Mathematics
Advanced
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen
Equivalence reference card

Fraction, Decimal and Percentage Equivalence Mastery

Switch fluently between fractions, decimals and percentages using an interactive model. Master equivalence chains, including recurring decimals, and learn which form works best for comparing, calculating or sharing.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at these three: 3/8, 0.375 and 37.5%. Are they the same amount, or three different ones? And if they are the same, which one did you recognise fastest? Hands up when you have decided.

    2 - Watch and Notice ~9 mins

    3/8 = 0.375 = 37.5%

    Watch the first battery. Three eighths of the way up, and the same amount reads as 0.375 and 37.5%. To get the decimal, we divide three by eight, which gives 0.375. To get the percentage, we use the fact that percent means 'out of 100': we multiply the decimal by 100. So 0.375 × 100 = 37.5, and we add a per-cent sign to get 37.5%. Multiplying by 100 slides the digits two places, which is why the decimal point ends up two places to the right. Notice this is our first amount that runs to a third digit after the point, the thousandths place.

    2/5 = 0.4 = 40%

    Here is a tidier one. Two fifths fills the battery to 0.4 and 40%. Again, 0.4 × 100 = 40, so 0.4 = 40%. This one stops cleanly after one decimal place, much friendlier than three eighths. Before the next battery, predict: will seven eighths give us a tidy decimal or a long one?

    7/8

    Seven divided by eight gives 0.875, and 0.875 × 100 = 87.5, so 7/8 = 0.875 = 87.5%. Notice it is the mirror of three eighths, sitting high up the battery instead of low, but with the same half-percent tail.

    1/3 = 0.333… = 33.3…%

    Now the surprise. One third divided out is 0.333, but the threes never stop. A decimal whose digits repeat forever like this is called a recurring decimal. As a percentage it is 33.3…% , the threes running on forever there too.

    Here is how we write it, not just read it. Worked example on the board with 1/3:

    1. Divide: 1 ÷ 3 = 0.3333… (the digit 3 repeats without end).
    2. Write it with the phrase and so on: 0.333… means 0.333 and so on.
    3. Or use dot notation: put a single dot above the repeating digit, so 0.3̇. That one dot stands for the threes going on forever.
    4. The percentage form is written the same way: 33.3…% or 33.3̇%.

    Both writings mean the same amount. This is the one that does not fit neatly, and that is exactly why it is worth knowing how to write it.

    3 - Try It Together ~10 mins

    Key point

    Today we work through these fifths and quarters together, one after another: 1/5, then 2/5, then 3/5, and finally 3/4. Each time, one of us sets the battery to the fraction and the rest of the class reads off the decimal and the percentage before we check. The jump from fifths to that last quarter is where it gets interesting, so watch for it.

    Read off each fraction

    4 - Complete the Equivalence Table in Your Copy ~3 mins

    COPYBOOK MOMENT

    Illustration for Complete the Equivalence Table in Your CopyIn your maths copy, draw a three-column table headed Fraction, Decimal and Percentage. Each row gives you one form and you fill in the missing two. Underline the simplest fraction on each completed row.

    • 1/4
    • 0.5
    • 60%
    • 7/10

    5 - Class Challenge ~8 mins

    Key point

    Today's challenge builds up: match the battery to 25%, then 0.8, then 3/8, and finally the recurring stretch 1/3.

    Each target is given in a different form, so first work out where the battery needs to sit, then set it and check. The battery reads to the nearest whole percent, so round when the exact value does not land on a whole percent. Predict the level before each pupil sets it.

    Match the equivalent form

    Pupil practice
    Module 3 · Fractions, Decimals and Percentages Number
    Lesson 37 · Fraction, Decimal and Percentage Equivalence Mastery
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