## Decimals Make Cents

### Sharla ShultsBay District Schools

#### Description

Look out real world, here we come! Due to new jobs, pay increases, taxes, money in the bank, and opportunities to spend, spend, spend, students learn there is no way to avoid working with decimals in making life -centsable!-

#### Objectives

Understands concrete and symbolic representations of real and complex numbers in real-world situations.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

#### Materials

-Copies of documents found in the associated file prepared for class discussion and formative assessment (See Teacher Preparation for list.)
-Students’ calculators (optional for problem solving only)

#### Preparations

1. Download and duplicate copies of the following documents located in the associated file:
a) Warm-Up Activity – one per student (See Associated File.)
b) Warm-Up Activity Answer Key – one copy for teacher use
c) Problem Solving Group Activity Cards – one per group (set up for 8 groups)
d) Answer Key for Group Activity – one copy for teacher use
e) Problem Solving Practice Sheet – one per student
f) Problem Solving Practice Sheet Answer Key – one for teacher use

2. Set up overhead projector and have enough overhead pens for demonstration.

3. Download, print, and make transparencies of the models (Transparency 1 and Transparency 2) developed for introduction of basic skills and common errors with decimals found in the associated file. Answer keys are also included in the associated file.

4. Secure a set of classroom standard FCAT calculators, or request students to furnish their own to be used with problem solving only. Students do not use calculators during the Warm-Up activities.

5. Prepare extra worksheets as needed for students having difficulty with basic arithmetic skills with decimals. These reflect areas of difficulty as demonstrated in the diagnostic check.

#### Procedures

NOTE: Inverse relationships are not addressed or assessed in this lesson.

1. What better way is there to demonstrate the understanding of the decimal than with money notation? However, it won’t just start and end there because in this lesson, students explore decimals with both rational and irrational numbers. Decimals must make sense as well as cents!

2. Display overhead Transparency 1. (See Associated File.) Cover the transparency with a sheet of paper and slowly display each problem one at a time. Allow students to volunteer to come to the overhead individually and circle the answer that seems to be more reasonable. Ask students to explain their choices.

3. Next, display overhead Transparency 2. (See Associated File) Tell students to look for and identify common errors with decimals. Explain to students the objective is to examine the problems and judge by observation where the error occurred in the decimal placement of the answers.

4. Distribute Warm-Up Practice (see Associated File) to diagnostically assess students’ abilities to add, subtract, multiply, and divide decimals. (No calculators allowed on this section.) Use the Warm-Up Practice Answer Key in the associated file to check answers and go over common errors with students before beginning the activity. Provide students that need practice in the basic operations with decimals additional practice sheets as deemed necessary.

5. Divide the class into groups of 3 or 4 depending on the size of the class. Distribute one problem card face down to each group. See Associated File for Problem Solving Group Activity Cards. Have the back of the card numbered from 1 to 8 corresponding with the problem number on the front of the card.

NOTE: For example, in a class of 32 use 8 groups. Allow 5 minutes per problem, then tell students to switch cards. Considering 30 seconds elapsed time for switching cards, 5 minutes per problem for 8 problems would take approximately 44 minutes. Use teacher discretion to determine how much time to allow or how many of these problems to require students to solve during the activity.

6. Instruct each group to assign the following roles to group members:
a) Information Manager – Keeps all group members solving the problems
b) Effective Communicator – Initiates and keeps discussion going relative to task
c) Recorder – Copies the problem in the event the group does not finish within time limits
d) Calculator/Checker – Responsible for data entry into the calculator & checking answers

7. Set up a timer and call time at the end of each 5 minutes. Tell students to switch and reset the timer. If a group finishes before the 5 minutes is up, tell students to go over the problem and check for accuracy and labeling or go back and work on an unfinished problem. Students use calculators during the problem solving for speed and to check accuracy.

8. Emphasize to all group members that each student is responsible for EXPLAINING the solutions to all of the problems. Tell students all work must be shown since answers only are not acceptable. Explanations must be clearly defined demonstrating understanding of the effects of operations on real numbers. Student responses will vary. Use teacher discretion to decide how many of these problems to require students to include in the activity. The number of problems required is not the issue, but the clarity by which the students demonstrate understanding of the concepts!

9. Have each group draw a number from 1 to 8 for a problem to explain the solution key to the class. Hold question and answer discussions as needed throughout the process.

10. Distribute the Decimals Make Cents Problem Solving practice sheets to students. (See Associated File.)

11. Use the remaining time in the class period for students to work independently on their problem solving skills. Monitor students’ progress through observation and lend assistance as needed. Again, emphasize to students the objective is to explain the effects of the operations, not just obtain an answer!

12. Take up students’ papers or have them complete for homework and formatively assess students’ understanding of concepts and problem solving skills using the answer key found in the associated file.

#### Assessments

Students demonstrate the understanding of the effects of operations on real numbers, and concrete and symbolic representations of rational numbers, on the Decimals Make Cents problem solving activity sheet. (See Associated File.) Students are formatively assessed using the answer key provided in the associated file. Students scoring low in multiple areas may require additional practice in basic operations and/or problem solving techniques.

#### Extensions

As an extension, instruct students to create their own math problems demonstrating Decimals Make Cents. Allow students to discuss real life experiences of their own and incorporate this information into actual problems for the class to solve.