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Maths Year 3 Summer 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 Mentally add/subtract 1-digit numbers (suggested as 2 days)

Objectives

Mentally add/subtract 1-digit numbers
Unit 1: ID# 3733

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 and subtract.
14. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display 347 + 5. Discuss different strategies to find the answer. Encourage children to use number patterns and knowledge of facts, e.g. 7+5 = 12, so 347 + 5 = 352, or ‘bridging’ the next multiple of 10, i.e. 347 + 3 + 2. Repeat with 236 + 7 and 878 + 6. Then repeat to cross 100s, e.g. 498 + 4.
Group Activities
-- Play a card game where 1-digit numbers are added to 3-digit numbers.
-- Play a card and dice game where 1-digit numbers are added to 3-digit numbers.

Day 2 Teaching
Write 342 – 6 = 339. Is this correct? How do you know? We can solve this using number facts: 12 – 6 = 6, so 342 – 6 = 336. Also use bridging to do 342 – 2 – 4. Repeat with 352 – 7. Ask children to write two other subtractions that involve crossing a multiple of 10. Choose some to solve as a class.
Group Activities
Use the ‘Magical subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Play a card and dice game where 1-digit numbers are subtracted from 3-digit numbers.
-- Play a mystery subtractions game where 1-digit numbers are subtracted from 3-digit numbers.

You Will Need

• 3-9 cards and counters
• Whiteboards and pens
• ‘Set A’ and ‘Set B’ cards with 3-digit numbers (see resources)
• 1-6 dice
• ‘Set C’ and ‘Set D’ cards with 3-digit numbers (see resources)
• Strips of paper

Mental/Oral Maths Starters

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

Day 2
Subtract 1-digit numbers from teens numbers (pre-requisite skills)

Procedural Fluency

Day 1
Add 1-digit numbers to 3-digit numbers using number facts and ‘Target the 10’ strategies, including bridging through 10s and 100s.

Day 2
Subtract 1-digit numbers from 3-digit numbers using number facts and bridging: through 10s and 100s.

Mastery: Reasoning and Problem-Solving

Complete the bar models:
Diagram 1:

 ? 347 7

Diagram 2:

 ? 555 8

Diagram 3:

 342 7 ?

Diagram 4:

 623 8
• How many times can 7 be subtracted from 232 before the answer is less than 200?
• Kit says ‘If I keep adding 6 to 152, I’ll eventually reach exactly 200’. Is he correct?

In-depth Investigation: Magical Subtractions
Children subtract the digital root of a 3-digit number from that number. Magic ensues!

Extra Support

Hops to Fours
Bridging 10 when adding 1-digit numbers to 2-digit numbers, e.g. 48 + 5.

Unit 2 3-digit expanded and compact addition (suggested as 5 days)

Objectives

Add 3-digit numbers using expanded then compact column addition
Unit 3: ID# 3761

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
Write 654 + 567. One child calculates answer using expanded addition, another using compact addition. Remind both children to leave a space before drawing the lines for the answer. When children have finished, compare their workings and answers. Write 478 + 245, and 837 + 367. Use your preferred strategy to calculate the two answers.
Group Activities
-- Add two 3-digit numbers, using expanded and compact addition methods.
-- Make two 3-digit numbers using dice. Then add the numbers using compact addition.

Day 2 Teaching
Write 426 + 217, 742 + 276 and 587 + 278. Children round each to nearest 100, then add to estimate the total. Repeat, this time children round each to nearest multiple of 10; then use addition of 2-digit numbers to estimate total. Give 1 addition to each third of the class to find an exact answer. Compare with estimates.
Group Activities
-- Think mathematically to use chosen digits to make two (or three) 3-digit numbers with a total as close as possible to 600 (or 1000). Use compact addition.
-- Estimate the total of two 3-digit numbers; find the exact total using compact addition.

Day 3 Teaching
Write 48 + 26 + 35. Agree we could do this by adding the larger two numbers (83) and then the smallest. BUT we can also use column addition. This is especially useful if we are adding four 2-digit numbers. Model both expanded and compact addition for 45 + 28 + 63 + 38. Here, we had an extra 20 to add to the 10s! Children have a go with 36 + 45 + 58 + 23.
Group Activities
-- Add three or four 2-digit numbers, using expanded and compact addition methods.
-- Estimate the total when adding three or four 2-digit numbers, then find the answer using compact addition.

Day 4 Teaching
Write 43, 86, 27, 36, 18, 54, 72 and 67. Look for 3 numbers that might have a total close to 100. They check using column addition. How did you choose your numbers? Rounding to the nearest 10 can help. Now choose 3 numbers with a total near 150. Check using column addition. Now choose 4 numbers with a total near 150.
Group Activities
-- Look for 3 or 4 numbers that children estimate will have a total near given multiples of 10.
-- Play ‘missing digits’. Children work out the missing 1s digit in addition calculations.

Day 5 Teaching
Add 3 numbers where the digits in each number are the same, e.g. 33 + 44 +55. Share answers; discuss observations. Ask them to choose other trios of similar numbers to check if this is always the case. Can we write a ‘rule’ to describe what happens with additions like these? If one doesn’t work, check! [If the answer is a 3-digit number, the middle digit is the sum of the two digits on either side - a function of this being one of a certain group of multiples of 11; If the answer is a 2-digit number, both digits are the same].
Group Activities
Use the in-depth, whole-class, problem-solving investigation– Investigating 11– as today’s group activity.
-- Investigate patterns when adding three or four 2-digit numbers that have a difference of 11, e.g. 89+ 78 + 67.

You Will Need

• Whiteboards and pens
• 3-digit number cards (see resources)
• 2-digit number cards (see resources)
• Calculators
• 0 – 9 Dice
• Counters
• 0-9 cards
• 100s, 10s and 1s place value cards
• 2-digit number cards
• ‘Addition’ sheets 1 and 2 (see resources)
• ‘Estimating totals’ sheets 1 to 3 (see resources)
• ITP: Spinners

Mental/Oral Maths Starters

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

Day 2
Round 3-digit numbers to nearest 10 and 100 (pre-requisite skills)

Day 3
Add 4 single-digit numbers (pre-requisite skills)

Day 4
Add multiples of 10 (pre-requisite skills)

Suggested Day 5
Subtract single-digit numbers (simmering skills)

Procedural Fluency

Day 1
Use expanded or compact addition to add two 3-digit numbers.

Day 2
Choose two 3-digit numbers from those given to target one of several given target numbers. Estimate and find exact totals.

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

Day 4
Choose three 2-digit numbers from those given to target one of several given target numbers. Estimate and find exact totals.

Day 5
Add 3 or four 2-digit numbers using compact addition.

Mastery: Reasoning and Problem-Solving

• Choose a different method to solve each addition:
375 + 567 =
638 + 51 =
24 + 36 + 25 =
• Use column addition to help you to find each missing number:
548 + 175 = ☐
☐ – 356 = 387
635 + 296 = ☐
☐ – 466 = 247
• Sally has 45 Pokémon cards, Bill has 67, Jon has 28 and Parvati has 86. How many do they have altogether?
• Choose four of these numbers likely to give a total close to 200:
73 68 56 75 66 37
Add them using column addition. Is the closest possible total to 200?

In-depth Investigation: Investigating 11
Look for patterns when adding numbers with a difference of 11. See Day 5 group activity 1 for details.

Extra Support

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

Unit 3 Revise expanded and column addition (suggested as 4 days)

Objectives

Revise/secure understanding of expanded and compact column addition
Unit 5: ID# 3779

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

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.
14. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate both expanded & compact written addition: 46 + 27 + 52 + 17. Remind children to leave a space above the answer for ‘carry’ digits.
Write 82 + 32 + 47 + 25. How could we estimate the answer? Recall strategy to round each number to the nearest 10, then add these multiples of 10. Agree estimates, then use expanded or compact addition to find exact answer. Repeat for 63 + 18 + 36 + 55.
Group Activities
Use the ‘Mobile Towers’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Revise estimating totals and adding three or four 2-digit numbers using compact addition.
-- Estimate the total of four 2-digit numbers; find exact totals using column addition.

Day 2 Teaching
Write 378 + 123 + 285. Ask children to estimate the answer by rounding to nearest 100. Check estimate using first expanded column addition then compact. Remind children to leave a line above the answer. Repeat for 416 + 389 + 534.
Group Activities
-- Practise adding trios of 3-digit numbers, using either expanded or compact addition. Totals <1000 and >1000.
-- Estimate, then calculate, three costs that add up to <£1000.

Day 3 Teaching
Record expanded addition for £3.55 + £2.26. Demonstrate how we add the 1ps, the 10ps, the pounds and then add the 3 amounts together. Repeat with £4.72 + £2.54 pointing out what happens when you add 70p and 50p – a total more than £1. Children have a go at £4.59 + £2.25 and £4.72 + £3.59, choosing to use expanded or compact addition.
Group Activities
-- Practise using expanded or compact addition to add amounts of money.
-- Estimate then calculate multiple costs that add up to under £10.

Day 4 Teaching
Show four holiday items with prices £2.74, £1.43, £8.53 and £5.72. Choose two to buy for less than £5. Find their total, then calculate the change from £5 using Frog. Repeat to choose two for less than £10 & find change. Repeat for a pair under £20.
Group Activities
-- Choose two items that add up to under £5, £10 or £20 then calculate change.
-- Buy multiple items that add up to under £20, then calculate change.

You Will Need

• Whiteboards and pens
• Cards with 2 digit numbers on them
• ‘Adding three 3-digit numbers’ sheets 1, 2 and 3 (see resources)
• ‘Bicycles for sale’ sheet (see resources)
• ‘Adding amounts of money’ sheets 1 and 2 (see resources)
• Books with price tags £4.79, £3.14, £6.01, £5.49, £5.88, £5.25, £3.23, £4.65, £4.29, £2.35, £5.17, £2.52
• Items that might be for sale in a seaside shop e.g. sun cream, beach towel, bucket, spade with prices £2.74, £1.43, £8.53 and £5.72
• ‘The beach shop’ sheet (see resources)
• Coins and dice

Mental/Oral Maths Starters

Day 1
Round 3-digit numbers to nearest 100 (pre-requisite skills)

Day 2
Round amounts of money to the nearest pound (pre-requisite skills)

Day 3
Say the amount needed to make £1 (pre-requisite skills)

Suggested for Day 4
Add 3 multiples of 10 (simmering skills)

Procedural Fluency

Day 1
Round 2-digit numbers to the nearest 10; choose three or four of them to add up to approximate one of several target numbers.

Day 2
Round 3-digit numbers to the nearest 10; choose two or three of them to add up to approximate one of several target numbers.

Day 3
Round to the nearest pound to estimate each total. Then use column addition to ﬁnd the exact answer.

Day 4
Calculate the price of 2 items, and then the change from £5, £10 or £20.

Mastery: Reasoning and Problem-Solving

• Choose three of these numbers and write an estimate of their total:
475 386 287 349 248
Add the three numbers and compare the actual answer with your estimate. Repeat, choosing three different numbers. Was your second estimate closer?
• Work out the missing numbers in this addition puzzle:
£4 ☐p 8p
£7 80p ☐p
£☐ 60p 1p

In-depth Investigation: Mobile Towers
Children create 4 or five 2-digit numbers and add these to get different totals.

Extra Support

Addition of Three-digit Numbers
Using the interactive tool from Harcourt School at http://www.harcourtschool.com, children use base-10 blocks to explore regrouping in addition