Maths Year 3 Autumn Addition and 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.

Unit 1 Number facts and inverse operations (suggested as 2 days)

Objectives

Number facts and inverse operations
Unit 1: ID# 3169

National Curriculum
Add/Sub (i) (iii)

Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20.
14. Solve problems, including those involving missing numbers.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use different sets of objects, including pegs on a coat hanger, to partition 12 into 2 sets. Then use bar diagrams and write 4 sentences. Learn the facts.
Group Activities
Use the in-depth problem-solving investigation ‘Are you well balanced?’ from NRICH as today’s group activity.
Or, use these activities:
-- Find as many ways of making given numbers.
-- Consolidate number bonds to 10 and 20.

Day 2 Teaching
Use the NRICH balances to show equality and use this to rehearse number facts. Write these facts as number sentences, using +, = and also – signs.
Group Activities
-- Play ‘what’s in the box’ exploring different number fact sentences.

You Will Need

  • Coat hanger and 12 pegs (2 colours)
  • Bar model pictures for pairs to 6, 7, 8, 9 & 12 (see resources)
  • Number balance (or an interactive one)
  • Small items for hiding, boxes or bags to hide items in

Mastery: Reasoning and Problem-Solving

  • Write 4 number sentences to relate these 3 numbers: 13, 19 and 6.
  • We know 13 + 7 = 20. So what is 130 + 70?
    We know 11 + 9 = 20. So what is 110 + 90?
    Write an addition with an answer of 20.
    Write a similar addition with an answer of 200.
    Repeat this.


In-depth Investigation: Are You Well Balanced?
Hang combinations of weights to make the scale balance. Are You Well Balanced? from nrich.maths.org.

Extra Support

Perfect Pairs
Addition factions for 6, 7, 8, 9 and 10

Patterns Practice
Using addition fact to add single-digit numbers to 2-digit numbers, e.g. using 5 + 3 = 8 to work out 25 = 3 (not crossing 10s)

Unit 2 Using number facts to add/subtract (suggested as 3 days)

Objectives

Using number facts to add/subtract
Unit 2: ID# 3181

National Curriculum
Add/Sub (i) (ii)

Hamilton Objectives

4. Add and subtract 1-digit numbers from 2-digit numbers using number facts.
9. Mentally add and subtract multiples of 1 to/from 2-digit and 3-digit numbers.
7. Know securely number pairs for all the numbers up to and including 20.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use a 1-100 bead bar to demonstrate 5 + 3 is similar to 15 + 3, 25 + 3, 35 + 3, etc. Repeat for 7 + 4, 17 + 4, 27 + 4, 37 + 4, etc. Repeat on landmarked lines.
Group Activities
Use the ‘Puzzling Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Identify mystery numbers by spotting the patterns of adding given 1-digit to 2-digit numbers.
-- Explore adding a given no. to any 2-digit no. that ends in the same digit.

Day 2 Teaching
Use the bead bar to show that 5 – 2 is similar to 15 – 2, 25 – 2, 35 – 2, etc. Repeat for 14 – 7, 24 – 7, 34 – 7. Show on landmarked lines.
Group Activities
-- Play subtraction bingo, taking 1-digit numbers from 2-digit numbers.
-- Card subtraction activity taking 1-digit numbers from 2-digit numbers.

Day 3 Teaching
Demonstrate spotting number facts and doubles to add several numbers.
Group Activities
-- Play tiddlywinks, adding 3 or more numbers.
-- Mystery number bags – adding 3 or more numbers.

You Will Need

  • 100 bead bars
  • 0-100 beaded line (see resources)
  • 0-100 landmarked line (see resources)
  • Additional activity sheets (see resources)
  • Number dice (regular, 8-sided and 12 sided)
  • Number cards
  • 4 bags or pots per group
  • 1-digit and 2- digit number cards

Mental/Oral Starters

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

Suggested for Day 2
Number facts (simmering skills)

Suggested for Day 3
Doubles 1 to 10 (simmering skills)

Procedural Fluency

Day 1
Add 1-digit to 2-digit numbers.

Day 2
Subtract 1-digit from a 2-digit-number.

Day 3
Add several numbers practice sheets.

Mastery: Reasoning and Problem-Solving

  • Write 8 + 4 = 12 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 sentences, each with a 2-digit number, using this central fact.
  • Always true, sometimes true or never true?
    Adding 7 to a number ending in 4 gives an answer ending in 1.
    Taking 6 away from a number gives an answer ending in 2.


In-depth Investigation: Puzzling Squares
Children use reasoning skills to solve a number puzzle. They use numbers 0 to 7 to make a total of 10 on each side of a square.

Extra Support

This unit has no separate Extra Support activities.

Unit 3 Add/subtract: efficient mental strategies (suggested as 3 days)

Objectives

Mental addition and subtraction including frog
Unit 3: ID# 3191

National Curriculum
Add/Sub (i) (iv)

Hamilton Objectives
6. Mentally add or subtract any pair of 2 digit numbers, e.g. 75 + 58 or 75 – 58.
10. Recognise that there are 2 ways of completing subtractions, either by counting up or by counting back.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
32. Give change by counting up; use both £ and p in practical contexts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Introduce maths Frog. Show how Frog hops up along a number line to help us count up to find a difference, e.g. 70 – 56, Frog hops from 56 to 60, and then to 70. Stress that Frog always hops first to the next 10.
Group Activities
-- Frog pairs game subtracting two 2-digit numbers.

Day 2 Teaching
Rehearse the list of rules for how Maths Frog counts up. Use these to help Maths Frog to find greater differences, e.g. 92 – 48.
Group Activities
Use the ‘Twisted Subtraction’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Jumping frogs & dog lengths - finding subtractions through counting on.

Day 3 Teaching
Explain that Maths Frog can help us find change from £1. Show how Frog hops from 67p to 70p to £1 to find change from 67p.
Group Activities
-- Pick a badge activity - finding change from £1.
-- Use bar models to create subtractions which require Frog to help us find the change from £1.

You Will Need

  • Maths Frog toy
  • 0-100 landmarked line
  • 0 to £1 (see resources)
  • 0-100 beaded lines (see resources)
  • Additional activity sheets (see resources)
  • Toy dogs (or similar) of different sizes
  • Money
  • Items to sell

Mental/Oral Starters

Day 1
Complements to multiples of 10, e.g., 57 + □ = 60 (pre-requisite skills)

Day 2
Subtraction number bonds to 10 (pre-requisite skills)

Suggested for Day 3
Use place value to add and subtract (simmering skills)

Procedural Fluency

Day 1
Subtract by counting up.

Day 2
Subtract two 2-digit numbers.

Day 3
Find change from £1.

Mastery: Reasoning and Problem-Solving

  • Write two 2-digit numbers with a difference of 8.
  • Write 3 different subtractions where Frog does 2 hops and they are both 7.
  • Use Maths Frog to help you write the missing digits:
    7 ☐ – 4 8 = 3 4
    ☐ 5 – 2 7 = 6 ☐
  • Write a subtraction where the 10s digit in the smaller number is 2 less than the 10s digit in the bigger number and the answer is 16.


In-depth Investigation: Twisted Subtractions
Children subtract a number which is the reverse of another, e.g. 62 - 26.

Extra Support

Tiptoe to 10
How many to the next 10, e.g. 36 + □ = 40?

Unit 4 Partitioning to add (suggested as 2 days)

Objectives

Partitioning to add
Unit 4: ID# 3203

National Curriculum
Add/Sub (ii)

Hamilton Objectives
8. Mentally add or subtract any pair of 2 digit numbers, e.g. 75 + 58 or 75 – 58.
5. Solve number problems and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate how we can add 2-digit numbers by partitioning each one into 10s and 1s. So 65 + 24 = 60 + 20 + 5 + 4. Use place value equipment to demonstrate this.
Group Activities
Use the in-depth problem-solving investigation ‘Diagonal Sums’ from NRICH as today’s group activity.
Or, use these activities:
-- Spinners: adding to make less than and more than 100.

Day 2 Teaching
Use place value equipment to add pairs of 2-digit numbers by partitioning each one into 10s and 1s, and noticing that if we wind up with more than ten 10s, we have 100.
Group Activities
-- Pocket money promotion activity adding to make more than & less than 100 in pounds and pence.

You Will Need

  • Place value cards
  • ITP: Place Value
  • Spinners (see resources)
  • Cards (to write additions on)
  • Pocket money badges (see resources)

Mental/Oral Starters

Day 1
Add pairs of multiples of 10 (pre-requisite skills)

Suggested for Day 2
Number bonds (simmering skills)

Mastery: Reasoning and Problem-Solving

  • Write 2 numbers which total 91 where one has a 1s digit of 6.
  • Write the missing digits:
    7 ☐ + 4 8 = ☐ 2 4
    ☐ 5 + 8 7 = 1 4 ☐
  • How many pairs of numbers between 20 and 30 can you find that total 51?


In-depth Investigation: Diagonal Sums
In a square of numbers on the 100-grid, explore the sum of the pairs of numbers that are diagonally opposite each other. Diagonal Sums from nrich.maths.org.

Extra Support

Splitting Sums
Adding 10s numbers; beginning to use partitioning to add pairs of 2-digit numbers

Unit 5 Using place value to add/subtract (suggested as 5 days)

Objectives

Using place value to add/subtract
Unit 5: ID# 3209

National Curriculum
Add/Sub (iv) (i)

Hamilton Objectives
9. Add and subtract multiples of 1, 10 and 100 to/from 3-digit numbers.
3. Understand place value in 3-digit numbers.
5. Solve number problems & practical problems involving place value.

Additional
Add and subtract near multiples of 1, 10 and 100 to/from 3-digit numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display a place value grid and write 3-digit numbers on it. Show which digit changes if you add multiples of 10. Repeat to show which digit changes if you add multiples of 100. Repeat for 1s.
Group Activities
-- Spinners: adding 1s, 10s and 100s to 3-digit numbers.
-- Making Money: adding multiples of 1s and 10s.

Day 2 Teaching
Use a place value grid to show which digit changes if you subtract multiples of 10. Repeat for multiples of 100 or 1.
Group Activities
-- Cake cards: subtracting 1s, 10s and 100s from 3-digit numbers.

Day 3 Teaching
Demonstrate how to add and subtract near multiples of 10 to/from 2-digit numbers using a number line, and also a 1-100 number grid.
Group Activities
Use the ‘Magic 147’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Near Multiples Game: adding and subtracting multiples of 10 and related near multiples.
-- Alien Attack: adding multiples of 10 and related near multiples

Day 4 Teaching
Use an empty number line to model the hops involved in adding a near multiple of 10 to a 3-digit number: 225 + 29 is 225 hop 30 along and then back 1, etc.
Group Activities
-- Hexagon Multiples Game: adding multiples of 10 and related near multiples.

Day 5 Teaching
Use an empty number line to model the hops involved in subtracting a near multiple of 10 from a 3-digit number. Demonstrate how we adjust the hops to subtract 51 or 49 rather than 50.
Group Activities
-- Hexagon Multiples Game: subtracting multiples of 10 and related near multiples.

You Will Need

  • Place value grid (see resources).
  • Spinners (see resources).
  • 10ps & 1ps.
  • Cake cards (see resources).
  • 100 square.
  • Near Multiples Game Board (see resources).
  • Coloured counters.
  • Number lines or 100 squares.
  • Alien Attack online game.
  • Hexagon Multiples Addition Game board and cards (see resources).
  • Hexagon Multiples Subtraction Game board and cards (see resources).

Mental/Oral Starters

Day 1
Add/subtract multiples of 10 to or from any 2-digit number (pre-requisite skills)

Suggested for Day 2
Pairs to 20, and related subtractions (simmering skills)

Suggested for Day 3
Add any pair of single-digit numbers (simmering skills)

Day 4
Count on and back in 10s from a 3-digit number (pre-requisite skills)

Suggested for Day 5
Count in 2s from any 3-digit number (simmering skills)

Procedural Fluency

Day 1
Add multiples of 1s, 10s and 100s to 3-digit numbers.

Day 2
Subtract multiples of 1s, 10s and 100s from 3-digit numbers.

Day 3
Find the missing number: near multiples.

Day 4
Add multiples and near multiples of 1s, 10s and 100s to 3-digit numbers.

Day 5
Subtract multiples and near multiples of 1s, 10s and 100s to 3-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Start with 789. Write 3 different subtractions to get a final answer of 500. How would these change if you wanted a final answer of 499?
  • Add 80 to 263 then subtract 1. How much bigger is your answer than 263?
  • Use number cards 9, 1, 5 and 7. How many additions of near multiples can you create?
  • Mystery number
    What ONE number makes this sentence true?
    76 – ? = 18 + ?
  • How many times will you add 19 to 24 to reach 100? What number will you start with if you add 18 repeatedly and reach 100 exactly?


In-depth Investigation: Magic 147
Children arrange the ‘nearly numbers’ in a square so that each row and column adds to Magic 147.

Extra Support

Jolly Jumping
Adding 9 to 2-digit numbers

Super Simple Subtractions
Subtracting 9 from 2-digit numbers

Unit 6 Mental calculation – complements to 100 (suggested as 2 days)

Objectives

Mental calculation – complements to 100
Unit 6: ID# 3221

National Curriculum
Add/Sub (i) (iii)

Hamilton Objectives
8. Mentally add or subtract any pair of 2 digit numbers, including pairs to 100.
7. Know securely number pairs for all the numbers up to and including 20.
12. Subtract larger numbers with confidence, using 'Frog' for counting up, e.g. either side of 100.

Additional
Know pairs of multiples of 5 that total 100.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use the bead bar to demonstrate the pairs of multiples of 5 that total 100, e.g. 10 and 90, 15 and 85, etc. Record and rehearse these aloud.
Group Activities
-- Pairs to 100 bar game: finding pairs of multiples of 5 that total 100.
-- Complements to 100: pairs of multiples of 5 that total 100 and corresponding subtractions.
-- Thumbs up, thumbs down: identifying pairs of multiples of 5 that total 100.

Day 2 Teaching
Use the bead bar to demonstrate that we can count up from 67 to 70 and from 70 to 100. So 67 + 33 = 100. Hide the complement of 56 under a cloth on the bead bar and encourage children to work it out by performing the hops in their heads.
Group Activities
Use the ‘Closest to 100’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Split the bead bar: complements to 100
-- Four in a row: complements to 100
-- Subtraction challenge: finding additions that help solve subtractions

You Will Need

  • 100 bead bar & bead string
  • Cloth & rectangles of coloured card
  • 0-100 landmarked line (see resources)
  • 0-100 beaded line (see resources)
  • Cubes
  • Additional activity sheets (see resources)

Procedural Fluency

Day 1
Practise multiples of 5: pairs to 100.

Day 2
Practise matching pairs to 100.

Mastery: Reasoning and Problem-Solving

  • Write 4 sentences to link the numbers 45, 100 and 55.
  • What mistake has Fred made in each of his sums?
    1. 63 + 47 = 100
    2. 26 + 84 = 100
    3. 41 + 69 = 100
    Correct each one for him.
  • Write all additions of this form: __ + __ = 100 where 1 of the numbers has 2 digits the same.


In-depth Investigation: Closest to 100
Following simple rules children find ways to make 100 based on four dice throws. They practise adding four numbers with a total around 100 and use this to find a solution.

Extra Support

100 Jigsaws
Finding, then knowing by heart pairs of numbers with a total of 10

Unit 7 Mental subtraction – counting up (suggested as 3 days)

Objectives

Mental subtraction – counting up
Unit 7: ID# 3229

National Curriculum
Add/Sub (i) (iv)

Hamilton Objectives
12. Find a difference between a 3-digit and a 2-digit number by counting up.
10. Recognise that there are 2 ways of completing subtractions, either by counting up or by counting back.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.


Teaching and Group Activities for Understanding

Day 1 Teaching
Remind children of Maths Frog. Demonstrate how we can count up along an empty number line using Frog to work out the difference between 87 and 102. Model several subtractions.
Group Activities
-- Frog jump cards: subtract 2-digit numbers from 3-digit numbers.
-- Investigation: subtract 2-digit numbers from 3-digit numbers to find answers of 15.

Day 2 Teaching
Demonstrate counting up using Frog hopping along a number line to show how we calculate 113 – 78. Stress how we add the hops to find the answer.
Group Activities
-- Cricket scores: finding the difference between 2 numbers.

Day 3 Teaching
Use Frog and the empty number line to perform subtractions (112 – 76) and make deliberate errors which children have to correct.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey Operations’ from NRICH as today’s group activity. Or, use these activities:
-- Making subtractions: 2-digit from 3-digit numbers with answers less than 40.
-- Change from £1: subtracting 2-digit numbers from 100.
-- Frog jumps or counting back: choosing the right approach.

You Will Need

  • Maths Frog toy
  • Red and blue Frog jump cards (see resources)
  • Table of jumps children made (see resources)
  • Additional activity sheets (see resources)
  • Money

Procedural Fluency

Day 1
Subtract 2-digit numbers from 3-digit numbers.

Day 2
Subtract by counting up: answers less than 30.

Day 3
Subtract by counting up: answers less than 40.

Mastery: Reasoning and Problem-Solving

  • Write 3 pairs of numbers with a difference of 17. 1 of the numbers must be more than 100, 1 must be less than 100.
    76 + __ = 112
    106 – 68 = ___
    11 ☐ – 8 7 = 2 5
  • What must be added to 88 to give 114?
    What must be added to 77 to give 115?
  • What change will I get if I buy two pairs of trainers for £33 each and pay with two £50 notes?
  • Tim has saved £112. He spends £87 on a new game. How much does he have left?


In-depth Investigation: Dicey Operations
Adapt Game 2 and use counting up to find a 3-digit-2-digit difference closest to 500. Dicey Operations from nrich.maths.org.

Extra Support

A Hop and a Jump
Finding how many are needed to make the next 10, and the next 10 after that, e.g. 37 + ? = 40, and 37 + ? = 50