Division: 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 nine remainder story cards, a match-four card game, 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 story cards and the match-four cards once, one set per group.
- 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: division makes equal groups, and the story decides what happens to whatever is left over. Split a number into parts that divide easily: 72 ÷ 6 = 60 ÷ 6 + 12 ÷ 6 = 12. When it does not divide exactly, the remainder can round the answer up (23 children need 6 cars of 4), round it down (23 lollies make 5 each), or be shared out as a fraction or a decimal (17 m cut into 5 equal lengths is 3 2/5 m, or 3.4 m).
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.
Calculators
On Day 5 children use a calculator for the bigger divisions and read its decimal answers. A calculator shows 5.75 for 23 ÷ 4, which means 6 cars, 5 whole lollies each, or 5.75 m of rope, depending on the story. One calculator per pair is enough.
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 | Split, then divide | Split a number into parts the divisor divides exactly, divide each part, add, and check by multiplying | Dividing by partitioning |
| 2 | What is left over | Ring equal groups, write remainders such as 17 ÷ 5 = 3 r 2, and spot a remainder that is too big | Division with a remainder |
| 3 | What the remainder means | Sort stories by what the remainder means: round up, round down, or share it out | Interpreting the remainder |
| 4 | Three ways to write it | Write a result with a remainder, as a fraction and as a decimal, and choose the form a problem needs | Whole number, decimal or fraction |
| 5 | Solve and check | Solve school fete problems with a split, a known fact or a calculator, and read calculator decimals; play the unit quiz | Solving division problems |
How the week builds
Days 1 and 2 divide, first exactly and then with something left over; Day 3 decides what the remainder means in a story; Day 4 writes it as a fraction or a decimal; and Day 5 solves problems, with a calculator where it helps. It builds on Year 4’s division with no remainder (AC9M4N06) and this year’s multiplication of larger numbers (AC9M5N06), and it leads to Year 6, where children divide decimals by powers of 10 (AC9M6N06) and solve problems with fractions, decimals and percentages (AC9M6N09).
Materials for the week (one trip)
- From the classroom: scissors, envelopes for the cards, coloured pencils, mini whiteboards, this pack printed.
- For Day 5: one calculator per pair.
- Cut out once: the nine story cards (Day 3) and the 24 match-four cards (Day 4). No maths equipment to buy.
Words for the word wall
division, divisor, quotient, remainder, equal groups, share, round up, round down, fraction, decimal, check
Dear families
This week in maths, Year 5 divides. We split a number into parts that divide easily: 72 ÷ 6 = 60 ÷ 6 + 12 ÷ 6 = 10 + 2 = 12. When something is left over, the story decides what to do: 23 children in cars that take 4 need 6 cars, but 23 lollies shared by 4 children make 5 each, with 3 left.
Try this at home
- Share 14 grapes between 4 people. How many each, and how many are left over?
- A car takes 5 people. How many cars are needed for 22 people?
- Share $10 between 4 people. Is it $2 each, or $2.50 each?
- Ask your child why 23 children need 6 cars of 4, not 5.75 cars.
My divisions this week
Fill one row a day. Share something at home, then say what happened to the remainder.
| Day | What we shared | The division | The answer | The remainder |
|---|---|---|---|---|
| Monday | ||||
| Tuesday | ||||
| Wednesday | ||||
| Thursday | ||||
| Friday |
Printed from the free seegongsik Division teaching pack · seegongsik.com/au/y5/number/AC9M5N07/pack
Split, then divide
Children divide two- and three-digit numbers by a one-digit number by splitting the number into parts the divisor divides exactly: for dividing by 6, 72 is 60 and 12. Each part is divided and the answers are added. Multiplying back checks the answer.
We are learning to
- split a number into parts that the divisor divides exactly,
- divide each part and add the answers,
- check a division by multiplying the answer by the divisor.
Success criteria
- I can work out 72 ÷ 6 by splitting 72 into 60 and 12.
- I can check a division answer by multiplying.
You need
Mini whiteboards. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Eighty-four in four Show the board (see the box). Ask for a split before pressing anything. Ask: “84 is 80 and 4. What is 80 ÷ 4? What is 4 ÷ 4? And together?” |
| 30 min | A friendly split Model 91 ÷ 7 = 70 ÷ 7 + 21 ÷ 7 = 10 + 3 = 13. Children do Parts A and B. Ask: “Why does 72 split into 60 and 12 for dividing by 6, and not into 70 and 2?” |
| 10 min | Check by multiplying Children do Parts C and D. Ask: “14 × 5 is 70, not 75. What does that tell us about 75 ÷ 5 = 14?” |
Two half-sessions instead? Split after Part A; start Session B by splitting 87 ÷ 3 together.
Watch for these ideas
- Splitting by place value when the parts do not divide: 72 ÷ 6 as 70 ÷ 6 + 2 ÷ 6. Choose multiples of 6: 60 and 12.
- Dividing only one part, so 84 ÷ 4 = 20. Every part is divided, then the answers are added.
- Skipping the check. The answer times the divisor should give back the number.
Answers
- Part A: 48 ÷ 4 = 40 ÷ 4 + 8 ÷ 4 = 10 + 2 = 12; 65 ÷ 5 = 50 ÷ 5 + 15 ÷ 5 = 10 + 3 = 13; 78 ÷ 3 = 60 ÷ 3 + 18 ÷ 3 = 20 + 6 = 26. Part B: 24, 12, 27, 26, 23, 28.
- Part C (other splits can work): 98 ÷ 7 = 70 ÷ 7 + 28 ÷ 7 = 10 + 4 = 14; 128 ÷ 8 = 80 ÷ 8 + 48 ÷ 8 = 10 + 6 = 16; 153 ÷ 9 = 90 ÷ 9 + 63 ÷ 9 = 10 + 7 = 17. Part D: 33 × 4 = 132, so right; 14 × 5 = 70, so wrong (75 ÷ 5 = 15); 12 × 9 = 108, so wrong (117 ÷ 9 = 13); 18 × 6 = 108, so right.
Split, then divide
A. Split the number into parts that divide easily, divide each part, then add
B. Divide by splitting
96 ÷ 4 = ________84 ÷ 7 = ________135 ÷ 5 = ________156 ÷ 6 = ________92 ÷ 4 = ________252 ÷ 9 = ________
C. Find a good split
98 ÷ 7 = ______ ÷ 7 + ______ ÷ 7 = ______ + ______ = ______
128 ÷ 8 = ______ ÷ 8 + ______ ÷ 8 = ______ + ______ = ______
153 ÷ 9 = ______ ÷ 9 + ______ ÷ 9 = ______ + ______ = ______
D. Check by multiplying
| Someone worked out | My check | Right? |
|---|---|---|
| 132 ÷ 4 = 33 | ______ × ______ = ______ | yes / no |
| 75 ÷ 5 = 14 | ______ × ______ = ______ | yes / no |
| 117 ÷ 9 = 12 | ______ × ______ = ______ | yes / no |
| 108 ÷ 6 = 18 | ______ × ______ = ______ | yes / no |
What is left over
Children divide when the groups do not come out evenly. They make equal groups, count the full groups and what is left over, and write 17 ÷ 5 = 3 r 2. The remainder is always smaller than the divisor; if it were not, another group could be made.
We are learning to
- make equal groups and find what is left over,
- write a division with a remainder, such as 23 ÷ 4 = 5 r 3,
- explain why a remainder is always smaller than the divisor.
Success criteria
- I can show 22 ÷ 3 = 7 r 1 by ringing groups of dots.
- I can spot a remainder that is too big and fix it.
You need
Coloured pencils. Mini whiteboards. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Rows of five Show the board (see the box). Ask how many full rows there are before pressing anything. Ask: “Seventeen in rows of five: how many full rows? How many are left?” |
| 30 min | Ring and record Model 27 ÷ 4: draw 27 dots, ring groups of 4, and write 27 ÷ 4 = 6 r 3. Children do Parts A and B. Ask: “For 100 ÷ 3, split 100 into 90 and 10. What is left over?” |
| 10 min | Too big? Children do Parts C and D. Ask: “26 ÷ 4 = 5 r 6. Can you make another group of 4 from the 6?” |
Two half-sessions instead? Split after Part A; start Session B with 27 ÷ 4 on dots again.
Watch for these ideas
- A remainder as big as the divisor, or bigger: 26 ÷ 4 = 5 r 6. Another group of 4 fits, so it is 6 r 2.
- Mixing up the groups and the leftovers: 17 ÷ 5 = 2 r 3. Check: 3 × 5 + 2 = 17, so it is 3 r 2.
- Thinking there is no answer when a number does not divide exactly. There is: full groups and a remainder.
Answers
- Part A: 19 ÷ 4 = 4 r 3; 22 ÷ 3 = 7 r 1; 26 ÷ 6 = 4 r 2. Part B: 4 r 5, 7 r 3, 5 r 2, 7 r 5, 33 r 1, 31 r 1.
- Part C: 5 r 6 is wrong, 6 r 2; 6 r 3 is right; 7 r 3 is right; 5 r 10 is wrong, 6 r 4. Part D: 7, 12, 17, 22, 27 and so on; 6, 10, 14, 18, 22 and so on; both: 22, 42, 62.
What is left over
A. Ring equal groups, then write the division
B. Divide. Write any remainder.
29 ÷ 6 = ________38 ÷ 5 = ________47 ÷ 9 = ________61 ÷ 8 = ________100 ÷ 3 = ________125 ÷ 4 = ________
C. Too big a remainder?
| Someone wrote | Right or wrong? | The right answer |
|---|---|---|
| 26 ÷ 4 = 5 r 6 | right / wrong | |
| 33 ÷ 5 = 6 r 3 | right / wrong | |
| 52 ÷ 7 = 7 r 3 | right / wrong | |
| 40 ÷ 6 = 5 r 10 | right / wrong |
D. Leave 2 over
Find three numbers that leave 2 over when you divide by 5: ______ ______ ______. Then three that leave 2 over when you divide by 4: ______ ______ ______. Can you find one that does both? ______
Hint: take a multiple of 5, then add 2.
What the remainder means
The same division can give different answers. 23 ÷ 4 = 5 r 3, so 23 children in cars of 4 need 6 cars (round up), 23 lollies shared by 4 make 5 each (round down), and 23 m of rope cut into 4 equal lengths is 5.75 m each (share it out). The story decides.
We are learning to
- read a division story to decide what the remainder means,
- round up when everyone must fit, and round down when only full groups count,
- share the remainder out when the leftover can be cut into parts.
Success criteria
- I can explain why 23 children need 6 cars of 4, not 5.
- I can sort a story into round up, round down or share it out, and give the answer.
You need
The story cards (cut-out sheet 1), one set per group. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Same division, different answers Show the board (see the box). Groups agree on each answer before anyone presses. Ask: “The cars and the lollies are both 23 ÷ 4. Why is one answer 6 and the other 5?” |
| 30 min | Sort the stories Groups sort the nine cards into three piles, then do Parts A and B. Ask: “Card D: would 6 cartons hold all 39 eggs? Where do the other 3 go?” |
| 10 min | One division, three stories Children do Part C, then share a story with a partner. Ask: “Tell a story for 23 ÷ 4 where the answer is 6.” |
Two half-sessions instead? Split after the sort; start Session B with Part B.
Watch for these ideas
- Rounding to the nearest, as with any number: 50 ÷ 12 = 4 r 2, so 4 minibuses. Does everyone get to the pool?
- Answering 5 r 3 cars or 5.75 cars. A car is a whole thing; the answer is 6 cars.
- Sharing a remainder that cannot be cut: 30 muffins in boxes of 4 make 7 full boxes, not 7 1/2 boxes.
Answers
- Part A: round up A, D, I; round down C, E, H; share it out B, F, G.
- Part B: A 50 ÷ 12 = 4 r 2, 5 minibuses; B 26 ÷ 4 = 6 r 2, $6.50; C 50 ÷ 8 = 6 r 2, 6 bows; D 39 ÷ 6 = 6 r 3, 7 cartons; E 30 ÷ 4 = 7 r 2, 7 boxes; F 7 ÷ 4 = 1 r 3, 1 3/4 pizzas; G 14 ÷ 4 = 3 r 2, 3.5 m; H 27 ÷ 5 = 5 r 2, 5 tickets; I 45 ÷ 8 = 5 r 5, 6 tables. Part C: any stories that give 6, 5 and 5.75 (or 5 3/4).
What the remainder means
A. Sort the story cards. Write the card letters.
| Round up | Round down | Share it out |
|---|---|---|
How did you decide? _______________________________________________________
B. Solve four cards
| Card | Division | The remainder means | Answer, with the unit |
|---|---|---|---|
C. One division, three stories
23 ÷ 4 = 5 r 3. Write a story for each answer.
The answer is 6:
The answer is 5:
The answer is 5.75, or 5 3/4:
Three ways to write it
Children write a division result three ways. The remainder shared by the divisor is a fraction: 17 ÷ 5 = 3 r 2 = 3 2/5. When the fraction is halves, quarters, fifths or tenths it is also a short decimal: 3 2/5 = 3 4/10 = 3.4. The problem decides which form fits.
We are learning to
- write a remainder as a fraction of the divisor, so 17 ÷ 5 = 3 2/5,
- write halves, quarters, fifths and tenths as decimals,
- choose the form a problem needs: a remainder, a fraction or a decimal.
Success criteria
- I can write 9 ÷ 4 as 2 r 1, 2 1/4 and 2.25.
- I can say which form fits $9 shared by 4 friends, and why.
You need
The match-four cards (cut-out sheet 2), one set per group. Mini whiteboards. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Three forms Show the board (see the box). Before pressing, children write 17 ÷ 5 with a remainder on whiteboards. Ask: “The 2 left over is shared between 5. How much of one whole does each share get?” |
| 30 min | Match four Groups find the four cards that belong together, then do Part A. Ask: “Someone puts 3 r 4 with 19 ÷ 4. How do you know it is 4 r 3?” |
| 10 min | Which form fits? Children do Parts B and C. Ask: “Money comes in dollars and cents. Which form does a money answer need?” |
Two half-sessions instead? Split after the card game; start Session B with Part A.
Watch for these ideas
- Turning the remainder straight into decimal digits: 17 ÷ 5 = 3 r 2, so 3.2. The 2 left over is 2/5 = 4/10, so 3.4.
- Putting the wrong number under the remainder: 3 2/17. The remainder is shared by the divisor: 2 out of 5.
- Using a decimal for whole things: 5.75 cars. Choose the form the story needs.
Answers
- Match four: 7 ÷ 2, 3 r 1, 3 1/2, 3.5; 11 ÷ 4, 2 r 3, 2 3/4, 2.75; 21 ÷ 5, 4 r 1, 4 1/5, 4.2; 19 ÷ 4, 4 r 3, 4 3/4, 4.75; 37 ÷ 10, 3 r 7, 3 7/10, 3.7; 23 ÷ 2, 11 r 1, 11 1/2, 11.5. Part A: 9 ÷ 2 = 4 r 1 = 4 1/2 = 4.5; 15 ÷ 4 = 3 r 3 = 3 3/4 = 3.75; 17 ÷ 10 = 1 r 7 = 1 7/10 = 1.7; 22 ÷ 5 = 4 r 2 = 4 2/5 = 4.4; 26 ÷ 4 = 6 r 2 = 6 1/2 = 6.5.
- Part B: $2.25 (decimal); 2 1/2 sandwiches (fraction); 9 marbles each, 2 left over (remainder). Part C: 7 ÷ 3 = 2 1/3. A third is not a whole number of tenths, hundredths or thousandths, so the 3s never stop; the fraction is exact.
Three ways to write it
A. Write each result three ways
| Division | With a remainder | As a fraction | As a decimal |
|---|---|---|---|
| 9 ÷ 2 | |||
| 15 ÷ 4 | |||
| 17 ÷ 10 | |||
| 22 ÷ 5 | |||
| 26 ÷ 4 |
B. Which form fits? Answer, then circle the form you used.
$9 is shared equally by 4 friends. How much does each friend get?
Answer: ____________________ remainder / fraction / decimal
5 sandwiches are shared equally by 2 children. How much does each child get?
Answer: ____________________ remainder / fraction / decimal
38 marbles are shared equally by 4 children. How many does each get, and how many are left?
Answer: ____________________ remainder / fraction / decimal
C. A third
7 ÷ 3 = 2 r 1. Write it as a fraction: __________. A calculator shows 2.3333333 for 7 ÷ 3. Why does the decimal never stop? _______________________________________
_____________________________________________________________________
Solve and check
Children solve school fete problems. They write the number sentence, choose a split, a known fact or a calculator, check by multiplying, and give the answer the story needs. A calculator shows a remainder as a decimal, so they read its answer in the words of the story.
We are learning to
- decide that a problem needs division and write the number sentence,
- choose a split, a known fact or a calculator, and check by multiplying,
- read a calculator’s decimal answer in the words of the story.
Success criteria
- I can solve a fete problem and give the answer the story needs.
- I can explain what 18.75 on a calculator means for 150 jars in boxes of 8.
You need
One calculator per pair. Mini whiteboards. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Work it out first Show the board (see the box). Children work out each division on whiteboards, then one child presses a button. Ask: “Someone picks 2 r 3 for 17 ÷ 5. Multiply back: what do you get?” |
| 30 min | Fete problems Children do Parts A and B, with a calculator per pair for the big numbers. Ask: “The calculator shows 18.75 for the jam jars. How many boxes do we need?” |
| 10 min | Quiz game Run the unit’s self-check quiz as a class game: pairs agree on an answer before it is pressed. Early finishers do Part C. |
Two half-sessions instead? Split after Part A; start Session B with Part B.
Watch for these ideas
- Giving the calculator decimal as the answer: 18.75 boxes. Read the story: 19 boxes.
- Reaching for the calculator first. 372 ÷ 4 splits: 360 ÷ 4 + 12 ÷ 4 = 90 + 3 = 93.
- Dividing the smaller number by the larger: 4 ÷ 372. Ask what is being shared, and into how many groups.
Answers
- Part A: 372 ÷ 4 = $93; 150 ÷ 8 = 18 r 6, so 19 boxes; 10 ÷ 4 = 2 r 2, so 2.5 m; 340 ÷ 25 = 13 r 15, so 13 books; 1236 ÷ 12 = 103 cupcakes.
- Part B: the screen shows 6.5; 7 tents, 6 stickers each, $6.50 each. Part C: answer × divisor gives back the number, plus any remainder.
Solve and check
A. Fete problems
1. The fete raised $372, shared equally between 4 school clubs. How much does each club get?
Number sentence: ______________ Answer: ____________________
2. Jam jars are packed in boxes of 8. How many boxes are needed for 150 jars?
Number sentence: ______________ Answer: ____________________
3. A 10 m roll of bunting is cut into 4 equal lengths. How long is each length?
Number sentence: ______________ Answer: ____________________
4. Raffle tickets come in books of 25. How many full books can be made from 340 tickets?
Number sentence: ______________ Answer: ____________________
5. There are 1236 cupcakes for 12 stalls, the same number for each stall. How many does each stall get?
Number sentence: ______________ Answer: ____________________
B. Read the calculator
A calculator shows 6.5 for 26 ÷ 4. Use it to answer each story.
26 children, 4 to a tent. How many tents? __________
26 stickers shared by 4 friends. How many whole stickers each? __________
$26 shared by 4 friends. How much each? __________
C. Check two answers by multiplying
______ × ______ = ______ ______ × ______ = ______
Remainder story cards
Cut out the nine cards (Day 3), one set per group. Every story is a division with something left over. Sort the cards into three piles: round up, round down, or share it out.
A minibus seats 12. How many minibuses are needed to take 50 children to the pool?
Four friends share $26 equally. How much does each friend get?
A ribbon is 50 cm long. How many 8 cm bows can be cut from it?
Eggs are packed in cartons of 6. How many cartons are needed for 39 eggs?
Muffins are sold in boxes of 4. How many full boxes can be made from 30 muffins?
Seven pizzas are shared equally by 4 children. How much pizza does each child get?
A 14 m rope is cut into 4 equal pieces. How long is each piece?
Movie tickets cost $5 each. How many tickets can you buy with $27?
Each table seats 8. How many tables are needed for 45 guests?
Teacher note: three cards of each kind. The sort and the answers are on the Day 3 plan.
Match four
Cut out the 24 cards (Day 4), one set per group. Each division has three more cards: its answer with a remainder, as a fraction and as a decimal. Find the four cards that belong together.
Teacher note: the six sets of four are listed on the Day 4 plan.
What we know: Division
Work on your own. Show your thinking if you can.
- Split, then divide: 96 ÷ 6 = __________
- Split, then divide: 117 ÷ 9 = __________
- 38 ÷ 5 = ______ r ______
- Which of these cannot be a remainder when you divide by 4: 1, 3, 5? Why?
- 29 children sit at tables of 6. How many tables are needed? __________
- $30 is shared equally by 4 friends. How much does each friend get? __________
- Write 13 ÷ 4 with a remainder, as a fraction and as a decimal: ________ ________ ________
- A calculator shows 12.5 for 75 ÷ 6. How many full boxes of 6 can be packed from 75 eggs? __________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 60 ÷ 6 + 36 ÷ 6 = 10 + 6 = 16
- 90 ÷ 9 + 27 ÷ 9 = 10 + 3 = 13
- 7 r 3
- 5: a remainder of 4 or more would make another group of 4.
- 29 ÷ 6 = 4 r 5, so 5 tables (round up: everyone sits).
- $7.50 each.
- 3 r 1, 3 1/4, 3.25
- 12 full boxes (round down: the half box is not full).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Splitting and checking (Q1, Q2) | divides only one part of the number | splits into parts the divisor divides, then adds | chooses a split quickly and checks by multiplying |
| Remainders (Q3, Q4) | leaves a remainder as big as the divisor | writes the full groups and a remainder smaller than the divisor | explains why a remainder must be smaller than the divisor |
| What the remainder means (Q5, Q8) | rounds to the nearest, whatever the story | rounds up or down to fit the story | explains the choice from the story, including a calculator decimal |
| Fractions and decimals (Q6, Q7) | writes 3 r 2 as 3.2 | writes the remainder as a fraction of the divisor and as a decimal | chooses the form a problem needs, such as dollars and cents |
Eight questions, four ideas. A child at standard answers most questions and can say why, by naming the groups they made or what the story needs from the remainder.
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 | Splits to divide | Finds remainders | Reads the story | Writes three forms | Solves problems |
|---|---|---|---|---|---|
The five columns are the five days: splitting to divide, finding remainders, reading the story, writing three forms, and solving problems.