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5-8

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## Linking Number Patterns and Algebraic Expressions

Students practice using algebraic expressions by recording data from a video segment in which two staircases ascend at different rates. They record the patterns in two-column tables, draw line graphs and write simple algebraic relations.

### Overview

In this Cyberchase activity, students are introduced to two-column representations of algebraic relations by recording data from a video clip, in which two staircases ascend at different rates. The students record the patterns in two-column tables, draw line graphs, and write simple algebraic relations.

5-8

one hour

### Media Resources

Staircases of Shangri-La Video
Speed of Ascent Video

### Materials

Handout 1: Comparing Algebraic Expressions Document
Assessment: Level A Document
Assessment: Level B Document

### Part I: Learning Activity

1. Read the following to your students: "Hacker has attacked ShangriLa, where Master Pi has established the rule of the 'Good Vibration' that keeps the kingdom peaceful and beautiful. Hacker and the CyberSquad race to reach the Good Vibrations tree, one choosing the red staircase, the other choosing the blue staircase. The staircases grow at different rates and have steps of varying sizes."

2. Distribute Handout 1: Comparing Algebraic Expressions.

3. Tell the students that they will watch video clips in which Hacker and the CyberSquad are climbing staircases to get to the top of the mountain where the Good Vibration tree stands.

4. Ask the students to fill in the columns on the first problem on Handout 1 for each staircase as they watch the video clips.

5. Play the Staircases of Shangri-La Video then play the Speed of Ascent Video. Pause the video after each staircase increase, as students may need to count the number of stairs.

6. Ask the students to complete the rest of Handout 1, "Comparing Algebraic Relationships." (Note: This handout is designed to elicit a discussion of the importance of the size of the units. Problems 1 through 4 ignore the different sizes of the steps that Hacker and the CyberSquad are on, and the point where the two graphs cross has no significance. Problems 5 through 11 introduce the relative sizes of the steps, and use the height of one of the steps as the common measure of the progress of both Hacker and the CyberSquad.)

7. Discuss Handout 1, and the issue of doubling vs. single-step changes.

### Part II: Assessment

Assessment: Level A (proficiency): Students fill in a table of values to complete patterns of data, and interpret their results.

Assessment: Level B (above proficiency): Students fill in tables of values based on algebraic expressions and graph them.

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