Short Blocks

Maths Year 4 Spring 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 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.