• Hamilton's Flexible Maths Blocks Explained

Open our sample 'Year 5 Autumn Unit 1' to find out how the blocks of units work.

• Go Deeper with Maths Investigations

Our Investigations provide the materials to confidently teach problem solving & investigation skills.

• Free Maths Resources on Hamilton

Find out which Hamilton maths units you can access for free, including our new slide presentations.

Maths Year 2 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 Count in 2s, 5s, 10s; 5x tables facts (suggested as 2 days)

Objectives

Count in 2s, 5s and 10s; begin to know the 5x tables facts
Unit 1: ID# 2557

National Curriculum
Mult/Div (i) (ii)

Hamilton Objectives
16. Begin to know 2x and 10x tables; use x [and ÷] signs correctly.
19. Write multiplications [and divisions], using x, [÷] and = signs; calculate answers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use the ITP Number grid to demonstrate counting in 5s. Look at the patterns, and identify large multiples of 5. Then count in 5s from numbers other than 0 or 5. Identify patterns.
Group Activities
Use the ‘Multiple Madness’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Complete and describe number patterns that involve 2s, 5s and 10s.
-- Investigate statements about patterns; decide if they are always true, sometimes true or never true.

Day 2 Teaching
Show children seven 5p coins. Count in 5s to establish how much. Create an array of 7 x 5 and state that 5 + 5 + 5 + 5 + 5 + 5 + 5 is seven lots of 5 or seven fives, which we can write as 7 x 5, read as seven times five. Repeat with other arrays for different multiples of 5.
Group Activities
-- Rolling a 1-10 dice then multiply the number by 5.
-- Multiply strips of 5 stickers up to 10 and record the calculation.

You Will Need

• Number grid ITP (see resources)
• Statement cards: Multiples of 5 end in 5; Multiples of 10 end in 0; Multiples of 2 end in 2; Multiples of 2 end in 7; Multiples of 5 two-digit numbers and headings cards: always true, sometimes true and never true
• ‘Patterns’ activity sheet (see resources)
• 1-100 grid (see resources)
• 1-10 dice & pots of ten 5p coins
• Additional activity sheets (see resources)
• Eight 5p coins
• Blutac

Mental/Oral Maths Starters

Day 1
Count in 5s (pre-requisite skills)

Day 2
Count in 5s (pre-requisite skills)

Procedural Fluency

Day 1
Identify and describe number patterns that count on or back in 2s, 5s and 10s.

Day 2
Buy multiple items at the 5p shop.

Mastery: Reasoning and Problem-Solving

• Peter counts in 5s.
When he says ‘40’, how many 5s has he counted?
• Circle the multiples of 5 in the list below:
20, 31, 65, 54, 15, 80, 17, 100
• Draw an array to show 8 lots of 5.
• Fran starts counting in 2s from 12: 12…14…16… Will she say the number 43?
• Fill in the missing numbers:
72 68 ☐ ☐ 56 ☐ 48 ☐ 40

Children arrange digit cards to form multiples of 2, 5 and 10 and explore different possibilities.

Give Me Five
Counting in 5s

Unit 2 Division as the inverse of multiplication (suggested as 3 days)

Objectives

Begin to relate multiplication to division as inverse operations
Unit 2: ID# 2579

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

Hamilton Objectives
16. Begin to know 2x and 10x tables; use x and ÷ signs correctly.
19. Write multiplications and divisions, using x, ÷ and = signs; calculate answers.
21. Solve multiplication/division problems in context, doubling, halving.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show children an array of 3 lots of 5 counters. Discuss how we can read it as 3 lots of 5, or 3 times 5. Write ☐ x 5 = 15. ‘3’. Mark 15 on a 0-20 beaded line; draw 3 lots of 5, labelling where they land. Rotate array to show 5 lots of 3. Record 5 x 3 = ☐ and ☐ x 3 = 15. Recognise that the multiplication can be written either way round and gives the same answer.
Group Activities
-- Write multiplication sentences to match arrays.
-- Create arrays for given multiplication facts.

Day 2 Teaching
Show 20 counters and ask how many groups of 5 we could make. Record as ☐ x 5 = 20. Show how we count in groups of 5 to find the answer. Use a beaded line or the Grouping ITP to work out how many 10s in 30 by counting in 10s. Record ☐ x 10 = 30. Repeat for other divisions, including some with ‘left overs’.
Group Activities
-- Answer division questions using grouping.
-- Group ‘eggs’ into egg boxes to make groups of 6 and note any leftovers.

Day 3 Teaching
Display: Sam has 10 stickers. He puts 5 on each page in his sticker book. How many pages will he fill? Read the story together; ask children to discuss it in pairs. Model using cubes as stickers and count 10. Group these in 5s. Record: ☐ x 5 = 10 or 10 ÷ 5 = ☐ Write the answer. Repeat for other problems.
Group Activities
Use the in-depth problem-solving investigation ‘Ip Dip’ from NRICH as today’s group activity.
Or, use these activities:
-- Solve a word problem after identifying it as a division or multiplication problem.
-- Find missing numbers in multiplication or division word problems.

You Will Need

• 0-20 beaded line (see resources)
• ‘Arrays’ activity sheets (see resources)
• Pegboards, pegs & counters
• Flipchart & coins
• ‘Gingerbread biscuits’ sheet (see resources)
• Number cards 1-9
• Additional activity sheets (see resources)
• Grouping’ ITP.
• 6 hole egg boxes (x25)
• Cubes

Mental/Oral Maths Starters

Day 1
Grouping lots of 10s (pre-requisite skills)

Day 2
Count in 2s, division facts (pre-requisite skills)

Suggested for Day 3
2 times table (simmering skills)

Procedural Fluency

Day 1
Match and write multiplications to match arrays.

Day 2
Solve and record sentences for division questions, using grouping.

Day 3
Solve word problems using multiplication or division.

Mastery: Reasoning and Problem-Solving

• The same number is missing from each number sentence. What is it?
☐ x 3 = 15
1 x ☐ = 5
30 = 6 x ☐
• Write each addition as a multiplication.
Work out the total.
5 + 5 + 5 + 5 + 5 + 5 + 5 = ☐
☐ = 2 + 2+ 2 + 2 + 2 + 2 =
10 + 10 + 10 + 10 = ☐
• How many groups of 3 make 18?
How many groups of 6 make 12?
How many groups of 5 make 45?
• Will there be any eggs left over if I put 50 eggs into boxes of 6?

In-depth Investigation: Ip Dip
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...? Ip Dip from nrich.maths.org.

Extra Support

Clever Counting
Carrying out early multiplication (in 10s)

Unit 3 Solve multiplication/division problems - 1 (suggested as 2 days)

Objectives

Solve multiplication and division problems using beaded lines
Unit 3: ID# 2591

National Curriculum
Mult/Div (ii) (iii)

Hamilton Objectives
19. Write multiplications and divisions, using x, ÷ and = signs; calculate answers.
20. Understand that multiplication can be done in any order (it is commutative) and division cannot.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use an array to show 4 lots of 3 counters. What do you see? Model using a beaded line to count in 3s. Record as 4 x 3 = 12. How many 3s in 12? Draw a ring round the groups of 3 up to 12. Four 3s are 12. Ring 3 groups of 4 to show that 3 lots of 4 gives the same answer. Repeat for a 7 by 2 array. Be explicit about the learning objective and key outcome for today that multiplication can be done in any order.
Group Activities
-- Work out all multiplication facts for various arrays.
-- Play an online array game, suggesting the multiplication facts before revealing them.

Day 2 Teaching
Show 6 x 3 as an array: 6 lots of 3 dots. On a beaded line, draw 6 hops of 3 to show that if we count in 3s we get to 18. Six 3s are 18. Record 6 x 3 = 18. Ask how many 6s there are in 18. Model drawing hops of 6 along the beaded line.
Group Activities
Use the ‘Mrs Multiple’s Cakes’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Record multiplication and division facts for various arrays.

You Will Need

• Counters
• ‘Array cards’ sheets 1, 2 and 3 (see resources)
• Beaded number lines (see resources)
• Counters
• Additional activity sheets (see resources)
• Mini-whiteboards and pens
• ITP: Number Grid

Mental/Oral Maths Starters

Suggested for Day 1
Count in 2s (simmering skills)

Suggested for Day 2
Count in 5s (simmering skills)

Procedural Fluency

Day 1
Derive all multiplication and division facts from various arrays.

Day 2
Create arrays from given numbers then identify the multiplication and division facts they represent.

Mastery: Reasoning and Problem-Solving

• How many hops to count in 3s along the bead bar to reach 21?
• How many hops to count in 5s to reach 50?
• Write 2 multiplications and two divisions to match this array:

• • • • • •
• • • • • •
• • • • • •
• • • • • •
• Can you work out the multiplication and division facts represented by this bar model?

 15 5 5 5

In-depth Investigation: Mrs Multiple's Cakes
Children arrange ‘cakes’ in arrays and find which numbers between 10 and 20 can be arranged in most ways.

Extra Support

Hopping Maths
Carrying out early multiplication (in 5s)

Unit 4 Solve multiplication/division problems - 2 (suggested as 3 days)

Objectives

Use arrays and beaded lines to solve multiplication and division problems
Unit 4: ID# 2609

National Curriculum
Mult/Div (ii) (iv)

Hamilton Objectives
17. Understand equivalence in simple calculations: 3 x 4 = 6 x ☐
20. Understand that multiplication can be done in any order (it is commutative) and division cannot.
21. Solve multiplication/division problems in context, using recall of x /÷ facts, doubling, halving, arrays and ‘clever counting’.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children work in pairs to draw an array on their boards. They record the multiplication, e.g. 4 lots of 3. Ask them to demonstrate that their array may also give them another multiplication if they turn it round, e.g. 3 lots of 4. Choose an array and turn it into a word problem. Leave arrays on whiteboards for group activity.
Group Activities
-- Create multiplication word problems based on an array.

Day 2 Teaching
Show 3 packets each with 6 buns inside. How many buns altogether? Children discuss and draw the array that shows this. Write the number sentence 3 x 6 = 18. Turn this into a division word problem. Write another word problem using the buns and packets to illustrate 15 ÷ 5.
Group Activities
-- Create division word problems based on an array.
-- Relate multiplication and division through the creation of word problems.

Day 3 Teaching
Give children a word problem.
Establish that we must work out how many 5s are in 15. Display a large beaded line. Children ring the groups of 5. How many? 3. Repeat but by drawing hops of 3 on the beaded line. Does this represent the problem in the same way? Use a different word problem and model using the beaded line to solve it.
Group Activities
Use the in-depth problem-solving investigation ‘Music to my Ears’ from NRICH as today’s group activity.
Or, use these activities:
-- Identify whether a word problem needs a multiplication or division calculation.
-- Create a pairs a game involving matching multiplication and division word problems.

You Will Need

• Mini- whiteboards and pens
• Selection of beaded number lines (see resources)
• Buns (3 packets of 6)
• Cubes & party bags
• Party bag contents, e.g. sweets, balloons, rubbers etc
• Selection of landmarked lines (see resources)
• ‘Word problems’ sheet (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
2 and 10 times tables (simmering skills)

Suggested for Day 2
Doubles to double 10 (simmering skills)

Suggested for Day 3
Doubles and halves (simmering skills)

Procedural Fluency

Day 1
Create multiplication word problems from a series of arrays.

Day 2
Create division word problems from a series of arrays.

Day 3
Sort multiplication and division problems; then solve them.

Mastery: Reasoning and Problem-Solving

• In the first triangle diagram (see download), can you see a relationship between the number on top and the two below? Can you write four number sentences to describe those relationships?
Work out the missing number in the other five triangles.

In-depth Investigation: Music to My Ears
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? Music to My Ears from nrich.maths.org.

Extra Support

Ring the Fives
Carrying out early division (in 5s)