A percentage is a share written out of 100, so shares of wholes of any size can be compared fairly. This unit builds the idea up: what per cent counts on a hundred grid and on wholes cut into other numbers of parts, how a fraction, a decimal and a percentage name one amount, how to find a percentage of an amount from 10%, 5% and 1%, how to work back to the whole, and how to increase, decrease and measure a percentage change.
Every idea is something you can move: shade a grid past 100%, slide a fraction onto a decimal line, build 35% of an amount from blocks, work back to the whole, set a change against its original. Lessons 3 and 6 use a scientific calculator, once each, to check an estimate.
The lessons, in order
- Lesson 1 · What a percentage is Per cent as out of 100, benchmark percentages, percentages above 100%, and the percentage for a share of a whole cut into any number of equal parts. Shade a hundred grid up to 200%, then cut one whole into 4 to 50 equal parts and read each part as a percentage. No calculator
- Lesson 2 · Fractions, decimals and percentages Converting between fractions, decimals and percentages, and comparing and ordering mixed forms. Slide a fraction onto aligned decimal and percentage lines, then put mixed numbers in order on a zoomed line. No calculator
- Lesson 3 · Percentage of an amount Finding a percentage of an amount from 10%, 5% and 1%, with the decimal multiplier on a calculator, and comparing percentages of different amounts. Build any percentage of an amount from blocks of 10%, 5% and 1%, then compare two percentages of two amounts. Scientific calculator
- Lesson 4 · Finding the whole Finding the whole from a part and its percentage by way of 1%, and finding what percentage one amount is of another, including above 100%. Go back from a part and its percentage to 1% and then to the whole, then see one amount as a percentage of another. No calculator
- Lesson 5 · Increasing and decreasing by a percentage Increasing and decreasing an amount by a percentage with a multiplier, and why successive changes of the same percentage do not cancel. Change an amount by a percentage in one step with a multiplier, then take it up and down by the same percentage. No calculator
- Lesson 6 · Percentage change Percentage increase and decrease from two amounts, using the original as the divisor, and finding the original from a new amount and a percentage change. Swap an original and a new amount to see the percentage change, then go back to the original from a new amount. 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.