# Maths Year 3/4 Autumn Fractions

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

## Doubling, halving and the concept of a half(suggested as 3 days)

### Planning and Activities

Day 1 Teaching
Quick practice doubling 1-digit numbers and multiples of 10 less than 50.
Model doubling of 2-digit numbers, using a jotting to show partitioning and recombining.
Further Teaching with Y3
Further doubling of 2-digit numbers, using place value cards to support, e.g. for 34, 46 and 57.
Group Activities: T with Y4
Use the ‘Doubling forever’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Doubling 2-digit numbers: either to 50, or numbers greater than 50.
Y4 -- Doubling any 2-digit number.

Day 2 Teaching
Model halving of 2-digit numbers by partitioning and recombining, including examples with odd tens digit.
Further Teaching with Y4
Revisit halving and doubling multiples of 100. Introduce doubling and halving of 3-digit numbers by partitioning and recombining.
Group Activities: T with Y3
Y3 -- Halving 2-digit numbers, including money amounts; check by doubling.
Y4 -- Doubling and halving 3-digit numbers; reasoning about strategies.

Day 3 Teaching
Quick practice halving multiples of 10 (to 90).
Model halving odd numbers (2-digts) using partitioning and recombining.
Further Teaching with Y3
Find half of 3, 5, 7, 9 then 5, 25, 45 and 65; reason about patterns.
Group Activities: T with Y4
Y3 -- Find halves, describing patterns of halves in different number sequences: 2-digit numbers.
Y4 -- Find halves, describing patterns of halves in different number sequences: 2- and 3-digit numbers.

### You Will Need

• ‘Double up’ (see resources)
• Hundreds, tens and ones place value cards
• Place value dice or number cards 0–9
• Flipchart and pens
• ‘Chocolate bars – half price sale!’ (see resources)
• Whiteboard and pens
• Cubes or counters
• ‘Halving even numbers’ (see resources)
• Interlocking cubes (including 1/2 cubes if you have them)

### Short Mental Workouts

Day 1
Doubles to Double 20

Day 2
Halve multiples of 10

Day 3
Count in 5s and 10s

### Worksheets

Day 1
Y3: Identify fractions of shapes shaded.
Y4: Identify equivalent fractions (visual models).

Day 2
Y3: Compare Fractions.
Y4: Compare Fractions.

Day 3
Y3: Shade parts of circles to show mixed numbers.
Y4: Write improper fractions as mixed numbers (and vice versa).

### Mastery: Reasoning and Problem-Solving

Y3

• Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? Repeat, starting at 4. How many this time?
• Write the missing number(s) in these bar diagrams:
Diagram 1
 ? 36 36

Diagram 2

 52 ? ?
• Starting with 72, keep halving until you reach a 1-digit number. What is half of that number?

Y4

• Write two sentences to relate these three numbers: 37, 74 and 148.
• Use a jotting to double these numbers:
i) 216 ii) 327 iii) 438
Describe any pattern in the answers.
• Starting with 576, keep halving until you reach a 1-digit number. What is half of that number?

In-depth Investigation: Doubling Forever
Children double numbers up to 10 (Y3) or 20 (Y4) and look for duplicate sequences.

### Extra Support

Y3: Double and Halves
Doubling multiples of 5; Halving multiples of 10

Y4: Double or Halve?
Doubling and halving 2-digit numbers using partitioning (whole number answers only)