Mathematical Practice #6 Grade 8 Cluster 8.G.2 Welcome, This presentation will assist you implementing Common Core Standards to your instruction. Mathematical Practice #6 Attend to Precision

Math standards MACC.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse. MACC.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- world and mathematical problems in two and three dimensions. MACC.8.G.2.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. The focus for the highlighted problem covers the following academic Common Core Standards for Mathematics. This will be a good point to explain to your students what is expected once delivery of the lesson is completed, and will assist you when describing the objectives while you are writing the lesson plans.

Practice Standards Mathematical Practice #6 Attend to Precision Common Core also includes a series of practice standards. While many can be used, the focus here will be on Mathematical Practice #6 : Attend to Precision. At this point you may want to engage your students in a conversation about what they believe this means.

Highlighted problem For the Highlighted problem the students will be introduced to the following scenario, in order to give the students a clear idea of what is expected by the end of the lesson. <Introduce the problem or have a student read it to the class> Your company has been hired to build a stage for the Super-Bowl’s half-time show. A scale model of the stage is 2 cm. tall, 10 cm. long and 2 √11 cm. wide. Your job is to design the trusses that connect all the joints (The diagonals of the polyhedron faces) and design an additional reinforcement that connects the opposite joints (The diagonal of the cuboid).

Use these pictures as a reference to demonstrate to your students the segments that are originally given, so that they can visualize the segments they need to construct. Before moving to the next slide, pause and ask the students: “How can you strengthen the stage?” Prompt them to think about variables such as cost, weight, safety, setup, etc.

Use this pictures to help explain that creating diagonals through each face will create extra support for the structure without adding excessive weight. Prompt the students to discuss the type of triangles that are created. Once they have identified that they are right triangles, introduce or reinforce the Pythagorean Theorem, and ask the students to calculate the lengths of the diagonals.

Diagonal Brace for Stage Use these pictures to demonstrate the final element of the problem, calculating the diagonal of the three-dimensional stage. Note that 6.6 is an approximation of the actual value 2√11 . This will be a great vehicle to prompt the students to discuss precision. Depending on your level of experience and comfort with technology you may want to try to incorporate animations using software such as Geogebra, to help the students visualize the problem. (A Geogebra file will be linked to the picture; you will need Geogebra 5.0 or higher installed)

This picture will help show the students the right triangle that they need to calculate the three-dimensional diagonal. Many students will have a difficult time identifying segment AC as a leg of the right triangle.

Critical Thinking What are the possible consequences of designing a stage using measurements that are not precise? What is margin of error? When is it ok to round a number? When is it ok to round an answer? What is the difference between estimation and calculation? Is the answer on your calculator always precise? Depending on the available time and comfort level you can use any of these questions to enrich the activities, wrap up the session, or have a discussion.

This slide allows you to expand and enrich the lesson This slide allows you to expand and enrich the lesson. Students may be asked calculate the distance between points using the spatial coordinates instead of calculating the different diagonals. The students should be able to identify the advantages in terms of time and precision.

ADAPTATIONS To adapt this activity you may use different size boxes. No additional materials or costs are involved.