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Maths Year 4 Autumn Addition and Subtraction (B)

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 added value for Hamilton Friends and School Subscribers.

Unit 1 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)

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 Maths 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 2 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

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

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 ones 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 Maths 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

• 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 3 Written subtraction (suggested as 5 days)

Objectives

Written subtraction
Unit 7: ID# 4253

National Curriculum

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 Maths 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