Maths Year 3/4 Autumn Addition and Subtraction

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.

• 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

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

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.

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.

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)

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.

• 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

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

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.

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.

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

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.

• 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

Day 1
Bonds to 20

Day 2
Add three 1-digit numbers

Day 3
Complements to 100

Day 4
Change from £1

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.

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

Diagram 2

Diagram 3

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.

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