Money and Modelling: a week of ready-to-teach maths
Five days of lessons for Year 3 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus story cards, shop price tags, 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 shop price tags once; they 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. Modelling means using a number sentence to stand for a real situation. It has three steps: formulate (read the story and write the number sentence), solve (choose a way to work it out) and interpret (check the answer fits the story and say it in words). Many of the week’s stories are about money: totals, change, and how many can be bought.
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.
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 | Which number sentence fits? | Decide whether a story is adding, taking away, multiplying or sharing, and write its number sentence | Which number sentence fits? |
| 2 | Equal groups, two strategies | Find the cost of equal groups by adding the same price again and again, or by multiplying, and check one way with the other | Equal groups at the canteen |
| 3 | Add up the basket | Total a purchase in dollars and cents, keeping dollars with dollars and cents with cents | Add up the basket |
| 4 | Change, then the whole purchase | Find change as pay minus cost by counting up or taking away, then model a purchase from total to change | Counting the change; The whole transaction |
| 5 | Does the answer make sense? | Check an answer against the story: round up when everyone must fit, round down when the money must last | Does the answer make sense? |
How the week builds
Day 1 is the first modelling step: turn a story into a number sentence. Day 2 is the second: choose a strategy, and check one way with another. Days 3 and 4 put both to work with money, totalling a basket and then finding the change. Day 5 is the last step: read the answer back into the story. It leans on Add and Subtract to Three Digits (AC9M3N03) and Multiply and Divide (AC9M3N04).
Materials for the week (one trip)
- From the classroom: scissors, pencils, mini whiteboards or scrap paper, this pack printed.
- Play money: coins and notes from the maths cupboard, or a handful of real coins for Days 3 and 4.
- A few real items for the class shop (a pencil, an eraser, a piece of fruit) to wear the price tags.
- Cut out once, use all week: the story cards and the shop price tags in this pack.
Words for the word wall
number sentence, add, take away, multiply, share, equal groups, total, cost, price, dollars, cents, change, round up, round down, make sense
Dear families
This week in maths, Year 3 is learning to model real situations: to turn a story into a number sentence, work it out, and check that the answer makes sense. Many of the stories are about money.
Try this at home
- At the shops, ask your child to add the prices of two or three things before you pay.
- When you pay, ask how much change you should get, then count it together.
- Tell a story with numbers (4 packs of 6 eggs, $10 shared between 2) and ask for the number sentence.
- Ask whether an answer makes sense: if 14 people need cars that take 4, do we need 3 and a half cars?
Our money maths this week
Fill one row a day: what we bought or planned, the total, and the change.
| Day | What we bought or planned | Total | We paid | Change |
|---|---|---|---|---|
| Monday | ||||
| Tuesday | ||||
| Wednesday | ||||
| Thursday | ||||
| Friday |
Printed from the free seegongsik Money and Modelling teaching pack · seegongsik.com/au/y3/number/AC9M3N06/pack
Which number sentence fits?
Modelling starts by turning a story into a number sentence. Ask what happens: are more joining, are some taken away or spent, are there equal groups, or is a total shared out? Then the sentence almost writes itself: 4 packs of 6 juice boxes is 4 × 6.
We are learning to
- decide whether a story is adding, taking away, multiplying or sharing,
- write a number sentence that models the story,
- work it out and say the answer in words that fit the story (25 children, not just 25).
Success criteria
- I can choose the operation that matches a story.
- I can write and solve the number sentence.
You need
The story cards (cut-out sheet 1), one set per pair. Counters. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Act it out Act out two stories: 5 children sit on the mat and 3 more join; then 12 counters are shared between 3 children. Ask what happened each time. Ask: “In the first story the group grew. What happened in the second?” |
| 30 min | Story to sentence Choose number sentences on the board (see the box). Pairs sort the story cards into adding, taking away, multiplying and sharing, then children do the worksheet. Ask: “What in the story tells you it is equal groups?” |
| 10 min | Write a story Give 4 × 5. Children write or tell a story it models; a partner checks that the number sentence fits. Ask: “Does your story have equal groups of 5? How do you know?” |
Two half-sessions instead? Split after the card sort; start Session B with the worksheet.
Watch for these ideas
- Choosing from a key word alone (“more” means add). Picture what happens instead.
- Adding any two numbers in a story. Ask: is anything joining, leaving, grouping or sharing?
- Writing a take-away or a share backwards (6 − 15). The starting amount comes first.
Answers
- 1. add: 26 + 8 = 34 books. 2. multiply: 5 × 10 = 50 pencils. 3. take away: $15 − $6 = $9.
- 4. share: 30 ÷ 5 = 6 oranges. 5. multiply: 3 × $4 = $12. 6. take away: 35 − 9 = 26 children.
- Story cards: the sort is in the cut-out teacher note. Own story: 4 equal groups of 5 (or 5 of 4); 4 × 5 = 20.
Story to number sentence
Circle what happens in the story. Write the number sentence, then work it out. Give the answer with its word.
1. There are 26 books on the shelf. Ms Lee puts 8 more on it. How many books are on the shelf now?
2. Pencils come in boxes of 10. The class has 5 boxes. How many pencils is that?
3. Jay had $15. He spent $6 on a book. How much money does he have left?
4. 30 oranges are packed equally into 5 bags. How many oranges are in each bag?
5. Pool tickets cost $4 each. How much do 3 tickets cost?
6. 35 children are at the pool. 9 go home. How many children are still at the pool?
Your own story
Write a story for 4 × 5. Then solve it.
Equal groups, two strategies
When every group is the same size there are two ways to the total: add the same number again and again, or multiply. Five sausage rolls at $3 each is 3 + 3 + 3 + 3 + 3 = 15, or 5 × $3 = $15 in one step. One way checks the other.
We are learning to
- find the cost of equal groups by repeated addition and by multiplication,
- choose the quicker strategy and check the answer with the other one,
- write the number sentence for sharing money ($20 shared among 4 is $20 ÷ 4).
Success criteria
- I can find the cost of equal groups two ways.
- I can say which way is quicker and why.
You need
Play money ($1 and $2 coins), a handful per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Coins in groups Pairs make 4 groups of three $1 coins and find the total. Record how they did it: some add 3 four times, some know 4 × 3. Ask: “One pair added 3 four times; one pair said 4 times 3. Who is right?” |
| 30 min | Add or multiply Grow the canteen order on the board (see the box). Children find each worksheet cost both ways, then solve the two sharing stories. Ask: “For 8 rolls, which way is quicker? Would you still add if there were 10?” |
| 10 min | Check each other Pairs swap worksheets and check one answer with the other strategy. Ask: “Did both ways give the same total? If not, which one slipped?” |
Two half-sessions instead? Split after the board; start Session B with the worksheet.
Watch for these ideas
- Adding the price to the number of items (5 + $3 = $8). There are 5 groups of $3.
- Losing count of the repeated adds. Tally the groups as you go, or use the multiplication fact.
- Expecting the two strategies to give different answers. They model the same groups.
Answers
- Orders: 2 + 2 + 2 + 2 + 2 + 2 = 12 and 6 × $2 = $12; 4 × $5 = $20; 3 × $4 = $12; 7 × $3 = $21; 3 × $10 = $30.
- Sharing: $20 ÷ 4 = $5 each; $15 ÷ 3 = $5 each.
- Ella: 9 × $3 = $27. Multiplying is quicker; adding 3 nine times checks it.
Add or multiply
Find each cost two ways
Example: 5 rolls at $3 each: 3 + 3 + 3 + 3 + 3 = $15, and 5 × $3 = $15.
| Order | Add the same price | Multiply |
|---|---|---|
| 6 muesli bars at $2 each | ||
| 4 pies at $5 each | ||
| 3 pool tickets at $4 each | ||
| 7 sausage rolls at $3 each | ||
| 3 art kits at $10 each |
Share the money
1. $20 is shared equally among 4 children. How much does each child get? Number sentence: ______________ Answer: ______
2. Three friends share $15 equally. How much does each friend get? Number sentence: ______________ Answer: ______
Which is quicker?
Ella buys 9 sausage rolls at $3 each. Would you add or multiply? Find the cost, then check it the other way.
Add up the basket
The cost of a basket is the sum of its prices. Keep dollars with dollars and cents with cents: $2.50 + $1.20 is $3 and 70 cents, so $3.70. When the cents reach 100 or more, trade 100 cents for $1.
We are learning to
- read a price in dollars and cents ($2.50 is 2 dollars and 50 cents),
- total two or three prices, adding dollars to dollars and cents to cents,
- trade 100 cents for $1 when the cents add up to a dollar or more.
Success criteria
- I can total a basket of two or three prices.
- I can trade 100 cents for $1.
You need
Play money. The shop price tags (cut-out sheet 2) on a few real items. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Read the price Hold up the tags for $2.50, $0.80 and $1.20. Children read each one in dollars and cents, then make it with play money. Ask: “$0.80 and $8.00 both have an 8. Which costs more, and how do you know?” |
| 30 min | Total the basket Build the basket on the board (see the box). Children total the worksheet baskets, adding dollars with dollars and cents with cents, then make $3 from the shop. Ask: “The cents came to 145. What do we do with 100 of them?” |
| 10 min | Class shop Pairs choose two tagged items from the class shop, total them, and check with play money. Ask: “How did the coins show that your total was right?” |
Two half-sessions instead? Split after the board; start Session B with the worksheet and the class shop.
Watch for these ideas
- Adding dollars to cents ($2.50 + $1.20 = $2.70). Line up dollars with dollars, cents with cents.
- Writing 145 cents as $0.145. 100 cents is $1, so 145 cents is $1.45.
- Reading $0.80 as 80 dollars. The digits after the point are cents.
Answers
- Basket A: $0.60 + $1.90 = $2.50.
- Basket B: $1.50 + $0.95 = $2.45.
- Basket C: $1.40 + $2.20 + $0.80 = $4.40.
- Basket D: $2.00 + $0.55 + $1.20 = $3.75.
- Make $3: the apple and the water; the pencil, the eraser and the ruler; or two bread rolls and the banana.
Add up the basket
The shop
| apple $0.80 | banana $0.60 | juice $2.50 | milk $1.90 |
| bread roll $1.20 | muesli bar $1.40 | water $2.20 | sausage roll $3.00 |
| pencil $0.95 | eraser $0.55 | ruler $1.50 | sticker sheet $2.00 |
Total each basket
Add dollars to dollars and cents to cents. Trade 100 cents for $1.
Basket A: banana, milk $______ + $______ = $______
Basket B: ruler, pencil $______ + $______ = $______
Basket C: muesli bar, water, apple $______ + $______ + $______ = $______
Basket D: sticker sheet, eraser, bread roll $______ + $______ + $______ = $______
Make $3
Choose items from the shop that cost exactly $3 altogether. Write the number sentence.
Change, then the whole purchase
Change is what you pay take away the cost. Count up from the cost to what you paid: from $4.50, 50 cents makes $5, so paying $5 gives 50 cents change. A whole purchase has two number sentences: add for the total, then subtract for the change.
We are learning to
- find change as the amount paid minus the cost,
- count up from the cost to the amount paid in friendly steps,
- model a whole purchase with two number sentences: the total, then the change.
Success criteria
- I can find the change by counting up or taking away.
- I can write both number sentences for a purchase.
You need
Play money. The shop price tags (cut-out sheet 2). The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Count up Play shopkeeper: sell a $2.70 item for a $5 note and count the change up aloud, 30 cents to $3, then $2 to $5, so $2.30. Ask: “Why count up from the cost instead of down from $5?” |
| 30 min | Change, then the whole Find change on the board, then run the whole transaction (see the box). Children count up the worksheet change, then model a whole purchase. Ask: “Which number sentence comes first, the total or the change? Why?” |
| 10 min | Shopkeepers Pairs take turns as shopkeeper with the price tags and play money, counting the change up aloud. Ask: “How can the customer check they were given the right change?” |
Two half-sessions instead? Split after Counting the change; start Session B with The whole transaction.
Watch for these ideas
- Adding instead of taking away ($5 + $4.50). The change is less than the amount paid.
- Losing a step when counting up (from $2.70: 30 cents, then $2). Write each step down.
- Finding the change before the total in a whole purchase. Total first, then pay minus total.
Answers
- Change: $5.00 for $2.45 gives $2.55; $10.00 for $6.50 gives $3.50; $2.00 for $1.15 gives $0.85; $5.00 for $4.40 gives $0.60; $20.00 for $14.50 gives $5.50.
- Whole purchase: $2.20 + $0.60 = $2.80; $5.00 − $2.80 = $2.20 change.
- Ben: not right. $10.00 − $7.40 = $2.60, so he was given $1 too much.
Change, then the whole purchase
Count up the change
Example: pay $5 for $4.50. Count up: 50 cents makes $5. The change is 50 cents.
| I pay | It costs | Count up from the cost | Change |
|---|---|---|---|
| $5.00 | $2.45 | ||
| $10.00 | $6.50 | ||
| $2.00 | $1.15 | ||
| $5.00 | $4.40 | ||
| $20.00 | $14.50 |
The whole purchase
You buy a water ($2.20) and a banana ($0.60) and pay with $5.
Total: ______ + ______ = ______ Change: ______ − ______ = ______
Check the change
Ben paid $10 for a $7.40 book and was given $3.60 change. Is that right? Show how you know.
Does the answer make sense?
The last modelling step reads the answer back into the story. 20 children each want a slice and a pizza has 8 slices: 2 pizzas give 16 slices, so 4 children miss out, and nobody sells half a pizza. The answer that works is 3 pizzas. The same kind of sum can need rounding up or rounding down.
We are learning to
- check that an answer works in the story, not only in the sum,
- round up when everyone must fit, and round down when the money must last,
- say the answer in a sentence that fits the story, with any leftover.
Success criteria
- I can decide if an answer makes sense in the story.
- I can say when to round up and when to round down.
You need
Counters or cubes to model the groups. The worksheet, one per child. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | One more table? Tell the story: 23 children, and each table seats 6. Model it with counters in groups of 6, then ask how many tables to set. Ask: “Three tables seat 18. What about the other 5 children?” |
| 25 min | Up or down? Test answers on the board (see the box). Children solve the worksheet problems and say whether they rounded up or down. Ask: “Why did we round up for the pizzas but down for the tickets?” |
| 15 min | Class quiz Run the self-check quiz as a team game: teams hold up one, two or three fingers for their choice. Ask: “Which picture from this week would prove that answer?” |
Two half-sessions instead? Split after the board; start Session B with the worksheet and the quiz.
Watch for these ideas
- Giving the sum’s answer without checking the story (2 and a half pizzas). Ask what really happens.
- Always rounding up. When the money must last, round down: $18 buys 4 tickets, not 5.
- Leaving out the leftover. Say it in full: 4 tickets, with $2 left over.
Answers
- Opening: 4 tables (3 tables seat 18, and the other 5 children need a fourth).
- 1. 4 minibuses, up (3 take 24, so 3 children are left). 2. 6 stickers, down ($18, with $2 left). 3. 3 cartons, up (18 eggs, 3 spare).
- 4. 5 benches, up (4 seat 20, so 3 children are left). 5. 4 pens, down ($8, with $1 left).
- Explain: round up when everyone must have a place; round down because you cannot spend money you do not have.
Does it make sense?
Work it out, then write the answer that works in the story. Circle whether you rounded up or down.
1. 27 children are going to the sports carnival. Each minibus takes 8 children. How many minibuses are needed?
2. Stickers cost $3 each and you have $20. How many stickers can you buy?
3. Eggs come in cartons of 6. The cake stall needs 15 eggs. How many cartons should we buy?
4. Each bench seats 5 children. There are 23 children. How many benches are needed?
5. Pens cost $2 each and you have $9. How many pens can you buy?
Explain
Why do we round up for the minibuses but round down for the stickers?
Story cards
Cut out the twelve cards. On Day 1, pairs sort them into four piles: adding, taking away, multiplying and sharing. Then they write the number sentence for each card.
Teacher note, the sort: adding, cards 1 (15 + 6 = 21), 7 ($8 + $5 = $13), 10 (23 + 9 = 32); taking away, cards 2 (30 − 12 = 18), 5 ($10 − $4 = $6), 12 (25 − 8 = 17); multiplying, cards 3 (3 × 6 = 18), 6 (5 × $2 = $10), 9 (4 × 5 = 20); sharing, cards 4 (20 ÷ 4 = 5), 8 ($12 ÷ 2 = $6), 11 (18 ÷ 3 = 6).
Shop price tags
Cut out the twelve tags and stick them on real items or pictures to set up a class shop for Days 3 and 4. The prices match the worksheets.
Teacher note: the Day 3 baskets and the Day 4 change both use these prices, so children can check a sheet against the shop.
What we know: Money and Modelling
Work on your own. Write a number sentence for each one.
- There are 6 boxes with 4 cupcakes in each box. How many cupcakes? ______________ = ______
- 28 stickers are shared equally among 4 children. Circle: add / take away / multiply / share. ______________ = ______
- Drinks cost $3 each. Find the cost of 6 drinks two ways. Add: ______________________ Multiply: ______________
- $1.60 + $2.30 = ______
- A banana costs $0.60, a juice $2.50 and an eraser $0.55. What is the total? ______________________
- You pay $5 for a book that costs $3.80. How much change do you get? ______________________
- You buy a milk ($1.90) and a muesli bar ($1.40) and pay with $5. Total: ______________ Change: ______________
- 13 children want to paddle, and each canoe takes 3 children. How many canoes are needed? ______ Why? ______________
Answers and marking guide
Answers
- 6 × 4 = 24 cupcakes.
- Share: 28 ÷ 4 = 7 stickers each.
- 3 + 3 + 3 + 3 + 3 + 3 = 18 and 6 × $3 = $18.
- $3.90.
- $0.60 + $2.50 + $0.55 = $3.65 (the cents make 165, so trade 100 cents for $1).
- $5.00 − $3.80 = $1.20 (count up: 20 cents to $4, then $1 to $5).
- $1.90 + $1.40 = $3.30; $5.00 − $3.30 = $1.70.
- 5 canoes: 4 canoes take 12, so 1 child is left, and you cannot send part of a canoe.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Formulate (Q1, Q2) | chooses the operation from a key word alone | decides whether a story is adding, taking away, multiplying or sharing and writes the number sentence | writes a story to match a given number sentence |
| Solve, with money (Q3 to Q7) | adds dollars to cents, or loses track when counting change | finds equal-group costs two ways, totals a purchase and counts up the change | checks a total or a change with a second strategy |
| Interpret (Q8) | gives the answer to the sum without checking the story (4 and a third canoes) | rounds up or down to suit the story and says the answer in words | explains when to round up and when to round down |
Eight questions, three ideas. A child at standard writes a number sentence that fits each story and says the answer in words, with its unit or its dollars and cents.
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 | Number sentences | Two strategies | Totals | Change | Makes sense |
|---|---|---|---|---|---|
The five columns are the five days: writing number sentences, two strategies for equal groups, totalling a basket, finding change, and checking that an answer makes sense.