Chenowith Mathematics Scope & Sequence

Geometric Relationships

CCG: Use given assumptions to determine properties of geometric figures, solve problems, and prove or justify relationships between figures.  

Content Standards: Relationships:

• Find and analyze relationships among geometric figures using transformations (e.g., reflections, translations, rotations, dilations).
• Make and test conjectures about geometric shapes and their properties, and prove relationships between them, incorporating technology where appropriate.
• Solve problems using geometric relationships, spatial reasoning, and coordinate geometry.

#	I=Introduce, P=Practice, S=State Benchmark Level, M=Master, A=Apply, O=Optional	K	1	2	3	4	5	6	7	8	9	10	11	12
1	Identify changes in figures as they move through reflections and rotations.	.	.	.	S	.	.	.	.	.	.	.	.	.
2	Identify properties of geometric figures and combinations of shapes.	.	.	.	S	.	.	.	.	.	.	.	.	.
3	Students will visualize three-dimensional shapes shown "unfolded" in two-dimensional representations.	.	.	.	S	.	.	.	.	.	.	.	.	.
4	Students will visualize folding of individual shapes to show symmetry.	.	.	.	S	.	.	.	.	.	.	.	.	.
5	Students will identify properties of geometric figures by determining which shape does not belong to a group of shapes.	.	.	.	S	.	.	.	.	.	.	.	.	.
6	Students will identify properties of geometric figures by indicating shapes that are identical in all properties.	.	.	.	S	.	.	.	.	.	.	.	.	.
7	Students will identify properties of geometric figures by recognizing similar shapes (those that maintain the same shape, but are different in size).	.	.	.	S	.	.	.	.	.	.	.	.	.
8	Shapes that may be reflected, rotated, or categorized include line segments, angles, triangles, quadrilaterals--(trapezoid, parallelogram, rectangle, rhombus, square) pentagons, hexagons, octagons, circles (including location of the diameter and radius).	.	.	.	S	.	.	.	.	.	.	.	.	.
9	Shapes that may be reflected, rotated, or categorized include spheres and cubes.	.	.	.	S	.	.	.	.	.	.	.	.	.
10	Students will identify closed and not-closed figures.	.	.	.	S	.	.	.	.	.	.	.	.	.
11	Students will identify concepts of inside and outside of a shape.	.	.	.	S	.	.	.	.	.	.	.	.	.
12	Investigate figures and make conjectures about their properties.	.	.	.	.	.	S	.	.	.	.	.	.	.
13	Identify and predict the effects of combining, dividing, reflecting, nd rotating figures.	.	.	.	.	.	S	.	.	.	.	.	.	.
14	Use geometric representations to solve problems.	.	.	.	.	.	S	.	.	.	.	.	.	.
15	Students will identify congruence, similarity, and symmetry of transformed figures.	.	.	.	.	.	S	.	.	.	.	.	.	.
16	Geometric figures include polygons of eight sides or less, simple irregular shapes, rectangular solids, spheres, and cylinders.	.	.	.	.	.	S	.	.	.	.	.	.	.
17	Transformational motions are translation--slide, rotation--turn, reflection--flip, dilation--shrinking or enlarging. (Either formal or informal terminology may be used. )	.	.	.	.	.	S	.	.	.	.	.	.	.
18	Represent transformations (translations, rotations, reflections) of geometric figures.	.	.	.	.	.	.	.	.	S	.	.	.	.
19	Use given assumptions and make conjectures to discover or verify properties of geometric figures.	.	.	.	.	.	.	.	.	S	.	.	.	.
20	Use geometric diagrams and models to solve problems.	.	.	.	.	.	.	.	.	S	.	.	.	.
21	Students will be asked about transformations (translation, rotation, reflection) with any geometric shape to prove congruence of wo whole figures or their corresponding component parts.	.	.	.	.	.	.	.	.	S	.	.	.	.
22	Students will be asked about identification of line (reflection) and rotational symmetry of a figure.	.	.	.	.	.	.	.	.	S	.	.	.	.
23	Geometric figures may include any polygons, simple irregular shapes, rectangular solids, spheres, or cylinders.	.	.	.	.	.	.	.	.	S	.	.	.	.
24	Use transformations (translations, rotations, reflections) to justify properties of figures.	.	.	.	.	.	.	.	.	.	.	S	.	.
25	Develop conjectures and arguments to discover or verify the properties of figures.	.	.	.	.	.	.	.	.	.	.	S	.	.
26	Use geometric models and properties of figures (e.g., Pythagorean Theorem) to solve problems.	.	.	.	.	.	.	.	.	.	.	S	.	.
27	Students will solve problems from any previous benchmark level.	.	.	.	.	.	.	.	.	.	.	S	.	.
28	Students will be asked about Euclidean theorems and definitions related to parallel and perpendicular lines.	.	.	.	.	.	.	.	.	.	.	S	.	.
29	Students will be asked about congruence and similarity of geometric figures and their corresponding parts.	.	.	.	.	.	.	.	.	.	.	S	.	.
30	Students will be asked about making conjectures and justifying geometric properties.	.	.	.	.	.	.	.	.	.	.	S	.	.
31	Students will use properties of geometric figures to solve problems, e.g., vertical angles, transversals.	.	.	.	.	.	.	.	.	.	.	S	.	.
32	Use transformations (translations, rotations, reflections, dilations) to justify properties of figures and relationships among figures.	.	.	.	.	.	.	.	.	.	.	.	.	S
33	Develop and evaluate conjectures and arguments to discover or verify the properties of figures.	.	.	.	.	.	.	.	.	.	.	.	.	S
34	Use geometric relationships, spatial reasoning, and models to solve problems.	.	.	.	.	.	.	.	.	.	.	.	.	S
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