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Maths Year 3 Spring 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. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Mental addition of 2-digit numbers (suggested as 2 days)

Objectives

Mental addition of 2-digit numbers
Unit 1: ID# 3413

National Curriculum

Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15.
8. Mentally add or subtract any pair of 2-digit numbers, e.g. 75 + 58 or 75 – 58.

Teaching and Group Activities for Understanding

Day 1 Teaching
Discuss what strategies we can bring to adding two 2-digit numbers. We start with the larger number. We look for number bonds to help us. We may partition or add multiples of 10 and near multiples of 10.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey addition’ from NRICH as today’s group activity.
-- Use spinners to generate 2-digit numbers to add. Children discuss which strategy to use each time.

Day 2
Explain that today we will add three 2-digit numbers.
Show 3 snakes each with their length labelled: 42cm, 18cm, 25cm. Children discuss in pairs and then share how they would find the total length.
Group Activities
-- Choose 2 or three 2-digit numbers to add, ring answer on a grid. Try to get 3 in a line.

You Will Need

• Large 1-100 grid
• Plastic/card spider and fly
• ‘2-digit number spinners’ sheet 1 (see resources, enlarge to A3)
• A paper clip, 10s and 1s place value cards
• ‘2-digit number spinners’ sheet 2 (see resources)
• 1 to 100 number grid (see resources)
• Six snakes/ribbons/caterpillars each with length labelled: 43cm, 18cm, 25cm, 57cm, 48cm, 23cm
• Red and blue pencils/pens
• Additional activity sheets (see resources)

Mental/Oral Maths Starters

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

Day 2
Add 3 or 4 numbers (pre-requisite skills)

Procedural Fluency

Day 1
Use Spider and Fly to add pairs of number which don’t cross 10s.
Add pairs of amounts of money. Find as many pairs with a total of less than £1 as they can.

Day 2
Add pairs then trios of 2-digit numbers, and then answer word problems.

Mastery: Reasoning and Problem-Solving

• Use a different strategy for each of these additions:
45 + 29
45 + 34
65 + 35
78 + 28
• Complete the bar model diagrams:
Diagram 1
 ? 36 37

Diagram 2

 ? 57 39

Diagram 3

 ? 48 24

In-depth Investigations: Dicey Addition
Use dice to generate two 2-digit numbers. Find the total. Whoever has the total closest to 100 wins. Dicey Addition from nrich.maths.org.

Extra Support

Do the Splits
Adding pairs of 2-digit numbers using partitioning (1s < 10, 10s < 100)

Unit 2 Use different strategies to subtract (suggested as 3 days)

Objectives

Use different strategies to subtract two numbers
Unit 2: ID# 3433

National Curriculum

Hamilton Objectives
8. Mentally add or subtract any pair of 2-digit numbers, e.g. 75 + 58 or 75 – 58.
10. Recognise that there are 2 ways of completing subtractions, either by counting up or by counting back.
14. Solve problems, including missing number problems.

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. If you would like to teach column subtraction in Year 3 please see Year 4 Addition and Subtraction autumn Unit 7, spring Unit 4 and summer Units 2 and 3.

Day 1 Teaching
Show items for sale (see resources). Children remove 10p from each price and show you on whiteboard. Then start again and remove 9p from each price. Practise reducing by other amounts, e.g. 12p, 21p, etc. Use Spider on the 1-100 grid to demonstrate.
Group Activities
-- Reduce prices by near multiples of 10p.

Day 2
Use Maths Frog. He helps us to subtract by counting up to find a difference. He ALWAYS hops to the next 10 and then to 100. He starts with the smaller number. Write notes. Use Frog for 45 – 32, 78 – 44, 54 – 23. Model: Below the line record the numbers where Frog lands and above the line the size of each hop.
Group Activities
Use the ‘Magic square differences’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Choose numbers between given multiples of 10, use Frog to subtract the smaller from the larger aiming to find the smallest and biggest answers that they can. Use landmarked lines.
-- Use Frog to work out how much dogs have grown. Draft own number line jottings.

Day 3
We’ve revised different ways of subtracting; we’ve looked at using Frog to count up and counting back to subtract near multiples. Write: Frog and Counting Back as column headings. Ask children to give an example for each. Correct misunderstandings.
Group Activities
-- Choose Frog or Counting Back to subtract.

You Will Need

• Subtracting near multiples sheet 1 (see resources)
• 1-100 number grid (see resources)
• Subtracting near multiples sheet 2 (see resources) or label actual items with the tags
• Blank-sided dice
• Toy frog
• Beaded and landmarked lines to display on the IWB (see resources)
• Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Add and subtract 1-digit numbers to/from 2-digit numbers (pre-requisite skills)

Day 2
Pairs to 100 (pre-requisite skills)

Suggested for Day 3
2 and 5 times tables (simmering skills)

Procedural Fluency

Day 1
Subtract multiples of 10 and near multiples.

Day 2
Use Frog to work out subtractions on landmarked lines.

Day 3
Choose Frog or counting back to work out given subtractions.

Mastery: Reasoning and Problem-Solving

• Frog, Counting Back (CB) and subtracting multiples of 10 or Near Multiples (NM) are 3 different ways of subtracting. Write CB, NM or Frog beside each subtraction below.
(i) 64 – 56
(ii) 53 – 9
(iii) 72 – 57
(iv) 86 – 5
(v) 37 – 19
(vi) 62 – 28
• Write the missing numbers
(a) ☐ + 30 = 55
(b) 100 - 79 = ☐
(c) ☐ + 19 = 65
(d) 73 – ☐ = 58
(e) 50 – ☐ = 43
(f) ☐ + 47 = 62
• Padma spends 39p on a drink. She uses a 50p coin to pay. How much change does she get?
• Sam has 76 cards. Tom has 92. How many more does Tom have than Sam?

In-depth Investigation: Magic Square Differences
Children use the magic square to generate two-digit numbers and explore difference patterns.

Extra Support

Hop, Jump, Hop
Subtracting pairs of 2-digit numbers either side of a multiple of 10, e.g. 54 – 37, using counting up (Frog).

Unit 3 Expanded addition: 3-digit numbers - 1 (suggested as 3 days)

Objectives

Unit 3: ID# 3449

National Curriculum

Hamilton Objectives
11. Add numbers with 3-digits using column addition, first expanded then compact method.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show 243 + 725 and say that we will use expanded column addition. First we partition numbers into 100s, 10s and 1s. Children partition the number using place value cards. Model layout and perform the addition. Repeat with 427 + 345 and other similar additions.
Group Activities
-- Work in 3s to partition pairs of 3-digit numbers, collect the 100s, 10s and 1s to find the total. Record the addition using the expanded layout.
-- Use place value cards and expanded addition to add pairs of 3-digit numbers, including those where the 1s >10.

Day 2 Teaching
Write 528 + 333. Who can show us how to solve this? Discuss solution given and the steps needed. Write 362 + 483. Point out how this time we need to add an extra 100 to the 100s column. Repeat with 473 + 253.
Group Activities
Use the ‘Expanded Elevens’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use place value cards and expanded addition to add pairs of 3-digit numbers, including those where the 1s >10.
-- Choose numbers from given sets to add using expanded addition. (10s >100).

Day 3
Write 318 + 235. Ask children how we estimate the answer. We round each number to the nearest 100. Write 200 + 300 = 500. Now find the answer using expanded addition and compare estimate. Repeat with 392 + 233, pointing out how 1 number rounds up and the other rounds down.
Group Activities
-- Work in 3s to partition pairs of 3-digit numbers, collect the 100s, 10s and 1s to find the total using expanded addition (10s >100).
-- Estimate which additions have totals </>800 (1s >10 OR 10s>100). Use expanded addition to find out.
-- Use place value cards to create additions where 1s>10 AND 10s> 100.

You Will Need

• 100s, 10s and 1s place value cards.
• Large sheets of paper.
• Flipchart and pens.
• Expanded addition activity sheet (see resources).
• Numbers to add sheet (see resources).
• Mini-whiteboards and pens.

Mental/Oral Maths Starters

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

Day 2
Use number facts to quickly add pairs of multiples of 10 (pre-requisite skills)

Suggested for Day 3
3 times table (simmering skills)

Procedural Fluency

Day 1
Use expanded addition (1s<10 and 10s<100).
Use expanded addition (to include 1s>10).

Day 2
Use expanded addition (to include 10s >100).

Day 3
Use expanded addition (to include 1s>10 or 10s >100).

Mastery: Reasoning and Problem-Solving

• 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 = ☐
☐ – 356 = 238
327 + 258 = ☐
☐ – 426 = 247
• 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?

In-depth Investigation: Expanded Elevens
Children use base 10 equipment to create 3-digit numbers to add using expanded column addition.

Extra Support

More Split Sums
Adding pairs of 2-digit numbers using partitioning (1s > 10 or 10s > 100).

Unit 4 Counting up subtraction with nos>100 (suggested as 2 days)

Objectives

Subtract 2-digit numbers from numbers over 100 using counting up
Unit 4: ID# 3457

National Curriculum

Hamilton Objectives
12. Subtract larger numbers with confidence, using 'Frog' for counting up.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
14. Solve problems, including missing number problems.

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. If you would like to teach column subtraction in Year 3 please see Year 4 Addition and Subtraction autumn Unit 7, spring Unit 4 and summer Units 2 and 3.

Day 1 Teaching
Show a toy frog. Maths Frog helps us with subtraction. He always knows where to start and where to end up. Remind children that Frog hops to the next 10 or 100. Then we add his hops to find the answer. Use Frog to work out 136 – 87, modelling how to draw the steps. Repeat for 143 – 75.
Group Activities
Use the ‘Pattern subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use Frog on landmarked lines to subtract numbers between 50 and 100 from number between 100 and 150.
-- Subtract numbers between 50 and 100 from number between 100 and 150. Use a bar model to show link with addition.

Day 2 Teaching
Children show you on whiteboards how to use Frog to solve 123 – 76. Check that they sketch a line from 76 to 123 and that they hop to the next 10, 100, etc. Write 126 – 73. Do you think this has a bigger or smaller answer? Why? Discuss how the difference between these 2 numbers is bigger. Solve.
Group Activities
-- Children replace the boxes in a subtraction calculation with different digits to get different answers, including smallest and largest possible answers, looking for patterns.

You Will Need

• Toy frog.
• 50 – 150 landmarked lines (see resources).
• ‘Subtract by counting up’ sheet (see resources).
• Flipchart and pens.
• Mini-whiteboards and pens.

Mental/Oral Maths Starters

Day 1
Complements to 100 (pre-requisite skills)

Day 2
Inverse number sentences (pre-requisite skills)

Procedural Fluency

Day 1

Use Frog to subtract numbers between 50 and 100 from number between 100 and 150.

Day 2
Use Frog to find missing numbers in bar models (subtracting numbers between 50 and 100 from number between 100 and 150).

Mastery: Reasoning and Problem-Solving

• Write the missing numbers:
123 – ☐ = 75
106 + ☐ = 78
111 – ☐ = 57
118 – ☐ = 85
123 + ☐ = 84
102 + ☐ = 98
• Write two numbers either side of 100 which have a difference of 26.
• Write 2wo numbers either side of 200 which have a difference of 34.
• Complete this bar diagram:
 121 86 ?

In-depth Investigation: Pattern Subtractions
Children subtract two-digit from three-digit numbers, by counting up, and look out for patterns in the numbers.

Extra Support

Frog's Brave Big Jumps
Subtracting pairs of 2-digit numbers with a bigger gap, e.g. 64 – 37, using counting up (Frog)

Unit 5 Expanded addition: 3-digit numbers - 2 (suggested as 2 days)

Objectives

Add 3-digit numbers using expanded column addition
Unit 4: ID# 3463

National Curriculum

Hamilton Objectives
11. Add numbers with 3-digits using column addition, first expanded then compact method.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
14. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 328 + 241. Children use expanded addition to solve this on their whiteboards. Repeat to add 728 + 153, demonstrating how we leave a line above the answer for the extra 10s. Now model adding 567 + 158 showing how we need to add an extra 10 and 100.
Group Activities
-- Shuffle given ranges of place value cards to generate additions. Use expanded addition to find totals.
-- Learn to use compact addition.

Day 2 Teaching
Write 654 + 218. Ask for an estimation of total. Model rounding to approximate. Draw a line down centre of board. Ask a child to use expanded addition on left hand side and another to use compact addition on right hand side. Stress that we must leave a space before drawing the lines for answer.
Group Activities
Use the ‘Next door additions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Write different digits in 2□□ + 2□□, aiming to make 2 sums with a total less than 500 and 2 sums with a total of more than 500. Use expanded addition.
-- Pick additions from a pot. Use expanded and compact addition to find the totals, then choose preferred layout to work out others.

You Will Need

• 100s, 10s and 1s place value cards
• Mini-whiteboards and pens
• ‘Adding two 3-digit numbers’ sheet (see resources)
• Flipchart and pens
• Addition cards (see resources)
• Pots/dishes for cards

Mental/Oral Maths Starters

Day 1
Addition facts (pre-requisite skills)

Suggested for Day 2
4 times table (x and ÷) (simmering skills)

Procedural Fluency

Day 1
Practise using expanded addition to add pairs of 3-digit numbers, moving extra numbers into the 10s and/or 100s column.

Day 2
Use expanded and compact addition to work out 2 answers, then choose preferred layout to work out other answers (1s>10, then 10s>100, then 1s>10 AND 10s> 100).

Mastery: Reasoning and Problem-Solving

• Choose 2 numbers and estimate the total. Write this. Then calculate and compare the actual answer with your estimate. Repeat, choosing 2 different numbers.
 475 386 248 349

Choose to use expanded or compact addition to add 484 to 368. Explain your choice.

In-depth Investigation: Next Door Additions
Children add pairs of three-digit numbers and look for patterns in the digital roots of the answers.

Extra Support

Adding any pairs of 2-digit numbers using partitioning (including 1s> 10 AND 10s > 100)

Unit 6 Strategies to subtract from nos>100 (suggested as 3 days)

Objectives

Subtract 2-digit numbers from 3-digit numbers using an efficient strategy
Unit 5: ID# 3469

National Curriculum
Add/Sub (i) (iii) (iv)

Hamilton Objectives
12. Subtract larger numbers with confidence, using 'Frog' for counting up.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
14. Solve problems, including word problems.

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. If you would like to teach column subtraction in Year 3 please see Year 4 Addition and Subtraction autumn Unit 7, spring Unit 4 and summer Units 2 and 3.

Day 1 Teaching
Show a toy Frog and discuss how Frog helps us subtract. Use Frog to do 162 – 135, modelling how to draw the steps on an empty number line. Write 471 – 425. Children use Maths Frog on whiteboards to work it out. Remind them that the ‘baby’ number goes on left hand side and Frog always hops to the next 10. Repeat with 893 – 838 and 673 – 606.
Group Activities
-- Learn to draw empty number line jottings for subtracting by counting up.
-- Draw own empty number line jottings to subtract numbers within the same century.
-- Use Frog to work out given calculations, discussing pattern in answers. Repeat with a similar set.

Day 2 Teaching
Children think, pair, share, how Frog helps us. Write 871 – 827. Children solve on whiteboards with Maths Frog. Ask children how we check it. Agree that we use addition, because the inverse of subtraction is addition – addition undoes subtraction: Repeat with 453 – 406 and 693 – 226.
Group Activities
Whole class investigation. Find different answers to 18◊ – 12☐. Find smallest and largest answers.

Day 3
Remind children of expanded and compact addition and using Frog to subtract by counting up. Today we choose addition and subtraction to find the answers to word problems. Reveal word problems (see resources) 1 by 1. Model using the bar model for the first 2 questions.
Group Activities
-- Draw bar models to represent word problems.
-- Write word problems to go with given bar models. Use bar models to represent 2-step problems.

You Will Need

• Toy frog
• Mini-whiteboards and pens
• Flipchart and pens
• ‘Finding a difference using Frog’ sheet (see resources).
• ‘Word problems’ sheet (see resources)
• ‘Problem cards’ (see resources)
• ‘Make up your own word problems’ sheet (see resources)
• ‘2-step word problems’ sheet (see resources)

Mental/Oral Maths Starters

Day 1
Pairs of 3-digit numbers with a difference of 5 (pre-requisite skills)

Day 2
Pairs to 100 (pre-requisite skills)

Suggested for Day 3
8 times table (simmering skills)

Procedural Fluency

Day 1
Use Maths Frog to subtract by counting up between pairs of numbers within the same century.

Day 2
Use Maths Frog to subtract by counting up between pairs of numbers within the same century and check some with addition.

Day 3
Read word problems, discuss whether they need addition or subtraction, and then calculate the answers.

Mastery: Reasoning and Problem-Solving

• Complete the bar model diagrams:
Diagram 1
 472 428 ?

Diagram 2

 581 548 ?

Diagram 3

 875 837 ?
• Tracy has 381 pennies saved in her ‘penny-jar’. If she takes out 329 to buy a Shopkins toy, how many pennies will she have left?
• Shane has 258 Pokémon cards and his mum buys a job-lot of 267 on-line. How many cards does he have now?
• In his exercise routines, Ahmed does 78 press-ups during the week. His fitness tutor says he needs to do 125 each week. So, how many more must he do each week?

In-depth Investigation: Smallest and Largest
Find different answers to 18◊ – 12☐. Find the smallest and largest answers. See group activity Day 2 for further details.

Extra Support

Frog's Ginormous Jumps
Subtracting pairs of 2-digit numbers with a bigger gap, e.g. 84 – 37, using counting up (Frog)