Level 4: Working with fractions and decimals

Numbers · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 you met fractions and decimals as numbers: you placed them on the number line and compared them. In this level you calculate with them: add, subtract, multiply and divide, and for every rule you learn why it works, so you never have to trust a rule you cannot explain. Then the number line grows to the left with the negative numbers, and the level ends with the agreement that tells everyone in the world how to read a long calculation the same way.

Lesson	You will be able to
Adding and subtracting fractions	Explain why the denominators must match, find a common denominator, and add and subtract mixed numbers
Multiplying fractions	Find a fraction of a fraction with the area model, and explain why multiplying can make a number smaller
Dividing fractions	Divide by a fraction, and explain two ways why "multiply by the reciprocal" works
Calculating with decimals	Add, subtract, multiply and divide decimals, and explain where the decimal point goes
Fractions to decimals and back	Turn any fraction into a decimal, and predict whether the decimal stops or repeats
Negative numbers	Compare negative numbers, and add and subtract them with chips and on the number line
Order of operations	Work out long calculations in the agreed order, and explain why the agreement is needed

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