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# Maths Year 2 Spring Place Value and Fractions

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 Ordinal numbers; properties of numbers (suggested as 4 days)

### Objectives

Ordinal numbers; place value, properties of 2-digit numbers and rounding
Unit 1: ID# 2521

National Curriculum
Num/PV (ii) (iii) (iv) (v)

Hamilton Objectives
3. Identify any number on 1-100 grid; understand that each is a multiple of 10 and some 1s. 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 to at least 100 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
Show children birthday cards with ordinal numbers. Ensure these include 1st, 2nd, 3rd and discuss how these are said and written differently. Children say these numbers. Look how 21st is written too. Show how ordinal numbers are written/said.

Group Activities
Use the ‘Racing Riddles’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Describe multi-coloured cube towers using ordinal numbers.
-- Work out secret messages using ordinal numbers.

Day 2 Teaching
Place 2-digit numbers on a large landmarked line. Discuss where different numbers go – between which multiple of 10. Make a flexible equals sign (see teaching) and then use this to demonstrate =, < and > with towers of cubes.
Group Activities
-- Record inequalities between two 2-digit numbers, using symbols for inequalities.
-- Pick 2-digit numbers to complete inequalities, using symbols for inequalities.

Day 3 Teaching
Write 32 on a tag, and ask a child to hang it after the 32nd bead on a 100 bead bar. Discuss how 32 is nearer 30 than 40 and explain that, if we are approximating, we round it to 30. Model how 37 rounds to 40. Continue with different numbers including 35, 25, 75 and 95.
Group Activities
-- Make 2-digit numbers and round them to the nearest 10.

Day 4 Teaching
Show children items priced: 17p, 25p, 32p, 49p, 55p, 63p, 74p, 86p and 99p. Round each to nearest 10p. Mark each on a 0-100 landmarked (in p) line. Discuss how 99p rounds to 100p which is £1.
Group Activities
-- Identify numbers that will round to a given 10.
-- Round prices to the nearest 10p to keep a running total.

### You Will Need

• Birthday cards
• Red, blue, green and yellow cubes
• Mystery messages sheets: ‘Work out the secret meeting spot’ and ‘Who will be at the secret meeting’ (see resources)
• 0-100 landmarked lines (see resources)
• Strips of black card, 2 brass fasteners and cubes to make =, < and > signs
• 1-9 digit cards and 1-100 grid
• 0-100 beaded lines (see resources)
• Two 100 bead strings and 100 bead bar
• Additional activity sheets (see resources)
• Objects and price labels up to £1

### Mental/Oral Maths Starters

Day 1
1 more/1 less (pre-requisite skills)

Day 2
Order 2-digit numbers (pre-requisite skills)

Suggested for Day 3
Place value (simmering skills)

Suggested for Day 4
Rounding (simmering skills)

### Procedural Fluency

Day 1
Solve puzzles with ordinal numbers.

Day 2
Complete a table showing inequalities.

Day 3
Round prices to the nearest 10p.

Day 4
Find numbers that round to given 10s – both down and up.

### Mastery: Reasoning and Problem-Solving

• In a race…
Ali came 4th, Bella came 2nd, Carrie came 6th and Dave came 3rd.
Draw the children (using stick drawings!) in the order they arrived. Draw and give names to the ones who came before and between them.
• Draw a line. Mark the ends 0 and 100. Draw marks for 59, 71, 19 and 91.
• Write numbers to make these sentences true.
☐ < 35
73 < ☐
13 < ☐ < 17
• How many numbers are less than 40 and more than 31?
• (a) Write all the numbers that round to 50 as the nearest 10.
(b) Write the numbers that round to 10 as the nearest 10.
Have you written the same number of answers in (a) and (b)?

In-depth Investigation: Racing Riddles
Children discuss the positions of four dogs in a set of four races using the information given. They attempt to use mathematical reasoning to answer questions and complete a table of results.

### Extra Support

Tag, You're It
Locating 2-digit numbers on a beaded line

More or Less
Comparing pairs of 2-digit numbers

## Unit 2 Properties of numbers, e.g. odd/even (suggested as 2 days)

### Objectives

Properties of numbers including odd/even
Unit 2: ID# 2531

National Curriculum
Num/PV (i) (iii) (vi)

Hamilton Objectives
1. Count from 0 in steps of 2.
3. Identify any number on 1-100 grid; understand that each is a multiple of 10 and some 1s.
6. Use place value and number facts to solve problems.
18. Double and halve numbers up to 20 and multiples of 5 to 50; recognise odd & even numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Highlight multiples of 2 on ITP Number grid. Discuss the stripy pattern. Ring 18 and ask a child to take 18 cubes and share them fairly with a friend. Try sharing 19 cubes. Write 3 really BIG numbers and discuss how we know they are even.
Group Activities
-- Sort numbers according to properties.
-- Play a choice of games to practise recognising odd and even numbers.

Day 2 Teaching
-- Show children a 100 grid; circle 24. Draw out what we can say about this number – its properties.
It’s even.
It’s between 20 and 30.
It’s a 2-digit number.
It’s greater than 20.
It’s not in the 10 times table.
Use properties of numbers to find other mystery numbers.
Group Activities
Use the in-depth problem-solving investigation ‘Part the piles’ from NRICH as today’s group activity.
Or, use these activities:
-- Decipher ‘mystery’ numbers from given clues.
-- Apply knowledge of number properties to decipher or write clues for ‘mystery’ numbers.

### You Will Need

• ITP: Number grid (see resources)
• 2 hoops
• Number cards 1-100
• ‘What am I?’ sheet (see resources)
• 1-50 number grid (see resources – preferably laminated)
• Blank cards to write on

### Mental/Oral Maths Starters

Day 1
Recognise multiples of 2 and 10 (pre-requisite skills)

Suggested for Day 2
Count in 2s (simmering skills)

### Procedural Fluency

Day 1
Make odd and even numbers from a range of given digits.

Day 2
Sort numbers into ‘sorting machines’ according to given criteria.

### Mastery: Reasoning and Problem-Solving

• How many numbers between 0 and 30 are even?
Are there the same number of odd numbers?
• True or False: Odd numbers are always made of ‘a multiple of 2 and 1 more’?
• Write even or odd beside each number:
(a) 368
(b) 492
(c) 661
How did you know the answer?
• Mystery number
My digits add to 10.
I am more than 65.
I am even. Is this the only possibility?
• Can you write a number which belongs in both the ‘multiples of 5’ set and the ‘even numbers’ set? And another? And another? What other property do all these numbers have in common?
• Can you write a number which belongs in both the ‘multiples of 10’ set and the ‘odd numbers’ set?

In-depth Investigation: Part the Piles
Find a strategy to stop an opponent from being able to split piles of counters into unequal numbers. Part the Piles from nrich.maths.org.

### Extra Support

Blues and Twos
Counting in 2s from 1 and from 2

## Unit 3 Find fraction of shapes (1/2, 1/4, 1/3) (suggested as 2 days)

### Objectives

Find fractions (1/2, 1/4, 1/3) of shapes
Unit 3: ID# 2539

National Curriculum
Fr (i) (ii)

Hamilton Objectives
23. Begin to recognise the equivalence of 2/4 & 1/2 on the number line & in other practical contexts.
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, and quantities.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate halves and quarters by asking children to fold a piece of A4 paper into first 1/2 and then into 1/4s. Stress that these are equal parts of the shape. Then fold another piece of paper into 1/3s.
Group Activities
Use the in-depth problem-solving investigation ‘Halving’ from NRICH as today’s group activity.
Or, use these activities:
-- Identify whether shapes are correctly divided into halves, quarters or thirds.
-- Fold shapes into halves, quarters or thirds.

Day 2 Teaching
Draw a square; divide it into 1/4s. Shade 3/4. How much is coloured? Record ‘three quarters’ and 3/4. Ask children to draw a square on their whiteboard and to colour in 3/4 in a different way to yours. Repeat for an oblong and a circle. Show a variety of children’s whiteboards.
Repeat for thirds, using a square, oblong and a circle.
Group Activities
-- Shade 1/4s or 1/3s of shapes.
-- Design then play snap or pairs with fractions and shaded shapes.

### You Will Need

• Pieces of A4 paper
• ‘Square and circle’ sheet (see resources)
• ‘Shapes divided into two or four parts’ sheet (see resources)
• ‘Shapes divided into two, three or four parts’ sheet (see resources)
• Additional activity sheets (see resources)
• Card & colouring pencils

### Mental/Oral Maths Starters

Suggested for Day 1
Odds and evens (simmering skills)

Suggested for Day 2
Doubles (simmering skills)

### Procedural Fluency

Day 1
Colour 1/2s, 1/4s and 1/3s of shapes.

Day 2
Match fractions to visual representations.

### Mastery: Reasoning and Problem-Solving

• Fold an oblong into quarters.
Can you take an identical oblong and fold it into quarters in a different way?
• Draw around 6 squares in a row in your maths book. Now colour one third of this ‘strip’.
• How much of each strip is shaded?
Diagram 1
 //

Diagram 2

 // //

Diagram 3

 // //

Diagram 4

 // //
• Katie says that the shaded part of this strip is 1/3 of the whole because there is 1 part shaded out of 3 parts in the whole.
Do you agree?

 //

In-depth Investigation: Halving
Find creative ways to split squares into halves. Halving from nrich.maths.org.

### Extra Support

Birthday Cards
Finding halves of shapes by folding

## Unit 4 Find fractions of amounts (1/2, 1/4, 1/3) (suggested as 3 days)

### Objectives

Find fractions of amounts (1/2, 1/4, 1/3)
Unit 4: ID# 2549

National Curriculum
Fr (i) (ii)

Hamilton Objectives
23. Begin to recognise the equivalence of 2/4 & 1/2 on the number line & in other practical contexts.
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, and quantities.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Count out 10 sweets and show how we can share these with a friend by splitting into 2 piles, or by knowing the number fact. Repeat to share 8 cubes between 4 friends - into quarters. Stress each quarter is the same. Repeat to share 12 cubes into thirds. Stress that each third is the same.
Group Activities
Use the in-depth problem-solving investigation ‘Fair Feast’ from NRICH as today’s group activity.
Or, use this activity:
-- Share cubes to find 1/2s, 1/4s and 1/3s of amounts.

Day 2 Teaching
Show children a box of 16 pens. Say the office has ordered pens and we are allowed to keep 1/4 of them. Discuss ways of finding 1/4 of 16. Include finding half and half again. Repeat to find 1/4 of 20 pens.
Group Activities
-- Solve stationery fraction problems.
-- Explore finding 1/2s and 1/4s of various numbers.

Day 3 Teaching
Show children 12 Smarties™ and 2 cakes. Discuss how we can share the Smarties™ fairly between the cakes. Repeat with 4 cakes. Now we need to find 1/4 of the sweets. Repeat with 3 cakes. Now we need to find 1/3 of the sweets.
Group Activities
-- Find Smartie™ fractions through sharing.
-- Sort numbers according to sharing results.

### You Will Need

• ‘Fractions cards’ sheets (see resources)
• Cubes, board pens & piece of A4 paper
• ‘Stationery problems’ sheet (see resources)
• ‘Number cards’ sheet (see resources)
• Doubles and halves dartboard from topmarks.co.uk
• Addtional activity sheets (see resources)
• Play dough, cupcakes & Smarties

### Mental/Oral Maths Starters

Day 1
Halving (pre-requisite skills)

Suggested for Day 2
Doubling (simmering skills)

Suggested for Day 3
Telling the time (simmering skills)

### Procedural Fluency

Day 1
Finding fractions of numbers using cubes.

Day 2
Halving and quartering numbers using number facts.

Day 3
Finding fractions of bigger numbers.

### Mastery: Reasoning and Problem-Solving

• Use the image to complete each number sentence, using <, > or =.
 1/2 1/2 1/3 1/3 1/3 1/4 1/4 1/4 1/4

1/2 ☐ 1/3
2/4 ☐ 1/2
1/4 ☐ 1/3

• Complete each sentence.
1/4 of 20 is _____
1/3 of 12 is _____
1/2 of 24 is _____
• Look at this bar diagram:
 12 3 3 3 3

It shows that 1/4 of 12 is 3
Write a fraction sentence to match each bar diagram below:
Diagram 1

 22 11 11

Diagram 2

 15 5 5 5

Diagram 3

 8 2 2 2 2
• 18 children are in a class and 1/3 are boys. How many are girls?
10 of the 15 children in a class are girls. What fraction are boys?

In-depth Investigation: Fair Feast
Help Petros and Michael to share a picnic equally. Fair Feast from nrich.maths.org.

### Extra Support

Fair Cakes
Finding half of quantities by sharing