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Dana Middle School team: Dena Hause, Cathy Garcia, Kathy Robertson, Susan Naujokaitis, Christy MacCabe

Format (whole class/small group): small group

What concept or idea is being developed in this lesson?

• Case 1: height of shadow is constant
• Case 2: distance from light is constant
• Case 3: height of prop is constant

Prior knowledge

• How to write a ratio
• How to simplify fractions
• How to write equivalent ratios
• Importance of labeling in ratios

What mathematical practice standards are addressed?

• 1 – Make sense of problems and persevere in solving them
• 2 – Reason abstractly and quantitatively
• 4 – Model with mathematics
• 5 – Use appropriate tools strategically
• 7 – Look for and make use of structure

• 1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• 3: Use ratio and rate reasoning to solve real-world and mathematical problems.
• 3a: Make tables of equivalent ratios relating quantities with whole number measurements. Use tables to compare ratios.

#### Activity or problems you will pose:

Day 1: Launch: If a 6 ft tall father and a 3ft. tall child were walking to school together, could their shadows ever be the same height? Where would the props be on the grid to make this true? (Use props to discuss ratio of child to father to shadow. Discuss use of Shadow Device and demonstrate use of props, measurements on device, importance of placement of light source.) Call out specific ratio language and background knowledge needed for inquiry task.)

Inquiry: "Two similar figures cast shadows that are the same height. The heights of the figures are different. Move the figures to different distances from the light source. What happens? Does a figure get larger or smaller as you move it toward the light? Where will the figures be on the grid when their shadows are the same height?

Day 2: Students make conjectures with their groups to test on Day 2 using the Shadow Device. Guiding questions: Which figure will be closer to the light source, which farther away? How far away from the light source do you think each figure will be? Why do you think so?