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# Maths Year 2 Summer Calculation

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 Fractions of amounts; count in fractions (suggested as 2 days)

### Objectives

Fractions of amounts; counting in fractions
Unit 1: ID# 2861

National Curriculum
Fr (i) (ii)

Hamilton Objectives
22. Count in halves and quarters, recognising fractions as numbers.
24. Understand 1/2, 1/4, 1/3, 3/4, 2/3 as fractions of quantities in a practical context. Solve problems using shapes, objects, quantities.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show 16 counters on the Interactive Whiteboard. Demonstrate how we can find 1/2 by sharing and then find 1/4 by halving a half. Display the sequence of ‘Design a flag’ images to model different ways to represent 1/2, then 1/4 of 24 squares.
Group Activities
-- Shade flag templates to show halves and quarters of amounts.

Day 2 Teaching
Show children 12 bricks in the centre of the circle. Write 1/4 of 12 and discuss how to find a quarter by sharing the bricks into 4 piles. Model sharing 15 bricks between 3 piles to find 1/3. Display a bar model (see resources) split into thirds. Discuss how this relates to sharing the bricks. Model finding 1/3 of 21. Repeat for 1/4 of 40, 3/4 of 40 and 2/3 of 12.
Group Activities
-- Find 1/3s and 1/4s of amounts, using bar models to represent whole and fraction parts.
-- Use an online game to practise calculating 1/4 and 3/4 of amounts.

Day 3 Teaching
Write 1/2 of □ = □. In pairs, children discuss what numbers might complete the sentence. Test ideas, using Interactive Whiteboard counters if required. Display 1/2 of 5 = 10. Now you be the teacher. Is this correct? Repeat with 1/4 of □ = □. Display 1/3 of 12 = 6. Is this correct? Repeat with 1/3 of □ = □.
Group Activities
-- In a game context, complete as many fraction number sentences as possible to show 1/2, 1/3 or 1/4 of amounts to 12 (or 20 or 30).

### You Will Need

• ‘Design a Flag’ sheets 1–6 (see resources)
• ‘Design your own flags’ sheets 1 and 2 (see resources)
• Coloured pencils and counters
• ‘Fractions: bar models’ (see resources)
• Additional activity sheets (see resources)
• Number cards or tiles: numbers 1 to 12 (and some to 20 or 30)
• ITP: Number Grid

### Mental/Oral Maths Starters

Day 1
Count on in 3s (pre-requisite skills)

Day 2
Understanding division as the inverse of multiplication (pre-requisite skills)

Suggested for Day 3
Equivalence (simmering skills)

### Procedural Fluency

Day 1
Design a range of bookmarks based on given combinations of 1/2s and 1/4s.

Day 2
Complete bar models.
Use to calculate 1/4, and 1/3 of amounts.
Use to calculate unit and non-unit fractions of amounts.

Day 3
Calculate the missing numbers or fractions in number sentences finding fractions of amounts.

### Mastery: Reasoning and Problem-Solving

• Find 1/2 of each amount.
£24
£44
£60
Now find 1/4 of each amount.
• What is 1/3 of 30? Use this answer to find 1/3 of 60.
• Complete each sentence using the bar models to help.
3/4 of 24 = ☐
 24

2/3 of 18 = ☐

 18

3/4 of 44 = ☐

 44

In-depth Investigation
Use the Group activity from Day 1.

### Extra Support

Fractions on the Beach
Finding 1/2 and 1/4 of amounts (whole number answers)

## Unit 2 Tell digital and analogue time confidently (suggested as 2 days)

### Objectives

Telling the time with confidence on digital and analogue clocks
Unit 2: ID# 2879

National Curriculum
Meas (vi) (vii) (viii)

Hamilton Objectives
29. Tell/write the time on digital/analogue clocks to 1⁄2 past, 1⁄4 past and 1⁄4 to the hour; draw hands on a clock face to show these times.
30. Begin to tell and write the time on digital and analogue clocks to the nearest 5 minutes.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a ‘Hamilton clock’, reminding children that when the minute (long) hand is in the pink it is a ‘past’ time, when it is in the blue it is a ‘to’ time. Relate this to digital times: minutes ‘past’ the hour. Count round the Hamilton clock in 5s to read digital times, such as 5:45. We don’t say 45 minutes past 5, as this is a blue ‘to’ time: 15 minutes to 6 or quarter to six. Repeat with other ¼- and ½-hour times, displaying the analogue clock alongside the hidden digital clock and asking children to write the corresponding digital time on their whiteboards. Reveal the digital display to allow children to self-check.
Group Activities
-- Match cards showing analogue and digital times.
-- Match cards showing analogue and digital times, one set showing times 15 minutes later than the other.

Day 2 Teaching
In pairs, children have a mini clock and a whiteboard/pen. Say a time: half past three. They show the time in analogue (on a clock) and in digital (written on a whiteboard). Repeat with other times. Model making times on Tell the time ITP clocks. Reiterate equivalences between ‘quarter to’ and ‘45’ past on the digital clock.
Group Activities
Use the in-depth problem-solving investigation ‘What Is the Time?’ from NRICH as today’s group activity.
Or, use these activities:
-- Given a time written in words, create analogue and digital equivalents.
-- Given a time written in words, create analogue and digital equivalents to the nearest 5 minutes.

### You Will Need

• ‘Analogue clock’ (see resources)
• ITP: Tell the time
• Digital clock and small analogue clocks
• Mini-whiteboards and pens
• ‘Matching analogue and digital times’ sheets 1 and 2 (see resources)
• ‘Clock time cards’ sheets 1 and 2 (see resources)
• (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count in 5-minute intervals (pre-requisite skills)

Day 2
Tell the time to the nearest 5 minutes in analogue and digital (pre-requisite skills)

### Procedural Fluency

Day 1
Find matching sets of three cards: one analogue, one digital and one written time.

Day 2
Read times and give analogue times 15 minutes later.

### Mastery: Reasoning and Problem-Solving

• What number is the minute hand pointing at when the clock shows these times? Count in 5s to find out.
(a) quarter past 8
(b) quarter to 4
(c) twenty past 1
(d) twenty to 7
(e) twenty-five past 9
(f) ten to 3
(g) five to 12
• Draw lines to match each written time to a digital time:
Quarter past 3 3:45
Ten past 12 10:50
Quarter to 4 3:15
Ten to 11 5:40
Twenty past 3 12:10
Five to 2 3:20
Twenty to 6 1:55

In-depth Investigation: What is the Time?
Can children put these times on the clocks in order? What is the Time? from nrich.maths.org.

### Extra Support

Time to Match
Telling the time to the half hour on analogue and digital clocks. Saying the time half an hour later.

## Unit 3 2- & 3-digit numbers on line; round to 10 (suggested as 3 days)

### Objectives

Placing 2-digit and 3-digit numbers on a line; rounding to nearest 10
Unit 3: ID# 2887

National Curriculum
PV (iii) (iv) (v) (vi)

Hamilton Objectives
4. Locate any 2-digit number on a 1–100 grid or a landmarked line; use this to order and compare numbers with <, > and = signs.
5. Read and write numbers in numerals; (make recognisable attempts to write in words).
6. Use place value and number facts to solve problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a line from 0–100 with only 0 and 100 land no other marks. Where can we mark 47? Discuss how it is helpful to mark 50. Then discuss how to place other numbers and agree that marking all multiples of 10 is helpful to locate other numbers. Then play ‘guess my number’ with two children forming the ends of the 0–100 line.
Group Activities
-- Sketch number lines; estimate the position of 2-digit numbers between 0 and 100 as accurately as possible.
-- Estimate the value of mystery numbers on a 0–100 sketched line by considering nearby 10s.

Day 2 Teaching
Display 0–10 number line (see resources), point to 3 and ask: Is this closer to 0 or 10? Repeat for other numbers. Explain that we call this ‘rounding to nearest ten’. Spend time talking about 5, explaining that, although it is in the middle, we always round up to the 10 above. Repeat for numbers between 30 and 40, to include 35.
Group Activities
Use the in-depth problem-solving investigation ‘Which scripts?’ from NRICH as today’s group activity.
Or, use these activities:
-- Mark 2-digit numbers on a line; round to nearest 10. Create a poster to explain rounding.
-- Play ‘Rounding Pelmanism’.

Day 3 Teaching
Show a 101–200 square (see resources). Count from 101 to 200, pointing at the numbers and noting they follow the same patterns as 1 to 100. Show a 0–100 beaded line. How could we change this 0–100 beaded line to be a 100–200 beaded line? Amend 0 to 100, 100 to 200. What should we change 10 to? And 20? etc. Count in 10s from 100 to 200. Mark on various 3-digit numbers to 200.
Group Activities
-- Order 3-digit numbers between 100 and 200; locate on a beaded or landmarked line.
-- Place 3-digit numbers on a landmarked line.

### You Will Need

• Mini-whiteboards and pens
• 1–9 digit cards
• A4 book with 1cm squared paper
• ‘0–100 landmarked line’ (see resources)
• ‘0–10 landmarked line’ (see resources)
• ‘30–40 landmarked line’ (see resources)
• 1–9 dice
• Additional activity sheets (see resources)
• Sticky notes
• ITP: Number Grid

### Mental/Oral Maths Starters

Day 1
Mark 2-digit numbers on a landmarked line (pre-requisite skills)

Day 2
Round 2-digit numbers to the nearest 10 (pre-requisite skills)

Suggested for Day 3
Recognise multiples of 2 and 5 (simmering skills)

### Procedural Fluency

Day 1
Identify numbers indicated by arrows on a 0-100 beaded or landmarked line. Mark given numbers on the line.

Day 2
Round 2-digit numbers to the nearest 10.

Day 3
Identify numbers indicated by arrows on a 100-200 beaded or landmarked line. Mark given numbers on the line.

### Mastery: Reasoning and Problem-Solving

• Rewrite these numbers in order, smallest to largest.
93
121
39
189
200
75
175
• Fill in the missing numbers in these portions of the 101–200 grid: Diagram 1
 153 154

Diagram 2

 174
• Round each of these numbers to the nearest 10:
71, 89, 124, 95, 147, 185

In-depth Investigation: Which Scripts?
There are six numbers written in five different scripts. Can children sort out which is which? Which Scripts? from nrich.maths.org.

### Extra Support

Placing numbers on a 0–100 landmarked line

## Unit 4 Place value in 3-digit numbers (suggested as 2 days)

### Objectives

Beginning to understand place value in 3-digit numbers
Unit 4: ID# 2897

National Curriculum
PV (ii) (iii) (vi)

Hamilton Objectives
3. Identify any number on 1-100 grid; understand that each is a multiple of 10 and some ones. Extend to 3-digit numbers.
6. Use place value and number facts to solve problems, e.g. 60 - ☐ = 20.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show children your large 100s, 10s and 1s place value cards. Hold up 100, 20 and 4, then combine them to make 124. Give each pair a set of small place value cards. They order the 100s, 100 to 900. Count along in 100s together. Lay out the tens and ones cards in order. Find 100, 30 and 5 to make the number 135. Make other 3-digit numbers, recording place value additions, i.e. 400 + 20 + 7 = 427. Use the Place value ITP to show how different 3-digit numbers are made.
Group Activities
Use the in-depth problem-solving investigation ‘Sixteen rocks’ as today’s group activity.
Or, use this activity:
-- Make a 3-digit number and write the corresponding place value addition. Create and solve place value additions with missing numbers.

Day 2 Teaching
Addition: Give children place value cards: hundreds, tens and ones. They make and say different 3-digit numbers. Model how to write each one as a place value addition: e.g. 123 = 100 + 20 + 3. Use these cards to write other additions, e.g. 120 + 3 = 123, 100 + 23 = 123, 103 + 20 = 123.
Children work with a partner to make 345, then write as many additions as they can that use these cards.
Subtraction: Make and display the number 342. How could we ‘zap’ the digit 4 to leave a zero in its place: 302. Would there be a zero if we subtracted 4? Why not? Make the number with your cards and try out some ideas. Record 342 – 40 = 302. The 4 is in the 10s place, so to ‘zap’ the 4, we need to subtract 4 tens: 40. How could we get the 4 digit back again? Agree that you must add 40. Record 302 + 40 = 342. Repeat to ‘zap’ the 2, recording 342 – 2 = 340.
Group Activities
-- ‘Zap’ digits in a 3-digit number by subtracting amounts with the appropriate place value.
-- Complete missing numbers in place value additions and subtractions.

### You Will Need

• Large place value cards
• Sets of small place value cards
• ITP: Place value
• Mini-whiteboards and pens
• ‘Place value addition’ (see resources)
• Calculators

### Mental/Oral Maths Starters

Day 1
Place value (pre-requisite skills)

Day 2
Compare numbers between 100 and 200 (pre-requisite skills)

### Procedural Fluency

Day 1
Partition and recombine 3-digit numbers to complete place value additions.

Day 2
Complete number sentences for place value additions and subtractions.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers:
400 + ☐ + 5 = 475
☐ + 40 + ☐ = 646
200 + ☐ + ☐ = 202
964 – ☐ = 904
731 – ☐ = 31
• Add 10 to each number.
452
200
673
101
395
• Roll a 1–9 dice three times to create three different digits, e.g. 2, 1, 6. What is the largest 3-digit number you can create? And the smallest? How many other numbers are there in between? List them all in order, smallest to biggest.

In-depth Investigation: Sixteen Rocks
Children arrange place value cards to make 3-digit numbers and then add the digits. They look at patterns.

### Extra Support

10s Neighbours
Saying a number between neighbouring multiples of 10, e.g. between 40 and 50.