Fractions, Decimals and Percentages of a Quantity: a week of ready-to-teach maths

Five days of lessons for Year 6 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus thirty-six matching cards, twelve sale tags, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the matching cards and the sale tags once; one set per pair serves Days 2 to 4.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. 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: a fraction, a decimal and a percentage can name the same part, so 25%, 0.25 and 1/4 of an amount are the same. To find a part, divide the amount into equal pieces and take some of them. Familiar percentages have quick routes: 50% is half, 25% is a quarter, 10% is a tenth, and the rest are built from those. A discount is a percentage taken off a price.

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.

Words to watch

Per cent means “out of 100”. The discount is the amount taken off; the sale price is what you pay. 20% off means you pay 80%. Calculators are welcome on Days 4 and 5 for awkward amounts, after an estimate.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 finds fractions of amounts; Day 2 connects percentages to fractions and decimals; Day 3 finds percentages of amounts; Day 4 works out discounts; and Day 5 chooses a strategy for mixed problems. It builds on the Year 5 work connecting familiar percentages to fractions and decimals, and on this year’s fractions and decimals units. It leads to estimating with percentages and to Year 7, where all four operations work with fractions, decimals and percentages.

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils, this pack printed.
• For Days 4 and 5: a calculator for each pair (a tablet or laptop calculator is fine).
• Cut out once, use all week: the thirty-six matching cards and the twelve sale tags, one set per pair.

Words for the word wall

fraction of, percentage, per cent, hundredths, equivalent, discount, sale price, original price, strategy, estimate

Dear families

This week in maths, Year 6 finds fractions and percentages of amounts and works out discounts. We learn quick routes for 50%, 25% and 10%, and why 20% off means paying 80% of the price.

Try this at home

• Shop catalogues: find a sale item and work out the discount and the sale price together.
• Ask: what is 10% of $50? Then 5%? Then 15%?
• Cooking: if a recipe needs 3/4 of 400 g of flour, how much is that?
• Is 25% off better than $10 off on a $36 item? Talk it through.

My amounts this week

Fill one row a day. Find a price or an amount at home, then find 10% and 25% of it.

Printed from the free seegongsik Fractions, Decimals and Percentages of a Quantity teaching pack · seegongsik.com/au/y6/number/AC9M6N07/pack

A fraction of an amount

To find a fraction of an amount, split it into as many equal parts as the denominator says, then take as many parts as the numerator says. A bar model shows both steps, and the same idea works for an hour, a kilogram or a metre.

We are learning to

• find a unit fraction of an amount by dividing,
• find a non-unit fraction by dividing, then multiplying,
• find fractions of measures and work back from a part to the whole.

Success criteria

• I can find 3/4 of 12 and 2/5 of 35 with a bar model.
• I can find 2/3 of an hour in minutes.

You need

Coloured pencils and the worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the measures in Part B.

Watch for these ideas

• Dividing by the numerator: 3/4 of 12 is not 12 ÷ 3.
• Stopping at one part: 2/5 of 35 is two parts of 7, so 14, not 7.
• Losing the unit: 2/3 of an hour is 40 minutes, not “2/3 minutes”.

Answers

• Part A: 3/4 of 12 = 9 (one part 3); 2/5 of 35 = 14 (one part 7); 5/6 of 42 = 35 (one part 7); 3/8 of 40 = 15 (one part 5).
• Part B: 2/3 of an hour = 40 minutes; 3/4 of a kilogram = 750 g; 3/10 of a metre = 30 cm; 1/4 of a day = 6 hours.
• Part C: 28, 30.
• Part D: $30.00 now and $15.00 later.

A fraction of an amount

A. Split, then take

Write the value of one part in each section. Shade the fraction. Then answer.

B. Fractions of measures

C. Back to the whole

1/4 of a number is 7. What is the number? ________

3/5 of a class is 18 children. How many children are in the class? ________

D. Paying in parts

A book costs $45.00. Sam pays 2/3 of the price now and the rest next week. How much is paid now, and how much next week?

Now: ________    Next week: ________

Percent means per hundred

Per cent means out of 100. A hundred square shows a percentage as squares shaded out of 100, which is also a fraction in hundredths and a decimal: 25% = 25/100 = 1/4 = 0.25. Children learn the familiar percentages in all three forms and use them to order a mixed set.

We are learning to

• explain what a percentage means,
• write familiar percentages as fractions and decimals,
• order a mix of fractions, decimals and percentages.

Success criteria

• I can write 75% as a fraction and as a decimal.
• I can order 0.3, 1/4 and 28% and say how I know.

You need

Coloured pencils, the worksheet, one per child, and the cut-out matching cards, one set per pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the table in Part B.

Watch for these ideas

• Reading 0.5 as 5%. It is 50 hundredths, so 50%.
• Thinking 1/5 is 5% because of the 5: 1/5 = 20/100 = 20%.
• Comparing by the digits: 0.3 is more than 0.25, because 30 hundredths is more than 25.

Answers

• Part A: 30 squares; 30% = 3/10 = 0.3; 75 squares; 75% = 3/4 = 0.75; 5 squares; 5% = 1/20 = 0.05.
• Part B: 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 1/10 = 0.1 = 10%; 3/4 = 0.75 = 75%; 1/5 = 0.2 = 20%; 1/100 = 0.01 = 1%; 2/5 = 0.4 = 40%; 1/20 = 0.05 = 5%.
• Part C: 1/4 < 28% < 0.3 < 2/5 (as percentages: 25%, 28%, 30%, 40%).
• Three of a kind: the trios are 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%; 1/10 = 0.1 = 10%; 1/5 = 0.2 = 20%; 2/5 = 0.4 = 40%; 3/10 = 0.3 = 30%; 1/100 = 0.01 = 1%; 7/10 = 0.7 = 70%; 3/5 = 0.6 = 60%; 1/20 = 0.05 = 5%; 9/10 = 0.9 = 90%.

Percent means per hundred

A. Shade, then write the fraction and the decimal

B. Fill the table

C. Smallest first

0.3, 1/4, 28%, 2/5

________  <  ________  <  ________  <  ________

A percentage of an amount

Familiar percentages have quick routes: 50% is half, 25% is a quarter, 10% is a tenth, 5% is half of 10%, and 1% is a hundredth. Other percentages are built from these, so 35% is 25% + 10%. A decimal of an amount works the same way: 0.25 of 80 is a quarter of 80.

We are learning to

• find 50%, 25%, 10%, 5% and 1% of an amount,
• build other percentages from these,
• find a decimal of an amount as a fraction of it.

Success criteria

• I can find 35% of 80 in two steps.
• I can explain why 5% is half of 10%.

You need

The worksheet, one per child, and the cut-out matching cards, one set per pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the building in Part B.

Watch for these ideas

• Taking 10% as “take away 10”: 10% of 240 is 24, not 230.
• Thinking 5% is a fifth. A fifth is 20%; 5% is half of 10%.
• Adding the percentages instead of the parts: 35% of 80 is 20 + 8 = 28.

Answers

• Part A: 50% = 120; 25% = 60; 10% = 24; 5% = 12; 1% = 2.4.
• Part B: 35% of 80 = 20 + 8 = 28; 15% of 60 = 6 + 3 = 9; 75% of 48 = 24 + 12 = 36; 20% of 45 = 4.5 + 4.5 = 9; 12% of 50 = 5 + 1 = 6.
• Part C: 0.25 of 80 = 20; 0.1 of 70 = 7; 0.75 of 36 = 27; 0.4 of 15 = 6.
• Part D: 54 students (36 + 18).

A percentage of an amount

A. Quick routes for 240

B. Build it from easier ones

35% of 80 = 25% + 10% = ______ + ______ = ______

15% of 60 = 10% + 5% = ______ + ______ = ______

75% of 48 = 50% + 25% = ______ + ______ = ______

20% of 45 = 10% + 10% = ______ + ______ = ______

12% of 50 = 10% + 2% = ______ + ______ = ______

C. A decimal of an amount

D. Walking to school

A school has 360 students. 15% of them walk to school. How many students walk? Show the two steps.

______________________________________________________________________

Discounts

A discount is a percentage of the price taken off; the sale price is what is left to pay. Children find the discount and take it away, then learn the shortcut that 20% off means paying 80%, and compare a percentage off with an amount off.

We are learning to

• work out a discount and the sale price,
• find a sale price in one step by paying the percentage that is left,
• compare two deals and say which is better, and by how much.

Success criteria

• I can find the sale price of a $40 item with 20% off in two ways.
• I can decide whether 25% off or $12 off is better on a $60 jacket.

You need

The worksheet, one per child, the cut-out sale tags, one set per pair, and a calculator for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the shortcut in Part B.

Watch for these ideas

• Taking the percentage number off the price: 20% off $40 is not $20.
• Giving the discount as the answer when the question asks for the sale price.
• Thinking a bigger percentage always saves more: 25% off $16 saves less than 10% off $65.

Answers

• Part A: $40.00, 20% off: discount $8.00, sale price $32.00; $65.00, 10% off: discount $6.50, sale price $58.50; $120.00, 25% off: discount $30.00, sale price $90.00; $36.00, 50% off: discount $18.00, sale price $18.00; $84.00, 15% off: discount $12.60, sale price $71.40.
• Part B: 80% of $45.00 = $36.00; 70% of $70.00 = $49.00; 75% of $16.00 = $12.00.
• Part C: $45.00 against $48.00, so Shop A, by $3.00; $81.00 against $80.00, so Shop B, by $1.00.
• Best buy sale prices: sneakers $60.00, backpack $36.00, headphones $51.00, board game $18.00, jacket $84.00, watch $45.00, scooter $135.00, book set $21.00, tent $156.00, lunch box $9.00, soccer ball $24.00, art kit $51.30.

Discounts

A. Discount, then sale price

B. Pay what is left

20% off means you pay 80%. Find each sale price in one step, then check by taking the discount off.

$45.00, 20% off: pay ______% of $45.00 = ________    check: ________

$70.00, 30% off: pay ______% of $70.00 = ________    check: ________

$16.00, 25% off: pay ______% of $16.00 = ________    check: ________

C. Which deal is better?

Choose a strategy

The same part can be found many ways: 25% of 80 is a quarter of 80, or 10% twice and 5%. Children choose the quickest way for each problem, in their heads, on paper or with a calculator for awkward amounts, and check every answer against an estimate.

We are learning to

• choose an efficient strategy for a fraction, decimal or percentage of an amount,
• use a calculator for awkward amounts after estimating,
• compare parts written in different forms.

Success criteria

• I can decide whether 3/5 of 50 or 55% of 50 is more.
• I can say why I chose my strategy for each problem.

You need

The worksheet, one per child, and a calculator for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Part B.

Watch for these ideas

• Reaching for the calculator first. Estimate, then decide whether the numbers are awkward enough.
• Typing 15% of 36.8 as 15 × 36.8 and reading 552 as the answer. The estimate (about $5) catches it.
• Comparing the numbers instead of the parts: 55% is not more than 3/5 because 55 is bigger than 3.

Answers

• Part A: 3/5 of 50 = 30, 55% of 50 = 27.5: the first; 0.3 of 90 = 27, 1/4 of 100 = 25: the first; 20% of 45 = 9, 1/5 of 45 = 9: equal.
• Part B: 50% of 86 = 43; 15% of 36.8 = 5.52; 2/3 of 75 = 50; 1% of 4500 = 45; 35% of 62.4 = 21.84. Head for 50% and 1%, paper or head for 2/3, calculator for the awkward 15% and 35%.
• Part C: (1) $17.43 (discount $7.47); (2) 900 mL left; (3) 8 students.

Choose a strategy

A. Which is more?

3/5 of 50 or 55% of 50? ______________________

0.3 of 90 or 1/4 of 100? ______________________

20% of 45 or 1/5 of 45? ______________________

B. Choose a strategy, then answer

C. Problems

1. A video game costs $24.90. It has 30% off. What is the sale price? ________

2. A 1.5 litre bottle of water is full. 2/5 of it is drunk. How many millilitres are left? ________

3. 25% of a class of 32 students buy lunch from the canteen. How many students is that? ________

Matching cards

Cut out the thirty-six cards once. Pairs use them on Days 2 and 3.

Three of a kind (Days 2 and 3)

1. Deal six cards each. The rest go face down in a pile, with one turned up beside it.
2. On your turn, take the top card from either pile, then put one card face up on the turned-up pile.
3. Three cards that name the same amount (a fraction, a decimal and a percentage) make a set: lay it down and say why.
4. The first player to lay down two sets wins.

Teacher note: the twelve sets are 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%; 1/10 = 0.1 = 10%; 1/5 = 0.2 = 20%; 2/5 = 0.4 = 40%; 3/10 = 0.3 = 30%; 1/100 = 0.01 = 1%; 7/10 = 0.7 = 70%; 3/5 = 0.6 = 60%; 1/20 = 0.05 = 5%; 9/10 = 0.9 = 90%.

Sale tags

Cut out the twelve tags once, one set for each pair.

Best buy (Day 4)

1. Shuffle the tags face down. Each player turns one over.
2. Each works out the sale price of their tag on paper; the partner checks it on a calculator.
3. The lower sale price wins both tags. Then say which tag saved more money.

Teacher note: the sale prices are sneakers $60.00, backpack $36.00, headphones $51.00, board game $18.00, jacket $84.00, watch $45.00, scooter $135.00, book set $21.00, tent $156.00, lunch box $9.00, soccer ball $24.00, art kit $51.30.

What we know: Fractions, Decimals and Percentages of a Quantity

Work on your own. Show your thinking if you can.

1. 3/4 of 28 = ________
2. 2/5 of 45 = ________
3. Write 35% as a decimal and as a fraction in its simplest form. ________ ________
4. 10% of 260 = ________
5. 25% of 96 = ________
6. 0.2 of 75 = ________
7. A $60.00 jacket has 15% off. What is the sale price? Show your steps. ______________________________
8. Which is more: 3/5 of 50 or 55% of 50? How do you know? ______________________________

Answers and marking guide

Answers

1. 21.
2. 18.
3. 0.35 and 7/20.
4. 26.
5. 24.
6. 15.
7. Discount $9.00 ($6.00 + $3.00); sale price $51.00.
8. 3/5 of 50 = 30 and 55% of 50 = 27.5, so 3/5 of 50 is more (3/5 = 60%).

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, with a bar, an easy percentage or a change of form.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: fractions of amounts, percentages as hundredths, percentages of amounts, discounts, and choosing a strategy.