Math Foundations
Fractions
Cut the world into equal parts — then learn to put it back together.
THE SYLLABUS dev · all lessons unlocked
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Finding Half
Colour one half of a shape, however it's cut.
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Combining Parts
Combine unequal pieces — even triangles — to make a fraction.
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Splitting Parts
A unit fraction is one of the SMALL equal parts — not any big region. Split a big piece into equal parts to read a fraction.
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Splitting and Combining
To make a fraction you can split a big piece OR combine small pieces. Pieces of the same size count equally, even when their shapes differ.
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Equal Parts
You can only name a fraction when the whole is cut into EQUAL parts — equal-looking is not enough.
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Level Review
Prove the whole level on fresh shapes — colour, combine, split, and judge equal parts on your own.
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II
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Sixths and Twelfths
Name fractions in sixths and twelfths, and see that finer parts give a new name for the same amount (4/6 = 8/12).
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Eighths and Sixteenths
Name fractions in eighths and sixteenths, and see that a finer split gives a new name for the same amount (6/8 = 12/16).
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Making Equivalent Fractions
Multiply the top and the bottom by the SAME number and the value is unchanged.
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Simplifying Fractions
Divide top and bottom by a common factor to write a fraction in its simplest form.
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Equivalent Fractions
Multiplying and dividing top and bottom are two directions of the one idea: renaming without changing the amount.
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Identifying Equivalents
Read shapes by their shaded amount to tell which fractions truly match and which only look close.
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Level Review
Prove the whole level on fresh numbers — recognise, make, simplify, and identify equivalents.
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Comparing Numerators
When the bottoms match, the parts are the same size — so more of them is more.
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Comparing Denominators
When the tops match, you're comparing piece sizes — the smaller bottom means bigger pieces.
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Comparing Equivalents
Compare two fractions when one denominator is a multiple of the other by renaming to a shared denominator, then comparing numerators.
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Comparing More Equivalents
To compare any two fractions, rewrite them with the same bottom, then compare the tops.
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Identifying the Greatest
Put all your comparison methods together to pick the greatest from a set of four.
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Level Review
One skill, tested on fresh numbers across all four methods — which fraction is greater?
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IV
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Adding Fractions
Add fractions by combining shaded areas — shade one part, then the other, and read the total (e.g. Find ¼ + ⅛).
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Adding Same-Sized Fractions
When denominators match, add the numerators and keep the denominator.
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Adding Unlike Parts
Make the parts the same size with equivalent fractions, then add the tops.
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Adding Unit Fractions
When neither bottom divides the other, multiply them: the grid has a×b cells.
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Adding Any Fractions
Non-unit tops and the cross-multiply rule: multiply each fraction by the other's bottom.
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Level Review
A ten-question spiral of everything in Level 4 — shade, rewrite, and add.
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Multiples of Fractions
Multiplying a whole number by a fraction is repeated addition — Find N × 1/d by shading N groups.
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Expressing Multiples
To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator.
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Fractions of Unit Fractions
Taking a fraction OF a fraction means multiplying — and 1/b of 1/d is one cell of a b×d grid.
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Products of Unit Fractions
To multiply two unit fractions, keep the one on top and multiply the denominators.
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Fraction of Any Fraction
For any two fractions, the answer is a block of the grid: multiply the tops and multiply the bottoms.
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Multiplying Fractions
To multiply any two fractions, multiply the tops and multiply the bottoms.
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Level Review
Prove the whole level on fresh numbers — multiples, a fraction of a fraction, and multiplying across.
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