Short Blocks

Maths Year 3 Summer 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 Counting in equal steps; sequences (suggested as 3 days)

Objectives

Counting in equal steps; sequences
Unit 1: ID #3863

National Curriculum
Num/PV (i)
Mult/Div (i)

Hamilton Objectives
4. Count from 0 in 2s, 4s, 8s, 10s, 100s, and 50s.
21. Solve problems, including missing number (and scaling) problems.
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Count in 10s from 0 to 100 using the counting stick, then in 100s from 0 to 1000. Count in 100s from different numbers. Count in 50s to 500, then to 1000. Write: 4, 54, 104, 154; explain that 4 + 50 = 54, 54 + 50 = 104, 104 + 50 = 154. Repeat with 23, 73, 123.
Group Activities
Use the in-depth problem-solving investigation ‘Dog Chews’ as today’s group activity.
Or, use these activities:
-- Play ‘Ping Pong’, alternating between counting in 100s and 50s to 1000.
-- Play ‘Jump 50, Jump 100’, counting on a given number of 100s or 50s.

Day 2 Teaching
Count in steps of 4 from 4 to at least 100, noting that the numbers are all even. Count in 8s to 96. Observe that these are also even. Explain how we find the digital root of a number; find digital roots of numbers in the 4x table.
Group Activities
-- Find the digital roots of numbers in the 4 and 8 times table and beyond.
-- Play the compound leaves game, counting in 4s and 8s.

Day 3 Teaching
Show the first three numbers of a sequence: 28, 24, 20. Children describe the rule for this sequence and write the next three numbers. Discuss how sequences can decrease as well as increase. Show a sequence starting at 2, e.g. 2, 6, 10. Can children write the next three terms? Children create their own sequences, then extend: 2, 4, 8, 16.
Group Activities
-- Play sequences card game, challenging a partner to spot the rule of a sequence and write the next three numbers.
---Play sequences game, identifying the rule for a given sequence of numbers.

You Will Need

  • Counting stick
  • Mini-whiteboards and pens
  • Bean bags
  • ‘Count in steps of 100’ sheet (see resources)
  • ‘Jump 50, Jump 100’ cards (see resources)
  • 0-9 Dice
  • Internet access
  • ‘Counting patterns’ (see resources)
  • Additional activity sheets (see resources)
  • 1–12 dice

Mental/Oral Maths Starters

Day 1
Count in 100s (pre-requisite skills)

Suggested for Day 2
Odd and even numbers (simmering skills)

Suggested for Day 3
Count back in 3s (simmering skills)

Procedural Fluency

Day 1
Complete missing numbers in a 10 to 1000 grid, counting in steps of 10 and 100.
Fill the missing numbers in sequences that count in 50s or 100s.

Day 2
Fill the missing numbers in sequences that count in 4s or 8s.

Day 3
Complete the sequences and state the counting rule.

Mastery: Reasoning and Problem-Solving

  • Write the next four numbers in these sequences:
    4, 8, 12, ,…
    13, 63, 113, …
    8, 16, 24, …
    100, 96, 92, …
    341, 441, 541, …
    601, 551, 501, …
  • Create a sequence of ten numbers where you count on in 8s from an odd number.
  • Harry says, ‘If I count in 4s, starting at 3, I won’t say 30, but I will say 303.’ Do you agree? Explain your ideas.

In-depth Investigation: Dog Chews
Children find a multiple of 50 and a multiple for 4 with a given total.

Extra Support

Ladders to Success
Counting in steps of 50 from 0 to 1000

Unit 2 Revise multiplication and division facts (suggested as 2 days)

Objectives

Revise multiplication and division facts
Unit 2: ID #3877

National Curriculum
Mult/Div (i)

Hamilton Objectives
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
15. Understand that multiplication is commutative, and write mathematical statements for multiplication and division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a partially completed multiplication grid. Explain how it works, model with 2 × 5, writing 10 in the corresponding space. This grid has lots of spaces! Point to some; ask children to write in the answers. Point out how we can use facts we know to find other facts, such as 7 × 5 to find 5 × 7.
Point to 21. How many threes are in 21? Follow rows and columns to find the answer 7. Discuss number sentences using 3, 7 and 21… Scribe: 7 x 3 = 21; 3 x 7 = 21, then the divisions: 21 ÷ 3 =7; 21 ÷ 7 =3. Point to other multiples of 3, 4, or 8. Can you write a division number sentence that starts with that number?
Group Activities
-- Ring certain times table numbers on a 1–50 grid and say the associated division fact.
-- Play division facts bingo for the 2, 3, 4, 5, 6, 8 and 10 times tables.

Day 2 Teaching
Play a game with class into 2 teams. Write 4 × 6 = ___ and agree the product (24). Each child writes a related tables fact on a whiteboard, e.g. 6 × 4 = 24, 4 × 12 = 48, 2 × 6 = 12, 3 × 8 = 24. On a count of 3, children show their facts. Award points and record team totals. Repeat with another fact, e.g. 5 x 8 = 40.
Group Activities
Use the in-depth problem-solving investigation ‘Ordering cards’ from NRICH as today’s group activity.
Or, use these activities:
-- Play multiplication/division ‘Ping Pong’ by writing a multiplication or division from the 2, 3, 4, 5, 8 or 10 times tables, followed by a partner who writes a related x or ÷, and so on…
-- Practise multiplication and division facts using online games.

You Will Need

  • ‘Partially completed multiplication grid’ (see resources)
  • ‘1–50 grid’ and ‘1–100 grid’ (see resources)
  • Mini-whiteboards and pens
  • Internet access

Mental/Oral Maths Starters

Day 1
3 and 4 times table (pre-requisite skills)

Day 2
5 and 8 times table (pre-requisite skills)

Procedural Fluency

Day 1
Fill in the incomplete multiplication grid for the 1, 2, 3, 4, 5, 8 and 10x tables.
Fill in the incomplete grid for all tables facts to 10 x 10.

Day 2
Write multiplication and division facts that relate to a given fact.

Mastery: Reasoning and Problem-Solving

  • Write the missing numbers.
    ☐ × 8 = 32
    6 × ☐ = 48
    9 = 36 ÷ ☐
    ☐ × 4 = 48
    5 = ☐ ÷ 8
  • Write 8 × 6 = 48 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 related number sentences using this central fact.
  • Always true, sometimes true or never true?
    6 × 8 is the same as 4 × 12.
    Dividing a number by 3 gives an odd answer.
    Even numbers divide by 8 to leave no remainder.

In-depth Investigation: Ordering Cards
Children use their knowledge of times table facts to find the order of a set of loop cards. Ordering Cards from nrich.maths.org.

Extra Support

Multiplication/division ‘Ping Pong'
Adapt this Group Activity from Day 2 to revise multiplication/division facts for 2-, 3-, 4-, 5- and 10-times tables.

Unit 3 Partition to double, halve and multiply (suggested as 4 days)

Objectives

Partition 2-digit numbers to double, halve and multiply using grid
Unit 3: ID #3889

National Curriculum
Mult/Div (ii) (iii)

Hamilton Objectives
20. Partition to double and halve numbers.
19. Multiply a 1-digit number by a 2-digit number using partitioning.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use the ITP Place value to show 20 and 7 = 27. Children work in pairs: one doubles 10s, the other doubles 1s. They add their answers. So, double 27 = 54. We worked it out using partitioning. Show 47, with the cards not split. Children repeat the process. Repeat for 2-digit numbers >50.
Group Activities
-- Play a 4-in-a-row grid game, doubling 2-digit numbers.
-- Play an online game to practise doubling using partitioning as a method.

Day 2 Teaching
Ask two children to make 48 using 10s and 1s cards. They partition the number. One child halves 40 and the other halves 8, then they add their answers. Record half of 48 is 24. Repeat with 56, then with 45. Remind children how to halve 5 to give 2¹/2. Repeat with 75. Create number chains.
Group Activities
-- Play a chain game, halving even numbers and adding 1 when numbers are odd.
-- Play an online game to practise halving using partitioning as a method.

Day 3 Teaching
Show a grid used to do 2 × 14. Point out that we do not need the grid but it is very useful to show partitioning. Use the grid to do 3 × 14. Then 6 × 14. Explain that grid method helps us keep track of the steps in multiplying.
Group Activities
-- Describe stepping stones in developing use of the grid method. Rehearse use of preferred image(s) to begin using the grid method.
--Practise multiplying teen numbers by single digit numbers.
--Play a multiplication game using the grid method.

Day 4 Teaching
Discuss solving 3 × 24 with the grid method. Children use the grid method to multiply 24 by 1, 2, 3, 4 … 9 so that they create the 24 times table.
Group Activities
Use the in-depth problem-solving investigation ’18 times table – wow!’ as today’s group activity.
Or, use these activities:
-- Investigate multiplying odd and even 2-digit numbers by 1-digit numbers using the grid method.

You Will Need

  • ITP: Place Value
  • ‘Doubling numbers’ sheets 1 and 2 (see resources)
  • Coloured pencils
  • Place value cards
  • Internet access
  • Mini-whiteboards and pens
  • ‘Steps towards using the grid method for 14 x 5’ sheets 1 and 2 (see resources)
  • ‘Using the grid method’ sheet (see resources)
  • Squared paper
  • Number cards 12–15, 22–25 and 32–35
  • 1–6 dice
  • Counters
  • Number cards 1-9, 11-30 and 21-40
  • ITP: Number Dials

Mental/Oral Maths Starters

Day 1
Multiply 1-digit numbers by 20 (pre-requisite skills)

Day 2
30 times table (pre-requisite skills)

Suggested for Day 3
Add 1-digit numbers to 2-digit numbers (simmering skills)

Suggested for Day 4
× and ÷ by 10 and 100 (simmering skills)

Procedural Fluency

Day 1
Double given numbers using partitioning.

Day 2
Halve given numbers using partitioning.

Day 3
Multiply teens numbers by 1-digit numbers using the grid method.
Multiply numbers 18 to 39 by 1-digit numbers using the grid method.

Day 4
Choose a series of grid multiplications to complete:
numbers 13 to 19 x 1-digit numbers, or
numbers 18 to 39 x 1-digit numbers, or
numbers 26 to 45 x 1-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Write the missing numbers in each diagram.
    Diagram 1:
?
5656

Diagram 2:

74
??

Diagram 3:

95
??
  • How many odd numbers between 50 and 100, when halved, give an answer ending 4¹/2?
  • Write the missing numbers in this grid.

x306
4
  • Now complete the addition to find the total of the partial products.
    ☐ + ☐ = ☐

In-depth Investigation: 18 Times Table – Wow!
Children use the grid method to work out the 18 times table and look for patterns in the answers.

Extra Support

Doubles Decisions
Doubling numbers up to 50

Harder Halves
Halving even numbers to 100