standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Narrative
The purpose of this activity is for students to create rectangles from colored paper. Students make identical rectangles that have one side length that is a whole number and one side length that is a fraction greater than 1. Then, as a group they create one mosaic. It is not necessary for students to use all of the rectangle pieces. It is important that all students in each group measure their rectangles using the same unit, either inches or centimeters.
Action and Expression: Provide Access for Physical Action.
Provide access to pre-cut materials to reduce barriers for students who need support with fine motor skills and students who benefit from extra processing time.
Supports accessibility for: Fine Motor Skills, Organization, Visual-Spatial Processing
Required Materials
Materials to Gather
Colored paper
Glue
Rulers
Scissors
Required Preparation
Each student needs a few sheets of the same colored paper.
Each group of 4 needs a ruler, scissors, glue and one large piece of poster paper.
Launch
Groups of 4
Distribute materials. Make sure each student in the group gets a different color paper.
Activity
10 minutes: independent work time
5 minutes: group work time
Monitor for students who:
write numerical expressions to represent the area of the rectangles.
use a diagram or write on the physical rectangles.
Student Facing
Use the colored paper and scissors to cut identical rectangles. Make sure the measurement of one side of the rectangle is a whole number and the other is a fraction greater than 1.
What is the area of one of your rectangles? Show your reasoning.
Use the rectangles from your group to make a group mosaic by arranging some of the different colored rectangles on a blank piece of paper.
Student Response
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Activity Synthesis
Invite a few students to share and describe their mosaic.
“What are some questions we can ask about the mosaics?” (Which color rectangle did we use the most of? What are some other ways we can arrange the same pieces? What are some other pieces that can make the same pattern? How much would this cost if we actually made this using hard materials?)


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