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Maths Year 4 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 Partitioning and column addition (suggested as 3 days)

Objectives

Partitioning and column addition
Unit 1: ID# 4177

National Curriculum

Hamilton Objectives
9. Solve number and practical problems involving place value.
11. Use column addition to add 3-digit numbers: first expanded, then compact method.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a grid (see resources) and model adding two numbers using partitioning into 10s and 1s. Write 137 + 19, 178 + 31, 125 + 26, 154 + 27 and 22 + 195 on the board. Discuss how to do each one, using partitioning for all except the first, where adding 20 then subtracting 1 is best.
Group Activities
Use the ‘Make 100’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Create and add 3-digit and 2-digit numbers, investigating finding totals with different criteria.

Day 2 Teaching
Display 324 + 439. Children work in pairs and use the written method to find the answer on their whiteboards. Note/share different strategies. Explain that today we focus on compact written addition. Model this, emphasising leaving a space above the answer for writing extra numbers (‘carry’ digits).
Group Activities
-- Add pairs of 3-digit numbers using compact written addition.

Day 3 Teaching
Display 592 + 235. Children use compact written addition on their whiteboards. Clarify any mistakes. Children then use this strategy to add three 3-digit numbers. Display:

 1 2 3 4 7 4 + 3 3 2

Children calculate the total.

Group Activities
-- Create and add three 3-digit numbers using compact written additions.
-- Use compact written addition to add three 3-digit numbers with ‘carries’ in different columns.

You Will Need

• ‘2-digit + 2-digit grid with missing totals’ (see resources)
• 1–9 dice or 1–9 digit cards
• ‘Adding 3-digit and 2-digit numbers’ (see resources)
• ‘Special magic squares’ (see resources)
• Calculators
• 0–9 digit cards
• Place value cards

Mental/Oral Maths Starters

Day 1
Count on in 10s from any 3-digit number (pre-requisite skills)

Day 2
Add any pair of 2-digit multiples of 10 (pre-requisite skills)

Day 3
Add three 1-digit numbers (pre-requisite skills)

Procedural Fluency

Day 1
Add pairs of 2-digit numbers.
Find missing numbers in a 2-digit + 2-digit addition grid.

Day 2
Use compact addition to add 3-digit numbers.

Day 3
Solve word problems with adding three 3-digit numbers.

Mastery: Reasoning and Problem-Solving

• Complete these additions mentally with only the answer written!
78 + 127 = ? and 348 + 39 = ?
Use a different method for each one and explain both your strategies.
• Write the missing numbers in this calculation
 200 ☐ 7 + 500 60 ☐ ☐ 40 5
• If 378 is subtracted from a number to leave 284, what was the number?
• Add 375 + 528 + 194 using expanded column addition.

In-depth Investigation: Make 100
Given a pattern of four one-digit numbers, children attempt to make a total of exactly 100.

Extra Support

Adding 2-digit numbers using partitioning

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

Unit 2 Mental subtraction incl. counting up (suggested as 3 days)

Objectives

Mental subtraction including counting up
Unit 2: ID# 4201

National Curriculum

Hamilton Objectives
10. Mentally add and subtract any pair of
2-digit numbers.
12. Subtract numbers from 2-digit and 3-digit numbers using counting up (Frog).
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Teaching and Group Activities for Understanding

Day 1 Teaching
Do we remember Maths Frog? He subtracts numbers by counting up from the smaller to the larger number; Frog hops along the number line; he always hops to the next 10. Ask children to use Frog to help them work out 78 – 47. Repeat for 85 – 47.
Group Activities
-- Use number bonds to complete bar models with complements to 20. Find the difference between 2-digit numbers using Frog.
-- Subtract 2-digit numbers from numbers just over 100, using Frog.

Day 2 Teaching
Display a 0–100 landmarked line. Write 100 – 85. Children use Frog to solve this, drawing hops on the line. Repeat, subtracting 2-digit numbers from 100. Sketch a bar model to go with 100 – 82 and ask children what number is missing.
Group Activities
Use the ‘Which is Quicker?’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Make 2-digit numbers and use Frog to find the complement to 100.

Day 3 Teaching
Write 123 – 41. Children think/pair/share how they would solve it. Model Frog counting up, and counting back mentally. Write 123 – 89, 123 – 32, 123 – 50 and discuss strategies.
Group Activities
-- Choose whether to count up or back to subtract 2-digit numbers from numbers over 100.

You Will Need

• 1–9 cards
• ‘Addition and subtraction facts for pairs to 20’ (see resources)
• ‘Subtraction cards’ (see resources)
• Additional activity sheets (see resources)

Mental/Oral Maths Starters

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

Day 2
Pairs to 20 and related subtractions (pre-requisite skills)

Suggested for Day 3
Count back in 10s from any 3-digit number, including crossing 100s (simmering skills)

Procedural Fluency

Day 1
Count up to subtract 2-digit numbers from 2-digit numbers.

Day 2
Use number bonds to find complements to 20 and 100.

Day 3
Choose whether to use Frog or counting up to subtract 2-digit numbers from numbers over 100.

Mastery: Reasoning and Problem-Solving

• Write three subtractions for Frog to do where his jumps add to 24. Show Frog’s hops and write the subtractions.
• Complete each diagram:
Diagram 1
 100 68

Diagram 2

 100 34

Diagram 3

 100 55
• Describe how you will complete each of these subtractions
102 – 67 =
134 – 23 =
113 – 78 =

In-depth Investigation: Which is Quicker?
Explore counting up in different sized steps; consolidate place value. Which is Quicker? from nrich.maths.org.

Extra Support

Find the Gap
Subtracting 2-digit numbers by using Frog (counting up), to give small answers, e.g. 53 - 47 and 70 - 55 (numbers either side of a multiple of 10, and subtracting from a multiple of 10)

Unit 3 Mental addition and subtraction (suggested as 2 days)

Objectives

Mental addition and subtraction
Unit 3: ID# 4211

National Curriculum
Num/PV (viii)

Hamilton Objectives
6. Add multiples of 1, 10, 100, 1000 without difficulty.
10. Mentally add and subtract any pair of 2-digit numbers or 3-digit multiples of 10.
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show 352 + 204 on a place value grid and demonstrate how we can add these numbers using number facts. Repeat to show 444 + 222 and 530 + 105. Then model using a place value grid for subtraction.
Group Activities
-- Choose the best method for adding and subtracting 3-digit numbers.
-- Generate 3-digit numbers to add and subtract using knowledge of place value.

Day 2 Teaching
Show labelled training shoes (see resources) on the Interactive Whiteboard. Pick 2 pairs. Children write the total cost on whiteboards. Discuss strategies. Repeat with other pairs. Say that each child has £99.99. Children pick one pair to buy and work out change.
Group Activities
Use the ‘Total £10’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use number facts and place value to add 4-digit amounts of money and find change from £99.99 and £100.

You Will Need

• Place value grids
• ‘Adding & subtracting using place value & number facts’ (see resources)
• ITP: Number spinners
• ‘Adding & subtracting 4-digit numbers' (see resources)

Mental/Oral Maths Starters

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

Suggested for Day 2
Add and subtract 10 and 100 to and from 4-digit numbers (simmering skills)

Procedural Fluency

Day 1
Use place value to add and subtract with 2-, 3- and 4-digit numbers.

Day 2
Use place value and number facts to add and subtract amounts of money.

Mastery: Reasoning and Problem-Solving

• Write the digits which will change when you do the following calculations:
(i) 367 – 31 = (ii) 405 + 200 =
(iii) 539 – 201 = (iv) 874 + 30 =
• Write the missing digits:
8☐5 + 33 = 918
74☐ – 42 = 701
☐56 – 236 = 4☐0
• True or false?
If you start with a 3-digit number and subtract 99 you will always have to change exactly 2 digits.

In-depth Investigation: Total £10
Using only digits 1-9 without the ‘5’, children find all possible pairs of amounts to make £10.

Extra Support

Perfect Pairs
Using place value to add and subtract amounts of money (without crossing multiples of 10p and one pound)

Unit 4 Subtraction: frog with 3-digit numbers (suggested as 3 days)

Objectives

Subtraction: frog with 3-digit numbers
Unit 4: ID# 4219

National Curriculum

Hamilton Objectives
12. Subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426–278, 321-87.
15. Estimate and use inverse operations to check answers to a calculation.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children ‘think, pair, share’ how Frog helps us. Maths Frog counts up to subtract. He starts at a smaller number and hops to the next 10 then 100. We then add his hops. Display 402 – 356. Draw an empty number line and model using Frog. Repeat for 513 – 469, 203 – 156, 612 – 565.
Group Activities
-- Make subtractions of 3-digit numbers and use Frog to solve them.

Day 2 Teaching
Write 421 – 356. Use Frog and model drawing a line starting at 356, draw a hop to 360, then a jump to 400, then a jump to 421. Use a bar diagram to show 534 – 479 and model using Frog to do it. Show how addition and subtraction relate. Write 416 – 363 = 53 and ask children to check the answer using addition (363 + 53 = 416).
Group Activities
Use the ‘Cats and Dogs’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Subtract 3-digit numbers to find given differences and check using addition to find incorrect answers.
-- Subtract 3-digit numbers from multiples of 100 and check using addition.

Day 3 Teaching
Work as a class to prepare a poster that will help children to subtract using Frog and check using addition. Use the poster to revise subtracting using Frog then checking the answer using addition. Demonstrate the whole class activity, playing one half of the class against the other, or Teacher against the class!
Group Activities
-- Subtract pairs of 3-digit numbers, target is to have the difference closest to 50 or 100. Check with addition.

You Will Need

• ‘Spinners’ sheets 1 to 3 (see resources)
• Paperclips
• Subtraction cards (see resources)
• The Subtraction Nasty Game (see resources)
• Subtraction grid game boards (see resources )
• 0–9 digit cards

Mental/Oral Maths Starters

Day 1
Pairs to 100 (pre-requisite skills)

Day 2
Change from £1 (pre-requisite skills)

Suggested for Day 3
Add pairs of 2-digit numbers, answer < 100 (simmering skills)

Procedural Fluency

Day 1
Use Frog to subtract 3-digit numbers.

Day 2
Use addition to check subtraction calculations with Frog.

Day 3
Use Frog to solve subtraction word problems, and check with addition.

Mastery: Reasoning and Problem-Solving

• Complete each diagram:
Diagram 1
 534 487

Diagram 2

 132 86

Diagram 3

 327 259
• Subtract 377, then 387, then 397 from 424.
• Find the difference between a pair of 3-digit numbers, each of whose digits adds to 9. For example, 306 – 261. Add the digits of your answer. Repeat three times. Say what you notice.

In-depth Investigation: Cats and Dogs
Children work to solve a puzzle involving adding two 3-digit numbers. They find several possible solutions, and then invent their own puzzle.

Extra Support

Frog Goes Further!
Subtracting 2-digit numbers from 100, e.g. 100 - 65
Beginning to subtract 3-digit numbers from the next multiple of 100, e.g. 200 - 165