Mathematics
Beginner
45 mins
Teacher/Student led
+90 XP
What you need:
IWB/Projector/Large Screen

Fractions of a Shape, a Length and a Set

Explore how fractions work across three different types: shapes, lengths and sets of objects. Use strips, chocolate bars and counters to see that one half, one quarter and one third mean the same thing everywhere.

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    1 - Getting Started ~4 mins

    Look at this chocolate bar and this tub of twelve counters. The bar is a long strip we can split along its length, and the counters are a pile we can share out. They are very different things, but here is a question for both of them: what would one half of each one look like?

    Key point

    Hands up: how would you split the chocolate bar to find one half? And how would you split the counters?

    2 - Watch and Notice ~9 mins

    Illustration for Watch and NoticeWatch the fraction strips on the board. Each strip is a length cut into equal parts, and we shade one part to show the fraction.

    One half of a strip

    Here a strip is split into two equal pieces and one is shaded. That shaded piece is one half.

    Before the next strip, hands up: which do you think is smaller, a half or a quarter?

    One quarter of a strip

    Now a strip is split into four equal pieces and one is shaded. That shaded piece is one quarter.

    One half and two quarters together

    The top strip shows one half shaded. The strip right below it is split into four pieces with two shaded — two quarters. Look across: the shaded part of the bottom strip lines up exactly with the shaded part of the top strip, so two quarters covers the same length as one half.

    One third of a strip

    This strip is split into three equal pieces with one shaded — one third.

    3 - Demonstrate a Shape ~5 mins

    We have seen a fraction of a length on the strips. Now let us see a fraction of a shape together on the board.

    Worked example

    Here is a rectangle. To find one quarter of it, we split it into four equal parts and shade just one. Watch how the rectangle is divided into four equal pieces first, then one piece is shaded. That shaded piece is one quarter of the whole rectangle.

    4 - Try It Together ~11 mins

    Now we work with sets of counters — a set of counters just means a group of counters. Each table has twelve counters. When I name a fraction, one pupil shares the counters at the board while the rest of us count along and predict how many will land in one group.

    Key point

    One half of the set, one quarter of the set, one third of the set — every time, we make equal groups and look at just one of them.

    Hands-on Task

    5 - Shade and Ring in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, draw a rectangle and shade one quarter of it. Then draw a line of eight dots and ring one half of them. Write how many dots are in your half.

    6 - Class Challenge ~8 mins

    Today we work through finding fractions of sets together at the board. Here are our four rounds:

    • One half of 6 counters
    • One half of 10 counters
    • One quarter of 8 counters
    • One third of 9 counters
    Key point

    Each time, share into equal groups and count just one group. We will tick each round off as we finish it.

    Hands-on Task

    7 - What Did We Notice? ~3 mins

    MATHS TALK

    How is finding one half of a shape the same as finding one half of a set of counters? What is the same about both, even though one is a strip and one is a pile of counters? Think about this: one half always means splitting into two equal parts and taking one, whether it is a shape, a length or a set.

    8 - What's Next ~2 mins

    What we learned today

    • A fraction can name a part of a shape, a part of a length or a part of a set of objects.
    • Every time, we split the whole into equal parts and look at one of them.
    • One half of a set means sharing into two equal groups and taking one group.

    Coming up

    Key point

    Next we will name more fractions — fifths, eighths and tenths — and see that the more equal parts we make, the smaller each piece becomes.

    Pupil practice
    Module 3 · Fractions and First Decimals Number
    Lesson 30 · Fractions of a Shape, a Length and a Set
    Download Activity Book page (PDF)
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