• Free Maths Resources on Hamilton Find out which Hamilton maths units you can access for free, including our new slide presentations.

• New Flexible English Blocks Take control of the balance between the parts of the English curriculum too.

• Looking for the Weekly Plans? Find the weekly plans by looking for the orange button that says 'weekly plans' on the short blocks page for your year group.

Short Blocks

Maths Year 3 Spring Addition & Subtraction (A)

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 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 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 3 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.