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Maths Year 3 Autumn Addition and 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 Number facts and inverse operations (suggested as 2 days)

Objectives

Number facts and inverse operations
Unit 1: ID# 3169

National Curriculum

Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20.
14. Solve problems, including those involving missing numbers.
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
Use different sets of objects, including pegs on a coat hanger, to partition 12 into 2 sets. Then use bar diagrams and write 4 sentences. Learn the facts.
Group Activities
Use the in-depth problem-solving investigation ‘Are you well balanced?’ from NRICH as today’s group activity.
Or, use these activities:
-- Find as many ways of making given numbers.
-- Consolidate number bonds to 10 and 20.

Day 2 Teaching
Use the NRICH balances to show equality and use this to rehearse number facts. Write these facts as number sentences, using +, = and also – signs.
Group Activities
-- Play ‘what’s in the box’ exploring different number fact sentences.

You Will Need

• Coat hanger and 12 pegs (2 colours)
• Bar model pictures for pairs to 6, 7, 8, 9 & 12 (see resources)
• Number balance (or an interactive one)
• Small items for hiding, boxes or bags to hide items in

Mental/Oral Maths Starters

Day 1
Addition facts for numbers 6 to 10 (pre-requisite skills)

Suggested for Day 2
Pairs to 10 (simmering skills)

Procedural Fluency

Day 1
Practise number facts.

Day 2
Practise equalities.

Mastery: Reasoning and Problem-Solving

• Write 4 number sentences to relate these 3 numbers: 13, 19 and 6.
• We know 13 + 7 = 20. So what is 130 + 70?
We know 11 + 9 = 20. So what is 110 + 90?
Write an addition with an answer of 20.
Write a similar addition with an answer of 200.
Repeat this.
• Write three different ways of making 14 by adding two 1-digit numbers.

In-depth Investigation: Are You Well Balanced?
Hang combinations of weights to make the scale balance. Are You Well Balanced? from nrich.maths.org.

Extra Support

Perfect Pairs
Addition facts for 6, 7, 8, 9 and 10

Patterns Practice
Using addition facts to add single-digit numbers to 2-digit numbers, e.g. using 5 + 3 = 8 to work out 25 + 3 (not crossing 10s)

Unit 2 Using number facts to add/subtract (suggested as 3 days)

Objectives

Using number facts to add/subtract
Unit 2: ID# 3181

National Curriculum

Hamilton Objectives

4. Add and subtract 1-digit numbers from 2-digit numbers using number facts.
9. Mentally add and subtract multiples of 1 to/from 2-digit and 3-digit numbers.
7. Know securely number pairs for all the numbers up to and including 20.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use a 1-100 bead bar to demonstrate 5 + 3 is similar to 15 + 3, 25 + 3, 35 + 3, etc. Repeat for 7 + 4, 17 + 4, 27 + 4, 37 + 4, etc. Repeat on landmarked lines.
Group Activities
Use the ‘Puzzling Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Identify mystery numbers by spotting the patterns of adding given 1-digit to 2-digit numbers.
-- Explore adding a given no. to any 2-digit no. that ends in the same digit.

Day 2 Teaching
Use the bead bar to show that 5 – 2 is similar to 15 – 2, 25 – 2, 35 – 2, etc. Repeat for 14 – 7, 24 – 7, 34 – 7. Show on landmarked lines.
Group Activities
-- Play subtraction bingo, taking 1-digit numbers from 2-digit numbers.
-- Card subtraction activity taking 1-digit numbers from 2-digit numbers.

Day 3 Teaching
Demonstrate spotting number facts and doubles to add several numbers.
Group Activities
-- Play tiddlywinks, adding 3 or more numbers.
-- Mystery number bags – adding 3 or more numbers.

You Will Need

• 100 bead bars
• 0-100 beaded line (see resources)
• 0-100 landmarked line (see resources)
• Additional activity sheets (see resources)
• Number dice (regular, 8-sided and 12 sided)
• Number cards
• 4 bags or pots per group
• 1-digit and 2- digit number cards

Mental/Oral Maths Starters

Day 1
Complements to multiples of 10 (pre-requisite skills)

Suggested for Day 2
Number facts (simmering skills)

Suggested for Day 3
Doubles 1 to 10 (simmering skills)

Procedural Fluency

Day 1
Add 1-digit to 2-digit numbers.

Day 2
Subtract 1-digit from a 2-digit-number.

Day 3
Add several numbers practice sheets.

Mastery: Reasoning and Problem-Solving

• Write 8 + 4 = 12 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 sentences, each with a 2-digit number, using this central fact.
• Always true, sometimes true or never true?
Adding 7 to a number ending in 4 gives an answer ending in 1.
Taking 6 away from a number gives an answer ending in 2.
Adding 9 to a number always gives a 1s digit which is one less than the number you started with.
• A + B – 12 = 3
What numbers could A and B stand for? Neither is more than 10.

In-depth Investigation: Puzzling Squares
Children use reasoning skills to solve a number puzzle. They use numbers 0 to 7 to make a total of 10 on each side of a square.

Extra Support

This unit has no separate Extra Support activities.

Unit 3 Add/subtract: efficient mental strategies (suggested as 3 days)

Objectives

Mental addition and subtraction including frog
Unit 3: ID# 3191

National Curriculum

Hamilton Objectives
6. 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.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
32. Give change by counting up; use both £ and p in practical contexts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Introduce maths Frog. Show how Frog hops up along a number line to help us count up to find a difference, e.g. 70 – 56, Frog hops from 56 to 60, and then to 70. Stress that Frog always hops first to the next 10.
Group Activities
-- Frog pairs game subtracting two 2-digit numbers.

Day 2 Teaching
Rehearse the list of rules for how Maths Frog counts up. Use these to help Maths Frog to find greater differences, e.g. 92 – 48.
Group Activities
Use the ‘Twisted Subtraction’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Jumping frogs and dog lengths: subtract by counting up.

Day 3 Teaching
Explain that Maths Frog can help us find change from £1. Show how Frog hops from 67p to 70p to £1 to find change from 67p.
Group Activities
-- Pick a badge activity - finding change from £1.
-- Use bar models to create subtractions which require Frog to help us find the change from £1.

You Will Need

• Maths Frog toy
• 0-100 landmarked line
• 0 to £1 (see resources)
• 0-100 beaded lines (see resources)
• Additional activity sheets (see resources)
• Toy dogs (or similar) of different sizes
• Money
• Items to sell

Mental/Oral Maths Starters

Day 1
Complements to multiples of 10, e.g., 57 + □ = 60 (pre-requisite skills)

Day 2
Subtraction number bonds to 10 (pre-requisite skills)

Suggested for Day 3
Use place value to add and subtract (simmering skills)

Procedural Fluency

Day 1
Subtract by counting up.

Day 2
Subtract two 2-digit numbers.

Day 3
Find change from £1.

Mastery: Reasoning and Problem-Solving

• Write two 2-digit numbers with a difference of 8.
• Write 3 different subtractions where Frog does 2 hops and the first is 4.
• Use Maths Frog to help you write the missing digits:
8 ☐ – 4 8 = 3 4
☐ 5 – 2 7 = 6 ☐
• Write a subtraction where the 10s digit in the smaller number is 2 less than the 10s digit in the bigger number and the answer is 16.

In-depth Investigation: Twisted Subtractions
Children subtract a number which is the reverse of another, e.g. 62 - 26.

Extra Support

Tiptoe to 10
How many to the next 10, e.g. 36 + □ = 40?

Unit 4 Partitioning to add (suggested as 2 days)

Objectives

Unit 4: ID# 3203

National Curriculum

Hamilton Objectives
8. Mentally add or subtract any pair of 2 digit numbers, e.g. 75 + 58 or 75 – 58.
5. Solve number problems and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate how we can add 2-digit numbers by partitioning each one into 10s and 1s. So 65 + 24 = 60 + 20 + 5 + 4. Use place value equipment to demonstrate this.
Group Activities
Use the in-depth problem-solving investigation ‘Diagonal Sums’ from NRICH as today’s group activity.
Or, use these activities:
-- Spinners: adding to make less than and more than 100.

Day 2 Teaching
Use place value equipment to add pairs of 2-digit numbers by partitioning each one into 10s and 1s, and noticing that if we wind up with more than ten 10s, we have 100.
Group Activities
-- Pocket money promotion activity adding to make more than & less than 100 in pounds and pence.

You Will Need

• Place value cards
• ITP: Place Value
• Spinners (see resources)
• Cards (to write additions on)
• Pocket money badges (see resources)

Mental/Oral Maths Starters

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

Suggested for Day 2
Number bonds (simmering skills)

Procedural Fluency

Day 1
Add two 2-digit numbers.

Day 2
Add two 2-digit numbers.

Mastery: Reasoning and Problem-Solving

• Write 2 numbers which total 91 where one has a 1s digit of 6.
• Write the missing digits:
7 ☐ + 4 8 = ☐ 2 4
☐ 5 + 8 7 = 1 4 ☐
• How many pairs of numbers between 20 and 30 can you find that total 51?

In-depth Investigation: Diagonal Sums
In a square of numbers on the 100-grid, explore the sum of the pairs of numbers that are diagonally opposite each other. Diagonal Sums from nrich.maths.org.

Extra Support

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