Fractions and bar models
Build and connect the representations and methods in fractions.
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Before you begin
Build and connect the representations and methods in fractions.
Learning goals
- Express a whole-number quotient as a fraction
- Express a general fraction as a decimal
- Add and subtract mixed-number amounts
- Multiply a proper fraction by a whole number
- Multiply an improper fraction by a whole number
- Multiply two proper fractions
- Multiply a proper and an improper fraction
- Multiply two improper fractions
- Multiply a mixed number by a whole number
Syllabus statements covered
- dividing a whole number by a whole number with quotient as a fraction
- expressing fractions as decimals
- adding and subtracting mixed numbers
- multiplying a proper/improper fraction and a whole number without calculator
- multiplying a proper fraction and a proper/ improper fractions without calculator
- multiplying two improper fractions
- multiplying a mixed number and a whole number
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- The unit and equivalent fractionsMake the chosen whole and equal unit explicit before comparing fraction representations.
- Division, fractions and decimalsRepresent a quotient as a fraction and use equivalent fractions or division for its decimal value.
- Add and subtract mixed numbersKeep the whole unit and part size consistent when combining or exchanging mixed numbers.
- Multiply fractions as parts of partsUse equal partitions to explain fraction multiplication before calculating.
- Fraction products beyond one wholeConvert complete mixed-number amounts before scaling and check products of improper fractions.
- Operate with fraction unitsAdd, subtract and multiply fractions using equal units, then check the size of the result.
- Fraction relationships in bar modelsRepresent known and unknown quantities with a labelled bar model, then interpret and check the result.