p380-421-Gr3ON-Number-Unit5-financial-pass2

Unit 5: Financial Literacy Lesson Content Page Financial Literacy Introduction 380 382 1 Introduction to Financial Literacy 386 391 2 Identifying, Describing, and Comparing Coins and their Values 395 399 3 Identifying, Describing, and Comparing Dollar Coins and Bills 400 402 4 Making Change 406 5 and 6 Making Totals and Change in More than One Way 410 5 Adding Totals and Making Change Using Coins 411 413 6 Adding Totals and Making Change Using Dollar Coins and Bills 418 7 Applying the Commutative and Associative Properties when Adding Money 8 and 9 Scaling Up Money Amounts and Making Change 8 Buying Relational Rods 9 Calculating the Cost of a Pattern Block Design 10 Guided Math Lesson: Arlo’s Busy Day

Financial Literacy Introduction About the Financial literacy is a critical lifelong skill. The Ontario Working Group on Financial Literacy defines financial literacy as “having the knowledge and skills needed to make responsible economic and financial decisions with competence and confidence” (Ontario Ministry of Education, 2010, p. 7). Being financially literate will help students make better, more informed choices in life. Some of the related concepts that the Working Group identifies include money, income or earning money, saving, spending, budgeting, and planning ahead with money (Ontario Ministry of Education, 2010, p. 13). The focus in the primary grades is on understanding the value and use of Canadian coins and bills. In grade three, students build upon their experiences of creating equivalent money amounts in grade two, and calculate the amount of change owing on simple transactions that include whole-dollar amounts or amounts less than one dollar. These concepts are best understood when presented in realistic contexts so students can relate to the situations, recognize that transactions play an important role in society, and learn about managing money. Students can also apply their understanding of operations as they perform the necessary calculations. On a more practical note, money is an excellent manipulative with which to reinforce other significant math concepts, such as equality. Students learn, for example, that a toonie has a value of $2 but simultaneously has a value of 200¢. The various coins also encourage skip counting, repeated addition or subtraction, and estimating larger quantities. As emphasized in A Guide to Effective Instruction in Mathematics Grade 1 to 3: Number Sense and Numeration, “although the penny coin is no longer produced in Canada, the penny still has value in our money system. Therefore, it is important that students understand the value of the penny” (Ontario Ministry of Education, 2016, p. 17). You may decide to initially include the penny in lessons until students understand and can unitize the values of the coins and bills. For example, by trading 10 pennies for a dime, students can internalize the value of one dime as being ten cents. About the Lessons The lessons have financial literacy contexts that focus on needs versus wants, spending goals, different ways of saving and earning money, and giving back to the community through donations. 380 Number and Financial Literacy

Lesson Topic Page 1 Introduction to Financial Literacy 382 386 2 Identifying, Describing, and Comparing Coins and their Values 391 395 3 Identifying, Describing, and Comparing Dollar Coins and Bills 399 400 4 Making Change 402 5 and 6 Making Totals and Change in More than One Way 406 5 Adding Totals and Making Change Using Coins 410 411 6 Adding Totals and Making Change Using Dollar Coins and Bills 413 418 7 Applying the Commutative and Associative Properties when Adding Money 8 and 9 Scaling Up Money Amounts and Making Change 8 Buying Relational Rods 9 Calculating the Cost of a Pattern Block Design 10 Guided Math Lesson: Arlo’s Busy Day Financial Literacy 381

1Lesson Introduction to Financial Literacy Math Financial Literacy Curriculum Expectations • F1. demonstrate an understanding of the value and use of Canadian Teacher currency Look-Fors Possible Learning Goals PMraotcheesmseast:ical arRenefdlaesscottrinanitgne,ggsiaeenlsed,cptirnogvitnogo,ls • Investigates the places a loonie may travel during its years in circulation to ccoomnnmecutninicga,trinegpresenting, gain insight into how we use money in society Math Vocabulary: cash, mlcoooosnntei,eyc,,hccaiorncinguesla, tbioilnls,, • Understands that money is a medium of exchange for goods and services • Identifies and describes the loonie and its features • Identifies the value of the loonie in both cents and dollars • Explains how the loonie can be used in everyday life • Distinguishes between wants and needs About the Lesson This whole-group lesson introduces students to financial literacy and the role money plays in their lives and in society. Together, students analyse and discuss the various places that a loonie may travel during its years in circulation. NOTE: Select the prompts that best suit the needs and interests of your students. Materials: Minds On (15 minutes) • Ask students what they know about money and how they have used it in their lives. Have them reflect on how their families use money. List some of their responses. at least 1 real loonie, • Ask students what they know about Canadian money. Discuss how there are “Loonie Adventure” (pages 12–13 in the various types of coins and bills that each have different values. Record Number and Financial money terms on the Math Word Wall as they come up in discussion. Literacy big book and little books) • Ask what they know about the loonie. Show a real loonie and pass it around Time: 45–50 to students so they can see its features. If possible, pass a loonie to groups of minutes three or four students. Ask students how they think the loonie got its name. Highlight that the loonie is an eleven-sided figure known as a ‘hendecagon.’ Loonies were first made from nickel and bronze, but now they are made from steel and brass to make production costs cheaper. Ask what other significant features they see on the coin (e.g., the words ‘Canada’ and ‘dollar,’ the picture of the queen, the year). 382 Number and Financial Literacy

Teaching Tip • Tell students that they are going to investigate the loonie and how it is used, You may decide and learn some interesting facts about it. to investigate the pictures over two Working On It (Whole Group) (20–25 minutes) sessions, depending on how long • Show “Loonie Adventure” (pages 12–13 in the Number and Financial Literacy discussions last. big book). Read the title then ask students to predict what the page might be about. Small groups of students can also share the little book versions of the big book to more closely examine some of the pictures. Royal Mint • Draw attention to the first picture on page 12, of the Royal Mint. Explain that it is in Winnipeg, Manitoba, and this is where the loonie is made. Loonie and $1 Bill • Show the picture of the loonie and the old $1 bill. Explain that the loonie replaced the $1 bill in 1987, over 30 years ago. Ask why the government may have decided to replace the bill. Explain that this was done to save money since the loonie costs less to make and it can last longer. Explain that loonies are used for about 20 years before they are taken out of circulation and are returned to the Mint to be recycled. Ask what they think ‘circulation’ means. Pay Phone • Explain that pay phones were very popular in the past and were found in places such as street corners, malls, airports, and railway stations. Now there are only about 10 000 pay phones left across Canada. Ask why there are fewer pay phones around now. Ask why loonies would be handy to use in pay phones. Ask how they think a pay phone works. Vending Machines • Ask students if they have ever used a vending machine and what they purchased. Ask where vending machines are located and what types of items they sell. Ask why there are vending machines when you can buy what you need in a store. Ask how vending machines work. Ask what happens if you put in more money than the item costs. Explain that the return of money beyond the cost is known as ‘giving change.’ Piggy Bank • Ask students what they see in the picture and what the purpose of a piggy bank is. Ask if they have a piggy bank or something else to store money that they are saving. Ask what it means to save money and why people do it. Ask what other coins they may put into a piggy bank. Gumball Machine • Ask students if they have ever seen a gumball machine or a candy machine. Ask how they think the machines work. Ask how many gumballs they might get for 1 loonie. Ask what they think happens to the money once it is in the gumball machine, how long it might stay in there, and who gets it. Financial Literacy 383

Newspaper Boxes • Ask what is being sold in the boxes. Ask students whether any of their family members get a newspaper and how they get it. Ask why people like reading newspapers. Ask why students think there are so many different boxes. Ask why some newspapers are free and why you need to pay for others. Ask why loonies would be good for buying newspapers. Ask, “About how often do you think people buy newspapers? Why?” Parking Meter • Ask what type of machine is in the picture and whether students have ever seen one before. Ask why people may have to pay to park on the street. Ask how a parking meter works. Explain that the more money a person puts in the meter, the longer that person can park. Ask students what they think happens if the time on the meter runs out before a car is moved. Women’s Hockey Game at the 2002 Olympic Games, Salt Lake City • Ask what a loonie might have to do with a hockey game. Explain that in 2002, a Canadian from Alberta was hired to make the ice for the hockey rink at the Olympic Games. He decided to secretly bury a loonie at centre ice to bring good luck to the Canadian teams. He only told people involved with Team Canada so they would be inspired to win. Both the men’s and women’s Canadian teams won that year. And, it was the first time in over 50 years that the men’s team had won. This loonie became known as a ‘lucky loonie’ and is now on display at the Hockey Hall of Fame. Ask students whether they think the loonie can really bring good luck. Ask why the icemaker might have chosen to bury a loonie and not a different kind of coin. (e.g., Loonies are gold in colour and he wanted the hockey teams to win gold medals.) Cashier’s Till • Ask students where these coins might be and whether they have ever seen a drawer of money like this in stores. Ask why loonies might make it to many stores during their 20 years in circulation, and what types of stores they might be in. Ask how the loonies are used (e.g., to pay for things, to give change for bills). Ask how long they think a loonie may stay in a cashier’s drawer. Laundromat • Ask students what they see in the picture and why there are so many driers in a row. Explain that the building is known as a laundromat. Ask why laundromats may be very important to some people and not to others. Ask why loonies would be a good way to pay for the service. Ask how students think the coin- operated driers work and who gets the money out of the machines. Ask who gets to keep the money. Differentiation • You may decide to revisit these pictures at another time and have students engage in partner investigations, such as exploring how many loonies can stretch across the length of the room. 384 Number and Financial Literacy

• For ELLs or any students who may need language support, review some of the words recorded on the Word Wall after the lesson. Assessment Opportunities Observations: Since this is an introductory lesson for this unit, it is important to listen to what students say about money and note their previous knowledge and experience. You can draw on these experiences to help them better connect to the concepts. You can also uncover any misconceptions that students may have and discuss them further to clarify their ideas. Consolidation (10 minutes) • Ask students what they found most interesting about the loonie. Ask what they still wonder about. Some of their responses could be topics for further investigations. • B uilding Social-Emotional Learning Skills: Critical and Creative Thinking: Tell students that they are just beginning to learn about money and how it is used in real life. They will learn much more in this unit and in the years ahead, which will help prepare them to use money wisely in the future. Ask what questions they have about money and what they wonder about. Create a chart of their responses, which can become starting points for inquiries. Further Practice • At another time, have students reflect on and discuss how many places a loonie might travel to in one day. Financial Literacy 385

2Lesson Identifying, Describing, and Comparing Coins and their Values Math Financial Literacy Curriculum Expectations • F1. demonstrate an understanding of the value and use of Canadian Teacher currency Look-Fors Possible Learning Goals Previous Experience with Concepts: • Identifies and describes Canadian coins and represents a monetary amount In grade two, students worked with coins and using various combinations of coins bills (coin amounts to 200¢ and dollar amounts • Estimates the value of a collection of coins, and counts them to find the to $200). Students have used the cent (¢) and actual total dollar ($) symbols. • Identifies and names coins and describes their appearance and value PMraotcheesmseast:ical • Compares coins based on their features and relative values arRenefdlaesscottrinanitgne,ggsiaeenlsed,cptirnogvitnogo,ls • Creates and solves riddles based on the features of various coins and bills ccoomnnmecutninicga,trinegpresenting, • Accurately uses coins to represent various money amounts • Counts coins and bills, adjusting their counting strategy for different values About the As John Van de Walle and LouAnn Lovin explain, recognizing the names and values of coins and bills is not a mathematical skill but a convention of society. Students learn these names the same way they acquire the names of any objects, and they learn the values by being told (Van de Walle & Lovin, 2006a, p. 150). Explicit teaching is necessary so students can learn and internalize these conventions. Students in grade two estimated, counted, and represented the value of a collection of coins to 200¢ and dollar coins and bills to $200, but they likely need to refresh this knowledge. It is also beneficial to review the strategies that can be used to count the coin values and represent a given amount. For example, students may use the largest coin as a starting point and count on as they add other coins in an order that makes the counting convenient (e.g., begin with 1 quarter, add on a nickel to make 30¢, and then count on by 10s for 2 dimes). Students may also subitize 386 Number and Financial Literacy

Mmvddaiaoomlutlnlheeae,,ry,V,lnoeociocqocknuianeiaebsll,,u, pqblaeuilnralsynr,:tyec,re,nts, familiar amounts of money (e.g., 4 quarters represents $1), or apply knowledge of addition facts to total small values of coins (e.g., 2 nickels is 10¢, 1 nickel and 1 dime is 15¢). Although the penny coin is no longer in circulation and we round cent values to the closest nickel for cash transactions, money values such as $3.62 still arise when paying with a debit card, a credit card, and cheques. After introducing the penny in this and other early lessons, you may decide to phase it out and have students round to the nearest 5¢ to make the situations more realistic. About the Lesson In this lesson, students identify and describe Canadian coins and establish their relative values. In the accompanying Math Talk, students make equivalent amounts of money. Materials: Minds On (15 minutes) chart paper, BLM 52: • Before the lesson begins, create a copy of BLM 52: Canadian Money on chart Canadian Money, Digital Slide 45: paper so you can co-create an anchor chart in the Consolidation. You will Canadian Penny, coin need 11 rows under the headings (bills will be added in a later lesson). manipulatives, slips of paper • Review the headings on the chart with the class. • Ask students how they could fill in the chart for the loonie based on what Time: 60 minutes they learned in the previous lesson. Record this information in the fifth row of the class chart. • Ask students what a riddle is. Clarify that riddles present clues that help people guess the mystery of the riddle. Ask what is important to remember when creating a good riddle. (e.g., The clues have to give enough information so the riddle can be solved, but the information should not make the solution too obvious or easy to guess.) Ask students how they could create a riddle for the loonie. Have them turn and talk to their partner. • Have students share their ideas. Together, create a riddle that has two or three clues. • Ask what the other Canadian coins are called. Write their names on the chart in their order of value. Include the penny. • Show students Digital Slide 45: Canadian Penny. Explain that although the penny is no longer produced in Canada, its value is important because it helps us understand the relative value of the rest of the coins. Working On It (20 minutes) • Students work in pairs. Provide each pair with a copy of BLM 52: Canadian Money and coin manipulatives. Financial Literacy 387

• Explain to students that they will examine the other Canadian coins and fill in the information on the BLM to develop a good description of each. They can also copy the information about the loonie into their charts. • When students have completed their BLM, have them develop riddles for two or three of the coins, recording each on a separate slip of paper. They do not include the answers. Ensure there is a riddle for each coin, for the Consolidation. Differentiation • You may want each pair of students to develop only one riddle. • For students needing more of a challenge, have them develop riddles for each of the coins. They can also develop a riddle with clues that make comparisons between two coins (answers name both coins). Assessment Opportunities Observations: Observe whether students are recording features of the coins but not comparing them. Conversations: If students are not making comparisons, pose some of the following prompts: – Y ou said this coin has a value of 5¢. How does this compare to other coins? – Y ou found a beaver on the nickel. Is there anything similar on the other coins? – E ach coin has a person on it. Does this make the coins similar or different? Consolidation (25 minutes) • Meet as a class. Together, complete the Canadian Money anchor chart started in the Minds On. As you do, make comparisons across the categories to highlight what makes the coins the same and what makes them different. • Discuss the features that are the same on all coins and why this is important. (e.g., They can be identified as Canadian coins; their amounts are printed on them; they all have a date to indicate when they were made.) • Discuss why it is important to have features that are different from coin to coin (i.e., features that differ among various types of coins, features that vary on the same type of coin). Ask why the coins might all be different sizes. • Have students retrieve their riddles. Create an inside/outside circle (i.e., two circles of students, one inside the other, with each student in one circle facing a student in the other circle). Have the pairs of students facing each other take turns reading one of their riddles to their partner, who guesses the mystery coin. After all the pairs are done, have one of the circles move to the left so that everyone has a new partner. Partners share their riddles again. 388 Number and Financial Literacy

Materials: Further Practice hundreds chart 1–100 (from BLM 3: Hundreds • M ath Game: Race to 100: Students play in pairs. Charts to 500), BLM 53: Coin Spinner, pencil and – P layer A spins the coin spinner from BLM 53 and moves his/her counter paper clip, counters or that number of spaces on the hundreds chart (e.g., for a nickel, move 5 tiles (a different colour or spaces). shape for each player), coin manipulatives – Player B takes a turn, moving his/her counter starting at the next empty (optional) cell in the hundreds chart to mark the progress throughout the game. Materials: – The winner is the first player to reach or surpass 100¢. anchor chart – V ariation 1: The winner is the first player to reach exactly 100¢. If a ‘Canadian Money’ from the Consolidation, player rolls an amount that will exceed 100¢, they lose a turn. coin manipulatives, – V ariation 2: Instead of using a hundreds chart, players accumulate coin chart paper manipulatives. This encourages them to track the total as they go or to periodically count up their money. In this way, players can confirm whether the winner actually reached 100¢. • Independent Problem Solving in Math Journals: Students can use coin manipulatives to solve one or more of the following problems. They should record the money amount and show how they counted. – You have 25 quarters. How much money do you have? – You have $3.10. Then you find 21 dimes. How much money do you have now? – S ammy has $7.24. He finds 14 nickels. How much money does he have now? – M arcy has $9.25 in quarters. How many quarters does she have? – You have 17 nickels. How much money would you have left if someone takes 9 nickels away, one at a time? Math Talk: Math Focus: Representing amounts of money up to 100¢ using various combinations of coins Note: You can choose to include the penny in the coin manipulatives, depending on the needs of your students. Students may still need to see the individual cents to be able to visualize the value of other coins (e.g., to see 5 pennies and mentally link them to the nickel, which is worth five cents). Let’s Talk Select the prompts that best meet the needs of your students. • Look at the chart we developed about Canadian coins. What is the value of 1 quarter? What does it mean that it is worth 25¢? What is the penny worth? How many pennies could be exchanged for the quarter? Work with a partner and find all of the ways that you can make combinations of coins that have the same value as 1 quarter. continued on next page Financial Literacy 389

Teaching Tip • W hat did you find? (e.g., 2 dimes and 1 nickel) How can you count this Integrate the math amount? What coin do you find best to start counting with? Why? Did you talk moves (see find any other combinations? (e.g., 1 dime and 3 nickels; 5 nickels) How did page 8) throughout you count these combinations? What coin did you start counting with? Draw Math Talks to the equivalent amounts on chart paper as students suggest them. maximize student participation and • Let’s imagine you have 50¢. How can you use the combinations for 25¢ to active listening. know what coins equal 50¢? (e.g., Double the number of coins in each combination, because 50¢ is double 25¢.) Are there any new ways to make 50¢ besides doubling these coin combinations? Turn and talk to your partner and use the coin manipulatives to find other ways. • W hat did you find? (e.g., 5 dimes; 1 quarter, 1 nickel, and 2 dimes) How would we count these combinations? Is there more than one way? What coin did you find easiest to begin counting with? Why? • Imagine you have 75¢. How do the coin combinations we found for the quarter help us this time? (e.g., Triple the number of coins in each case, because 75¢ has the value of 3 quarters.) How would you count these combinations? What new ways can you find? Work with your partner. • W hat did you find? (e.g., 3 quarters; 2 quarters, 2 dimes, and 1 nickel) How would you count each of these combinations? Which coin was best to start counting with? • Imagine you have 100¢. How could you make this amount with the least number of coins? Which combination would have the greatest number of coins? [Ask this question either with the penny or without the penny.] • W ork with your partner to find a way to make 100¢ with exactly 8 coins. What did you find? • When you are counting combinations of coins, which coin seems to be best to start counting with? Why? 390 Number and Financial Literacy

3Lesson Identifying, Describing, and Comparing Dollar Coins and Bills Math Financial Literacy Curriculum Expectations • F1. demonstrate an understanding of the value and use of Canadian Teacher currency Look-Fors Possible Learning Goal Previous Experience with Concepts: • Identifies, describes, and represents the value of a collection of dollar coins In grade two, students worked with coins and and bills bills (coin amounts to 200¢ and dollar amounts • Identifies, names, and describes coins and bills to $200). • Identifies some features of the $5 bill and the $10 bill • Identifies the $20, $50, and $100 bills PMraotcheesmseast:ical • Uses the anchor chart ‘Canadian Money’ to support their work arRenefdlaesscottrinanitgne,ggsiaeenlsed,cptirnogvitnogo,ls • Estimates the value of a collection of money in dollars, and gives reasons for ccoomnnmecutninicga,trinegpresenting, their estimation Math Vocabulary: mblboioilolllsnn,,ei$edy2,,o0tcloloaboirnnislsli,e(,$$,c)$5,e50nvatbbsluii(lle¢ll,,,),$10 • Accurately uses dollar coins/bills to represent various money amounts $100 bill • Counts dollar coins and bills, adjusting their counting strategy for different values of dollar coins/bills • Represents the same money amount with different combinations of dollar coins and bills • Exchanges dollar coins/bills for equivalent amounts of other dollar coins/bills • Correctly uses the dollar symbol, and accurately reads money amounts in dollars About the Grade three students work with coins and bills; they calculate dollar amounts and make change with full dollar amounts. It can be challenging to work with coins and bills. For example, there are some coins that represent cent amounts (e.g., dimes) and other coins and bills that represent dollar amounts. Students may be confused when learning that a nickel is worth 5¢ and there is a bill worth $5. Both are worth 5 units, but the units are different, so students need to understand the difference between cents and dollars and the relationship between them. Financial Literacy 391

About the Lesson In this lesson, students investigate the features of the $5 bill and the $10 bill. They also investigate the $20, $50, and $100 bills and their relative values. Materials: Minds On (20 minutes) anchor chart from • Revisit the co-created anchor chart ‘Canadian Money’ from Lesson 2. Lesson 2 (“Canadian • Draw attention to the row about the loonie. Say, “We wrote on the chart that Money”), real $5 bill or Digital Slide 46: the loonie has a value of 100 cents (100¢). What is the value in dollars? How Canadian $5 Bill, real do we write the value in two different ways?” Add information about the $10 bill or Digital Slide toonie to the next row. 47: Canadian $10 Bill, Digital Slides 48–50 • Show students the most recent version of an actual $5 bill available, or show (more Canadian bills), BLM 54: Money Digital Slide 46: Canadian $5 Bill. (An actual bill is preferable.) Note and Challenges, money discuss some of the features of the bill, adding information to the anchor manipulatives (coins chart as you go. Below are some interesting facts that you can include (not and bills), chart paper, all will apply to all bill versions): markers – It is blue, made out of a plastic material, and some parts are transparent. Time: 60 minutes – O ne side has a picture of former prime minister Sir Wilfrid Laurier. There is also part of a building, the West Block of the Parliament Buildings in Ottawa. – T he other side has a picture of the Canadarm, a robotic arm used on space missions from 1981 to 2011. The astronaut represents all the Canadians who have contributed to the space program. – S ecurity features include: the large 5 has raised ink; the three maple leaves turn colour when you tilt the bill; there is a hidden 5 you can see when you tip the bill; and if you look at the bill under ultraviolet light, Canada’s coat of arms and the word FIVE can be seen. • Show students the most recent version of an actual $10 bill available or Digital Slide 47: Canadian $10 Bill. Note and discuss the features of the bill, adding information to the anchor chart as you go. Include in the discussion any of the facts below that are applicable: – It is purple, made out of plastic material, and some parts are transparent. – T he images on the bill are vertical instead of horizontal. – O ne side has a picture of Viola Desmond, who is the first woman to appear on a Canadian bill other than the Queen. Desmond refused to leave a segregated whites-only section of a theatre, thereby standing up for her human rights. – T he other side has a picture of the Canadian Museum for Human Rights in Winnipeg, and an eagle feather representing truth, power, and freedom. 392 Number and Financial Literacy

– S ecurity features include: the large 10 has raised ink; the colours on the eagle feather change when you tilt the bill; the images in the transparent window change when you tilt the bill; the largest maple leaf appears to be three-dimensional. • Using Digital Slides 48–50, introduce the $20, $50, and $100 bills. Ask students how they would effectively count a set of like bills. • Make a distinction between the bills and the two coins that represent dollars, and the other coins that represent cents. Working On It (20 minutes) • Students work in pairs. Give them BLM 54: Money Challenges and money manipulatives with which to count out the combinations of bills and dollar coins. Students can record each amount and show how they counted on chart paper. Remind students to estimate the total before they count. • You could also ask students to represent each amount using a different combination of bills and dollar coins. Differentiation • Adjust the amounts in the challenges as needed, so they meet the abilities of your students. Assessment Opportunities Conversations: If students are having difficulty counting a combination of coins and bills, pose some of the following prompts: – H ow could we sort this money so it will be easier to count? Let’s sort the coins/bills by their values. – T ry counting the larger bills first. Record what you found. Now count in the smaller bills. How can you count in the dollar coins? Consolidation (20 minutes) • Have pairs share their problems with another pair. Encourage students to count the bills/coins shown by other students to check for accuracy. • Strategically select two or three student examples to share and discuss with the class. Have the students explain how they were able to represent the same amount using different bills/coins. Explicitly discuss what coins and bills could be exchanged for others. • Encourage students to use correct vocabulary for bills and coins and for describing the money amounts. • Review how money amounts are written using the dollar sign. • B uilding Social-Emotional Learning Skills: Critical and Creative Thinking: Conclude the discussion by asking students for one or two things they learned today that were new. Emphasize that they may not know how to represent all money amounts yet, but they will be learning and practising how to use the dollar coins and bills throughout this unit. They will also work with Financial Literacy 393

the other coins to make amounts using the unit of ‘cents.’ Encourage them to refer to the anchor chart “Canadian Money” as they work through the rest of the lessons. • Challenge students to find written money amounts in their environment (e.g., at the store, gas station, on advertisements). Give them paper to take home so they record their findings. They can also take photos of what they observe. A few days later, have students bring in their findings and discuss them as a class. Emphasize that money plays a very important role in our society, and that it is important to learn about money so as they grow up they can buy groceries, get gas for the car, count the money they earn, and read the prices of the items they want to save for and buy. Making this connection to everyday life is important so students see the value in learning about money. Further Practice • Independent Problem Solving in Math Journals: Have students draw a collection of dollar coins and bills and write its total value. Have them represent the same value in another way. 394 Number and Financial Literacy

4Lesson Making Change Math Financial Literacy Curriculum Expectations • F1.1 estimate and calculate the change required for various simple cash Teacher transactions involving whole-dollar amounts and amounts of less than one Look-Fors dollar Previous Experience Number with Concepts: Students have experience • B2.5 represent and solve problems involving the addition and subtraction of adding money amounts and subtracting two-digit whole numbers that add up to no more than 1000, using various tools and and three-digit whole algorithms numbers. Possible Learning Goal PMraotcheesmseast:ical arPenrfodlebsclettrimantges,gosileevlsien,cgt,ing tools • Creates change and counts it by calculating the differences in money ccoomnnmecutninicga,trinegpresenting, amounts, using a variety of strategies Math Vocabulary: cpeunrctsh,arseeg,rotoutpailn, g, • Understands that the context of the problem requires finding the difference in change, money amounts dollars, subtracting • Selects and uses a reasonable strategy and explains how it works • Makes money amounts using appropriate bills and coins • Makes change by providing the correct bills and coins and counting to confirm accuracy About the Realistic contexts for finding the difference between money amounts arise when people a) spend money and want to know how much they have left, or b) pay for an item with a coin or bill that is greater than the item’s value and require change. For these scenarios, students will most likely adapt many of the strategies they used for adding and subtracting two-digit whole numbers. While they may subtract the two amounts in different ways, they also may use ‘think-addition’ and count on from the lower amount. Adding on from the lower amount is frequently used when making change. For example, if something costs $27 and a person pays with a $50 bill, students can visualize starting at $27 and getting to the nearest ten-dollar amount by adding 1 toonie and 1 loonie. It is important that students work with money manipulatives as they calculate the amount of change owed so they form visual images of money in terms of the values of coins and bills. Financial Literacy 395

Materials: Minds On (20 minutes) BLM 55: Making • Say, “I have a $10 bill to buy my lunch. I bought a sandwich for $3 and a Change, money manipulatives, chart drink for $1. How much money will I get back from my $10 after paying for paper, markers these items? What dollar coins and bills might I get back?” Have students discuss the problem with their partner. They can use money manipulatives if Time: 60 minutes they would like to. • Discuss students’ responses. Have students justify how all of the ways of making change represent the same amount. • Discuss what ‘change’ means and whether they have ever seen a cashier make change for a customer. Reinforce the idea that ‘change’ means the difference between the amount paid and the amount owed. Ask why it is important that the customer knows how to make change (e.g., to make sure they get the correct change back). • Ask how much change students would get back from a loonie if they bought something that cost 45¢. Ask how this amount could be represented in different ways. • Discuss the difference between dealing with money amounts in dollars versus money amounts in cents. Working On It (20 minutes) • Have students work in pairs. Provide students with money manipulatives, BLM 55: Making Change, chart paper, and markers. Read over the instructions and the challenges on the BLM so students are clear on what they are to do. Differentiation • For students who need more support, have them solve only one or two of the challenges on BLM 55 and only represent their change in one way. • For students who need more of a challenge, encourage them to solve each problem in more than one way. Students can also create their own problem and solve it. Assessment Opportunities Observations: Pay attention to how students are making change. Are they exchanging coins/bills with intentionality or are the using trial and error? Are they using a strategy (e.g., counting) to confirm their solution? Do they understand that they are finding the difference between two monetary values? Conversations: If some students are having difficulty understanding that they are finding the difference between two amounts (the total amount owing and the total amount paid), pose some of the following prompts: – W hich of the two money amounts do I have already? – W hich of the two money amounts do I need to give away? Would the remaining amount be more or less? – W hat coins or bills do you need to make the change? What coins or bills could you exchange to make the problem easier? 396 Number and Financial Literacy

Consolidation (20 minutes) • Have student pairs meet up with another pair to share their answers. Encourage them to explain how they solved the problems, and have the other pair check for accuracy. • Meet as a class. Strategically select different strategies to discuss. Some possibilities include: – S tudents made the larger amount—the money paid—and then took away the money owed, making exchanges as needed. – S tudents made the smaller amount—the money owed—and then added money to it to make the larger amount (adding on). • Discuss how cashiers often count the money that they are giving to a customer, starting with what is owed and ending at the amount that was paid. Explain that the cashier’s machines often calculate the amount of change that the customer should get. Ask how the cashier would figure out what coins or bills to get from this information. Materials: Math Talk: coin manipulatives Math Focus: Counting back by 5s, 10s, and 25s to make change Teaching Tip Let’s Talk Integrate the math talk moves (see Select the prompts that best meet the needs of your students. page 8) throughout Math Talks to • Put out 9 nickels in a random arrangement. What is your estimate of the maximize student participation and value of these coins, and how do you know? Turn and talk to your partner. active listening. • W hat are your estimates, and why are they reasonable? How can you count the money? • Imagine we are taking 1 nickel away at a time until none are left. How would we count the money? How would this counting pattern look on the hundreds chart? How would it look on a number line? • Put out 19 nickels randomly arranged. Estimate how much money there is now. Turn and talk to your partner. • How did you estimate? Do you think there is more or less than 200¢? Why? Is there more or less than 100¢? How could we arrange the nickels so it is easier to estimate? Let’s count the value of the nickels together, one nickel at a time. What is our total? (95¢) • How could we count the value of the nickels if we take 1 nickel away at a time? Let’s do it together. What patterns are there in the numbers? How can the hundreds chart help with this count? What would this count look like on a number line? continued on next page Financial Literacy 397

• How many nickels do we need to put out to make 100¢? How does our previous problem help you? Let’s count them by 5s to make sure. If an item costs 95¢ and you pay with a loonie (100¢) how much change do you receive? • Let’s imagine that we bought something that cost 65¢ and we paid with a loonie. How could we make change in nickels by counting back from 100¢? What amount do we need to count down from so we can make change? Let’s count together as I take a nickel away for each count (e.g., 95, 90, …, 65). • H ow many nickels did I take away? (7) How much money is that? How do you know? So, we can make change with 7 nickels and they have a value of 35¢. • If the change is 35¢, what other coins could we use to represent it? Turn and talk to your partner. You can use your coin manipulatives to help show your thinking. • If we used 3 dimes and 1 nickel for the change, how could we count that back from 100¢? (e.g., 90, 80, 70, 65) How could we count back 1 quarter and a dime? (e.g., 75, 65) What coins did we use to start counting backwards? (e.g., The coin with the greatest value.) Why is this a good strategy? Can you do it any other way? • Which combinations of coins do you think people would prefer getting for their change? Why? • How can counting backwards help us make change? Further Practice • Independent Problem Solving in Math Journals: Students can use money manipulatives to help them solve the following problem: – K iran pays for her school supplies with a $20 bill and a $10 bill. As change, she receives 1 loonie and 1 toonie. How much did her school supplies cost? 398 Number and Financial Literacy

and5 6Lessons Making Totals and Change in More than One Way Math Financial Literacy Curriculum Expectations • F1.1 estimate and calculate the change required for various simple cash Previous Experience transactions involving whole-dollar amounts and amounts of less than one with Concepts: dollar Students have had experience with Number identifying, describing, and representing coins • B2.5 represent and solve problems involving the addition and subtraction and bills, and making change. of whole numbers that add up to no more than 1000, using various tools and algorithms PMraotcheesmseast:ical arrPeenrfadolesbsocltetnrimanintgge,sgoasileenvlsdien,cpgtr,ionvgintogo, ls About the ccoomnnmecutninicga,trinegpresenting, Students need to understand how to make equivalent amounts of money Math Vocabulary: in order to calculate and make change in different ways. This can be ecqeunitvsa, ldeonltl,aersq,ucahl,avnagleu,e, important in real-life situations, when certain coins and/or bills are not total available. As students explore money equivalency, they need several experiences using money manipulatives to physically exchange coins or bills and create equivalent values. Hands-on activities also help students form visual images of equivalent amounts, such as visualizing 25¢ as 1 quarter or as 2 dimes and 1 nickel. As students count out change, they also need to adjust their method for counting the different representations, thereby applying their skip counting skills and ability to count on from various amounts. It can be helpful to reinforce this ability using a hundreds chart, where students can see how the number of spaces between counts changes when counting by different quantities (e.g., 5s, 10s, 25s). This understanding supports students as they learn to pay for items in different ways and to make change when the amount paid is more than the amount owed. About the Lessons In Lesson 5, students exchange coins to make equivalent amounts and calculate change. In Lesson 6, students do the same for dollar amounts. Financial Literacy 399

5Lesson Adding Totals and Making Change Using Coins Teacher Possible Learning Goals Look-Fors • Determines equivalent representations of an amount of money, using various combinations of coins (cents) • Calculates the amount of change and represents the change in more than one way • Uses various coins when counting or representing an amount of money • Independently represents the same value in different ways • Explains the equivalence of various money amounts • Calculates change and makes the change in more than one way Materials: Minds On (20 minutes) Digital Slide 51: For • Ask students how many cents there are in 1 loonie. Have student pairs use Sale, BLM 56: For Sale, coin manipulatives, coin manipulatives to represent 100¢ in another way. chart paper • As a group, compare the various combinations. Have students prove how Time: 60 minutes they know the amounts are equal. Reinforce their counting methods and how students switch from counting by one amount, such as counting the dimes by 10s, to counting by another amount, such as counting the nickels by 5s. • Ask how much change they would receive if they bought something for 55¢ and paid for it with a loonie. Have them show how to make the change in more than one way. • Discuss how students calculated the change (e.g., 100¢ − 55¢; adding up from 55¢ to 100¢) and the various combinations of coins they could use. Challenge students to prove that the various combinations are equivalent in value. 400 Working On It (20 minutes) • Show and discuss Digital Slide 51: For Sale, which shows a number of sweet treats for sale. • Students work in pairs. They make simulated purchases of treats, which they pay for using a loonie. They must receive some change from their purchase. • Provide copies of BLM 56: For Sale and challenge students to create at least two different lists of purchases. In each case, they show how they totalled the amount of money owed and the how they calculated the change. They also make the change in at least two different ways. • Students can use coin manipulatives as they solve the problem and record their answers on chart paper. Number and Financial Literacy

Differentiation • Some students may benefit from focusing on only one list of purchases and showing their change in several different ways. • For students who need more of a challenge, specify the number of items they need to buy and still receive some change. • For students who need more of a challenge, have them work with total values up to 200¢ (you could change the cost of some treats or ask students to buy more of them) and pay with a toonie. Assessment Opportunities Observations: Observe whether students trade in coins of the same value to create new representations or if they start over each time. Conversations: • If you notice students using the same coins each time (e.g., only dimes), ask, “What would you do if you didn’t have any dimes?” • If students are starting over with each representation, ask, “Could you exchange any of these coins for others?” Consolidation (20 minutes) • Meet as a class to discuss some of the students’ purchases. Strategically select solutions that use various strategies for arranging and counting the money, and making the change owed. You may want to choose solutions that highlight some of the following strategies: – S tudents start counting with the largest value first and progressively add in the next largest values. Ask how starting with the largest values might be easier when counting the coins. – S tudents strategically count coins to make more-friendly numbers for counting. For example, for 1 quarter, 3 dimes, and 1 nickel, they count the quarter and then the nickel to make 30¢, and then count in the dimes by 10s (since it is easier to count by the decade numbers). – S tudents strategically group some coins together to make benchmark values and then count. For example, they group 1 quarter, 2 dimes, and 1 nickel together to make 50¢. Have students explain the reasoning for their groupings. – W hen making change, students subtract the amount owed from the amount paid. – W hen making change, students add on from the amount owed to the amount paid. • Have students prove that the different ways they represented the change for the same purchase produce equivalent amounts. Financial Literacy 401

6Lesson Adding Totals and Making Change Using Dollar Coins and Bills Teacher Possible Learning Goals Look-Fors • Determines equivalent representations for dollar amounts, using various combinations of coins and bills • Calculates the amount of change and represents the change in more than one way • Uses various dollar coins and bills when counting or representing an amount of money • Independently represents the same value amount in different ways • Explains the equivalence of various money amounts • Calculates change and makes the change in more than one way About the Lesson In this lesson, students solve realistic problems that involve finding the difference between money amounts. This provides a good opportunity to reinforce the mathematical modelling process and its four components: • Understand the Problem • A nalyse the Situation • C reate a Model • A nalyse and Assess the Model Use an anchor chart to highlight how students may move among the components. For example, students may need to understand the context (Analyse the Situation) before they can be presented with the problem. As they test out their model, they may find it necessary to revisit the problem (Understand the Problem) or reconsider the context (Analyse the Situation) to gather more information and select more appropriate tools and strategies to refine their model. There are suggestions on how and when to reinforce the model throughout, although these will need to be adjusted so they are reflective of how your students are progressing through the process. 402 Number and Financial Literacy

Materials: Minds On (15 minutes) • Use the following Math Talk to set the context for the problem. (Analyse the Situation) Math Talk: “Holiday Toy Drive!” Math Focus: Investigating transactions that give back to the community and “Earn and Spend” (pages 14–17 in the Let’s Talk Number and Financial Literacy big book and Select the prompts that best meet the needs of your students. little books) Time: 60 minutes • Show “Earn and Spend” on pages 16–17 in the big book. Draw attention to Teaching Tip the donations jar. What do you see in this picture? What are donations? Have you ever donated money? Who was the money going to? Why do we donate Integrate the math talk money? moves (see page 8) throughout Math Talks • Look at all of the pictures. Which ones could be examples of donating money to maximize student participation and active or raising money for a good cause? Turn and talk to your partner. You can listening. look at the pictures in the little books. • W hat did you find? • Let’s discuss the picture of the poppies. When and where have you seen poppies being worn or sold? What do poppies stand for? Why do people wear them in November? How can you buy a poppy? This is a way of earning money. Who does the money go to? How much might a poppy cost? (e.g., Usually, you can donate whatever amount you wish.) Why is it a good idea to give people a choice on the amount that they donate? • Look at the picture of the students running. What kind of event is this? How does it raise money? (e.g., Runners get pledges from people who sponsor them to run in the race.) Why do you think people run in the race rather than just giving money to the cause? Have you participated in an activity to raise money for a good cause? How did you feel after participating in the event? • Could the lemonade sale be raising money for a good cause? Are there times when the money raised is not considered a donation? (e.g., If you raise money to buy a toy or something for yourself.) • What other events have you participated in to raise money for a good cause? Why is this important? (e.g., It is giving back to the community.) • Imagine you don’t have any money. What other ways could you give back to your community and help people who need assistance? (e.g., Donate old clothes; volunteer your time to help a neighbour who can’t shovel their driveway or can’t walk their dog.) How are these actions good for the community? Financial Literacy 403

Working On It (20 minutes) • Turn to “Holiday Toy Drive!” on pages 14–15 in the big book. Ask students what they think a ‘toy drive’ is and how it helps people in the community. Have students imagine that they have raised $500 to spend on toys for this toy drive. Explain that they must receive some change from their $500. They choose their items, add them up, represent the total with dollar bills and coins in more than one way, and then calculate the change they would receive from $500. They can represent the change in more than one way. Have students explain the problem in their own words. (Understand the Problem) • Ask what factors students need to consider as they buy toys (e.g., having a variety of toys for different interests and age groups). (Analyse the Situation) • Students can use any tools and strategies that they think are appropriate. They can record their solutions on chart paper. (Create a Model) Differentiation • Change the dollar values and the parameters of the challenge so they meet the needs of your students. • Add other requirements for students’ purchases to make the problem more challenging. For example, students need to buy between 4 and 6 items and can’t buy any duplicates, or they need to get change that is between $35 and $15. Assessment Opportunities Observations: Pay attention to how students represent and count their money amounts. • Ddeosctehnedyinsgtavratlubey? adding the largest bill first and then add more in • eDxoamthpelye, make benchmark amounts of money and then count on? For if they have $46, they may add 2 toonies to make $50 and then add $50 bills or $100 bills thereafter. Conversations: If students are having difficulty representing money amounts, present the questions using numbers alone, and use a number line or a hundreds chart to help students see how they can make benchmark numbers and then count on. Make the connection that numbers to 500 and monetary values to 500 represent the same quantities and that money problems can also be solved on a number line. Students can then convert their numerical results from the number line to dollar values. Consolidation (25 minutes) • Have students meet with another pair. They can take turns explaining one of their scenarios and checking each other’s work for accuracy. 404 Number and Financial Literacy

• Meet as a class. Select two or three students to share their solutions. Highlight the strategies that they used to represent the total cost of the toys (e.g., making benchmark dollar amounts, using bills/dollar coins in descending order of value), and the strategies they used to make change (e.g., counting on, finding the difference between the amount owed and the amount paid and making the change). • Have students prove that the different ways of representing the same value are equivalent. • Discuss the various strategies students used and which they found to be most effective. Ask how they might do the problem differently if they were to do it again. (Analyse and Assess the Model) • Discuss why being accurate with money amounts is important in real-life situations. Further Practice • Have students use estimation to find another combination of toys they could buy for about $100. Have them show how they estimated, then prove that their estimation is reasonable by calculating the total. Then, have them calculate the change they would receive from $150. Financial Literacy 405

7Lesson Applying the Commutative and Associative Properties when Adding Money Math Financial Literacy Curriculum Expectations • F1.1 estimate and calculate the change required for various simple cash Teacher transactions involving whole-dollar amounts and amounts of less than one Look-Fors dollar Previous Experience Number with Concepts: Students had experience • B2.1 use the properties of operations, and the relationships between using the commutative property in grade two. multiplication and division, to solve problems and check calculations Possible Learning Goal • Applies the commutative and associative properties to add money amounts, using a variety of tools • S olves money addition problems using a variety of strategies and explains the strategies • Understands, uses, and explains the commutative property when adding two money amounts (knowing the term is secondary to understanding the concept) • Understands, uses, and explains the associative property when adding three or more money amounts (knowing the term is secondary to understanding the concept) • Accurately writes addition equations for money amounts • Counts on from larger numbers when adding PMraotcheesmseast:ical About the Problem solving, ccssrooetermnalaenstmceoetgncuinitinenignisgcgt,ao,artoenrinelfdslgpepracerntosidnevginn,tgin, g, Applying the commutative and associative properties can help students work more efficiently when totalling money amounts. In grade two, students learned about the commutative property—the concept that two numbers can be added in any order and the sum will be the same. This 406 Number and Financial Literacy

Mccc(pooooarnpsmotjttehp,imocetVnotruutatotyarlace)l,(t,,aoiavdbbpesouutsilypolloa,arncrporaisypual,:)retcicrvehteynatsse,, concept appears in other units and can be applied when adding two costs to find a total; for example, students may reverse the order of the costs so they can start with the greater amount and add on the lesser amount. In grade three, students study the associative property, which states that three or more numbers can be added in any order and the sum will be the same. This is handy for adding money values in any order, but also has other advantages. As Marian Small explains “as a consequence of this property, you can take away from one number and add what you took away to the other number without changing the sum” (Small, 2009, p. 109). For example, when adding $2 + $3 + $7, students may group and add $2 + $3 and then add in the $7, or they may add $3 + $7 first to make $10 and then add in the $2. Students apply mental math strategies as they make friendly numbers by composing and recomposing. About the Lesson In this lesson, students can apply the commutative and associative properties, as well as their other strategies, as they practise adding money amounts and making change. Materials: Minds On (15 minutes) money manipulatives, NOTE: Students also prove the conjecture about the associative property in chart paper, markers, Unit 4: Addition and Subtraction. If you are studying the Financial Literacy BLM 57: Adding Money unit first, have students prove the conjecture and then conclude the lesson by Amounts saying that it seems to be a rule, but they will test it further later in the year with different numbers and situations. If students have already completed Unit Time: 60 minutes 4, tell them this is a further test of the conjecture. It is important for students to understand that it takes many examples before a conjecture can be considered a rule. • Pose the following problem: If you buy an item for $2 and then go to another store and buy another item for $5, how much money did you spend altogether? • Ask students how the information in this problem could be recorded using an equation (e.g., $2 + $5 = $7). Ask whether it matters if you add the $5 first and why students think so. Review the commutative property if students have used it with whole numbers. Ask why you might want to add the $5 first (e.g., starting with the larger amount can be easier). Record the commutative property on an anchor chart (if you haven’t already done so). Explain that this is a proven rule and it works every time. • Pose the following problem for students to solve with a partner: On your birthday, you got $20 from your uncle, $17 from your cousin, and $13 dollar from your sister. How much money did you get? Financial Literacy 407

• Have students turn and talk to their partner. Discuss as a group, with students explaining their reasoning. From the discussion, record a possible rule. (e.g., You can group and add three or more money amounts in different ways and it will not affect the total.) • Tell students that this statement is known as a ‘conjecture.’ A conjecture is a possible rule based on a limited number of experiences that may not always work. Explain that a conjecture must be tested many times and must work each time before it can be considered a rule. Tell them that it takes only one example that doesn’t work to disprove a conjecture. Working On It (20 minutes) • Have students work in pairs. Provide them with money manipulatives, chart paper, markers, and BLM 57: Adding Money Amounts. • Challenge students to test the conjecture by solving four problems and then creating their own problem (Challenge 5). Encourage them to record their strategies and solutions using pictures, numbers, and/or words on chart paper. They can also use money manipulatives to solve a problem or confirm a solution. Differentiation • Limit the number of challenges to one or two if completing all of them is overwhelming. Assessment Opportunities Observations: Pay attention to the strategies students are using. • D o they apply the commutative property, which they already know is a rule? • Are they decomposing and recomposing values so they are easier to work with? • How are students proving or disproving the conjecture? Are they adding the numbers in more than one way? • Are they using manipulatives to verify their answers? Conversations: If students are adding the values in only one way, pose some of these prompts: – How did you add your numbers? Did your partner add them the same way? Are you convinced that the conjecture we made is a rule? Is there another way that you could add the numbers? Try using the manipulatives to help you prove that your adding is correct. Consolidation (25 minutes) • Have pairs meet with another pair. Have them compare strategies and see if they all found the same totals for each problem. Have the pairs exchange the 408 Number and Financial Literacy

problems they created and solve them. Students can compare their solutions to see if they found the same answer. • As a class, discuss whether students think the conjecture is true or not and why they think so. Discuss how meeting with another pair helped them to decide. • Focus on one problem and strategically select as many different strategies used to solve it as possible. Display the strategies on an anchor chart. For each strategy, have students who solved the problem with that strategy explain it. • Ask students whether they found any examples that did not follow the conjecture. Explain that the conjecture seems to work in all cases FOR NOW, but they may need to test it further in other circumstances. If you have started an anchor chart on properties, you can add the associative rule for addition (if you haven’t already done so). You may refer to it by its name or adopt another name. • Record the strategies students used on the anchor chart. Some possibilities include: – A dd the numbers in a different order – D ecompose amounts in order to build friendly amounts, such as $10 • B uilding Social-Emotional Learning Skills: Critical and Creative Thinking: Explain that mathematicians have been proving conjectures for thousands of years. Inform them that there are some conjectures that seem to be true but are not yet considered rules, and that mathematicians continue to look for examples that don’t work just to be sure that the conjectures are correct. Explain that mathematicians create conjectures because they are curious about math and they persistently work to prove or disprove them. It takes time and patience for mathematicians to continually test their ideas. During their testing, they also discover new information that may lead to new conjectures. Explain that in today’s class, students have shown some of these characteristics as they also worked to prove or disprove a conjecture. Financial Literacy 409

8 9Lessonsand Scaling Up Money Amounts and Making Change Math Financial Literacy Curriculum Expectations • F1.1 estimate and calculate the change required for various simple cash Previous Experience transactions involving whole-dollar amounts and amounts of less than one with Concepts: dollar Students are familiar with coins and bills and have Number used various strategies to add and subtract • B2.5 represent and solve problems involving the addition and subtraction quantities up to 1000. of whole numbers that add up to no more than 1000, using various tools and algorithms • B2.9 use the ratios of 1 to 2, 1 to 5, and 1 to 10 to scale up numbers and to solve problems Spatial Sense (Lesson 9) • E1.2 compose and decompose various structures, and identify the two- dimensional shapes and three-dimensional objects that these structures contain PMraotcheesmseast:ical About the Problem solving, As students work with various coins and bills and their relative values, reasoning and they are working with ratios and using proportional thinking. For representing, proving, example, the value of a loonie in relation to a $5 bill represents a ratio of 1:5. This kind of thinking supports grade three students as they work communicating, with ratios of 1:2, 1:5, and 1:10. sscteorlanetnceetgicniteginstgo,orlesflaencdting, Relational rods are effective for representing ratios in a concrete manner using the attribute of length. For example, if students know that a white Math Vocabulary: rod is worth $1, they can figure out that the yellow rod, which is 5 times total, purchase, change, as long, is worth $5, and the orange rod, which is 10 times as long, is scale up worth $10. Students learn to think flexibly about ratios when the values are adjusted. For example, if students know that the white rod is worth $2, the yellow rod is worth five times as much, or $10. About the Lessons In Lesson 8, students are given the value of one relational rod and need to find the value of the other rods. They are given a certain amount of money to spend, buy rods in a variety of ways, and then calculate any change that is owing in more than one way, using dollar coins and bills. In Lesson 9, students scale up money amounts by ratios of 1 to 2, 1 to 5, and 1 to 10, and make change if any is due after the total value is calculated. 410 Number and Financial Literacy

8Lesson Buying Relational Rods Teacher Possible Learning Goals Look-Fors • Calculates the relative dollar values of relational rods by scaling up in Materials: relational rods, chart various ways paper, money manipulatives • Purchases rods up to a given total amount and makes change for their Time: 60 minutes purchases in more than one way using dollar coins and bills • Understands and explains how the dollar values of the rods are relative to each other • Calculates the values of all of the rods, based on the dollar value of one of the rods • Purchases rods within the total amount of money given and accurately sums up the total cost • Creates more than one combination of rods that meets the given parameters • Accurately calculates the amount of change owing and represents it in more than one way using dollar coins and bills Minds On (20 minutes) • Give pairs of students a set of relational rods. Ask how much each rod would be worth if the white rod was $1. • Discuss students’ responses and have them explain their reasoning. Ask how many times more the red rod is worth than the white rod. Repeat this with the yellow rod and the orange rod. • Tell students that the orange rod is worth $20. Have them work with their partner to find the values of all of the other rods. Discuss their strategies. Some students may figure out the costs one rod at a time, while others may realize that the orange rod is worth double the amount in the previous scenario and thus double all of the amounts in the previous scenario. • Tell students that the yellow rod is worth $25. Ask how much the white and orange rods are worth. Some students may double the value for the orange rod. Some strategies for finding the value of the white rod include: – P ut 5 white rods alongside the yellow rod and then use guess-and-check and skip counting to find out how to count to 25. – D ivide 25 by 5 (25 ÷ 5). – W ork from the value of the orange rod and divide 50 by 10 (50 ÷ 10). • Discuss what the values of the other rods would be. Highlight how counting by 5s to 50 can reveal the value of each rod as the rods progressively increase in length. Financial Literacy 411

Working On It (20 minutes) • Students work in pairs. Tell students that the red rod is worth $8. • First, students need to find out the value of all of the other rods. • Next, students have to ‘buy’ some rods. They have a total of $113 to spend, but they must receive some change. Students will – find at least two combinations of rods to buy, – c alculate the total cost of each combination and the change they will receive from $113, and – m ake the change with coins and/or bills in at least two ways. Differentiation • Adjust the cost of the rods and the money students have to spend so the quantities are within the needs of your students. • For students who need more of a challenge, add other parameters. For example, challenge students to buy exactly 5 rods, or 6 rods that are all different in value. You can also challenge them to spend as much of their money as possible on the fewest number of rods. Assessment Opportunities Observations: Notice how students find the relative values of the rods and how they make various combinations. • Do they start with the red rod, work down to find the value of the white rod, and then work up for the rest of the rods? Do they build an orange rod with red rods and then skip count or add repeatedly? • Do they exchange rods for other rods to create different combinations or do they start over again? Conversations: If students are having difficulty finding the values of the other rods, work with a small group. Have the students build the length of the orange rod using red rods, which are each equivalent to two white rods. Encourage them to count by 4s to find the values of all the rods. Consolidation (20 minutes) • Have students meet with another pair and share their purchases. They can check each other’s work for accuracy. • Meet as a class. Discuss how students figured out the values of all of the rods. Have students prove that their values make sense by using the rods to show the relative values. • Discuss how students chose the rods to purchase. Ask how they created different combinations. • Ask how they calculated the total and the change. Have students prove that their change, represented by various dollar coins and bills, is accurate and that different ways of making the change are equivalent. Discuss whether they subtracted or counted up to make their change. 412 Number and Financial Literacy

9Lesson Calculating the Cost of a Pattern Block Design Teacher Possible Learning Goals Look-Fors • Scales up the value of pattern blocks by factors of 2, 5, and 10, using various Math Vocabulary: tsdswrhihymoamo-pmedmenimbsse,uiteotsrnhyn,,srateicrloaeoonp-sbaetjl,zeotcritidas,n, gle, strategies hexagon • Accurately adds up the total value of the blocks used and calculates change if Materials: any is owing BLM 58: Pattern Block Design Challenge, • Creates a design using pattern blocks (optional: a variety of • Identifies the relative sizes of the pattern blocks (e.g., the trapezoid is half the tools, e.g., number lines, ten frames, hundreds size of the hexagon) charts, etc.) Time: 50–60 minutes • Calculates the relative value of different pattern blocks by knowing the value of one block and scaling up by factors of 2, 5, or 10 • Accurately calculates the value of the blocks in their design • Calculates the amount of change that is owing and represents it with coins/ bills in various ways About the Lesson On Day 1, students create pattern block designs according to set criteria and count the number of each type of block used. On Day 2, students calculate the total cost of the blocks used and show the coins or bills they might receive in payment. They also calculate the amount of change owing and show various ways to represent it. Day 1 Minds On (15 minutes) • Show students a set of pattern blocks. Ask whether they are three- dimensional objects or two-dimensional shapes and why they think so. Reinforce that they are three-dimensional because they have depth. Ask what two-dimensional shapes are on the shapes’ surfaces. • Tell students that they are going to complete a design challenge using pattern blocks. Show them an example by having a model prepared. • Present the challenge to students: Your challenge is to create a pattern block design that must meet this criteria: – Has symmetry – Has at least 3 different shapes Financial Literacy 413

– Has between 12 and 16 pattern blocks – Uses any one shape 4 or less times • After presenting the challenge, refer to your prepared design and have the students help you justify whether your design meets all of the criteria or needs to be revised. Show students BLM 58: Pattern Block Design Challenge and explain how to record the number of each kind of pattern block used in the second column. Tell them that they will need to find out how many blocks they used altogether (to complete the first sentence at the bottom of the page) but do not model a process for them. You may brainstorm possible tools that they may use to help them (e.g., number line, ten frames, hundreds charts). Working On It (20–30 minutes) • Provide time for students to create their pattern block designs according to the set criteria. Hand out copies of BLM 58 and ask students to record on their recording sheets the number of blocks used in their design. Students may also colour in the shapes on their recording sheets to match the colours of the pattern blocks. Point out that the rest of the table will be completed later. Differentiation • Create parallel tasks by adjusting the numbers of blocks that may be used. • Make this an open problem by allowing students to determine the number of blocks they’ll use. If you choose this option, ensure students know that they’ll have to add up the cost of the blocks before they make their decisions. • Present the challenges in even smaller chunks, if necessary. Provide check-ins along the way for students who have difficulty with multi-step instructions. Assessment Opportunities Observations: Observe students as they work. Ask students to think aloud as they work through a strategy. This way you can understand what process they are using, and you are providing oral rehearsal in preparation for sharing during consolidations and for their representing their strategies on paper. If you notice that students are continually counting on, scaffold the process of using a different strategy (e.g., making a ten, using counting patterns, decomposing or using near doubles) through strategic questioning. Observe whether or not students can apply this strategy to another question. Conversations: For example, a student is solving 5 + 5 + 5 and starts at 5 then counts on 5 more to 10, then counts on the remaining 5 to get to 15. Teacher: I notice that you are counting on the 5s. Is there another strategy that you could use? Student: I don’t know. Teacher: Look at our strategy anchor chart. Which other strategy might work for you? 414 Number and Financial Literacy

Student: I can count by 5s. Teacher: Great. Show me. Student: Touches each 5 and says: 5, 10, 15. Teacher: Wow, that was faster than counting on, wasn’t it? Let’s look at another question that you used counting on for and see if a different strategy might work. Let’s solve 4 + 4 + 6. Student: I see a double. 4 + 4. Teacher: Do you know this doubles fact. Student: No, I’d have to count. Teacher: Can we try the make a ten strategy? Do you see two numbers that add up to 10? Student: 6 + 4 = 10? Teacher: You don’t seem sure. Do you want to check? Student: Counts on from 6: 7, 8, 9, 10. Teacher: So you were right. Now what do you do? Student: Add on the other 4. I know 10 and 4 are 14. Teacher: How do you know? Student: I just think about a ten frame being full and then 4 more. Teacher: That works! So when you’re adding, try to use some of the strategies we’ve been working on in class. Counting on works and is a good strategy too but I’d like you to practise the other strategies so that they become easy for you to use too. Consolidation (15 minutes) • Analyse the student work that shows how students found the total number of blocks used. Look for a variety of strategies and models to highlight in the Consolidation (added by , make a ten, decomposing, used a number line, etc.). • Choose three to five students to share their strategy. If there is a student who made addition errors but used an efficient strategy, include him in the sharing to reinforce the message that process and making mistakes are as valuable as finding the correct answer. • Encourage students to ask the ‘sharers’ questions about the work or to explain how their strategies are similar or different to the ones being shared. Ask clarifying questions as students explain their thinking and provide any necessary math language (e.g., decomposed) by restating their explanations. Financial Literacy 415

Materials: Day 2 students’ Pattern Block Design Challenge Minds On (10–15 minutes) sheets from Day 1, BLM 59 and Digital Slide • R eview what students accomplished on Day 1. Then introduce the second part 52: Pattern Block Costing Sheet of the challenge by projecting Digital Slide 52: Pattern Block Costing Sheet and Time: 55–65 minutes reading the problem: A company would like to buy your design and make it into an Teaching Tip ornament. They will pay you for each pattern block you used in your When most students design. This chart shows how much they will pay for each kind of are nearly finished block. drawing or pasting the coins, stop the • A dd the costs per block to the table. Use cents or dollars, depending on your class and revisit the second part of the task students’ needs. You could also make the values of the blocks proportional to (working in partners to their sizes (e.g., If the hexagon is worth $12, the trapezoid is $6, the rhombus find the total cost per $4, and the triangle $2.). Provide copies of BLM 59: Pattern Block Costing block). Ask students Sheet to students as a reference while they solve the problem. to explain what they are to do next and Working On It (30 minutes) ensure that everyone understands the task. • Explain the task by saying, “Your job is to find out how much money the company will pay you for each kind of block you used based on the given price of one of the blocks.” Have students record the cost for each pattern block on their Pattern Block Design Challenge sheet (column 3), figure out the total cost per block, and draw the coins or bills that they might receive for each kind of block used. • Once students have completed this challenge, have them work with a partner to find the total cost of their designs. Encourage students to record on a large sheet of paper so that they can share their work during the Consolidation. You can also tell students what coins or bills the company will use to pay for the design. Students can calculate how much change they will need to give back to the company. They can represent the change in different ways, using coins and bills. Consolidation (15–20 minutes) • Meet as a class. Discuss the strategies students used to scale up and find the relative values of the pattern blocks used. • Analyse the student work to determine what strategies students used to solve the problem of finding the total cost of the blocks. Look for a variety of strategies (e.g., make a ten, counting by 5s, decomposing, etc.) and models (number line, coins, ten frames, etc.) to be shared. Choose a few partners to share how they solved the problem. Have a few students show their coin combinations as well and demonstrate how to use counting patterns. • Discuss how students calculated the change owing. Make connections between subtracting and adding on strategies, highlighting how they both are finding the difference between the two amounts. Students can share how they made the change using various combinations of coins and bills. 416 Number and Financial Literacy

Further Practice • Building Social-Emotional Learning Skills: Positive Motivation and Perseverance: Jo Boaler (www.youcubed.org) asserts that teachers have the power to influence how students view themselves as mathematicians. Thus we need to give them positive growth mindset messages such as ‘I believe in you’ not only through our words but by giving them challenging tasks. As you present the challenges to the class, have them review what it means to have a fantastic, elastic brain (see the introductory lesson on page 15). Discuss how mistakes actually help our brains grow and that it is important to try again if our first try does not work. Listen for and reinforce positive talk and behaviour as they work. For example, when you hear a student say, “That was hard, but I finally did it,” reinforce the statement by saying something such as, “Yes, I bet you stretched your brain by working through the challenging part.” Financial Literacy 417

10Lesson Guided Math Lesson: Arlo’s Busy Day Math Financial Literacy Curriculum Expectations • F1.1 estimate and calculate the change required for simple cash transactions Teacher involving whole-dollar amounts and amounts less than one dollar Look-Fors Possible Learning Goal Previous Experience with Concepts: • Applies understanding of adding, subtracting, and counting money amounts Students have added, subtracted, and counted to solve problems presented in a context, using a variety of strategies various amounts of NOTE: Adjust the learning goal to meet the needs of each group and create money throughout the Teacher Look-Fors that reflect the goal (see possible Teacher Look-Fors unit. below). • Selects appropriate materials and/or tools to solve the problem • Uses some mental math strategies to estimate and solve some of the problems • Uses mental math strategies or money manipulatives to make change by finding the difference between two money amounts • Adds two or more money amounts together, using mental math strategies or math manipulatives • Explains or shows their strategies and why they work • Explains or shows why their solutions work and other amounts will not work PMraotcheesmseast:ical About the Lesson Problem solving, arreenfadlessocttnrianintgge,gasieenlsde,cptrionvgintogo, ls This is an example of a guided math lesson that can be used with the math little ccoomnnmecutninicga,trinegpresenting, book Arlo’s Busy Day. The lesson can be differentiated to meet the specific needs of students in each group. You can select from the prompts, which vary in Math Vocabulary: difficulty, so they provide an appropriate challenge for each group. anplollutoesf,dtshiunempv,roedcviafiofbeuursleanlrecysesons; You can carry out this guided math lesson with a small group, while the rest of the students engage in activities that are set up at centres. Students can rotate through the centres over the course of a few days, or they can freely visit the centres, depending on what best suits the needs of your class. Remember that the purpose of the little book is to provide the context for the math, and raise curiosity about solving related problems concerning money. The reading is not supposed to be a barrier to the math, nor is the goal to have students independently read the text, although this would be a welcome secondary outcome. If students are struggling with the text, read it to them. In this way, they can effectively solve the problems and apply their mathematical thinking. 418 Number and Financial Literacy

Differentiation • The major purpose of a guided math lesson is to differentiate instruction. The money amounts in this book are designed so they can be differentiated to meet the needs of your students. If students are less confident, they can find solutions by using money manipulatives to represent the money amounts depicted in the text. • For students who need more of a challenge, you can scaffold the learning by having them solve the problems with progressively less support, from more concrete materials to using mental math strategies. Assessment Opportunities Observations: Pay attention to how students solve the given problems. • Do they know where to start or how to select appropriate tools? • Can they represent and count money amounts in various ways? • Do they check their solution for accuracy? Conversations: If students have difficulty getting started with a problem, or are unsure about their solution, pose some of the following prompts: – W hat tool or money manipulative have you used before to help you add and subtract money amounts? – What are you trying to find? (e.g., the difference between two money amounts) – H ow could you represent one of the money amounts? Are you going to end up with more or less money after solving the problem? Why? – How could you prove that you made the correct change? What different strategy could you use to check? Materials: Small-Group Guided Math Lesson Arlo’s Busy Day little • G ive each student a copy of the little book. Draw students’ attention to the books, money manipulatives, hundreds cover of the book and read the title. Ask what they think the book may be chart (optional) about. Time: 20–25 minutes per session • R ead the book together, choosing from the prompts given below to discuss the context and solve the embedded problems. For pages 2–14, select the prompts that are best suited to the students in the group. Read pages 2 and 3: • How else could Miss Dara pay Arlo $20? • How else could the money in Arlo’s money box be represented? How would he count the various ways? If the $5 was all in quarters, how many quarters would that be? How did you figure that out? How does knowing how many quarters are in $1 help solve the problem? How could you count the quarters? Read pages 4 and 5: • How do you think Arlo is feeling about having his best friend move away? Have you ever had a close friend move away? Financial Literacy 419

• W hat does the phrase “He was on a mission” mean? • How do you think Arlo will spend his $25? Why do you think so? Read page 6: • H ow much change should Arlo get? How do you know? How might the cashier have given the change to Arlo? Read page 7: • How much change would Arlo receive if he had bought the glossy paint? The glow-in-the-dark paint? How else could Arlo have paid for the glossy paint and the glow-in the-dark paint if he didn’t want to receive any change? • What paints could Arlo buy if he wanted to spend the $20 only on paint? Read pages 8 and 9: • W hat does “Sale! $2 off purchase” mean? • H ow much will the square photo cost at the sale price? • How did Arlo pay for the photo if he received no change? Is there more than one way he could have paid for the photo? • How much change would Arlo have received if he paid for the photo with his remaining bill? Would he still have the same amount of money left over? Why? • How much would Arlo need to pay if he bought a different photo size? Solve the cost for two or three of the photos. Read pages 10 and 11: • H ow did Arlo pay for the frame? How do you know? Is there another way he could have paid for it? Why? • H ow much money did Arlo have left? What coins or bills might he have? • W hat stickers could Arlo buy if he was going to spend one loonie? • Select one of the purchases that Arlo could make. How much change would he receive from his purchase? What coins might he receive? Is there more than one way he could get the change? Why do you think so? • What could Arlo buy with two loonies? Read pages 12 and 13: • How much money did Arlo spend on stickers? • H ow much change did Arlo receive? What coins might he have received? • H ow much money does Arlo have left? How many dollars? How many cents? What coins or bills might make up the dollar that Arlo has left? How else could the dollar value be represented? What coins make up the cents that he has left? Is there another way to represent this amount? 420 Number and Financial Literacy

Read pages 14–16: • H ow must Arlo and Lucy be feeling now? • H ow do you think Lucy feels after getting Arlo’s gift? • D o you think Arlo spent his money wisely? Why? • B uilding Social-Emotional Learning Skills: Positive Motivation and Perseverance: Ask students how they felt throughout the problem-solving process, especially when they were uncertain about what to do. Ask what helped them move forward (e.g., using money manipulatives to represent the amounts). Ask how they started solving a problem that could have more than one solution. Discuss how they can try one way and, if it doesn’t work, they use what they learned from a strategy that didn’t work or an incorrect answer to find a solution that will work. Emphasize to students that they can learn from their mistakes, and that doing so helps their brain to grow. Financial Literacy 421