Ohio Standards Connection Number, Number Sense and Operations Benchmark D Determine the value of a collection of coins and dollar bills. Indicator 4 Represent and write the value of money using the sign and in decimal form when using the $ sign. Benchmark E Make change using coins for values up to one dollar. Indicator 3 Count money and make change using coins and a dollar bill. Mathematical Processes Benchmarks E. Explain to others how a problem was solved. F. Draw pictures and use physical models to represent problem situations and solutions. Lesson Summary: Students count collections of coins and one-dollar bills. They solve problems and learn to use the cent sign ( ) and the dollar sign ($) with the decimal point to represent money amounts. Estimated Duration: Four hours Commentary: Students have varying experiences counting money and making change in school and daily-life settings. Many students can recognize and name coins when they enter kindergarten. Some students can state the value of each coin, for example, a dime is worth 10 cents, yet not understand what it means. An understanding of key numbers, such as 1, 5 and 10, is needed in order for students to develop meaning for a penny is worth 1 cent, a nickel is worth 5 cents and a dime is worth 10 cents. More importantly, students must be able to link these quantities to a single item. Working with money is often the first context in which young students must think or say this is five or this is ten when pointing to a single item. New money-related ideas and skills are introduced in grade one. These include counting small collections of coins, selecting coins to match a specified value, and showing different combinations or collections of coins having the same total value. These tasks involve mental computation and/or skip counting restricted to multiples of 25, 10 and/or 5 with some ones added at the end. These concepts and skills are expanded in grade two. Paper money (one-dollar bills) and making change are incorporated into money activities. Students also begin representing and writing money values using the cent sign and in decimal form using the $ sign. Fluency in performing these tasks develops over time and requires multiple experiences, including authentic tasks. In this lesson, a skip counting activity plays an important role in preparing students for activities and problem situations involving counting and comparing collections of coins and making change. 1
Pre-Assessment: Assess students knowledge of coins and their values. Attachment A, Pre-Assessment Activity, provides an example activity that can provide insight into students recognition of coins and their values as well as skill in counting a small collection of coins. Distribute copies of Attachment A, Pre-Assessment Activity. Introduce the context: Kip has some coins in his pocket. His coins are shown on your activity sheet. Ask students to think about Kip s coins and write statements that describe his coins. Pose guiding questions to help students start the task; such as what can you tell me about the types of coins Kip has? what can you tell me about the value of Kip s coins? Collect and review students responses. Look specifically for responses that indicate possible gaps in recognition of coins and their values. Scoring Guidelines: Record observations based on the review of student responses on a checklist, Attachment B, Pre- Assessment Checklist. Use + to indicate that the student performed the skill successfully and to indicate difficulty demonstrating the skill. Individual follow-up or additional questioning may be needed when responses for this task are incomplete; e.g., a student s response provides insufficient descriptions or fails to address some of the coins. Also pay attention to how the student responds to the question about the total value of Kip s coins. For example, did the student find the actual value or use reasoning skills to determine whether the value is less than one dollar? Does the student s response show a counting on approach or standard algorithm? Brief anecdotal records are also helpful. Record evidence from other sources, such as informal observations made during routine classroom tasks; e.g., collecting milk money or purchasing school supplies. Post-Assessment: A formal post-assessment has not been included in this lesson as assessment of student understanding and skill is on-going throughout the lesson. The activities and journal entries provide rich evidence of students progress and serve as both instruction for and assessment of the target benchmarks and indicators. Student discussion and products from each part of this lesson can be used as one piece of evidence to categorize student progress. Anecdotal notes can be used to capture informal assessment of student progress through observations and discussions. Products, including journals entries, can be gathered, reviewed and shared with parent(s) to illustrate student progress. Scoring Guidelines: Use Attachment C, Post-Assessment Observation Summary, to record student performance. Brief anecdotal records are evidence of student understanding and skill in counting money and making change. Evidence of misconceptions should be noted such as counting errors that occur when counting combinations of coins. This checklist can be updated throughout the school year as students use these skills in informal and formal classroom or school-related activities. 2
Instructional Tip: Research shows that using actual coins when learning money concepts is beneficial. Consider strategies to make coins available for student use, particularly when tasks involve finding the value of collections of coins and making change. Many children may need to model the problem situation, organize or group like coins and touch or move coins as they count to find the value of a collection of coins. One strategy is to create sets of coins that can be used during money-related tasks for example, baby food jars or film canisters each containing collections of coins. These sets of coins could be made available, one or two per table, during instructional and assessment activities. Plastic or paper replicas should be made available if classroom/school conditions make it difficult to make actual coins available. Make smaller student sets when sufficient quantities are available; for example, some instruction materials include plastic or laminated paper coins. Students should also be encouraged to draw simple pictures to record their thinking and solutions. Instructional Procedures: Part One: Counting Activity 1. Introduce a counting activity by counting 10, 20, 30, 40, 50 and using a non-verbal signal for students to join in. Continue counting together to at least 150 to 200. 2. Ask students how they knew which number came next. 3. Select a student to be the leader by counting by a different number and signaling students to join in. Signal students to stop counting, as appropriate, after adding 10 to 15 additional numbers. Help students moderate the pace of the skip counting not too fast nor too slow a comfortable pace that allows all students time to respond based on the difficulty of the unit ; for example, counting by 5s versus counting by 8s. Ask students (other than the leader) to identify by what number they are counting. Repeat the process two or three times. Note: This activity can be done as a transition activity or while students are lining up to go to lunch, art, music or physical education. 4. Explain to students that they are ready for a new, more difficult counting activity. This time they will start counting by one number. When you give them a signal, they will then start counting by a different number. Write the numbers 10 and 2 on the board or on chart paper. (Another option is to write the numbers on sheets of paper and post the number cards where all students can see them easily. Tell students that they will start counting by 10s (point to the 10) and then change to counting by 2s when you point to the 2. Model the process by pointing to the 10 and counting 10, 20, 30, 40 and then point to the 2 and continue counting 42, 44, 46, 48, 50. (Students may join in without being prompted.) 5. Practice the process again using 10 and 2. Always start with the larger number and vary the point at which students are to switch from counting by 10s to counting by 2s. 6. Add the numbers 5, 25 and 100 to the numbers on the board, chart paper or the cards posted. Inform students that they should start counting by the number you point to and continue counting by that number until you signal them to switch to another number. Practice by point to the 100, having them count by 100 until they reach 400, then switch to 5s and count until they reach 425. 3
7. Organize students into small groups to practice their counts. Give each group a set of five cards each with one of the following numbers: 2, 5, 10, 25 and 100. Provide directions for the small groups: a. Direct students take turns as the leader. b. The leader picks two numbers, points to the larger number and leads students in counting by that number. The leader then decides when to switch to the second number and points to that number. Students continue counting by that number until the leader signals them to stop. c. Students practice counting for 5 minutes or until each student has a turn as leader. 8. Facilitate a brief discussion with the class about which combinations of numbers were easy to count, which were more difficult to count and why. 9. Set the stage for the next several components of the lesson by asking students to respond to two questions in their mathematics journal. Beth has 60 cents in her pocket. What coins could she have? Do you think you are good at counting money? Have students work individually and write their responses in their mathematics journal. Part Two: Ordering and Counting Collections of Coins 10. Begin this portion of the lesson by having students share a combination of coins Beth could have in her pocket (journal activity from Part One of the lesson). Record or have the students record combinations on the board or chart paper. Have students explain how they know the coins total 60 cents. Record all the combinations that students have found at this time. Keep the information on the board or chart paper so students can continue to add combinations as they are found throughout the remainder of the lesson. 11. Select one of the combinations from the board or chart paper to use as a model for connecting the counting activity from Part One to counting collections of coins; e.g., six dimes. Model six dimes by placing 6 dimes (or overhead versions) on the overhead or drawing six circles on the board, each marked 10. Ask students to count the dimes aloud as you point to each one: 10, 20, 30, 40, 50, 60 cents. 12. Select another combination of two coins, such as dimes and nickels. Model the combination or have a student model the combination on the overhead, board or chart paper. Ask students how to arrange the coins to make them easier to count. (Group the like coins together) and which coin they would like to count first. Have the students count as they point to each coin. 13. Repeat with the process with a combination that has at least one quarter. Ask questions to focus attention to when the order in which the coins were arranged made the counting the value easier. For example, do you think it would be easier to begin counting the quarters then the dime or counting the dime first and then add on the quarters? Have students count the values both ways: 25, 50, 60 cents than 10, 35, 60 cents. 14. Organize students into pairs. Provide each pair with Attachment D, Coin Jars. Create a set of eight cards, each with one jar of coins, by copying and cutting each sheet into fourths. Also provide each pair or table with a supply of coins (actual or replicas). Ask students to find a jar that contains more than 60. Give them time to examine the jars, but not too much time. The goal is to encourage students to use what they know about coins rather than counting to find the exact value of all of the coins; e.g., recognize that the jars with three quarters must have more than 60 because 3 quarters are worth 75 and a jar with 2 quarters and 2 dimes 4
must have more than 60 because one of the combinations on the table created earlier for 60 is two quarters and one dime. 15. Select pairs to identify one jar that contains more than 60 and to explain to the class how they know it contains more than 60. Have students indicate whether they agree or disagree with the choice by using thumbs up or thumbs down. Encourage students to ask the student-pair questions and to tell them why they disagree. Allow the pairs to change their response based on the questions and comments of others. 16. Select two or three other pairs to identify other jars that contain more than 60 or jars that contain less than 60 and explaining how they know it contains more or less than 60 using a similar process for the other students to indicate whether they agree or disagree. 17. Introduce the counting task by asking pairs to find the value of all the coins in Jar A (contains 2 quarters, 1 nickel, 4 pennies). Ask students to identify the coins in the jar and to tell how many of each coin. Select a pair to demonstrate how to find the value of the coins by counting the value of the coins starting with the quarters then the nickel and the pennies (25, 50, 55, 56, 57, 58, 59 cents). Draw students attention to how this is like the counting activity they did in Part One lesson; e.g., the coins tell them what number to count by and when to change from one number to another. 18. Have students practice by using the counting technique to find the value of the coins in Jar B (contains 1 quarter, 2 dimes, 1 nickel and 2 pennies). First ask students what coins are in the jar and how many of each. Then ask a student-pair to demonstrate how to find the value by counting which coin would you count first (quarters), next (dimes, then nickels, then pennies). Have students model the combination in the jar using their coins (or replicas) and rearranging the coins in order from quarters to pennies on the overhead or by drawing pictures to represent the coins on the board or chart paper. Ask the student-pair (or one student) to then lead the class in finding the value by counting (25, 35, 45, 50, 51, 52 cents). Have the student point to the coin on the overhead or board/chart paper as they count the value. 19. Have pairs work together to find the value of coins in the remaining six jars by counting and write the value on the card. Jars G and H have values greater than one dollar. Use these jars to pre-assess students skill of counting collections of coins greater than one-dollar. 20. Ask students to record the values for the remaining jars on paper. Encourage students to use diagrams, charts, pictures and symbols to explain how they found each answer. Collect responses and review to assess students level of skill in counting collections of coins and in expressing what they know. 21. Set the stage for the next several components of the lesson by also asking students to respond to the following questions in their mathematics journal. What did I learn that helps me count money? What do I know about a one-dollar bill? Part Three: Working with One-Dollar Bills 22. Display a jar containing a collection of coins. The jar should include at least two or three of each type of coin and have a total value between $1.00 and $1.50. Give the jar to a student and ask the student to empty the jar on their table/desk and tell how many of each coin is in the jar; for example, there are 3 quarters, 4 dimes, 2 nickels and 6 pennies. Record (or have a student record) the information on the board or chart paper. 5
23. Ask a student to demonstrate how to find the total value of the coins by counting in a manner similar to that used in the previous parts of the lesson. Have the student use overhead coins or draw circles on the board to represent the coins in the collection. Ask the student to point to each coin as he or she counts to find the total 25, 50, 75, 85, 95, 105, 115, 120, 125, 126, 127, 128, 129, 130, 131 or 131 cents. 24. Allow students to share other strategies for counting the coins. For example, some students may recognize easy-to-count combinations based on their experiences in and out of school, such as recognizing that two dimes and one nickel have the same value as a quarter. They may notice that they can make two sets of two dimes and one nickel each that can be exchanged for two quarters. There are then 5 quarters and 6 pennies 25, 50, 75, 100, 125, 126, 127, 128, 129, 130, 131. 25. Ask what the 131 represents 131 cents. Check students use of symbols for writing money amounts greater than $1.00 by writing 131 cents on the board. Ask what symbols or ways used to write this amount -- 131, one-dollar and 31 cents, $1.31. Many students may be familiar with decimal notation for monetary amounts greater than one dollar and connect the number in front of the decimal point to the number of dollars and the number behind the decimal point to the number of cents and that one-dollar is the same as 100 cents. Instructional Tip: Proper use of the cent sign and dollar sign notation is very important. The cent sign is often used inappropriately on highly visible signs, in stores, and possibly in the school store or cafeteria; e.g., using a decimal and a cent sign for values less than one dollar such as.99 instead of 99. Be prepared to talk to students about this common error, when appropriate, and to collaborate with school staff to always use appropriate notation. 26. Distribute Attachment E, Coins Work Mat, to each student. Have students make a collection of coins equivalent to one dollar and forty cents. Observe students as they create the collection. Note which coin students use to start the collection. Ask students questions about their collections. Some students may try to make a collection with the fewest number of coins. 27. Organize students into small groups of two or three. Have students share their responses with the members of their small group. Ask students to explain to each other how they know the coins in the jar have a total value matching the given amounts. Circulate around the room looking and listening for responses that reflect a variety of approaches to the task. 28. Create a table on the board or chart paper to record combinations of coins. One example of a table is shown: Ways to Make $ 1.40 Quarters Dimes Nickels Pennies How I Know 4 4 0 0 4 quarters is the same as 100 cents and 4 dimes is the same as 40 cents, so together they are 140 cents 5 1 1 0 Counted 25, 50, 75, 100, 125, 135, 140 140 100 pennies make one dollar plus 40 more pennies makes $1.40 6
Record three or four different combinations for each jar. Have students post their solutions on the wall or bulletin board. 29. Give each small group (or student) two or three replicas of a one-dollar bill. Ask several students to share with the class some of the things they wrote in their journal in response to the questions, What do I know about a one-dollar bill? Summarize student responses on the board or chart paper. 30. Ask students to create a table or chart to record combinations of coins whose total value are one-dollar in their journal. Use one of their responses that may have been given in response to the journal question in step 21 to help them get started, such as: $1.00 is the same as 25 25 25 25 Part Four: Making Change 31. Have students share their responses to the task from the previous step. Record responses in a table or chart. Focus students attention on key equivalences; e.g., a one-dollar bill is the same as 4 quarters, 10 dimes, 20 nickels and 100 pennies. 32. Ask students to think about how they can create combinations of coins and a one-dollar bill that have a value of $1.67. Have students share combinations and record them on the board or chart paper using a table similar to that used in step 28. Ways to Make $ 1.67 One-Dollar Quarters Dimes Nickels Pennies How I Know Bills 1 2 1 0 7 You need one dollar bill and two quarters are worth 50 cents plus a dime makes 60 cents and 7 pennies makes 67 cents 1 6 1 2 Counted 100, 110, 120, 130, 140, 150, 160, 165, 166, 167 1 67 Dollar bill is the same as 100 pennies plus 67 more pennies makes $1.67 33. Provide or post a price list from the school store or cafeteria that lists various items and their cost or create a price list using actual costs of common school-related or snack items from a local store. It is recommended the prices or the items range from about 25 cents to between one and two dollars. Include some prices written using the cent sign and the dollar sign. 34. Pose a scenario in which a student has 2 one-dollar bills and three quarters. Suggest that the student wants to buy one of the items from the list; e.g., an eraser that costs 40. Ask students what coins or bills could be used to buy the eraser two quarters or one-dollar bill. Ask one 7
student to hand you two quarters (or replicas). Ask students what change you should give back to the student. Model the situation on the overhead, board or chart paper by drawing a simple illustration of the price and the money received and an area for the change. An example provided. What I want to buy How much it costs What bills and coins I need to pay for the item What bills and coins I should get as change eraser 40 2 quarters 1 dime because 2 quarters is the same as 50 cents and 40 plus 10 is 50 eraser 40 one-dollar bill 1 dime and 2 quarters because a dollar is 100 so I counted 40, 50, 75, 100. Instructional Tip: This may be the first exposure to making change for some students while other students will have prior knowledge and experience making change. Encourage students to share their thinking strategies. Recognize that some students will determine the amount of change by subtracting the cost of the item from the amount of money given to the clerk. This can be done using mental computation for some students and as a paper pencil activity for other students. Other students can determine the amount of change by starting with the price on the price tag and counting on until reaching the amount given to the clerk. For example, if the price tag reads 40 cents, students count, 41 cents, 42 cents, 43 cents until they reach 50 cents. Others will count on in a more efficient manner by recognizing they can count by 5 s or 10 s to reach 50 cents. At this grade level, encourage the use of counting strategies for making change, including those that appear inefficient (use lots of coins). The focus of initial experiences in making change should developing the concept of making change rather than performing computations or using the fewest coins possible. Additional opportunities, both informal and formal should be provided through out the school year to reinforce and extend students understanding and skill in counting collections of coins and one-dollar bills and making change. 35. Organize students into pairs and distribute multiple copies of Attachment F, Student Record Sheet, to each pair. Provide a price list, a collection of coins and three one-dollar bills. One student (the buyer) receives the three one-dollar bills and the other student (the clerk) receives all of the coins. The buyer selects an item to purchase and uses the one-dollar bill(s) to pay for the item. The clerk determines and gives back the change and then records the information on the record sheet. The buyer then uses the bills and coins left to buy another item, gives the clerk bills and/or coins to pay for it. The clerk determines the amount of change, gives the buyer the appropriate coins and records the information. The students reverse roles, redistribute the money so the buyer only has bills and the clerk has all the coins, and the process repeats. 36. Circulate around the room observing student pairs as they complete the task. Ask probing questions and provide assistance as needed. Use observations and record sheets as evidence of student understanding and skill in counting money and making change. 8
37. Bring closure to this portion of the lesson by asking students to respond to the following questions in their mathematics journal. Identify an item from a newspaper advertisement or in a store that they would like to purchase. List the price of the item and identify a combination of coins and one-dollar bills whose value is equal to the price of the item. Tell what you have learned that will help you know how much change you should get when you buy something. 38. Complete post-assessment using observations, record sheets, and journal entries as evidence of student understanding and skill in counting money and making change. Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). Visual learners can use the hundred chart to help them visualize making change. Students highlight the column of numbers with 5 as the ones digit. Use a different color to highlight the column with zero as the ones digit. Use a third color to highlight the multiples of 25 (25, 50, 75, 100). Explore and practice various moves, such as a move of one space to the right represents a penny. Other moves include, a jump horizontally from the 5s column to the 10s column represents a nickel, a vertical move down one row that represents a dime, and a move from 25 to 50, from 50 to 75, and from 75 to 100 each represent a quarter. Kinesthetic-tactile learners can play the Money Game using number cubes. The first player rolls two number cubes, adds the two numbers and selects that amount of money from the coins. For example when a sum of 7 is rolled, the player chooses a nickel and two pennies. The next player takes a turn, repeating the process. The game continues until one of the players accumulates a total of one dollar. This game can also be played in reverse where each player is given one dollar and the goal is to end up with no money. Another variation to increase the challenge to have the numbers rolled represent a two-digit number. For example when a 3 and 4 are rolled, the student may collect coins whose total value is 34 or 43. Students can represent money, using base ten blocks. A cube represents one penny, a tower represents one dime (or two nickels) and a flat (100 block) represents one dollar. Many literature books correlate well with teaching money. Have students model the money amounts used in the story. Extensions: Set up a store in a learning center using items cut out of the ads in the newspaper or catalog. A play cash register and play coins can be used. One student is the customer and the other student is the cashier. Students take turns buying items and making change. Examine state quarters, the new nickel, Susan B. Anthony dollar and the coins. Have students bring in coins from other countries. Compare how they are like U.S. coins and how they are different. Home Connections: Ask parents to allow their child to count the change that their parents have in their pockets, wallets, purses, or car. 9
Encourage parents to ask questions like: I have some coins in my pockets that equal 90 cents. What combinations of coins could be in my pocket? Practice writing the value of money using the cent sign ( ) and in decimal form using the dollar sign ($). Provide activities and tips to model ways that parents can help their child practice counting money and making change, such as providing a list of appropriate books involving money contexts and suggestions for modifying simple games or play activities to incorporate counting money and making change. Interdisciplinary Connections: Content Area: English Language Arts Standard: Writing Process Benchmark: A. Generate ideas for written compositions. Students discuss ideas and write stories and story problems that use money. Content Area: Social Studies Standard: Economics Benchmark: B. Explain how people are both buyers and sellers of goods and services. Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: For the student: Classroom items such as chart paper, a supply of coins (or replicas), overhead coins optional, replicas of one-dollar bills, price list from school store or cafeteria, if available. A film canister or small jar containing coins or replicas of coins, replicas of one dollar bills, copies of activity sheets Vocabulary: change dime dollar nickel one-dollar bill penny quarter 10
Research Connection: Van de Walle, John. Elementary and Middle School Mathematics: Teaching Developmentally, Fourth Edition. New York: Addison Wesley Longman. Attachments: Attachment A, Pre-Assessment Attachment B, Pre-Assessment Checklist Attachment C, Post-Assessment Observation Record Attachment D, Coin Jars Student Handout Attachment E, Coins Work Mat Attachment F, Student Record Sheet 11
Attachment A Pre-Assessment Name Date Things I know about Kip s coins Does Kip have more than one dollar or less than one dollar? How do you know? 12
Attachment B Pre-Assessment Checklist Name Identifies Coins Identifies Values Counts Small Collections Notes 13
Attachment C Post-Assessment Observation Summary Name Date Counting Money Making Change Notes Name Date Counting Money Making Change Notes Name Date Counting Money Making Change Notes 14
Attachment D Coin Jars Student Handout 15
Attachment D (continued) Coin Jars Student Handout 16
Attachment E Coins Work Mat 17
Attachment F Student Record Sheet Buyer: Clerk: Item Price What bills and coins are used to pay for the item What coins should be are given as change 18