Maths Year 3/4 Autumn More Addition & 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 +/- 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.

Teaching and Group Activities for Understanding

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.

Teaching and Group Activities for Understanding

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.

Teaching and Group Activities for Understanding

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