• 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 Autumn More Addition & Subtraction

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 Add/subtract using facts and place value (suggested as 2 days)

### Objectives

Add/subtract using facts and place value
Unit 1: ID# 2281

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 - 40 = 20.
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 or 17.
14. Recognise that addition and subtraction are inverse operations; use addition to check subtractions and solve missing number problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use a 20-bead frame to show 5 + 2 on lower bar, hiding all other beads behind the whiteboard. What is 5 add 2? Slide top 10 beads across and discuss how we now have 15 add 2. Tell children that we only needed to know one number fact (5 + 2) to find 15 + 2. Recall ‘Spider’ from earlier in term, for adding 10. Refer to 1-100 grid.
Use the bead frame to show further additions and subtractions. If we know what 5 - 2 is, then we can use this fact to find 15 – 2.
Group Activities
Use the ‘Cross Additions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Solve additions and subtractions using number facts.
-- Apply knowledge of number facts to add and subtract.

Day 2 Teaching
Write 35 + 3, 27 - 5, 30 + 5, 46 + 6, 27 - 7, 56 + 3, 99 – 3. Draw out using number fact 5 + 3 = 8 for first question. Stick card under heading Number fact. How about 30 + 5? Use place value! Stick card under a heading Place value. Discuss which use PV, which use a number fact. Sort cards into 2 sets. Answer some.
Group Activities
-- Sort calculations according to the strategy used to solve them.
-- Investigate equality using an on-screen interactivity.

### You Will Need

• 1-100 number grid (see resources)
• Number fact cards (see resources)
• Multilink cubes or Numicon shapes
• Calculations on cards or on IWB
• ‘Sorting calculations’ (see resources)
• Paper strips

### Mental/Oral Maths Starters

Day 1
Number facts (pre-requisite skills)

Suggested for Day 2
Pairs to 20 (simmering skills)

### Procedural Fluency

Day 1
Children show how to solve addition and subtraction problems using number facts.

Day 2
Children solve addition and subtraction calculations to play a game of 4 in a row with a partner or to complete an individual challenge.

### Mastery: Reasoning and Problem-Solving

• Fact families. Write 4 number sentences that link each ‘trio’ of numbers:
3, 8, 5
27, 2, 25
• Number Balance from nrich.maths.org
Can you hang weights in the right place to make the ‘equaliser’ balance?
• Fill in the missing numbers:
62 + ☐ = 69
48 = 43 + ☐
37 + ☐ = 41
☐ – 5 = 74
• Write the missing number in each diagram
Diagram 1

 ? 45 3

Diagram 2

 37 ? 2

Diagram 3

 90 70 ?

Using number facts including pairs to 10 children find totals of 5 numbers less than 10 to give different totals.

### Extra Support

Using place value to add, e.g. 20 + 4 = 24

## Unit 2 Use facts/patterns to add/subtract (suggested as 3 days)

### Objectives

Add/subtract single digit numbers using facts and patterns
Unit 2: ID# 2287

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 - 40 = 20.
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 or 17.
14. Recognise that addition and subtraction are inverse operations; use addition to check subtractions and solve missing number problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a bead bar and demonstrate adding 8 and 5 by doing 8 + 2 + 3 (‘bridging’) to land on a multiple of 10. Call this strategy ‘Target the 10s’ or ‘T10’ for short. Model 18 + 5, 28 + 5… Repeat for 6 + 7, 16 + 7, 26 + 7, etc. Use the bead bar to show the pattern. Model recording strategy (see detailed plan).
Group Activities
-- Children develop understanding of bridging 10 when adding a 1-digit number to a 2-digit number using beaded lines or landmarked lines.

Day 2 Teaching
Colour multiples of 10 on a 1-100 grid in red. Point these numbers out on the 0-100 bead bar. Write 37 + 6. Ask a child to point to 37. Recall that we can use number facts to help us (37 + 6 = 37 + 3 + 3). Repeat for other additions, crossing a 10s number and not crossing a 10s number, e.g. 33 + 4.
Group Activities
Use the ‘Pyramids’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Children sort and solve additions by bridging 10, using 1-100 number grids, beaded or landmarked lines.

Day 3 Teaching
Write 32 - 6. Use a 1-100 grid with multiples of 10 shaded. Point at 32. If we count back 6, we will cross a multiple of ten (30). Count back 2 then 4 more. 32 - 6 = 26. Be explicit that this the opposite (inverse) of the T10 strategy they have been using for addition. Repeat, using grid to find 45 - 7.
Show: 22 - 5, 27 - 5, 38 - 4, 33 - 4, 22 - 5, 27 - 6, 48 - 6, 53 – 7. Which will cross a multiple of 10?
Group Activities
-- Children sort and solve subtractions by bridging 10, using 1-100 number grids, beaded or landmarked lines.

### You Will Need

• Target the 10s calculation cards (see resources)
• Sheets of 0-100 beaded lines (see resources)
• Target the 10s recording sheet (see resources)
• Additional activity sheets (see resources)
• 1-100 number grid with 10s shaded red (see resources)
• 5-9 digit cards
• Addition calculations on cards or IWB

### Mental/Oral Maths Starters

Day 1
Complements to multiples of 10 (pre-requisite skills)

Suggested for Day 2
Place value (simmering skills)

Day 3
Subtraction facts for 10 (pre-requisite skills)

### Procedural Fluency

Day 1
Train Journey. Children add single digit numbers to keep a running total of the number of passengers on a train.

Day 2
Being a teacher. Children mark addition problems that have been solved. Children to use their chosen method for each addition.

Day 3
Match subtraction calculations to correct answers by counting back or using number facts.

### Mastery: Reasoning and Problem-Solving

• Write the next multiple of 10.
45 -> ☐
63 -> ☐
38 -> ☐
Write how many you add to get there.
• The answer is 53. What ‘T10’ addition did do you do?
• Circle the calculations that cross a multiple of 10.
34 + 8
53 + 5
78 – 5
18 + 4
26 + 7
66 – 5
Explain how you know.
• The answer is 67. What subtraction did do you do that crossed 70? Is that the only possibility?

In-depth Investigation: Pyramids
Children explore addition patterns in pyramids. They arrange numbers in a pyramid to create the largest and smallest possible totals.

### Extra Support

What's the gap?
Saying the next 10s number; Finding how many to the next 10s number, e.g. 36 + ? = 40

## Unit 3 Add/subtract multiples of 10 (suggested as 2 days)

### Objectives

Add/subtract multiples of 10 to/from 2-digit numbers
Unit 3: ID# 2297

National Curriculum

Hamilton Objectives
10. Add a 2-digit number and 10s.
11. Count back in 1s or 10s and use number facts to take away.
12.Recognise that addition and subtraction are inverse operations; use addition to check
subtractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use Spider on the 1-100 grid to demonstrate how we can add multiples of 10 to a 2-digit number, e.g. 46 + 30. Stress that Spider doesn’t have to count in 1s! Repeat, using Spider to subtract multiples of 10, e.g. 63 – 40.
Group Activities
-- Children play a game using Spider on the 1-100 grid to rehearse adding and subtracting multiples of 10.

Day 2 Teaching
Use a bead string to demonstrate how we can add multiples of 10 to a 2-digit number. Note that the 1s digit does not change. Repeat to show how we can subtract multiples of 10.
Group Activities
Use the in-depth problem-solving investigation ‘The Number Square!’ from NRICH as today’s group activity. Or, use these activities:
-- Children use a 100-beaded line to add or subtract 20, 30, 40 or 50. They choose their own calculations to solve.
-- Some children investigate patterns when adding and subtracting given multiples of 10 to 2-digit numbers.

### You Will Need

• 1-100 grids (see resources)
• Small cubes
• Plastic Spider
• ‘Add or Subtract 10s’ cards (see resources)
• ‘Spider counters’ (see resources)
• Small circles of card
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count on and back in 10s, with 100 grid (pre-requisite skills)

Day 2
Count on and back in 10s, using a bead bar (pre-requisite skills)

### Procedural Fluency

Day 1
Children practise adding and subtracting multiples of 10 to/from 2-digit numbers using a 1-100 grid and Spider.

Day 2
Children use a beaded line to solve addition and subtraction calculations. Some will find the missing number in a number sentence.

### Mastery: Reasoning and Problem-Solving

• Complete this grid:
 + 20 54 67 97
• Explain what Bill has done wrong in his homework:
 54 + 40 = 84 76 - 30 = 73 23 + 50 = 28 64 - 40 = 20
• Choose a number to write in the first empty box:
☐ + 20 – 30 + 10 = ☐
Repeat with a different starting number.
Explain what is happening.

In-depth Investigation: The Number Square!
Focus on strategies involving adding/subtracting multiples of 10 to put numbers back in the correct place on the 100-grid, e.g. 14 + 40 = 54, 87 - 60 = 27. The Number Square! from nrich.maths.org.

### Extra Support

Spider's Workout
Adding and subtracting 10 using a 1-100 grid

## Unit 4 Add/subtract 11, 12, 21, 22, etc (suggested as 3 days)

### Objectives

Add/subtract 11, 12, 21, 22, etc. to/from 2-digit numbers
Unit 4: ID# 2311

National Curriculum

Hamilton Objectives
10. Add a 2-digit number and 10s; add two 2-digit numbers that total <100 by counting on in 10s and 1s.
11. Count back in 1s or 10s or use number facts to take away, e.g. 27-3 = or 54-20 =.
15. Solve problems involving addition and subtraction of numbers, quantities and measures, using recall of number facts and appropriate models and images.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use the 1-100 grid to demonstrate how we can add 11, 12, 13, 21, 22 or 23 using Spider first and then adding the ones. Share plenty of examples, with children recording number sentences.
Group Activities
Use the ‘Count down to Zero’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Create, describe and begin to explain patterns created by repeated addition of 11, 12, 13, 21, 22 and 23.

Day 2 Teaching
Children show 40 on bead strings. Add 12 by sliding 10 beads then 2 more. Record 40 + 12 = 52. Show how to record hops of 10 and 2 on a beaded line. Also show on a 1-100 grid. Which do children find easier? Repeat for adding 13, 21, 22, 23, 31, 32 and 33.
Group Activities
-- Play a game to practise adding 11, 12, 13, 21, 22, 23, 31, 32, and 33. Some children will reason about number choices.

Day 3 Teaching
Write 65 – 11. Ask children how to the find answer. Demonstrate jumping back on the beaded line and also moving up and across on the 1-100 grid. Repeat for other subtractions, e.g. 48 – 11 and 48 – 21.
Group Activities
-- Using a 1-100 grid, children play a game in pairs where they rehearse adding or subtracting near multiples of 10, beginning to predict and reason about their answers.

### You Will Need

• 1-100 grids (see resources)
• Counters of different colours & coins
• Additional activity sheets (see resources)
• Coins, including lots of 10ps and 1ps
• Biscuits

### Mental/Oral Maths Starters

Day 1

Suggested for Day 2
2 more/less than 2-digit numbers (simmering skills)

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

### Procedural Fluency

Day 1
Most children create their own questions by selecting pairs of numbers to add. Some will complete a challenge involving missing numbers.

Day 2
Children are set different challenges to add 11, 12, 13, 21, 22, 23, 31, 32 or 33 to other 2-digit numbers; answers ≤110.

Day 3
Children calculate which of a set of given numbers is required to make a set of given calculations correct.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers in these calculations:
56 + ☐ = 86
86 + ☐ = 87
So, 56 + ☐ = 87

51 – ☐ = 31
31 – ☐ = 29
So, 51 – ☐ = 29
• Complete these diagrams:
Diagram 1:

 ? 48 21

Diagram 2

 63 31 ?
• I think of a number, then add 11, then 22, then 33 to it. My answer is 70. What number did I start with?

In-depth Investigation: Count Down to Zero
Children take turns to subtract 1, 2 or 3 from a 2-digit number greater than 20. They use strategies to help them win a game by reaching zero first.

### Extra Support

Down the Stairs

Up the Stairs
Subtracting 11 from 2-digit numbers

## Unit 5 Add/subtract near multiples of 10 (suggested as 3 days)

### Objectives

Add near multiples of 10 to/from 2-digit numbers
Unit 5: ID# 2333

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 - 40 = 20.
10. Add a 2-digit number and 10s; add two 2-digit numbers that total <100.
15. Solve problems involving addition and subtraction of numbers, using recall of number facts and appropriate models and images.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 36 + 19. 19 is nearly..? 20! Ring 36 on a 1-100 grid. Count on to 2 steps of 10 to work out 36 + 20. But 19 isn’t a multiple of 10 - it is only nearly 20, so we have to take off 1. Add other near multiples of 10 by adding a multiple of 10 and adjusting.
Group Activities
-- Children practise adding ‘nearly numbers’ by adding a multiple of 10 and then adjusting to find the answer. Children use a 1-100 grid to support addition and/or investigate patterns.

Day 2 Teaching
Display a 1-100 grid, with multiples of 10 coloured red. Identify numbers that are nearly multiples of 10 - ‘nearly numbers’ - 9, 19, 29 etc. 29 is nearly..? 30. Repeat for each ‘nearly number’. Use a calculator to add nearly numbers to 2-digit numbers. Notice patterns.
Group Activities
Use the ‘Nines to Zero’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Whole class investigation. In order to focus on mathematical reasoning, children use calculators. Describe and explain patterns by recording the calculations and answers that occur when adding ‘nearly numbers’.

### You Will Need

• 1-100 grid with multiples of 10 squares coloured red (see resources)
• 1-100 grids (see resources)
• Nearly numbers board (see resources)
• Small square Post-it notes
• Calculators

### Mental/Oral Maths Starters

Day 1
Count in 10s (pre-requisite skills)

Day 2

### Procedural Fluency

Day 1
Children rehearse adding ‘nearly numbers’ using the strategy of adding the multiple of 10 and then subtracting 1.

Day 2
Children use calculators to help them look for patterns when adding 9, 19, 29 and 39.

### Mastery: Reasoning and Problem-Solving

• Write 3 additions which include a 2-digit number and the number 22.
• Complete each number sentence:
27 + ☐ = 46
☐ + 29 = 73
☐ – 19 = 56
• Complete the patterns:
17, 26, __, 44, __, __.
5, 34, 63, __, __.
• Start with 18 and do the same 6 calculations. Can you predict the answer before doing the last 3 calculations?

In-depth investigation: Nines to Zero
Children repeatedly add 9 or 19 to numbers until they reach a multiple of 10. Look for patterns. Make and test predictions based on the patterns.

### Extra Support

More Spider Counting
Counting back in 10s

## Unit 6 Add pairs of 2-digit numbers (suggested as 2 days)

### Objectives

Unit 6: ID# 2341

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 - 40 = 20.
10. Add a 2-digit number and 10s; add two 2-digit numbers that total <100.
15. Solve problems involving addition and subtraction of numbers, using recall of number facts and appropriate models and images.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show 4 items priced 45p, 38p, 49p, 33p, & 4 different items priced 21, 22p 23p and 24p. Use these to find totals of pairs of prices, e.g. 49p and 22p, by adding the 10s and then the 1s.
Group Activities
-- Play games involving adding pairs of 2-digit numbers.

Day 2 Teaching
Group Activities
Use the in-depth problem-solving investigation ‘Five Steps to 50’ from NRICH as today’s group activity.
Or, use these activities:
-- Most children play Bingo to practise adding ‘ordinary’ and ‘nearly’ numbers, choosing and using appropriate strategies. Some may sort then solve calculations.

### You Will Need

• Four items priced 45p, 38p, 49p and 33p, & four priced 21, 22p 23p and 24p
• 1-100 grid (see resources)
• 0 to 100 beaded line to display on the board (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Add 3 to 2-digit numbers (pre-requisite skills)

Suggested for Day 2
Number facts (simmering skills)

### Procedural Fluency

Day 1
Most children use ‘Choose your own’ sheets to generate and solve different addition problems involving adding 2-digit numbers.

Day 2
Children practise adding ‘ordinary’ and ‘nearly’ numbers using a chosen method.

### Mastery: Reasoning and Problem-Solving

• Here are the prices for 5 pencils:
A 34p
B 29p
C 45p
D 52p
E 19p
The total is 53p. Which 2 pencils did you buy?
What is the most you can spend on 2 pencils?
What is the least you can spend on 2 pencils?
• What’s the same, what’s different?
54 + 39 = 93, 59 + 34 = 93
39 + 54 = 93, 34 + 59 = 93

In-depth investigation: Five Steps to 50 (NRICH.maths.org)

Children navigate the number line by adding or subtracting 1, 10 or 100.

### Extra Support

Sum Patterns
Using pattern and number bonds to work out related additions, e.g. 3 + 2 = 5, so 13 + 2 = 15, 23 + 2 = 25, 33 + 2 = 35