Money Jar
Est. Class Sessions: 1Developing the Lesson
Divide Coins. Read the short story about the Franklins on the Money Jar pages in the Student Guide. The Franklins save their coins in a jar. Once each month they divide the coins among the family members. Pennies are divided among the four children. Nickels and dimes are divided among all the family members. Any leftovers are returned to the jar.
Distribute the collection of coins or copies of the Pennies, Nickels, and Dimes Masters to each group. Encourage students to use the money as manipulatives to solve the problems. Since there are four children in the Franklin family, put students into groups of four so each member of the group can act as one of the children.
Assign Questions 1–10. In Question 2, the family divides 18 dimes among six people. To determine how much money each person gets, students can use the coins to distribute the dimes equally. They should find that 18 dimes divided among six people means each person has three (18 ÷ 6 = 3). Therefore, each person gets thirty cents.
Allow students to develop their own methods for sharing the coins. Some groups may pass out the appropriate coins one by one to each member of the group until all the coins have been distributed. Others may start with a guess, such as two coins per child, and then adjust the number of coins as needed. For some problems, students may have had enough experience with the numbers to use number sentences immediately.
Students must also interpret the remainders. In Question 3 the family divides 22 nickels among the six members. In this case, each person gets 3 nickels or 15 cents, and 4 nickels are returned to the jar.
Explain Numbers and Symbols in Number Sentences. As students work on the problems, talk with individual groups, asking them how they are solving the problems. In this way you can help them verbalize the division process. Ask them to explain their methods for dividing the coins evenly and interpreting the remainders. Then ask them to match their work with manipulatives to the numbers in their number sentences.
Sample discussion prompts for these conversations follow:
More than one number sentence is possible for each problem. For example, Question 6 requires students to divide 38 pennies among four children. Students may see the problem as repeated subtraction and write their solution as shown in Figure 1.
As a division sentence, this can be written as 38 ÷ 4 = 9 R2. The corresponding multiplication sentence is 9 × 4 + 2 = 38. Students can use other combinations of addition, subtraction, and multiplication to record their solutions.
Have a class discussion highlighting the relationships between the various number sentences. Ask the reporter from each group to display their group's number sentence for Question 6.
Ask:
Refer to Question 7 in which Flora, Frankie, and Ben each wrote different number sentences to show how they divided 38 pennies. Ask students to compare the number sentence their group wrote for Question 6 to each of the Franklins'. Then ask students to explain the numbers and symbols in Flora's, Frankie's, and Ben's number sentences.
Interpret Remainders.
Share the following problem with the class:
Understanding the Calculator. It is recommended that students use manipulatives for support when solving problems in this lesson. For most students, a collection of coins will provide all the support needed. However, some students struggling with the mental division involved in the problems in this lesson may benefit from using calculators. Be aware that they may have difficulty when faced with the task of interpreting the results. Point out that they will get different results depending on whether they enter the number of coins or the amount of money into the calculator. The table illustrates the different answers students will see on the windows of their calculators and an appropriate interpretation. Experimenting with the calculator in conjunction with using the manipulatives may allow students to explore the decimal representation of money.
If students choose to use calculators, the following problems may help in their understanding of how to interpret the answers displayed on a calculator:
- Jason used a calculator to solve 15 ÷ 6. His calculator read 2.5. How many coins should he give each person? (2 coins per person)
- Linda had 18 dimes to divide between 6 people. She knew 18 dimes was the same as $1.80 so she entered 1.80 ÷ 6. The window showed 0.3. How many dimes should each person get? (3 dimes. The 0.3 on the window means 30 cents.)
Discuss Question 10. It differs from the previous problem in that after the initial division, the money remaining in the jar can still be divided fairly among the family members. After the fifteen dimes have been divided among the six members (15 ÷ 6 = 2 R3), students can trade nickels for the remaining three dimes so that each person can have two dimes and one nickel.
Ask:
