Percentages: a week of ready-to-teach maths
Five days of lessons for Year 5 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out hundred-squares, a percentage strip and trio cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the two card sheets once; the squares, strip and cards are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: per cent means out of one hundred. 100% is the whole, so 25% is 25 out of 100, the same part as the fraction 25/100 = 1/4 and the decimal 0.25. Because every percentage is out of the same hundred, percentages make it easy to compare parts, even of wholes of different sizes.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Which percentages
Year 5 works with percentages of one whole, from 0% to 100%, and connects the familiar ones to fractions and decimals: 100%, 50%, 25%, 75%, 10%, 20% and 1%. Finding a percentage of an amount, such as 25% of $80, comes in Year 6, so this pack only scales scores out of 10, 20, 25 or 50 to 100 when comparing them.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Out of a hundred | Read and shade percentages on hundred-squares, and find the part that is left | Per cent means out of one hundred |
| 2 | 100% is the whole | Estimate how full a bar is, mark 25%, 50% and 75%, and find what is left of 100% | One hundred per cent is the whole |
| 3 | Three names for one part | Write familiar percentages as fractions and decimals, and fractions and decimals as percentages, with trio cards | Percentages, fractions and decimals |
| 4 | Compare shares | Compare and order percentages, and turn scores out of 20, 25 and 50 into percentages to compare them fairly | Comparing relative size with percentages |
| 5 | Familiar percentages | Know the familiar percentages by heart, use them in everyday sentences, and play the unit quiz | Matching familiar percentages |
How the week builds
Day 1 reads percentages as so many out of a hundred; Day 2 makes 100% the whole of anything, not only a hundred-square; Day 3 connects each familiar percentage to its fraction and decimal; Day 4 compares shares, even of different totals; and Day 5 puts the familiar percentages to work in everyday sentences. It builds on Year 4 tenths and hundredths and this year’s equivalent fractions, and it leads to finding percentages of amounts in Year 6.
Materials for the week (one trip)
- From the classroom: scissors, coloured pencils, envelopes for the cards, this pack printed.
- For Day 2: a phone or tablet showing its battery percentage, or a picture of one (optional).
- For Day 5: a shop catalogue or a sale sign with 50% off (optional).
- Cut out once, use all week: the hundred-squares, the percentage strip and the 24 trio cards. No maths equipment to buy.
Words for the word wall
per cent, percentage, %, whole, hundredth, fraction, decimal, equivalent, share, compare, out of, familiar
Dear families
This week in maths, Year 5 learns percentages. Per cent means out of one hundred: 25% is 25 out of 100, the same as a quarter and as 0.25. 100% is the whole of something. We use percentages to compare parts, so a score of 18 out of 20 (90%) can be set beside 22 out of 25 (88%).
Try this at home
- Look at a phone or tablet battery. If it shows 65%, ask how much is still to charge (35%).
- Spot percentages on packets, signs and sale tags. Ask what fraction each one is: 50% off is half price.
- Ask: is 10% of a pizza more or less than a quarter of it?
- Score a game out of 10 or 20, then turn the score into a percentage together.
Percentages I found this week
Fill one row a day. Write a percentage you saw and what it means.
| Day | The percentage | Where I saw it | As a fraction or a decimal |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Percentages teaching pack · seegongsik.com/au/y5/number/AC9M5N04/pack
Out of a hundred
Children meet per cent as “out of one hundred”: a hundred-square is the whole, and a percentage counts how many of its hundred squares are taken. They read, shade and write percentages, and find the part that is left.
We are learning to
- explain that per cent means out of one hundred, and read the % sign,
- show a percentage on a hundred-square, and read one from it,
- find the percentage that is not shaded, because the two parts make 100%.
Success criteria
- I can shade 45% of a hundred-square.
- I can say what percentage is left when 37% is shaded.
You need
The hundred-squares (cut-out sheet 1), one per pair. Coloured pencils. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Per cent Write “per cent = out of 100” and the % sign. Show the board (see the box). Ask: “25% shades 25 of the hundred squares. How many would 50% shade? And 100%?” |
| 30 min | Shade and read Pairs shade 45% on a cut-out square and check each other’s count, then do Parts A and B. Ask: “How can you count 45 squares quickly? A row is ten squares: what per cent is one row?” |
| 10 min | What is left? Children do Parts C and D. Ask: “37% is shaded. How do we find the percentage that is not shaded?” |
Two half-sessions instead? Split after Part A; start Session B by shading 45% together.
Watch for these ideas
- Thinking 45% means 45 squares of any grid. A percentage is so many out of 100 equal parts of the whole.
- Counting every square one at a time. A row of ten is 10%: count rows, then squares.
- Thinking the unshaded part is also 37%. The two parts together make 100%.
Answers
- Part A: 37%, 60%, 5%. Part B: 45% is 4 full rows and 5 squares; 8% is 8 squares; 90% is 9 full rows.
- Part C: 63%, 9%, 100%; 48 out of 100, 7 out of 100. Part D: 63%, 40%, 95% not shaded.
Out of a hundred
Each big square is one whole, cut into 100 small squares.
A. What percentage is shaded?
| ______ % | ______ % | ______ % |
B. Shade each percentage
C. Write it two ways
63 out of 100 = ______ %9 out of 100 = ______ %100 out of 100 = ______ %
48% = ______ out of 1007% = ______ out of 100
D. The part that is left
In Part A, what percentage of each square is not shaded? ______ % ______ % ______ %
100% is the whole
Children see that 100% is the whole of anything, not only a hundred-square, and 0% is none of it, so every percentage of one whole sits between them. They estimate how full a bar is, mark 25%, 50% and 75%, and work out the percentage that is left.
We are learning to
- explain that 100% is all of a whole and 0% is none of it,
- estimate a percentage on a bar, using 25%, 50% and 75% as markers,
- find what is left by counting on to 100%.
Success criteria
- I can estimate how full a bar is, to the nearest 10%.
- I can say what percentage is left when a battery is 65% charged.
You need
The percentage strip (cut-out sheet 1), one per child. A device showing its battery percentage, or a picture of one (optional). The worksheet.
Lesson flow (about 50 minutes)
| 10 min | The whole bar Show the board (see the box). Ask what 100% of the bar looks like, then 0%. Ask: “The bar is 50% full. What percentage of the bar is empty?” |
| 30 min | Fold and estimate Children fold the percentage strip in half, then in half again, and label 50%, 25% and 75%. They use it to do Parts A and B. Ask: “Is this bar more or less than half full? More or less than 75%?” |
| 10 min | What is left? Children do Parts C and D. Ask: “Could 130% of a class be at school today? Why not?” |
Two half-sessions instead? Split after the folding; start Session B with Part A.
Watch for these ideas
- Thinking a percentage needs a hundred-square. Any whole, a bar, a cake or a class, can be 100%.
- Calling a nearly full bar 100%. Compare it with the 75% mark first, then decide.
- Adding the two parts to more than 100% (65% charged and 45% to go). The two parts make exactly 100%.
Answers
- Part A: about 90%, 25%, 50%, 10%, 75% (within 10% is fine). Part B: 25% a quarter of the way along, 50% halfway, 75% three quarters of the way.
- Part C: 35%, 20%, 60%. Part D: true, false, false, true, true; 130% would be more than the whole class, and a full tank is 100% full.
100% is the whole
Each bar is one whole: 100%.
A. About how full is each bar?
B. Mark 25%, 50% and 75% on the empty bar
C. What is left?
A phone battery is 65% charged. What percentage is still to charge? ______ %
A download is 80% done. What percentage is left to download? ______ %
A jug is 40% full of water. What percentage of the jug is empty? ______ %
D. True or false? Circle one.
100% of a cake is all of the cake.true / false
130% of the class is at school today.true / false
A full tank of fuel is 50% full.true / false
Half a pizza is 50% of the pizza.true / false
0% of a jug of water is none of it.true / false
Three names for one part
Children connect a percentage to its fraction and its decimal: 25% is 25 out of 100, the fraction 25/100, the same as 1/4, and the decimal 0.25. Trio cards turn the connections into a game.
We are learning to
- write a percentage as a fraction out of 100, and simplify the familiar ones,
- write a percentage as a decimal by reading it in hundredths,
- write a fraction or a decimal as a percentage.
Success criteria
- I can write 75% as a fraction and as a decimal.
- I can find the odd one out in 50%, 1/2 and 0.05.
You need
The trio cards (cut-out sheet 2), one set per group of four. A hundred-square from cut-out sheet 1. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | One part, three names Shade 25 squares of a hundred-square and write 25%, 25/100 = 1/4 and 0.25 beside it. Show the board (see the box). Ask: “25 hundredths, one quarter and 25%: how can all three be the same part?” |
| 30 min | Table and trios Children do Parts A and B. Groups then play trio snap: deal the cards face down, turn them over in turn, and claim three cards that name the same part. Ask: “37% stays as 37/100. Why can it not be written more simply?” |
| 10 min | Odd one out Children do Parts C and D. Ask: “Is 0.05 the same as 50%? Say both in hundredths.” |
Two half-sessions instead? Split after Part B; start Session B with trio snap.
Watch for these ideas
- Writing 7% as 0.7. Seven hundredths is 0.07.
- Writing a quarter as 4% or 0.4. A quarter of 100 is 25: 25% and 0.25.
- Writing 10% as 1/100. Ten out of a hundred is one tenth.
Answers
- Part A: 50% = 50/100 = 1/2 = 0.5; 25% = 25/100 = 1/4 = 0.25; 75% = 75/100 = 3/4 = 0.75; 10% = 10/100 = 1/10 = 0.1; 30% = 30/100 = 3/10 = 0.3; 1% = 1/100 = 1/100 = 0.01; 37% = 37/100 = 37/100 = 0.37 (37/100 and 1/100 do not simplify).
- Part B: 0.6 = 60%; 3/10 = 30%; 1/4 = 25%; 0.07 = 7%; 3/4 = 75%; 0.5 = 50%. Part C: 0.05, 1/100, 0.34. Part D: any three that name one part, such as 40%, 2/5, 0.4. Trios: 50%, 1/2, 0.5; 25%, 1/4, 0.25; 75%, 3/4, 0.75; 10%, 1/10, 0.1; 1%, 1/100, 0.01; 20%, 1/5, 0.2; 30%, 3/10, 0.3; 60%, 3/5, 0.6.
Three names for one part
A. Fill the table
| Percentage | Out of 100 | Simplest fraction | Decimal |
|---|---|---|---|
| 50% | ____ /100 | ||
| 25% | ____ /100 | ||
| 75% | ____ /100 | ||
| 10% | ____ /100 | ||
| 30% | ____ /100 | ||
| 1% | ____ /100 | ||
| 37% | ____ /100 |
B. Write each as a percentage
0.6 = ______ %3/10 = ______ %1/4 = ______ %0.07 = ______ %3/4 = ______ %0.5 = ______ %
C. Odd one out: circle the one that names a different part
50% 1/2 0.05
0.1 10% 1/100
3/4 0.34 75%
D. Make your own trio
A percentage: ________ its fraction: ________ its decimal: ________
Compare shares
Children compare percentages as shares of the same 100, then use percentages to compare results out of different totals: 18 out of 20 and 22 out of 25 become 90% and 88%, so they can be set side by side fairly.
We are learning to
- compare and order percentages as shares of the same whole,
- turn a score out of 10, 20, 25 or 50 into a percentage by scaling it to 100,
- use percentages to compare results out of different totals.
Success criteria
- I can turn 22 out of 25 into a percentage.
- I can say which class has the larger share of walkers, and why.
You need
The worksheet, one per child. Mini whiteboards (optional).
Lesson flow (about 50 minutes)
| 10 min | The larger share Show the board (see the box). Ask: “Both are out of the same 100. Why does that make comparing easy?” |
| 30 min | Make it out of 100 Model 17 out of 20: 20 × 5 = 100, so 17 × 5 = 85, which is 85%. Children do Parts A, B and C. Ask: “Bea scored 22 and Ali scored 18. How can Ali’s score be the better one?” |
| 10 min | Fair comparisons Children do Part D. Ask: “Class 5B has more walkers. Does it have the larger share of walkers?” |
Two half-sessions instead? Split after Part B; start Session B by modelling 17 out of 20.
Watch for these ideas
- Comparing raw scores out of different totals, so 22 beats 18. Make both out of 100 first.
- Scaling only the score, so 18 out of 20 becomes 18%. Multiply the score and the total by the same number.
- Thinking 4% and 40% are close because both show a 4. 40% is ten times as much.
Answers
- Part A: 54%, 90%, 33%, 10%. Part B: 4%, 14%, 40%, 41%, 100%. Part C: Ali 90%, Bea 88%, Cal 92%, Dee 80%; best Cal; lowest first Dee, Bea, Ali, Cal.
- Part D: Class 5A 48% and Class 5B 26%, so Class 5A; The Possums 70% and The Wombats 75%, so The Wombats.
Compare shares
A. Circle the larger share
45% 54%9% 90%33% 30%1% 10%
B. Put them in order, smallest first
40%, 4%, 14%, 100%, 41%
______________________________________________
C. Four test scores, four different totals
| Name | Score | Out of 100 | Percentage |
|---|---|---|---|
| Ali | 18 out of 20 | ____ out of 100 | ____ % |
| Bea | 22 out of 25 | ____ out of 100 | ____ % |
| Cal | 46 out of 50 | ____ out of 100 | ____ % |
| Dee | 8 out of 10 | ____ out of 100 | ____ % |
Who did best? ________ Lowest first: ________, ________, ________, ________
D. Larger share
In Class 5A, 12 of the 25 children walk to school. In Class 5B, 13 of the 50 children walk. Which class has the larger share of walkers?
________________ because ______________________________
The Possums won 7 of their 10 games. The Wombats won 15 of their 20 games. Which team won the larger share of its games?
________________ because ______________________________
Familiar percentages
Children learn the familiar percentages by heart and use them in everyday sentences: 50% off is half price, 25% of a class is a quarter of it, 10% is one tenth. They shade familiar percentages of bars with fewer than a hundred parts, and the week ends with the unit quiz.
We are learning to
- match 100%, 50%, 25%, 75%, 20%, 10% and 1% to their fractions and decimals,
- explain an everyday percentage as a fraction,
- shade a familiar percentage of a bar cut into 4, 5, 8 or 10 parts.
Success criteria
- I can say the fraction for 50%, 25%, 75%, 20%, 10% and 1% without working it out.
- I can shade 75% of a bar cut into four parts.
You need
The trio cards (cut-out sheet 2). A sale sign or a catalogue (optional). The worksheet. The interactive unit open for the quiz game.
Lesson flow (about 50 minutes)
| 10 min | Quick match Show the board (see the box). Pairs answer each question before a child presses. Ask: “10% of the class is how many children in every ten?” |
| 30 min | Everyday percentages Read a sale sign or a catalogue together: 50% off is half price. Children do Parts A, B and C. Ask: “75% of a bar with four parts: how many parts do we shade, and why?” |
| 10 min | Quiz game Run the unit’s self-check quiz as a class game: pairs hold up their answer before you reveal it. Ask: “Which question tricked us most? What would you tell a friend about percentages?” |
Two half-sessions instead? Split after Part B; start Session B with the bars in Part C.
Watch for these ideas
- Thinking 20% is 1/20. 20 out of 100 is the same as 1 out of 5.
- Shading 75 parts for 75% of a four-part bar. 75% is three quarters: 3 of the 4 parts.
- Mixing up 1% and 10%. One hundredth is ten times smaller than one tenth.
Answers
- Part A: 100% = 100/100 = 1; 50% = 1/2 = 0.5; 25% = 1/4 = 0.25; 75% = 3/4 = 0.75; 20% = 1/5 = 0.2; 10% = 1/10 = 0.1; 1% = 1/100 = 0.01.
- Part B: 1/2, 1/4, 3/4, 1/10, 1/100. Part C: shade 3 of 4; 3 of 10; 1 of 5; 4 of 8.
Familiar percentages
A. Fill the gaps
| Percentage | Fraction | Decimal |
|---|---|---|
| 100% | ||
| 1/2 | ||
| 0.25 | ||
| 75% | ||
| 1/5 | ||
| 0.1 | ||
| 1% |
B. Everyday percentages
A shop has 50% off everything. What fraction of the price comes off? ________
25% of the class wear glasses. What fraction of the class wear glasses? ________
A water tank is 75% full. What fraction of the tank holds water? ________
10% of the trees in the park are gum trees. What fraction of the trees are gum trees? ________
1% of the beans in a jar are red. What fraction of the beans are red? ________
C. Shade each percentage of the bar
Two hundred-squares and a percentage strip
Each big square is one whole, 100%. Shade it to show a percentage: every small square is 1%, and every row of ten is 10%. One sheet per pair.
Percentage strip (Day 2)
Cut out the strip. Fold it in half and mark 50%, then fold it in half again and mark 25% and 75%.
Trio cards
Cut out the 24 cards, one set per group. Three cards make a trio when they name the same part: a percentage, a fraction and a decimal. Play trio snap, or lay all the cards face up and find the eight trios.
Teacher note: the eight trios are listed in the answers on the Day 3 plan.
What we know: Percentages
Work on your own. Show your thinking if you can.
- What does 64% mean? ______________________________
- What percentage is shaded? ______ % What percentage is not? ______ %
- A water bottle is 30% full. What percentage of the bottle is empty? ______ %
- Write 75% as a fraction: ________ and as a decimal: ________
- Write as percentages: 0.4 = ______ % 1/10 = ______ %
- Circle the larger share: 19% 91%
- Put these in order, smallest first: 50%, 5%, 15%, 55%. ______________________________
- Mia scored 16 out of 20. Jack scored 21 out of 25. Who did better? Show both as percentages. ______________________________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 64 out of 100.
- 23% shaded; 77% not shaded.
- 70% (the two parts make 100%).
- 3/4; 0.75.
- 0.4 = 40%; 1/10 = 10%.
- 91%.
- 5%, 15%, 50%, 55%.
- Mia 80%, Jack 84%; Jack did better.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Out of a hundred (Q1, Q2) | reads or shades a percentage by counting every square | reads and shows a percentage as so many out of 100, using rows of ten | finds the part that is left without counting |
| The whole is 100% (Q3) | lets the two parts add to more than 100% | finds the part that is left by counting on to 100% | explains why a part of one whole cannot be more than 100% |
| Fractions and decimals (Q4, Q5) | matches 50% to a half | writes familiar percentages as fractions and decimals, and back | writes any whole-number percentage as a decimal |
| Comparing (Q6, Q7, Q8) | compares scores out of different totals as they stand | compares and orders percentages, and scales scores to 100 | explains why percentages make the comparison fair |
Eight questions, four ideas. A child at standard answers most questions and can say why, reading every percentage as so many out of the same hundred.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Out of 100 | The whole | Three names | Compares shares | Familiar ones |
|---|---|---|---|---|---|
The five columns are the five days: out of a hundred, the whole, three names, comparing shares and the familiar percentages.