A fraction is a number of equal parts of a whole, and a point on the number line. This unit builds the idea up: how cutting parts finer gives the same amount a new name, how fractions bigger than one are written, how to compare and order them, and how to add, subtract, multiply and divide them, each from a picture before a rule.
Every idea is something you can move: cut a bar finer and watch its shaded end stay put, fill boxes with parts, recut two fractions into the same size of part, overlap columns and rows, lay copies along a length, and run long division one digit at a time. Lesson 7 uses a scientific calculator, once, to see what a display does with a decimal that never ends.
The lessons, in order
- Lesson 1 · Equivalent fractions A fraction as a number of equal parts of a whole and a point on the number line, equivalent fractions by multiplying or dividing top and bottom, and simplest form. Cut every part of a bar finer and watch the shaded end stay put, then divide top and bottom until nothing else divides both. No calculator
- Lesson 2 · Improper fractions and mixed numbers Improper fractions and mixed numbers: writing a count of equal parts as wholes and a part, and writing a mixed number as a count of equal parts. Fill whole boxes with parts to turn a count into a mixed number, then walk a number line from a mixed number to a count of parts. No calculator
- Lesson 3 · Comparing and ordering fractions Comparing and ordering fractions with a common denominator found from the lowest common multiple, with one half as a benchmark, and placing fractions on a number line. Recut two fractions into parts of the same size to see which is greater, then order three fractions on a zoomed number line. No calculator
- Lesson 4 · Adding and subtracting fractions Adding and subtracting fractions and mixed numbers by writing them over a common denominator, and why the bottom number is not added. Recut two fractions into the same size of part and join or take away, then see what adding the bottoms too would give. No calculator
- Lesson 5 · Multiplying fractions Multiplying fractions, whole numbers and mixed numbers with an area model, simplifying before multiplying, and a fraction of an amount. Draw a fraction of a fraction as an overlap of columns and rows, then cancel common factors before multiplying. No calculator
- Lesson 6 · Dividing fractions Dividing by a fraction as how many fit, the reciprocal, dividing with whole and mixed numbers, and the order of operations with fractions. Lay copies of a fraction along a length to count how many fit, then group parts of a whole to see the reciprocal. No calculator
- Lesson 7 · Terminating and recurring decimals Fractions as divisions, terminating and recurring decimals, which fractions terminate, and writing a recurring decimal as a fraction. Run long division one digit at a time to see a decimal stop or repeat, then line a repeating decimal up with a shifted copy to find its fraction. Scientific calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.