Using Clairaut’s historic-dynamic approach and dynamic geometry tools in middle school can develop students’ conceptual understanding before they encounter formal proof in geometry.

Grades: 6th to 8th

Geometry

Mathematical Practices

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Draw construct, and describe geometrical figures and describe the relationships between them.

Look for and express regularity in repeated reasoning.

Look for and make use of structure.

Attend to precision.

Use appropriate tools strategically.

Model with mathematics.

Construct viable arguments and critique the reasoning of others.

Reason abstractly and quantitatively.

Make sense of problems and persevere in solving them.

Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.A.5, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP3, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7, CCSS.Math.Practice.MP8, 7.G.A.2, 7.G.B.5

Address the needs of diverse learners with a class structure that is designed around a crime scene theme and based on student choice and perceptions of the math being studied.

Grades: 6th to 8th

Geometry

Mathematical Practices

Expression/Equation

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Look for and express regularity in repeated reasoning.

Look for and make use of structure.

Attend to precision.

Use appropriate tools strategically.

Model with mathematics.

Construct viable arguments and critique the reasoning of others.

Reason abstractly and quantitatively.

Make sense of problems and persevere in solving them.

Understand the connections between proportional relationships, lines, and linear equations.

Understand and apply the Pythagorean Theorem.

8.G.B.7, 8.EE.B.6, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP3, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7, CCSS.Math.Practice.MP8, 7.G.B.4