 3-digit by 1-digit numbers.

Day 3 Teaching
Write 6 × 376, 319 × 5, 3 × 482, 407 × 4. Which will have the largest answer? Support children in estimating and writing approximate answers for each one. Children use grid or ladder methods, as they prefer, to solve them. Model both layouts.
Group Activities
-- Whole-class investigation: apply 3-digit × 1-digit multiplications, then find the digital root of the answers.

You Will Need

  • ‘Using the grid method’ (see resources)
  • 100s, 10s and 1s place value cards
  • Flipchart
  • Whiteboards and pens
  • ITP: Number Dials

Mental/Oral Maths Starters

Day 1
6 and 60 times table (pre-requisite skills)

Day 2
7 and 70 times tables (pre-requisite skills)

Suggested for Day 3
Find remainders after division (simmering skills)

Procedural Fluency

Day 1
Use the grid method to multiply 3-digit numbers by 1-digit numbers.

Day 2
Use ‘ladder’ and/or grid methods for 3-digit x 1-digit calculations.

Day 3
Choose a partitioning method to multiply: grid or ladder.
Practise using the ladder method for 3-digit × 1-digit calculations.

Mastery: Reasoning and Problem-Solving

  • Use the grid method to complete each of these:
    424 × 6 = ☐
    3 × 848 = ☐
    What do you notice?
    Why does this happen?
  • Use the grid and ladder methods to solve 354 × 6.
    Say which method you prefer and why.
  • Write the missing numbers:

x300
416024

What is the final product?


In-depth investigation
Use the Group activity on Day 3 as this unit’s in-depth problem-solving activity.

Extra Support

Grid Genius
Using the grid method to multiply 2-digit numbers by 1-digit numbers

Unit 5 Division: chunking with remainders (suggested as 2 days)

Objectives

Division using efficient chunking with remainders
Unit 5: ID# 4621

National Curriculum
Mult/Div (ii) (v)

Hamilton Objectives
20. Know how to use ‘efficient chunking’ for division above the range of the tables facts, e.g. 84 ÷ 6 = ? Begin to extend this to 3-digit numbers.
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Revise the concept that tables facts can be written as divisions. Write division as ‘multiplications with a hole’, i.e. with a missing number, e.g. 32 ÷ 4 = 8 can be written ☐ × 4 = 32. Show 83 ÷ 3 and model starting with ☐ × 3 = 83 then using the vertical layout to solve it (see Teaching and Group Activities document).
Group Activities
-- Divide 2-digit numbers by 1-digit numbers as ‘multiplications with holes’; use remainders to score a game.

Day 2 Teaching
Model solving 47 ÷ 3 on an empty number line. How many 3s in 47? More than 10? Fewer than 10? More than 20? Show ten lots of 3 on the line. How much is left? 17. Complete and show the remainder. Now demonstrate using a more compact vertical layout (see Teaching and Group Activities document).
Group Activities
Use the in-depth problem-solving investigation ‘Rocking remainders’ as today’s group activity.
Or, use these activities:
-- Play a game to target division calculations with a given remainder.
-- Investigate patterns of remainders in sequences of division calculations.

You Will Need

  • ‘Divide multiples’ sheets 1 to 3 (see resources)
  • Mini-whiteboards and pens
  • Number cards for 67, 73, 74, 87, 89, 90, 93, 97, 99

Procedural Fluency

Day 1
Use multiplications with missing numbers to solve divisions of 2-digit numbers by 1-digit numbers.

Day 2
Use empty number line jottings to divide 2-digit numbers by 1-digit numbers (with remainders).

Mastery: Reasoning and Problem-Solving

  • Write the missing numbers in this division:
x4=97
x4=80
x4=
1

So, complete the division:
97 ÷ 4 =

  • Use a number line to solve these two divisions.
    (i) 115 ÷ 5
    (ii) 65 ÷ 5
    What is the relationship between the second hop on the two lines?
  • Look at the remainders in each of these divisions. Compare the remainder with the divisor.
    54 ÷ 4
    99 ÷ 6
    100 ÷ 8
    Can you write another division where the remainder is half the divisor?

In-depth Investigation: Rocking Remainders
Children divide 11, 22, 33… 99 by 3, 4, 5 and look for patterns in the remainders.

Extra Support

Leftovers
Using ‘chunking’ to divide numbers just beyond the times tables, including with remainders