Short Blocks

# Maths Year 1/2 Autumn Fractions and Multiplication

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Understanding halves and quarters (suggested as 2 days)

### Objectives

Understanding halves and quarters
Unit 1: ID# 12348

Y1: Find 1/2 and 1/4 of shapes.
Y2: Find 1/2 and 1/4 of shapes.

National Curriculum
Y1: Fr (i) (ii)
Y2: Fr (i)

Y1 Hamilton Objectives
15. Recognise, find, name a half as 1 of 2 equal parts of an object or shape.
16. Recognise, find and name a quarter as 1 of 4 equal parts of an object or shape.

Y2 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.

### Planning and Activities

Day 1 Teaching
Discuss colouring mats so that half is green and half is yellow. Stress that halves are equal.
Further Teaching with Y2
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, label each part.
Group Activities: T with Y2
Use the in-depth problem-solving investigation ‘Same shapes’ from NRICH as today’s group activity.
Or, use these activities:
Y1 -- Find half of shapes in different ways, including folding.
Y2 -- Identify whether shapes are correctly divided into halves or quarters; some children will fold shapes into halves and quarters.

Day 2 Teaching
Discuss colouring mats so that 1/4 is red and 3/4 is blue. Stress that quarters are equal.
Group Activities: T with Y1
Y1 -- Design party mats for Maisie by finding and shading quarters of shapes.
Y2 -- Find 1/4 by folding; shade 1/4s of shapes in different ways. Some children begin to find quarters of quantities.

### You Will Need

• A4 paper (including one pre-painted)
• Square of paper and yellow, green, red and blue paint
• Pre-cut shapes (circles, squares, semi-circles, equilateral triangles)
• ‘Shapes divided into two or four parts’ sheet (see resources)
• ‘Shapes to cut out and fold’ sheet (see resources)
• Rulers
• Additional activity sheets (see resources)
• Colouring pencils

Day 1
Count in 10s

Day 2
Doubles

### Worksheets

Day 1
Y1: Make party mats for Teddy by colouring halves of shapes.
Y2: Colours 1/2s and 1/4s of shapes.

Day 2
Y1: Colour 1/4 and 3/4 of shapes; recognise shapes that are not divided into equal quarters.
Y2: Match fractions to visual representations.

### Mastery: Reasoning and Problem-Solving

Y1

• Draw a line through each shape to cut it in half (including trapezium, octagon, oblong: see download).
• This strip of paper has been folded into four parts. Is each part a quarter?
• How many quarters in 1 whole cake?

Y2

• Fold an oblong into quarters. Can you take an identical oblong and fold it into quarters in a different way?
• Draw around 8 squares in a row in your maths book. Now colour three quarters of this ‘strip’.
• This strip of paper has been folded into four parts. Is each part a quarter? Explain your ideas clearly.

In-Depth Investigation: Same Shapes
Investigate how a selection of irregular shapes can be cut in half to make two shapes the same shape and size. Same Shapes from nrich.maths.org.

### Extra Support

Y1: Happy Halving
Spend time on this investigation to secure children’s understanding that each of 2 halves must be equal in size. Happy Halving from nrich.maths.org.

Y2: Birthday Cards
Finding halves of shapes by folding

## Unit 2 Doubling & halving; odd & even numbers (suggested as 3 days)

### Objectives

Doubling and halving; odd and even numbers
Unit 2: ID# 12364

Y1: Doubling and halving; odd and even numbers.
Y2: Doubling and halving; odd and even numbers.

National Curriculum
Y2: Mult/Div (iv)

Y1 Hamilton Objectives
2. Count in 2s.
13. Recognise doubles to double 5 and find related halves (half even numbers up to 10).
14. Solve simple problems involving multiplication/ division, find answers with support using objects, pictorial representations or arrays.

Y2 Hamilton Objectives
18. Double and halve numbers up to 20.
21. Solve multiplication/ division problems in context, doubling, halving.

### Planning and Activities

Day 1 Teaching
Show how to use fingers to double numbers 1-5.
Further Teaching with Y2
Use two bead strings to show doubles up to double 20.
Group Activities: T with Y2
Use the ‘Sock Doubles’ (Y1) or ‘Digit Sums’ (Y2) in-depth problem-solving investigations below as today’s group activity.
Or, use these activities:
Y1 -- Find the doubles dominoes and record the double fact, or play ‘Doubles Bingo’.
Y2 -- Use bead strings to find doubles of numbers up to 20. Some children will use recall of doubles to 20 to play a ‘Follow me’ game.

Day 2 Teaching
Double up to 10 pennies, say the corresponding half.
Further Teaching with Y1
Decide which numbers up to 10 (tomatoes) can be halved for two lunch boxes.
Group Activities: T with Y1
Y1 -- Investigate which numbers of cubes are odd and even numbers; note pattern on a 1-20 number track.
Y2 -- Investigate which amounts of money between 10p and 30p, or 20p and 40p, can be halved.

Day 3 Teaching
Whisper count in 2s along a number track, emphasising the even numbers. Recall definitions of odd and even.
Further Teaching with Y2
Halve strips of objects to find halves of even numbers up to 30. Introduce relationship between having and doubling on a bar model.
Group Activities: T with Y2
Y1 -- Game of finding odd and even numbers on a number track. Match up the socks to find the even numbers.
Y2 -- Find halves and their corresponding doubles.

### You Will Need

• Flipchart and pens
• Two 100-bead strings, rulers and sets of dominoes
• Bead strings and 1 to 6 Dice
• ‘Double numbers up to 20’ sheet (see resources)
• ‘Doubles to 20’ follow-me game cards (see resources)
• Pots of 20 pennies/counters
• Tomatoes or pictures of tomatoes on IWB
• 1-20 number track (see resources)
• Additional activity sheets (see resources)
• Pots of 10p and 1p coins
• 1-20 cards on washing line and pegs

### Short Mental Workouts

Day 1
Count to 100

Day 2
Count in 2s

Day 3
Double 1–5 and halves

### Worksheets

Day 1
Y1: Double numbers 1-6, or 2-10.
Y2: Find the doubles of numbers on a dartboard: 1-10 or 11-20.

Day 2
Y1: Recognise and order odd and even numbers 2-10 or 9-17.
Y2: Halve cake prices 2p-36p.

Day 3
Y1: Recognise odd and even numbers 2-9 or 2-15.
Y2: Double numbers 4-15; halve again. Use fraction strips to find missing numbers in doubling and halving sentences.

### Mastery: Reasoning and Problem-Solving

Y1

• Draw arrows to match each number to its double:
 4 4 2 10 5 6 3 2 1 8
• True or false?
An even number is always followed by an odd number.
One more than an odd number is an even number.
2 less than an even number is another even number.
• Who has an odd number of socks?
Edward: 20 socks
Jacob: 17 socks
Rachel: 16 socks
Bella: 10 socks
Charlie: 7 socks

Y2

• 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’?
• Double ☐ is 28. Half of ☐ is 16.
• Maia thought of a number. She doubled it and got 30. What was her number?
• I double a number, then subtract 2. My answer is 4. What was my number?
• Start on 1. Double and add 1. Double the answer and add 1. Keep going as long as you can!

In-Depth Investigations
Y1: Sock Doubles

Children double numbers 1 to 5 as part of a game, and find which answers from 1 to 10 are possible.

Y2: Digit Sums
Children find the sum of the digits in a sequence of numbers and compare the pattern found to that identified in the digits sums of the doubles.

### Extra Support

Y1
Double Trouble

Finding doubles up to double 5

Y2
Seeing Double

Finding and beginning to know by heart doubles from double 1 to double 10

Be Fair
Halving even numbers to 20

## Unit 3 Counting in steps of 5 and 10 (suggested as 2 days)

### Objectives

Counting in steps of 5 and 10
Unit 3: ID# 12380

Y1: Count in steps of 10 and 5.
Y2: Count in steps of 10 and 5; early multiplication.

National Curriculum
Y1: PV (ii); MD (i)
Y2: PV (i) MD (i) (ii)

Y1 Hamilton Objectives
2. Count in (2s) 5s, 10s.
14. Solve simple problems involving multiplication/division. Find answers with support using objects, pictorial representations or arrays.

Y2 Hamilton Objectives
16. Begin to know 10× and 5× tables; use × sign correctly.
19. Write multiplications, using × and = signs. Calculate answers.

### Planning and Activities

Day 1 Teaching
Count in 10s from 10 to 100 on the 1-100 grid. Count in 10s to find total of seven 10p coins. Write matching repeated addition and multiplication sentences. Discuss use of x symbol to show ‘lots of’.
Group Activities: T with Y1
Use the ‘Inside out’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y1 -- Spotting missing multiples of 10. Count 100 cubes in 10s.
Y2 -- Apply knowledge and understanding of counting in 10s to money. Begin to write number sentences using the multiplication sign.

Day 2 Teaching
Count in 5s from 5 to 50 on the 1-100 grid. Note ‘stripes’ pattern of multiples of 5, and that alternate numbers end in 0 or 5.
Further Teaching with Y2
Count in 5s to find total of 5p coins, write matching multiplication. Count in 5s to find total numbers of fingers, write matching multiplication.
Group Activities: T with Y2
Y1 -- Identify missing multiples of 5. Make handprint strips, to match given multiples of 5.
Y2 -- Count in 5s to find total numbers of fingers or amounts of money; record matching ‘lots of’ sentences or multiplication sign.

### You Will Need

• 1-100 number grid (see resources)
• 5p and 10p coins
• Multiples of 5 and multiples of 10 cards
• A box of 100 interconnecting cubes, e.g. Multilink
• 1-6 dice, 1–10 dice and 10p coins
• 10 strips of 10 stickers and Blu-tack
• Large strips of paper with multiples of 5 written at one end
• Trays of paint
• ‘Hands’ cards (see resources)

### Short Mental Workouts

Day 1
Count from 50 to 100 in 1s.

Day 2
Count in 10s.

### Worksheets

Day 1
Y1: Count on and back in 10s to fill in missing multiples.
Y2: Count in 10s to find totals and to find how many 10p coins are needed to pay for given items.

Day 2
Y1: Fill in missing multiples of 5 on ladder rungs.
Y2: Count in 5s to find totals of 5p coins.

### Mastery: Reasoning and Problem-Solving

Y1

• James has five of each coin in three separate piles.
2p 5p 10p
How much does he have in each pile?
• Write the missing numbers:
15, 20, 25, ☐, ☐, ☐
50, 60, 70, ☐, ☐, ☐
8, 10, 12, ☐, ☐, ☐, ☐
• Complete each sentence:
(a) 3 lots of 5 is ☐
(b) ☐ lots of 5 is 30
(c) 9 lots of ☐ is 90
(d) ☐ lots of 10 is100

Y2

• How many lots of 10 in 40?
• 25 is how many 5s?
• There are ☐ tens in 90.
• 2 × 10p = 20p; 10 × 2p = 20p What do you notice?
• 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: Inside Out
Children use their knowledge of inverse operations to calculate missing numbers in multiplication grids.

### Extra Support

Y1: Spider Counting
Counting in 10s from 10

Y2: Clever Counting
Counting in 10s from 10