Maths Year 3/4 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. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Strategies for adding and subtracting (suggested as 3 days)

Objectives

Strategies for adding and subtracting
Unit 1: ID# 34158

Y3: Use number facts to add and subtract.
Y4: Use number facts to add and subtract.

National Curriculum
Y3: Add/sub (i) (iii)
Y4: Add/Sub (iii)

Y3 Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20.
14. Solve problems, including those involving missing numbers.
4. Add and subtract 1-digit numbers from 2-digit numbers using number facts.

Y4 Hamilton Objectives
10. Mentally add and subtract any pair of 2-digit numbers or 3-digit multiples of 10.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use bar models to support writing addition and subtraction facts. Use number balances to model equalities; explore pairs to 13.
Further Teaching with Y4
Add 2-digit numbers in addition grids using an appropriate mental strategy.
Group Activities: T with Y4
Y3 -- Explore and write equalities (‘balancing’ sums).
Y4 -- Investigate ways in which digits can be arranged in an addition grid to give ascending totals, totals <100 and totals >100.

Day 2 Teaching
Use a 100 bead bar to demonstrate how 5 + 3 is similar to 15 + 3, 25 + 3, 35 + 3, …105 + 3, 125 + 3, 245 + 3, 845 + 3. Repeat for 17 + 7, 27 + 7, 37 + 7, 47 + 7, using ‘Target the 10’ strategy. Show on beaded, landmarked and empty number lines.
Group Activities: T with Y3
Y3 -- Identify mystery numbers by spotting patterns when adding 1-digit to 2-digit numbers.
Y4 -- Repeatedly add a 1-digit number to a 3-digit number; describe and explain any patterns in the ones digits.

Day 3 Teaching
Use the bead bar to show how 5 – 2 is similar to 15 – 2, 25 – 2, 35 – 2, 105 – 2, 145 – 2, 475 – 2. Repeat for 24 – 7, 34 – 7, etc. Show on beaded, landmarked and empty lines.
Group Activities: T with Y3
Y3 – Play a dice or card game to practise subtracting 1-digit from 2-digit numbers.
Y4 -- Dice game subtracting from 3-digit numbers.

You Will Need

  • Pairs to 12, sheets 1 and 2 (see resources)
  • Number balance (or use an interactive version from e.g. www.nctm.org)
  • 2-digit + 2-digit grid with missing totals (see resources)
  • Mini-whiteboards and pens
  • 100 beaded bar
  • 0 to 100 beaded line (see resources)
  • Additional activity sheets (see resources)
  • 0 to 9 dice (or 1 to 10) and 1 to 9 cards
  • Flipchart and pens

Short Mental Workouts

Day 1
Addition facts for numbers 6 to 10

Day 2
Know by heart totals of any pair of 1-digit numbers

Day 3
Complements to multiples of 10

Procedural Fluency

Day 1
Y3: Write missing numbers in equalities.
Y4: Add 2-digit numbers in addition grids.

Day 2
Y3: Add 1-digit to 2-digit numbers.
Y4: Add 1-digit to 3-digit numbers.

Day 3
Y3: Subtract 1-digit from a 2-digit-number.
Y4: Subtract 1-digit from a 3-digit-number.

Mastery: Reasoning and Problem-Solving

Y3

  • Write 4 number sentences to relate these three 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 for two more pairs of numbers that total 20, then 200.

Y4

  • Write 4 number sentences to relate these three numbers: 240, 390 and 150.
  • Use a mental method to find:
    150 + 50
    35 + 65
    192 + 6
    66 + 29
    153 + 39
    200 – 52
    240 + 550
    73 – 25
    630 – 150

In-depth Investigation
Use the games from the Day 3 group activities.

Extra Support

Y3
Perfect Pairs

Using addition facts 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)

Y4
Split and Add

Adding 2-digit numbers using partitioning

Collect 'em Up!
Adding 2-digit numbers using partitioning (total more than 100); Beginning to add 3-digit numbers (total less than 1000)

Unit 2 Number bonds to 100 (suggested as 3 days)

Objectives

Number bonds to 100
Unit 2: ID# 34174

Y3: Add 3 or 4 small numbers; pairs to 100.
Y4: Add 3, 4 or 5 small numbers; pairs to 100.

National Curriculum
Y3: Add/Sub (iii) (iv)
Y4: Add/Sub (i) (ii)

Y3 Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20.
8. Mentally add or subtract any pair of 2-digit numbers, including pairs to 100.
32. Give change by counting up; use both £ and p in practical contexts.

Additional
Know pairs of multiples of 5 that total 100.

Y4 Hamilton Objectives
10. Mentally add and subtract any pair of 2-digit numbers.
12. Subtract numbers from 2-digit and 3-digit numbers using counting up (Frog).

Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate spotting number facts, e.g. bond and doubles, to help add several numbers.
Group Activities: T with Y3
Use the ‘Puzzling squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Play ‘Mystery number bags’, adding three or four 1-digit more numbers.
Y3/Y4 -- Play tiddlywinks, adding 3 or more numbers.

Day 2 Teaching
Use a 100 bead bar to show pairs to 100, then locate a 2-digit number on landmarked line and calculate the complement to 100.
Group Activities: T with Y3 or Y4
Y3 -- Pairs to 100 bar model or bead string games: finding pairs of numbers to total 100.
Y4 -- Play ‘Four in a row’, finding complements to 100.

Day 3 Teaching
Count up using Frog to find the difference between 2-digit numbers and 100 on a 0-100 landmarked line. Show matching bar model. Use Frog to find change from £1.
Group Activities: T with Y3 or Y4
Y3 -- Find change from £1.
Y4 -- Make 2-digit numbers and find the complement to 100, while playing a game on a 1 to 100 grid.

You Will Need

  • 1 to 20 number cards.
  • 4 bags or pots, each containing number cards 1 to 10
  • A set of 11 to 20 number cards
  • ‘Tiddlywinks’ mats (see resources) and counters
  • 100 bead bar and cloth
  • ‘0 to 100 landmarked line’ (see resources)
  • ‘Pairs to 100’ bar models sheet and game board (see resources)
  • Coloured pens/pencils
  • 100-bead strings
  • Flipchart and coloured pens
  • Additional activity sheets (see resources)
  • Money and sticky notes
  • Items to ‘sell’ and 1 to 9 cards

Short Mental Workouts

Day 1
Pairs to 20 and related subtractions

Day 2
Complements to multiples of 10, e.g. 57 + □ = 60

Day 3
Complements to multiples of 10

Procedural Fluency

Day 1
Y3: Add 3 or more numbers. Add 4 or more numbers.
Y4: Add 4 or more numbers. Add 5 or more numbers.

Day 2
Y3: Find complements to 100 (multiples to 5).
Find compliments to 100 (any 2-digit numbers).
Y4: Fill in missing digits to make pairs to 100.

Day 3
Y3: Find change from £1.
Y4: Subtract 2-digit number from 100.

Mastery: Reasoning and Problem-Solving

Y3

  • What number pairs or facts can you spot to add these strings of numbers:
    7 + 4 + 7 = ☐
    1 + 5 + 9 + 5 = ☐
    ☐ = 8 + 7 + 5
    14 + 3 + 3 = ☐
  • Find the missing numbers:
    ☐ + 35 = 100
    48 + ☐ = 100
    100 = ☐ + 27
  • How much change does Ally get from £1 if she spends:
    93p, 59p, 17p, 64p?

Y4

  • What number pairs or facts can you spot to add these strings of numbers:
    6 + 7 + 4 + 7 = ☐
    11 + 5 + 9 + 5 = ☐
    ☐ = 8 + 17 + 5
    14 + 3 + 3 + 6 + 6 = ☐
  • Find the missing numbers:
    ☐ + 32 = 100
    27 + ☐ = 100
    100 = ☐ + 74
  • Each week, Anna spends a different amount from her £1 pocket money.
    Week 1: 59p
    Week 2: 83p
    Week 3: 97p
    How much change did she receive in total?

In-depth Investigation: Puzzling Squares
Use numbers 0 to 7 (or multiples of 10 from 0 to 70) to make a total of 10 (or 100) on each side of a square.

Extra Support

Y3
Tens Jigsaws

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

Y4
How High Can You Jump?

Adding and subtracting 1-digit numbers to and from 3-digit numbers

Unit 3 Subtract by counting up: frog (suggested as 4 days)

Objectives

Subtract by counting up: frog
Unit 3 (ID 34190)

Y3: Count up to subtract 2-digit numbers from 2-digit numbers and numbers over 100.
Y4: Count up to subtract 2-digit numbers from 2-digit numbers and numbers either side of a multiple of 100.

National Curriculum
Y3: Add/Sub (i) (iv)
Y4: Add/Sub (ii) (iii)

Y3 Hamilton Objectives
6. Mentally add or subtract any pair of 2-digit numbers, e.g. 75 + 58 or 75 – 58.
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.

Y4 Hamilton Objectives
10. Mentally add and subtract any pair of 2-digit numbers.
12. Subtract numbers from 2-digit and 3-digit numbers using counting up (Frog) and subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426–278, 321-87.
15. Estimate and use inverse operations to check answers to a calculation.

Teaching and Group Activities for Understanding

Day 1 Teaching
Model and discuss use of ‘Maths Frog’ to find differences between pairs of 2-digit numbers.
Group Activities: T with Y3
Y3 -- Frog pairs game to subtract two 2-digit numbers.
Y4 -- Frog investigation: think of a 2-digit number, 1st digit greater than 2nd, reverse digits, then subtract, e.g. 85 – 58.

Day 2 Teaching
Rehearse the list of ‘rules’ for using Maths Frog. Use these to help Maths Frog to find greater differences, e.g. 65 – 37.
Further Teaching with Y4
Write 123 – 45. Model Frog counting up, and counting back mentally. Model both strategies for 123 – 89, 123 – 32, 123 – 50; discuss preferences.
Group Activities: T with Y4
Y3 -- Count up to find out how many centimetres dogs have grown.
Y4 -- Explore counting up and counting back to subtract 2-digit numbers from numbers >100. Discuss preferences.

Day 3 Teaching
Use Frog to subtract numbers either side of 100, then challenge Frog to subtract numbers either side of multiples of 100.
Group Activities: T with Y3
Use the ‘Hole-y subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Create 3-digit - 2-digit subtractions; solve by counting up.
Y4 -- Find the difference between numbers either side of 200, or other multiples of 100.

Day 4 Teaching
Use Frog to calculate subtractions either side of 100, e.g. 113 – 78. Recall how we add the hops to find the answer.
Further Teaching with Y4
Calculate 534 – 479; use a bar diagram to represent 534 – 479 and discuss how addition and subtraction are related. Write 416 – 363 = 53. Children check using addition.
Group Activities: T with Y4
Y3 -- Making subtractions: 2-digit from 3-digit numbers with answers less than 40.
Y4 -- Subtract 3-digit numbers either side of/from multiples of 100 and check answers using addition.

You Will Need

  • Maths Frog toy
  • ‘Using Maths Frog’ sheet (see resources)
  • Mini-whiteboards and pens
  • Frog ‘Pairs cards’ sets 1 and 2 (see resources)
  • ‘0 to 100 landmarked lines ‘(see resources)
  • ‘Rules’ for Maths Frog drawn up on day 1
  • ‘Dog lengths’ sheets 1 to 3 (see resources)
  • Additional activity sheets (see resources)
  • Toy dogs (or similar) of different sizes
  • Paperclips

Short Mental Workouts

Day 1
Bonds to 20

Day 2
Add three 1-digit numbers

Day 3
Complements to 100

Day 4
Change from £1

Procedural Fluency

Day 1
Y3: Subtract by counting up to multiples of 10, then other 2-digit numbers (answers <20).
Y4: Subtract 2-digit numbers (answers >20).

Day 2
Y3: Use Frog to subtract 2-digit numbers.
Y4: Choose whether to use Frog or counting up to subtract 2-digit numbers from numbers over 100.

Day 3
Y3: Subtract 2-digit numbers from 100 and numbers over 100.
Y4: Subtract numbers either side of multiples of 100.

Day 4
Y3: Subtract 2-digit numbers over 100.
Y4: Use addition to check subtraction calculations with Frog.

Mastery: Reasoning and Problem-Solving

Y3

  • 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 3 pairs of numbers each having a difference of 17. One of the numbers must be more than 100, the other must be less than 100.

Y4

  • Describe how you will complete each of these subtractions:
    102 – 67 = ☐
    134 – 23 = ☐
    113 – 78 = ☐
  • Find the missing numbers represented in these bar diagrams:
    Diagram 1
212
157

Diagram 2

327
259

Diagram 3

534
487

In-depth Investigation: Hole-y Subtractions
Y3: Children look for patterns when subtracting numbers with identical digits from 101, 102, 103...
Y4: Children create 3-digit palindromic numbers with a zero in the middle, subtract 3-digit numbers with equal numbers of 1s, 10s and 100s and identify patterns.

Extra Support

Y3
Tiptoe to 10

Finding how many to the next 10

A hop and a Jump
Finding how many are needed to make the next 10, and the next 10 after that

Y4
Find the Gap

Subtracting 2-digit numbers by using Frog (counting up), to give small answers (numbers either side of a multiple of 10, and subtracting from a multiple of 10)

Frog Goes Further!
Subtracting 2-digit numbers from 100, e.g. 100 - 65; Beginning to subtract 3-digit numbers from the next multiple of 100, e.g. 200 - 165