Stated assumptions, definitions, and previously How are assumptions and definitions used in proof? Why are proofs an integral part of geometry? How does established results help in the construction of proofs. How can you prove relationships between angles writing a proof deepen your understanding of (MA10-GR.HS-S.4-GLE.1-EO.c) formed when transversal intersects parallel lines? geometric concepts? How do previously proved ideas about parallel lines support conjectures and proofs about triangles and parallelograms? The coordinate plane models algebraically What information is needed to calculate the perimeters Why is it helpful to model geometric relationships on the geometric relationships. of polygons and area of triangles and rectangles in coordinate plane? the coordinate plane? How can you determine the slope of line parallel or perpendicular to a given line? Geometric transformations create functions that take What function operations work with transformations? Why are transformations functions? points in the plane as inputs and give unique How can you compare transformations? corresponding points as outputs. Rigid transformations preserve distance and angle. What do non-rigid transformations preserve? Why is it important that rigid transformations preserve (MA10-GR.HS-S.4-GLE.1-EO.a) How can I use transformations to prove to figures are distance and angle? congruent? What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined. Key Knowledge and Skills: My students will…
Stated assumptions, definitions, and previously established results help in the construction of proofs. (MA10-GR.HS-S.4-GLE.1-EO.c) How are assumptions and definitions used in proof? How can you prove relationships between angles formed when transversal intersects parallel lines? How do previously proved ideas about parallel lines support conjectures and proofs about triangles and parallelograms? Why are proofs an integral part of geometry? How does writing a proof deepen your understanding of geometric concepts? The coordinate plane models algebraically geometric relationships. What information is needed to calculate the perimeters of polygons and area of triangles and rectangles in the coordinate plane? How can you determine the slope of line parallel or perpendicular to a given line? Why is it helpful to model geometric relationships on the coordinate plane? Geometric transformations create functions that take points in the plane as inputs and give unique corresponding points as outputs. What function operations work with transformations? How can you compare transformations? Why are transformations functions? Rigid transformations preserve distance and angle. (MA10-GR.HS-S.4-GLE.1-EO.a) What do non-rigid transformations preserve? How can I use transformations to prove to figures are congruent? Why is it important that rigid transformations preserve distance and angle? Key Knowledge and Skills: My students will… What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.