### Grade 7: Stained Glass

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#### Common Core Standards

7.G.4  Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.EE.3  Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Standards for Mathematical Practice

MP.1 – Make sense of problems and persevere in solving them

MP.2 – Reason abstractly and quantitatively

MP.3 – Construct viable arguments and critique the reasoning of others

MP.8 – Look for and express regularity in repeated reasoning

#### Description of Unit

This lesson titled, "Stained Glass" from illustrativemathematics.org is intended to engage students in a real-world application of area and perimeter, specifically associated with area and circumference of circles and semicircles. Students are provided a contextual problem and asked to use appropriate problem solving strategies to reach a conclusion on the price of making a stained glass window. Students are provided minimal information on the window’s dimensions and must deduce different measurements, such as radius and diameter of the given semicircles. Within this lesson, students are also using skills from the Expressions and Equations domain to use algebraic thinking when finding the total cost of making the window and comparing it to the provided money to pay for such a window.

#### Cautions

This lesson is lacking a formal lesson structure, including the possible questions to include during instruction. Connecticut teachers also should be aware that they would need to include supports for students working above/below grade level, those students who are identified as students with disabilities, and for English Language Learners. However, there are easy ways to adjust this to meet the needs of the diverse learners in Connecticut classrooms, such as marking the picture or asking students to find the dimensions of a new window so the cost matches the money set aside for window construction. While there are solutions, rubrics are missing from the lesson. This lesson may not be the most efficient for teachers, since there is a significant lack of lesson plan and instructional details.

#### Rationale for Selection

This lesson attends to the rigor of the Common Core. Students are required to construct an argument around if it is possible to make the window with the given money. The lesson provides a real-world context and requires students to reason abstractly about how the portions of the window can be put together to create circles and using that reasoning to quantify the amount of edging needed between panes of glass. There is a balance of conceptual learning and procedural fluency. This task is a great tool to use for assessing students’ understanding of the geometric concepts of area and perimeter. For the end user, this would a valuable tool to gauge students’ ability to transfer skills to a more realistic context.