Short Blocks

Maths Year 3/4 Autumn Addition & Subtraction (B)

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?
Open Unit 1 and download the PowerPoint from 'Planning and Group Activities': a brilliant and ready-to-use maths lesson for your white board!

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

Unit 1 +/- near-/multiples of 10, 100, 1000 (suggested as 4 days)

Objectives

Add/subtract multiples and near-multiples of 10, 100, 1000
Unit 1: ID# 34300

Y3: Use place value to add/subtract multiples of 1, 10, 100 to/from 2-digit and 3-digit numbers. Add/subtract near multiples of 10 and 100 to/from two and three-digit numbers.
Y4: Use place value to add and subtract multiples of 1, 10, 100, 1000 to/from numbers with up to 4 digits. Add/subtract near multiples of 1, 10, 100, 1000 to/from numbers with up to 4 digits.

National Curriculum
Y3: Add/Sub (i) (iv), Num/PV (ii)
Y4: Num/PV (iv) (viii)

Y3 Hamilton objectives
5. Solve number problems and practical problems involving place value.
9. Mentally add and subtract multiples of 1s, 10s and 100s to/from 3-digit numbers.

Y4 Hamilton objectives
6. Add multiples of 1, 10, 100, 1000.
9. Solve number and practical problems involving place value.

Planning and Activities

Day 1 Teaching
Use place value to add multiples of 1, 10, 100 to 2-digit and 3-digit numbers.
Further Teaching with Y4
Place value additions with up to 4-digits.
Group Activities: T with Y4
Y3 -- Add multiples of 1s, 10s (and 100s) to 3-digit numbers.
Y4 -- Use place value and number facts to add 3-digit and 4-digit numbers.

Day 2 Teaching
Add near multiples of 10 to 2 and 3-digit numbers.
Group Activities: T with Y3
Use the in-depth problem-solving investigation for this unit ‘Magic 147’ as today’s group activity.
Or, use these activities:
Y3 -- Hexagon Multiples addition game: add multiples of 10 and related near multiples.
Y4 -- Solve and make up word problems involving adding multiples and near multiples of 10 or 100 to a 3-digit number.

Day 3 Teaching
Use place value to subtract multiples of 1, 10, 100 from 2-digit and 3-digit numbers (Y4 4-digits).
Further Teaching with Y3
More guided practice on whole-class teaching.
Group Activities: T with Y3
Y3 -- Subtract 1s, 10s and 100s from 3-digit numbers.
Y4 -- Subtract multiples of 1, 10 and 100 from 3-digit and 4-digit numbers.

Day 4 Teaching
Subtract near multiples of 10 and 100 from 2 and 3-digit numbers.
Group Activities: T with Y3
Y3 -- Subtract multiples of 10 and related near multiples.
Y4 -- Use an empty number line to subtract near multiples of 10 and 100 from 3-digit numbers.

You Will Need

  • ‘Place value grid’ (see resources)
  • ‘Adding using place value’ sheets 1 and 2 (see resources)
  • Coins (£1s, 10ps and 1ps)
  • Whiteboards and pens
  • 1–6 dice, 1–8 dice and 3-minute sand timer
  • ITP: Number spinners (see resources)
  • ‘Hexagon Multiples Addition Game’ boards A and B plus cards (see resources)
  • ‘Word Problems’ sheet (see resources)
  • ‘Cake cards’ sheets 1 to 4 (see resources)
  • ‘Hexagon Multiples Subtraction Game’ (see resources)
  • ‘Subtracting multiples of 10/100 and multiples of 10/100 + 1, – 1’ sheets 1 to 3 (see resources)
  • Pencils and paperclips (to use with spinners)

Short Mental Workouts

Day 1
Add any pair of 1-digit numbers

Day 2
Add/subtract 10/100 to/from 3-digit and 4-digit numbers

Day 3
Add/subtract multiples of 10 to or from any 2-digit number

Day 4
Count on and back in 10s from a 3-digit number

Procedural Fluency

Day 1
Y3: Add multiples of 1s, 10s and 100s to 3-digit numbers.
Y4: Use place value to add to 3- and 4-digit numbers.

Day 2
Y3: Add multiples of 10 and near multiples.
Y4: Add multiples of 10 and 100 and multiples + 1, – 1.

Day 3
Y3: Subtract multiples of 1s, 10s and 100s from 3-digit numbers; some worded problems.
Y4: Place value subtractions from 3- and 4-digit numbers.

Day 4
Y3: Subtract multiples of 10 and near multiples.
Y4: Subtract multiples and near multiples of 10 and 100; 100 and 1000.

Mastery: Reasoning and Problem-Solving

Y3

  • 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?

Y4

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

Extra Support

Y3
Jolly Jumping

Adding 9 to 2-digit numbers

Super simple subtractions
Subtracting 9 from 2-digit numbers

Y4
Swapping Digits

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

Unit 2 Partitioning and column addition (suggested as 3 days)

Objectives

Partitioning and column addition
Unit 2: ID# 34316

Y3: Add two then three 2-digit numbers by partitioning.
Y4: Add two 3-digit numbers and three or four 2-digit numbers using compact written addition.

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

Y3 Hamilton objectives
8. Mentally add any pair of 2-digit numbers, e.g. 75 + 58.
11. Add numbers with 3-digits using column addition, first expanded then compact method
Y4 Hamilton objectives
11. Use column addition to add 3-digit and 4-digit numbers: first expanded, then compact method.

Planning and Activities

Day 1 Teaching
Add 2-digit numbers by partitioning and recombining.
Further Teaching with Y4
Add two 3-digit numbers using compact written addition; if necessary, remind some children of expanded addition alongside.
Group Activities: T with Y4
Y3 -- Add to make totals less than and greater than 100.
Y4 -- Add 2-digit and 3-digit numbers using compact written addition.

Day 2 Teaching
Add using partitioning and column addition (expanded and compact).
Further Teaching with Y3
Further partitioning examples, introducing and discussing answers greater than 100.
Group Activities: T with Y3
Y3 --Identify pairs of 2-digit numbers with totals greater/less than 100.
Y4 -- Add 3-digit numbers using compact written additions. Some children will ‘carry’ between different columns.

Day 3 Teaching
Add three 2-digit numbers using partitioning and expanded column addition.
Further Teaching with Y4
Add three or four 2-digit numbers using expanded and compact addition.
Group Activities: T with Y4
Use the in-depth problem-solving investigation for this unit ‘Reach 100’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Add sets of three 2-digit numbers.
Y4 -- Use compact addition to add three 2-digit numbers.

You Will Need

  • Place value cards and 0–9 digit cards
  • ITP: Place value
  • Whiteboards and pens
  • ‘Adding pairs of 2-digit numbers’ spinners sheets 1–3 (see resources)
  • Paperclip and pencils
  • 0–9 dice or sets of 1–9 cards
  • ‘Pocket money promotion’ sheets 1 and 2 (see resources)
  • ‘1–100 grid’ (see resources)
  • Counters, 10s and 1s cards and flipchart

Short Mental Workouts

Day 1
Adding multiples of 10

Day 2
Add three 1-digit numbers

Day 3
Add 3 or 4 numbers

Procedural Fluency

Day 1
Y3: Add pairs of 2-digit numbers by partitioning.
Y4: Add pairs of 3-digit numbers using compact addition.

Day 2
Y3: Add pairs of 2-digit numbers; answers >100.
Y4: Addition word problems with three 3-digit numbers.

Day 3
Y3: Add two, then three 2-digit numbers.
Y4: Add three or four 2-digit numbers.

Mastery: Reasoning and Problem-Solving

Y3

  • Write 2 numbers which total 91 where one has a 1s digit of 6.
  • Write the missing digits:
    7☐ + 48 = ☐24
    ☐5 + 87 = 14☐
  • How many pairs of numbers between 20 and 30 can you find that total 51?

Y4

  • Write 2 numbers which total 391 where one has a 1s digit of 6.
  • Write the missing digits:
    37☐ + 148 = ☐24
    5☐5 + 287 = 82☐
  • How many pairs of numbers between 120 and 130 can you find that total 251?

In-depth Investigation: Reach 100
Find four different digits that give four 2-digit numbers which add to a total of 100. Reach 100 from nrich.maths.org.

Extra Support

Y3: Splitting Sums
Adding 10s numbers; Beginning to use partitioning to add pairs of 2-digit numbers

Y4: Collect ’em Up!
Adding 2-digit numbers using partitioning (total more than 100); Beginning to add 3-digit numbers (total less than 1000)

Unit 3 Formal addition & subtraction algorithms (suggested as 5 days)

Objectives

Formal algorithms in addition and subtraction
Unit 3: ID# 34332

Y3: Add 3-digit numbers using expanded addition; estimating totals; subtraction using counting up.
Y4: Subtract 3-digit numbers using expanded decomposition; comparing subtraction methods.

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

Y3 Hamilton objectives
11. Add numbers with 3-digits using column addition, first expanded then compact method.
12. Subtract larger numbers with confidence, using 'Frog' for counting up, e.g. 302 – 288.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.

Y4 Hamilton objectives
12. Subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426 – 278, 321 – 87.
14. Use column subtraction to subtract 3-digit and 4-digit numbers: first expanded, then compact method.

Planning and Activities

Day 1 Teaching
Add 3-digit numbers using expanded addition.
Further Teaching with Y4
Subtract 3-digit numbers using expanded decomposition.
Group Activities: T with Y4
Y3 -- Use place value cards and expanded addition to add pairs of 3-digit numbers.
Y4 -- Begin to subtract 3-digit numbers using expanded decomposition, represented with base-10 equipment.

Day 2 Teaching
Add 3-digit numbers using expanded addition. Y3 look at adding in an extra 10; Y4 an extra 100.
Further Teaching with Y4
Subtract 3-digit numbers using expanded decomposition.
Group Activities: T with Y4
Y3 -- Add a pair of 3-digit numbers using expanded addition, variously where 1s total >10 and/or 10s total >100.
Y4 -- Use expanded decomposition to find the difference between two 3-digit numbers, finding and correcting mistakes if necessary.

Day 3 Teaching
Y4 teach Y3 how to complete subtraction by decomposition. Introduce Y4 task.
Further Teaching with Y3
Model estimating before completing additions.
Group Activities: T with Y4
Y3 -- Estimate the total of two 3-digit numbers and use expanded addition to find exact answers.
Y4 -- Use expanded decomposition to find the difference between two 3-digit numbers; some children create ‘top tips’ posters.

Day 4 Teaching
Subtract a 2-digit number from a 3-digit number using counting up (Frog). Compare subtraction strategies. Check subtraction with addition.
Group Activities: T with Y3
Use the in-depth problem-solving investigation for this unit ‘Hole-y subtractions’ as today’s group activity.
Or, use these activities:
Y3 -- Use Frog on landmarked lines to subtract numbers between 50 and 100 from numbers between 100 and 150; some children use bar models to show the link to addition.
Y4 -- Subtraction cards: Choose whether to use Frog or expanded decomposition to subtract 3-digit numbers.

You Will Need

  • Place value cards (100s, 10s, 1s)
  • ‘Expanded addition’ sheets 1 and 2 (see resources)
  • Dienes or Base 10 equipment
  • Whiteboards and pens
  • Top Marks ‘Decomposition’ demonstration
  • ‘Numbers to add’ sheet (see resources)
  • ‘Subtraction Cards’ (see resources)
  • 50–150 landmarked lines (see resources)
  • ‘Subtract by counting up’ sheets (see resources)
  • Flipchart and pens
  • ‘Subtracting using expanded decomposition or Maths Frog’ sheet (trim so each subtraction is on a separate card - it may be helpful to enlarge to A3 - see resources)

Short Mental Workouts

Day 1
Add multiples of 10p

Day 2
Subtraction facts

Day 3
Round 3-digit numbers to the nearest 10 or 100

Day 4
Complements to 100

Procedural Fluency

Day 1
Y3: Expanded addition for adding pairs of 3-digit numbers: no moving across columns; Begin to move a 10.
Y4: Use written subtraction to subtract 3-digit numbers with expanded decomposition; begin to explore regrouping.

Day 2
Y3: Expanded addition for adding pairs of 3-digit numbers: move a 10 or a 100.
Y4: Subtract 3-digit numbers using expanded decomposition with one move.

Day 3
Y3: Expanded addition (to include 1s>10 or 10s >100).
Y4: Use expanded decomposition to solve subtractions.

Day 4
Y3: Use Frog to subtract numbers between 50 and 100 from a number between 100 and 150.
Y4: Choose whether to use Frog or expanded decomposition to subtract pairs of 3-digit numbers.

Mastery: Reasoning and Problem-Solving

Y3

  • Add four hundred and fifty-six to three hundred and seventy-two.
  • What is the total of two hundred and sixty-eight and two hundred and eighty-six?
  • Write the missing numbers
    643 + 174 = ☐
    327 + 258 = ☐
    416 + ☐ = 888
  • Amit uses 346 Lego pieces in building his model X-wing, and his sister uses 287 in building her Millennium Falcon. How many Lego pieces have they used altogether?
  • Fill the gaps in this subtraction:
    81☐ – 4☐7 = ☐46

Y4

  • Complete each diagram.
    Diagram 1:
604
387

Diagram 2:

912
868

Diagram 3:

1003
578
  • Here is Ali’s homework.
    a. 403 – 265
    b. 648 – 356
    c. 752 – 199
    d. 812 – 754
    Advise him on the most efficient or error-proof subtraction strategy to calculate each one, explaining why you are suggesting that method. Calculate the answers.
  • Complete this subtraction calculation that uses decomposition:
700304
_300605

In-depth Investigation: Hole-y Subtractions
Y3: Children subtract numbers with identical digits from 101, 102, 103 ... and look for patterns in the answers.
Y4: 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.

Extra Support

Y3
More Split Sums

Adding pairs of 2-digit numbers using partitioning

Frog’s Brave Big Jumps
Subtracting pairs of 2-digit numbers with a bigger gap

Y4
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