## Gummy vs. Gum

### Rita Williams

#### Description

Students discover a number pattern and write an equation that describes it. This lesson should be conducted after students have worked with patterns and one- and two-step equations.

#### Objectives

The student describes a wide variety of patterns, relationships, and functions through models, such as manipulatives, tables, graphs, expressions, equations, and inequalities.

The student uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities.

#### Materials

-Gummy bears (8 for each student)
-Sticks of gum (2 for each student)
-Clean paper to place gum and gummy bears on
-Pencils
-One copy of the student activity sheet per student (See Associated File)
-One copy of the rubric per student (See Associated File)

#### Preparations

1. Make sure students have been exposed to patterns and one- and two-step equations.
2. Gather materials.
3. Line up gummy bears on a stick of gum and record how many gummy bears equal the length of one stick of gum. Write an equation(s) that describes this. For instance, if 3.5 gummy bears equal one stick of gum, then the equation would be 3.5x=y, where x=# of gum sticks and y=# of gummy bears. You need to know this in order to evaluate your students’ work.
5. Make copies of the student activity sheets with the rubric on the reverse side for each student.

#### Procedures

1. Distribute a student activity sheet (with the rubric copied on the opposite side), 8 gummy bears, 2 sticks of gum, and 1 clean sheet of paper to each student.

2. Put students in pairs. Encourage them to work cooperatively with their partners throughout this activity.

3. Ask them if they ever thought that the gummy bear company was cheating them because 1 gummy bear is not nearly as tall as 1 stick of gum? For a minute or two, allow them to share their responses.

4. Instruct them to estimate the number of gummy bears that would measure the length of 1 stick of gum. Briefly discuss their estimations.

5. Inform them that they are actually going to compare the measurements of gummy bears and gum sticks. Direct their attention to their activity sheet. Instruct them to line the gummy bears along 1 gum stick and determine how many gummy bears equal one gum stick. Encourage them to record their findings on their T-charts. Repeat for 2 gum sticks, 3 gums sticks, and 4 gum sticks.

6. Ask them how they could use their data to determine how many gum sticks it would take to equal any number of gummy bears (such as 237) without having to buy it all. Lead them into a discussion of patterns, if they do not automatically jump to this topic themselves. Inform them how patterns can be used to formulate equations, which help us make predictions. Point out how this procedure is used in the “real world.” For example, explain how this procedure is used when corporations project their sales for the following year(s). It is also used for population projection.

7. At this point, it would be appropriate to review the rubric with the students.

8. Instruct students to work with their partners and discover any patterns between their numbers.

9. Ask them if their pattern is consistent through both number lists. If not, encourage them to find a pattern that is consistent. Once they have discovered a consistent pattern, they should describe the pattern on their activity sheet.

10. Instruct students to use their data to formulate an equation that describes the pattern they just discovered. Tell them if their formula is accurate, it will yield the same responses listed on their T-chart. Have them record their equation on the activity sheet.

11. Now, ask them to use their equation to predict how many gummy bears would equal the measurement of 10, 20, and 237 gum sticks, and record their responses.

#### Assessments

Each student completes the student activity sheet; the activity sheet is assessed using the rubric. (See Associated File)

#### Extensions

Extensions
1. Students can translate their T-chart data into ordered pairs and graph the points. Ask students if certain points will be found on their graph, such as (12,-13) or (-7,24) or (0,0). Lead them to discover that all points on this line will be in Quadrant I, with the exception of (0,0) which lies on the origin.
2. Students can translate their equations in terms of the other variable. Next, they can graph the results. Discuss the differences between the graphs and point out that the equations are inverses of each other.

Modifications
1. Instead of having students come up with an equation without any assistance (procedure #10), give them three equations and have them find the one that fits the pattern.

#### Attached Files

Student activity sheet and rubric.     File Extension: pdf