Maths Year 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.

Unit 1 Partitioning and column addition (suggested as 3 days)

Objectives

Partitioning and column addition
Unit 1: ID# 4177

National Curriculum
Add/Sub (i)

Hamilton Objectives
9. Solve number and practical problems involving place value.
11. Use column addition to add 3-digit numbers: first expanded, then compact method.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a grid (see resources) and model adding two numbers using partitioning into 10s and 1s. Write 137 + 19, 178 + 31, 125 + 26, 154 + 27 and 22 + 195 on the board. Discuss how to do each one, using partitioning for all except the first, where adding 20 then subtracting 1 is best.
Group Activities
Use the ‘Make 100’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Create and add 3-digit and 2-digit numbers, investigating finding totals with different criteria.

Day 2 Teaching
Display 324 + 439. Children work in pairs and use the written method to find the answer on their whiteboards. Note/share different strategies. Explain that today we focus on compact written addition. Model this, emphasising leaving a space above the answer for writing extra numbers (‘carry’ digits).
Group Activities
-- Add pairs of 3-digit numbers using compact written addition.

Day 3 Teaching
Display 592 + 235. Children use compact written addition on their whiteboards. Clarify any mistakes. Children then use this strategy to add three 3-digit numbers. Display:

123
474
+332
_____ Children calculate the total.
Group Activities
-- Create and add three 3-digit numbers using compact written additions.
-- Use compact written addition to add three 3-digit numbers with ‘carries’ in different columns.

You Will Need

  • ‘2-digit + 2-digit grid with missing totals’ (see resources)
  • 1–9 dice or 1–9 digit cards
  • ‘Adding 3-digit and 2-digit numbers’ (see resources)
  • ‘Special magic squares’ (see resources)
  • Calculators
  • 0–9 digit cards
  • Place value cards

Mental/Oral Starters

Day 1
Count on in 10s from any 3-digit number (pre-requisite skills)

Day 2
Add any pair of 2-digit multiples of 10 (pre-requisite skills)

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

Procedural Fluency

Day 1
Add pairs of 2-digit numbers.
Find missing numbers in a 2-digit + 2-digit addition grid.

Day 2
Use compact addition to add 3-digit numbers.

Day 3
Solve word problems with adding three 3-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Complete these additions mentally with only the answer written!
    78 + 127 = ? and 348 + 39 = ?
    Use a different method for each one and explain both your strategies.
  • Write the missing numbers in this calculation
2007
+50060
405
  • If 378 is subtracted from a number to leave 284, what was the number?
  • Add 375 + 528 + 194 using expanded column addition.


In-depth Investigation: Make 100
Given a pattern of four one-digit numbers, children attempt to make a total of exactly 100.

Extra Support

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 Mental subtraction incl. counting up (suggested as 3 days)

Objectives

Mental subtraction including counting up
Unit 2: ID# 4201

National Curriculum
Add/Sub (ii) (iii)

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).
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Teaching and Group Activities for Understanding

Day 1 Teaching
Do we remember Maths Frog? He subtracts numbers by counting up from the smaller to the larger number; Frog hops along the number line; he always hops to the next 10. Ask children to use Frog to help them work out 78 – 47. Repeat for 85 – 47.
Group Activities
-- Use number bonds to complete bar models with complements to 20. Find the difference between 2-digit numbers using Frog.
-- Subtract 2-digit numbers from numbers just over 100, using Frog.

Day 2 Teaching
Display a 0–100 landmarked line. Write 100 – 85. Children use Frog to solve this, drawing hops on the line. Repeat, subtracting 2-digit numbers from 100. Sketch a bar model to go with 100 – 82 and ask children what number is missing.
Group Activities
Use the ‘Which is Quicker?’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Make 2-digit numbers and use Frog to find the complement to 100.

Day 3 Teaching
Write 123 – 41. Children think/pair/share how they would solve it. Model Frog counting up, and counting back mentally. Write 123 – 89, 123 – 32, 123 – 50 and discuss strategies.
Group Activities
-- Choose whether to count up or back to subtract 2-digit numbers from numbers over 100.

You Will Need

  • 1–9 cards
  • ‘Addition and subtraction facts for pairs to 20’ (see resources)
  • ‘Subtraction cards’ (see resources)
  • Additional activity sheets (see resources)

Mental/Oral Starters

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

Day 2
Pairs to 20 and related subtractions (pre-requisite skills)

Suggested for Day 3
Count back in 10s from any 3-digit number, including crossing 100s (simmering skills)

Procedural Fluency

Day 1
Count up to subtract 2-digit numbers from 2-digit numbers.

Day 2
Use number bonds to find complements to 20 and 100.

Day 3
Choose whether to use Frog or counting up to subtract 2-digit numbers from numbers over 100.

Mastery: Reasoning and Problem-Solving

  • Write three subtractions for Frog to do where his jumps add to 24. Show Frog’s hops and write the subtractions.
  • Complete each diagram:
    Diagram 1
100
68

Diagram 2

100
34

Diagram 3

100
55
  • Describe how you will complete each of these subtractions
    102 – 67 =
    134 – 23 =
    113 – 78 =

In-depth Investigation: Which is Quicker?
Explore counting up in different sized steps; consolidate place value. Which is Quicker? from nrich.maths.org.

Extra Support

Find the Gap
Subtracting 2-digit numbers by using Frog (counting up), to give small answers, e.g. 53 - 47 and 70 - 55 (numbers either side of a multiple of 10, and subtracting from a multiple of 10)

Unit 3 Mental addition and subtraction (suggested as 2 days)

Objectives

Mental addition and subtraction
Unit 3: ID# 4211

National Curriculum
Num/PV (viii)
Add/Sub (iii)

Hamilton Objectives
6. Add multiples of 1, 10, 100, 1000 without difficulty.
10. Mentally add and subtract any pair of 2-digit numbers or 3-digit multiples of 10.
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show 352 + 204 on a place value grid and demonstrate how we can add these numbers using number facts. Repeat to show 444 + 222 and 530 + 105. Then model using a place value grid for subtraction.
Group Activities
-- Choose the best method for adding and subtracting 3-digit numbers.
-- Generate 3-digit numbers to add and subtract using knowledge of place value.

Day 2 Teaching
Show labelled training shoes (see resources) on the Interactive Whiteboard. Pick 2 pairs. Children write the total cost on whiteboards. Discuss strategies. Repeat with other pairs. Say that each child has £99.99. Children pick one pair to buy and work out change.
Group Activities
Use the ‘Total £10’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use number facts and place value to add 4-digit amounts of money and find change from £99.99 and £100.

You Will Need

  • Place value grids
  • ‘Adding & subtracting using place value & number facts’ (see resources)
  • ITP: Number spinners
  • ‘Adding & subtracting 4-digit numbers' (see resources)

Mental/Oral Starters

Day 1
Add any pair of 1-digit numbers (pre-requisite skills)

Suggested for Day 2
Add and subtract 10 and 100 to and from 4-digit numbers (simmering skills)

Procedural Fluency

Day 1
Use place value to add and subtract with 2-, 3- and 4-digit numbers.

Day 2
Use place value and number facts to add and subtract amounts of money.

Mastery: Reasoning and Problem-Solving

  • Write the digits which will change when you do the following calculations:
    (i) 367 – 31 = (ii) 405 + 200 =
    (iii) 539 – 201 = (iv) 874 + 30 =
  • Write the missing digits:
    8☐5 + 33 = 918
    74☐ – 42 = 701
    ☐56 – 236 = 4☐0
  • True or false?
    If you start with a 3-digit number and subtract 99 you will always have to change exactly 2 digits.


In-depth Investigation: Total £10
Using only digits 1-9 without the ‘5’, children find all possible pairs of amounts to make £10.

Extra Support

Perfect Pairs
Using place value to add and subtract amounts of money (without crossing multiples of 10p and one pound)

Unit 4 Subtraction: frog with 3-digit numbers (suggested as 3 days)

Objectives

Subtraction: frog with 3-digit numbers
Unit 4: ID# 4219

National Curriculum
Add/Sub (ii) (iii)

Hamilton Objectives
12. 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
Children ‘think, pair, share’ how Frog helps us. Maths Frog counts up to subtract. He starts at a smaller number and hops to the next 10 then 100. We then add his hops. Display 402 – 356. Draw an empty number line and model using Frog. Repeat for 513 – 469, 203 – 156, 612 – 565.
Group Activities
-- Make subtractions of 3-digit numbers and use Frog to solve them.

Day 2 Teaching
Write 421 – 356. Use Frog and model drawing a line starting at 356, draw a hop to 360, then a jump to 400, then a jump to 421. Use a bar diagram to show 534 – 479 and model using Frog to do it. Show how addition and subtraction relate. Write 416 – 363 = 53 and ask children to check the answer using addition (363 + 53 = 416).
Group Activities
Use the ‘Cats and Dogs’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Subtract 3-digit numbers to find given differences and check using addition to find incorrect answers.
-- Subtract 3-digit numbers from multiples of 100 and check using addition.

Day 3 Teaching
Work as a class to prepare a poster that will help children to subtract using Frog and check using addition. Use the poster to revise subtracting using Frog then checking the answer using addition. Demonstrate the whole class activity, playing one half of the class against the other, or Teacher against the class!
Group Activities
-- Subtract pairs of 3-digit numbers, target is to have the difference closest to 50 or 100. Check with addition.

You Will Need

  • ‘Spinners’ sheets 1 to 3 (see resources)
  • Paperclips
  • Subtraction cards (see resources)
  • The Subtraction Nasty Game (see resources)
  • Subtraction grid game boards (see resources )
  • 0–9 digit cards

Mental/Oral Starters

Day 1
Pairs to 100 (pre-requisite skills)

Day 2
Change from £1 (pre-requisite skills)

Suggested for Day 3
Add pairs of 2-digit numbers, answer < 100 (simmering skills)

Procedural Fluency

Day 1
Use Frog to subtract 3-digit numbers.

Day 2
Use addition to check subtraction calculations with Frog.

Day 3
Use Frog to solve subtraction word problems, and check with addition.

Mastery: Reasoning and Problem-Solving

  • Complete each diagram:
    Diagram 1
534
487

Diagram 2

132
86

Diagram 3

327
259
  • Subtract 377, then 387, then 397 from 424.
  • Find the difference between a pair of 3-digit numbers, each of whose digits adds to 9. For example, 306 – 261. Add the digits of your answer. Repeat three times. Say what you notice.


In-depth Investigation: Cats and Dogs
Children work to solve a puzzle involving adding two 3-digit numbers. They find several possible solutions, and then invent their own puzzle.

Extra Support

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

Unit 5 Mentally add/subtract near multiples (suggested as 2 days)

Objectives

Mental calculation: addition and subtraction including near multiples
Unit 5: ID# 4229

National Curriculum
Num/PV (viii)
Add/Sub (iii)

Hamilton Objectives
6. Add multiples of 1, 10, 100, 1000 without difficulty.
9. Solve number and practical problems involving place value.
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
Demonstrate using an empty number line to add 40 to 356. Use the same empty number line to model adding 41 and then 39. Show how the empty number line is useful when we add near multiples. Children use the same process to add 50 and 49 to 736. They then add 200, 199 and 201 to 358.
Group Activities
-- Make up word problems involving adding multiples and near multiples of 10 or 100 to a 3-digit number.
-- Add multiples and near multiples of 10 or 100 to a 3-digit number where the answer is more than 1000.

Day 2 Teaching
Ask children to show 385 – 50 on an empty number line on their whiteboards. What happens if we subtract 51, not 50? Children draw a hop back to 334, label it – 1, and label 334. How do we subtract 49 not 50? Draw a hop labelled + 1 to 336. Make sure that children are clear about which way to adjust. Repeat to subtract 200, 201 and 199 from 645.
Group Activities
Use the in-depth problem-solving investigation ‘Images of Addition and Subtraction’ from NCETM as today’s group activity.
Or, use these activities:
-- Use an empty number line to subtract near multiples of 10 and 100 from 3-digit numbers.

You Will Need

  • ‘Word Problems’ sheet (see resources)
  • Whiteboards
  • ‘Spinners’ sheets 1 to 3 (see resources)
  • Paperclips

Mental/Oral Starters

Day 1
Adding multiples of 10 (pre-requisite skills)

Suggested for Day 2
6 times table (simmering skills)

or

Suggested for Day 2
8 times table (simmering skills)

Procedural Fluency

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

Day 2
Subtract multiples and near multiples of 10 and 100 from 3-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Complete this sequence by adding 198 each time.
    169, 367, ___, 763, ___, ___
  • What needs to be subtracted from 985 to get 587?
  • Harry subtracted 59 from 354 and got 293. Explain what he did wrong.
  • Complete the number sentences:
    438 + 39 = ___
    356 – ___ = 307
    ___ – 198 = 314


In-depth Investigation: Images of Addition and Subtraction
This activity looks at a range of models and images used for addition and subtraction. Challenge the children to sort the cards and think about all the skills they are using. Images of Addition and Subtraction from ncetm.org.uk

Extra Support

Swapping Digits
Adding and subtracting 1s, 10s, 100s to/from 3-digit numbers

Unit 6 Mentally add/subtract 1-digit numbers (suggested as 2 days)

Objectives

Mental addition and subtraction with single-digit numbers to big numbers
Unit 6: ID# 4241

National Curriculum
Add/Sub (iii)

Hamilton Objectives
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Additional
44. Develop mental facility when calculating with big numbers using number facts.

Teaching and Group Activities for Understanding

Day 1 Teaching
What is 5 + 2? 25 + 2? 425 + 2? 3425 + 2? Point out that we can use the fact that 5 + 2 = 7 to answer each of these questions. These are ‘no work sums’! Use a counting stick to show 3995 to 4005 and demonstrate 3995 + 6 then 3997 + 8. Repeat with 4200 then 4550 as the central number.
Group Activities
Use the in-depth problem-solving investigation ‘Amy’s Dominoes’ from NRICH as today’s group activity.
Or, use these activities:
-- Repeatedly add a 1-digit number to a 4-digit number and look at the pattern in the units digit.

Day 2 Teaching
Write 8 – 5? 38 – 5? 738 – 5? 3738 - 5? Point out that we can use the fact that 8 – 5 = 3 to answer each of these questions. Use Post-its to mark one end of a counting stick as 6995, the other as 7005. Mark the centre as 7000. What is 7005 subtract 6? Subtract 8? And 7003 – 8? Repeat with 5600 then 3240 as the central number.
Group Activities
-- Repeatedly subtract a 1-digit number from a 4-digit number.

You Will Need

  • Post-its
  • Counting stick
  • 0–9 dice
  • 0–6 dice for one group

Mental/Oral Starters

Day 1
Count on and back in steps of 1 (pre-requisite skills)

Suggested for Day 2
Add 1, 10, 100 and 1000 to 4-digit numbers (simmering skills)

Procedural Fluency

Day 1
Add 1-digit numbers to 3- and 4-digit numbers.

Day 2
Subtract 1-digit numbers from 3- and 4-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Write the unit pattern of answers if you add 8 to any 2-digit number. E.g. ?1 + 8 = ?9, ?2 + 8 = ?0, ?3 + 8 = ?1 etc.
  • A 3-digit number had 5 added to it. The answer then has 4 digits and ends in 1. What was the number?
  • Continue this sequence.
    8 + 3 + 8 + 3 + 8 + 3…..gives 11, 19, 22 ..…
    What do you notice about every other number in the sequence? Can you explain this?

In-depth Investigation: Amy's Dominoes
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing? Amy's Dominoes from nrich.maths.org.

Extra Support

How High Can You Jump?
Adding and subtracting 1-digit numbers to and from 3-digit numbers

Unit 7 Written subtraction (suggested as 5 days)

Objectives

Written subtraction
Unit 7: ID# 4253

National Curriculum
Add/Sub (i) (ii)

Hamilton Objectives
6. Add or subtract multiples of 1, 10, 100, 1000 without difficulty.
14. Use column subtraction to subtract 3-digit and 4-digit numbers: first expanded, then compact method.
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Teaching and Group Activities for Understanding

Although column subtraction is specified for Year 3 in the National Curriculum, Hamilton believe that teaching column subtraction in Year 4 will be more successful. The National Curriculum Guidance specifies that teachers can teach areas of study in different year groups than those mentioned in the Curriculum, so long as they are taught within the same Key Stage. You can choose to teach this column subtraction content in Year 3 or in Year 4.

Day 1 Teaching
Write 654 – 321 on the board. How would we work this out? Draw out partitioning into 100s, 10s and 1s. Record an expanded column subtraction and model each stage of the process. Repeat with 651 – 324 and 742 – 328. Children work in pairs to work out 445 – 339.
Group Activities
-- Start to subtract 3-digit numbers that need one move to the ones column.

Day 2 Teaching
Display Top Marks ‘Decomposition’ on the Interactive Whiteboard. Show 657 – 432. Ask children how to work this out, then click on the ‘partition’ arrow to split into 100s, 10s and 1s. Work through then repeat with 657 – 472, 465 – 283, 625 – 362, 936 – 571.
Group Activities
-- Use expanded decomposition to find the difference between two 3-digit numbers.
-- Find and correct mistakes when using expanded decomposition to subtract 3-digit numbers.

Day 3 Teaching
Use 460 – 238 and 734 – 351 to revise how to move from 100s to 10s or from 10s to 1s. Introduce 966 – 177 and repeat with 842 – 467 (two moves needed).
Group Activities
Use the ‘Hole-y Subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use expanded decomposition to find the difference between two 3-digit numbers.

Day 4 Teaching
Show a glass of squash. It has 533ml of squash. Pour some out (251 ml). Children estimate how much is left. Discuss strategies for estimating. Then use expanded decomposition to work out the answer and compare this to estimates. Repeat with other amounts.
Group Activities
-- Give tips for using expanded decomposition to subtract 3-digit numbers.

Day 5 Teaching
Share 802 – 374. Model using expanded decomposition. Ask if children can think of an easier method. Discuss Maths Frog and model using this. Repeat for 904 – 785, comparing methods.
Group Activities
-- Choose whether to use Frog or expanded decomposition to subtract 3-digit numbers.

You Will Need

  • Dienes or Base 10 equipment
  • Decomposition’ tool from topmarks.co.uk
  • ‘Subtraction Cards’ (see resources)
  • Pint glass filled with squash
  • Empty number line
  • ‘Subtracting using expanded decomposition or Maths Frog’ (see resources)

Mental/Oral Starters

Day 1
Subtract any 1-digit number from a teens number (pre-requisite skills)

Day 2
Subtract multiples of 10, crossing 100 (pre-requisite skills)

Day 3
Subtract any pair of 2-digit numbers (pre-requisite skills)

Day 4
Bonds to 100 (pre-requisite skills)

Suggested for Day 5
Round 3-digit numbers to the nearest 10 and 100 (simmering skills)

Procedural Fluency

Day 1
Use written subtraction to subtract 3-digit numbers with expanded decomposition.

Day 2
Subtract 3-digit numbers using expanded decomposition with one move.

Day 3 and 4
Use expanded decomposition to solve subtractions.

Day 5
Choose whether to use Frog or expanded decomposition to subtract 3-digit numbers.

Mastery: Reasoning and Problem-Solving

  • What would need to be added to 547 to give 752?
  • Complete each diagram:
    Diagram 1

534
351

Diagram 2

273
186

Diagram 3

903
787
  • Here is Janie’s homework:
    (i) 502 - 468 =
    (ii) 673 - 348 =
    (iii) 713 - 583 =
    (iv) 919 - 845 =

Advise her how to do each one, explaining why you are suggesting that method. Then work out the correct answers.


In-depth Investigation: Hole-y Subtractions
Children create 3-digit palindromic numbers with a ‘hole’ (i.e. a zero) in the middle. They subtract 3-digit numbers with equal numbers of 1s, 10s and 100s and identify patterns in their answers.

Extra Support

Frogs Get Fitter
Using counting up (Frog) to subtract pairs of 2-digit numbers

Teach the Frog
Using counting up (Frog) to subtract pairs of 2-digit numbers; Using counting up (Frog) to subtract pairs of 3-digit numbers within the same century, e.g. 352 - 327