## Reflection: Diverse Entry Points Quadratic Modeling (DAY 3) - Section 2: Collaborative Solution

Like many of the tasks from the Math Assessment Project, the Cutting Corners activity can be considered a “low floor, high ceiling task.”  All students can find an entry point, but there is sufficient challenge available to all students.

Assigning groups by ability allows me to differentiate the task so that it is both rich and approachable for all. In its raw form, students are probed to recognize and apply right triangle properties, simplify quadratic equations with three variables, substitute values for given quantities, solve an unfactorable quadratic equation, interpret the solution in context, and extend the reasoning to solve a new (but related) problem. Advanced students will have no trouble finding an endless supply of depth and challenge in this scenario. Many other students will benefit from a teacher demonstration of part 1 (applying Pythagorean Theorem), effectively entering the task at part 2 (substituting values and solving a quadratic). When faced with interpreting the solutions, further scaffolding can be provided, if necessary, by teacher questioning: “What is x supposed to be measuring?” “Do both of your answers seem reasonable?” “Do you remember the value and meaning of r?” Finally, part 3 can be differentiated by either eliminating or scaffolding the question.

Differentiating by Ability
Diverse Entry Points: Differentiating by Ability

Unit 3: Polynomial Functions and Expressions
Lesson 13 of 16

## Big Idea: How do large vehicles determine how wide to take the turns so they don't run over sidewalks and bike lanes? The math behind these calculations involves quadratic equations!

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80 minutes

### Colleen Werner

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