At a glance. One lesson of about 60 minutes. Students read a hundred grid as a percentage, go past 100%, then find the percentage for a share of a whole cut into 4, 8, 20 or 50 equal parts.
Calculator: no calculator. Nothing here needs one. Every number divides into 100 cleanly or by halving, and the skill is seeing the share, not computing it.
What students will learn
Know
- Per cent means out of 100, and 100% is the whole.
- 50% = 1/2, 25% = 1/4, 10% = 1/10 and 1% = 1/100.
- A whole cut into n equal parts has 100 ÷ n per cent in each part.
Understand
- A percentage is a share of a whole, so it needs the whole to give an amount.
- The same share can be 18 out of 40 or 45 out of 100, and a percentage puts both on one scale.
- A percentage above 100% means more than the starting whole.
Do
- Read and shade percentages on a hundred grid and on grids with other numbers of parts.
- Find the percentage for a share by scaling the whole to 100.
- Move between a share written as a count, a fraction and a percentage.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: per cent as out of 100, benchmarks and parts of a whole (questions 1 to 6).
- Criterion B. Investigating patterns: the equal-parts figure. Ask students to find the rule that links the number of parts to the percentage for one part, then test it on a number they choose.
- Criterion C. Communicating: explaining why 8 out of 20 is 40% and not 8%, using the words whole, part and out of 100 (questions 7, 8 and 9).
- Criterion D. Applying mathematics in real-life contexts: batteries, school gardens, match results and test scores (the hook and questions 2 and 5).
The one thing to do with the figure
Ask for a prediction before the first slide. “35 squares are shaded. What fraction of the grid is that, in its simplest form?” Take 7/20 and 35/100 from the room and let the figure and the read-outs settle it.
Then drag past 100 and ask what has happened to the whole. Name it on the board: more than 100% means more than the starting whole. In the second figure, keep the shaded parts fixed and change the number of parts, so the same count gives a different percentage.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook and the first figure, with predictions first. Include 150%. |
| 10 min | Key idea; the second figure. Students choose a number of parts and say the percentage for one part aloud. |
| 10 min | Worked example on the garden beds; students finish the faded netball example in pairs. |
| 5 min | Question 1, the check. If many choose A or C, go back to the second figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 0.3; 360; 20. |
|---|---|
| Worked example | 28%. |
| Faded example | 60%. |
| 1. Percentage of a whole of 20 parts | D, 25%. A reads the count as the percentage; B subtracts to get the unshaded parts; C uses the total number of parts as the percentage. |
| 2. Percentage from a count | 36. 9/25 = 36/100. |
| 3. Per cent as a fraction | C, 7/100. A and B are both 70%; D is 70/100, also 70%. |
| 4. More than 100% | 35. 135 − 100 = 35. |
| 5. Percentage from a score | 90. 4 marks lost is 10%, so 100% − 10% = 90%. |
| 6. Percentage for one equal part | 12.5. 100 ÷ 8 = 12.5, or 1/8 = 0.125 = 12.5%. |
| 7. Same percentage on a different whole | 12. 12/50 = 24/100. |
| 8. Parts from percentages | 5. 30% is 6 parts, 45% is 9 parts, 20 − 15 = 5. |
| 9. Same share, different totals | C. A and B compare a count with a percentage; D misses that a percentage puts different totals on one scale. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A in question 1; 9 in question 2 | Read the count as the percentage. | Ask what one part is worth when the whole is 100%. Write 1 part = 4% or 5% before counting. |
| B in question 1; 16 in question 2 | Found the parts that are not shaded or not chosen. | Underline the question word: shaded, walk. Say aloud which group is being asked for. |
| A, B or D in question 3 | Placed the 7 in the tenths or tens place, or confused 7/10 with 7/100. | Write 7% as 7 hundredths on a place-value chart (Unit 1, lesson 1). |
| 135 in question 4 | Gave the total instead of the second grid. | Shade the first grid in a different colour and ask what is left. |
| 0.9 in question 5; 0.125 in question 6 | Divided correctly and left it as a decimal. | Ask: out of 100, how many? Multiply by 100 and say the percentage. |
| 48 in question 7 | Scaled the count the wrong way because the whole is not 100. | Ask whether 50 squares is a bigger or smaller whole than 100, and what happens to the count. |
| A, B or D in question 9 | Compared a count with a percentage, or thought different totals cannot be compared. | Put both out of 100: ask what one mark is worth in each test, then compare percentages. |
| 25 or 75 in question 8 | Gave a percentage when a number of parts was asked for. | Write the unit on the answer line before starting: parts or per cent. |
Questions worth asking
- Why is 8 out of 20 not 8%? The 8 counts parts, not hundredths. Listen for “each part is 5%” or “it is 40 out of 100”.
- Can you have 120% of a whole? Yes, a whole and a fifth of another. Listen for “more than the whole”.
- Is 50% of a large pizza more than 50% of a small one? Yes in amount, equal as a share. A percentage needs its whole.
- Which is the better score: 17 out of 20 or 80 out of 100? 17/20 = 85/100, so 17 out of 20. Scale both to out of 100.
Differentiation
A way in for anyone stuck
- Give each student a printed hundred grid and a ten-by-ten strip they can cut. Every question can be done on it.
- Start with the whole-number benchmarks only: 50%, 25%, 10%, then 20 equal parts at 5% each.
- Use bars of 20 and 25 parts before 8 and 40, where each part is a decimal percentage.
Stretch
- Question 7, then: which wholes give a whole-number percentage for every single part? (Wholes of 1, 2, 4, 5, 10, 20, 25, 50 and 100 parts.)
- A bar is cut into 3 equal parts. What percentage is one part? Can any hundred grid show it exactly? (33.3...% repeating; no.)
Students learning in English as an additional language
“Per cent” is Latin for “by the hundred”, and many languages share the root. Say the phrase “out of one hundred” each time a % sign appears.
| Word | Plain meaning | Example |
|---|---|---|
| per cent (%) | out of 100 | 35% means 35 out of 100 |
| percentage | an amount written as a number of hundredths | a percentage of 25 is 25 out of 100 |
| whole | the full amount a share is taken from | the whole grid is 100 squares |
| part | one piece of the whole | one slice of 8 equal slices |
| equal parts | pieces that are all the same size | a bar cut into 20 equal parts |
| benchmark | a percentage worth knowing by heart | 50%, 25%, 10% and 1% |
Sentence starters for explaining aloud or in writing:
- The whole is cut into … equal parts, so one part is …%.
- … out of … is the same as … out of 100 because …
- This percentage is more than 100% because …
Two things not to say
“Just move the decimal point two places.” That is a method for later, and it needs the reason: per cent is hundredths.
“Put it over 100.” Over 100 means scaling the whole to 100, which is a multiplication or division by a number you have to find first.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- Reading a grid64 squares of a hundred grid are shaded. Write this as a percentage and as a fraction in simplest form.
64%, 16/25. - BenchmarksWhat fraction is 25%? What percentage is 1/2?
1/4; 50%.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA phone screen has 20 equal battery bars and 9 are lit. What percentage of the battery is left?
45%. Each bar is 5%, and 9 × 5 = 45. - Earlier work (Unit 1, lesson 7)Round 0.847 to two decimal places, then say how many squares of a hundred grid that shades.
0.85, so 85 squares: 85%.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningA bar is cut into 40 equal parts. Which numbers of shaded parts give a whole-number percentage?
Each part is 2.5%, so any even number of parts: 2 parts is 5%, 4 parts is 10%. - Over 100%This year's crowd is 3 times last year's crowd. Write this year's crowd as a percentage of last year's.
300%.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Draw a ten-by-ten grid on squared paper and shade it by rows of ten.