##
* *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*

# Quadratic Modeling (DAY 3)

Lesson 13 of 16

## Objective: SWBAT apply their understanding of quadratic equations and the Pythagorean Theorem to solve a spatial problem.

#### Warm-up

*10 min*

I provide students with a warm up almost every day in order to make the best use of class time. When I don't structure the first 10 minutes or so with a warm-up, students will spend the time chatting and waiting for announcements. The simple act of providing a warm-up helps me reclaim that time and also gets students in the right frame of mind to do some productive work.

For this warm-up, students practice solving quadratic equations by factoring, completing the square and using the Quadratic Formula. Warm-up Solve Quadratics has 6 equations to solve that encourage the use of all three methods.

#### Resources

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#### Collaborative Solution

*30 min*

In the previous class, students had the opportunity to attempt an individual solution to the MAP Assessment Task, Cutting Corners. Today, I will assign students to groups of three based on facility with problem solving. Each group will be assigned at least one student who is confident with word problems.

I hand back student work from the previous day and give students a chance to read my comments. I then ask them to get into their groups and share their work with their peers. The goal is for the group to come up with something better than any of the individuals came with. Everyone in the group has to agree on the method that is submitted in the end [MP1, MP4].

Working with an enlarged copy of the diagram and a large piece of paper, students will work out their group solution that will be hung on the bulletin board.

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After students come up with their group solution, they are provided with four possible selections of sample work to review and critique. If a group has been successful in solving the task before looking at sample responses, I ask the group to find a sample in which the task was solved in another way.

Groups take 20 minutes to look over the samples and answer questions provided in Cutting Corners. Students are asked to describe the method used, correct errors, and conjecture about why the student took the steps they did [MP3].

When students have had a chance to critique the work samples, we have a whole-group discussion about each sample. I project each sample response on the board and ask one of the groups to lead the discussion about the sample.

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#### Self-Evaluation

*10 min*

The final step in this assessment task is a for each group to evaluate how well they worked together. Students will complete the form group work evaluation, which is provided in the Cutting Corners activity in order to give each other and me feedback on how well they worked as a group [MP3]. I ask students to reflecting on how the group functioned because I care that they leave my class with a better understanding of how to collaborate to get a job done. Although not explicitly stated in the CCSS, teaching students to work together productively is considered one of the primary goals of K-12 education in my school district.

#### Resources

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- LESSON 1: Introduction to Polynomials
- LESSON 2: Seeing Structure in Expressions - Factoring GCF's and Quadratics
- LESSON 3: Connecting Polynomials to Sequences
- LESSON 4: Connecting Polynomials to Geometric Series
- LESSON 5: Quadratic Functions: Standard and Intercept Forms
- LESSON 6: Quadratic Functions: Vertex Form
- LESSON 7: Flexibility with Quadratic Functions
- LESSON 8: Connecting Quadratic Functions and Quadratic Equations
- LESSON 9: Solving Quadratic Equations
- LESSON 10: Quadratic Performance Task
- LESSON 11: Quadratic Modeling (DAY 1)
- LESSON 12: Quadratic Modeling (DAY 2)
- LESSON 13: Quadratic Modeling (DAY 3)
- LESSON 14: Quadratic Modeling (DAY 4)
- LESSON 15: Review Workshop: Polynomial Functions and Expressions
- LESSON 16: Unit Assessment: Polynomial Functions and Expressions