MATHEMATICS CURRICULUM SCOPE & SEQUENCE
CONTENT STANDARD #6: Spatial Relationships and Geometry PreK-12
Students will analyze and use spatial relationships and basic concepts of geometry to construct, draw, describe and compare geometric models and their transformations, and use geometric relationships and patterns to solve problems.
Preschool Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
1. Use vocabulary related to 1. Sort, describe likenesses and 1. Recognize, name, build, 1. Build, draw and classify 2- 1. Build models, draw with and 1. Build, classify, and describe 1. Build, draw, and classify 2-
position and order. MA4:6c differences, compare two- draw and sort two- and dimensional shapes and without technology; classify 2- and 3-dimensional figures and 3-dimensional shapes
and three-dimensional three-dimensional shapes describe similarities and polygons and solids and and describe the properties and use geometric
Examples: Near, far, top, shapes, and identify and objects. MA4:6a, d differences using explore similarities and that define classes of vocabulary (such as parallel
bottom, under, over, first, frequently used shapes and 2. Solve tessellation problems characteristics such as differences using polygons and solids, such as and perpendicular lines,
second, last. solids such as triangles, by filling a region with number of sides and angles, characteristics such as triangles and cubes. equal angles) to describe the
square, cube, circle, etc. concrete objects in one or and identify the shapes in the relationship of sides MA4:6a, d, e attributes and properties of
2. Recognize and identify MA4:6a, d, e more ways. MA4:6b ,c environment. (parallel, perpendicular), 2. Make and test conjectures sets and subsets of shapes.
simple shapes. MA4:6a 2. Use a variety of 3. Use a variety of concrete MA4:6a, d, e kinds of angles (right, acute, about geometric properties MA8:6a, b
manipulative materials to objects to create and copy 2. Build and identify shapes obtuse, congruent), and relationships involving 2. Make and test conjectures
Examples: circle, square, create geometric shapes and two- and three-D designs that have one or more lines symmetry and congruence. shape, position, movement, about geometric
diamond, triangle. solids and make copies of from visual memory. of symmetry, recognize and MA4:6a, d, e subdivision, tessellation and relationships involving
simple shapes and designs MA4:6a, c construct slides, flips and 2. Build, describe and identify transformations. MA4:6b, c congruence and
by observation and by visual 4. Name relative position, turns of simple polygons polygons and solids in 3. Make and use coordinate transformations (translations,
memory. MA4:6a, b, d direction, and location with using a variety of various orientations, systems to specify locations. reflections, rotations), and
3. Describe the position, simple relationships such as manipulative materials, and including combining, MA4:1c & MA4:6c develop logical arguments to
location and direction of "above/below" and" near to". explore covering a region subdividing, sliding, rotating 4. Explore congruence, justify conclusions.
objects, or parts of objects, MA4:6b, e (tessellate) with irregular and reflecting. MA4:6c similarity, line symmetry MA8:6c, d
using terms such as inside, 5. Create designs that have a shapes. MA4:6c, e 3. Use concrete models to and predict the results of 3. Plot positions on a
outside, top, bottom, close, line of symmetry. 3. Describe and predict the investigate ways of covering slides, flips, and turns of coordinate system and
closer, etc. MA4:6c MA4:6a, e results from different regions and filling spaces two-dimensional shapes. describe the distance
6. Identify shapes that are the perspectives, of combining, and ways of counting the MA4:6c, d, e between points horizontally
same even when flipped or subdividing and moving results. MA4:6b, c, d, e 5. Relate geometric shapes to and vertically. MA8:6c
turned. MA4:6c, e shapes and solids and 4. Build and draw geometric nature and the real world and 4. Explore and describe
reconstruct figures from shapes and create and solve real-world problems rotational symmetry,
visual memory. MA4:6b describe mental images of using geometric concepts. congruence, and similarity
4. Build and take apart models objects and patterns. MA4:6d (of 2-D shapes) as a dilation,
of 3-D shapes and describe MA4:6a, b, c and construct and interpret
the similarities and 5. Use coordinate systems, scale drawings. MA8:6d
differences of simple 3-D such as maps, to describe, 5. Identify, describe and build
shapes. MA4:6d name, and interpret direction nets (2-dimensional models)
5. Relate geometric shapes to and relative positions in that will form 3-D figures, or
nature and the real world. space. MA4:6c vice versa. MA8:6b, e
MA4:6d 6. Identify and describe line 6. Relate geometric shapes to
symmetry in 2- and 3- nature and the real world and
dimensional shapes and solve real-world problems
designs. MA4:6e using geometric concepts.
7. Relate geometric shapes to MA8:6d
nature and the real world and
solve real-world problems
using geometric concepts.
MA4:6d
CDGoals\Bk 9-12\Chp2\Scope & Seq #6.doc 06/21/02 VI - 1
MATHEMATICS CURRICULUM SCOPE & SEQUENCE
CONTENT STANDARD #6: Spatial Relationships and Geometry PreK-12
Students will analyze and use spatial relationships and basic concepts of geometry to construct, draw, describe and compare geometric models and their transformations, and use geometric relationships and patterns to solve problems.
Grade 6 Grade 7 Grade 8 Grade 9 & 10 Grade 11 & 12
1. Identify congruence and symmetry and 1. Classify and describe polygons and solids 1. Visualize, make and test conjectures about 1. Draw, construct, classify, analyze and use 1. Use trigonometric relationships to
investigate similarities in many settings using defining characteristics. MA8:6b, c relationships among angles, side lengths, the properties and attributes of various determine lengths and angle measures.
including art, architecture and everyday 2. Draw geometric objects with specified perimeters, areas and volumes of similar polygons and solids to solve problems. MA12:6b, e
life. MA8:6a, f properties, including angle measures. objects. MA8:6b, c MA12:6d 2. Visualize three-dimensional objects from
2. Describe sizes, positions and orientations MA8:6b 2. Create and critique inductive and deductive 2. Interpret algebraic equations and different perspectives and analyze their
of shape under informal transformations 3. Examine the congruence, similarity, and arguments concerning geometric inequalities geometrically and describe cross-sections, surface area and volume.
such as flips, turns, slides and scaling. line and rotational symmetry of objects. relationships, such as congruence, geometric objects algebraically. MA12:6f MA12:6d, e
MA8:6d MA8:6d similarity, and the Pythagorean 3. Model and solve 2- and 3-dimensional 3. Make geometric conjectures and establish
3. Use models to create and draw front, side 4. Use two-dimensional representations of relationship and investigate these geometric situations, including those in their validity using deduction, prove
and top views and cross sections of 3- three-dimensional objects to visualize and relationships in nature & everyday life. nature, using a variety of tools. theorems and critique arguments made by
dimensional figures. MA8:6b solve problems such as those involving MA8:6a, c MA12:6d, e others. MA12:6c
4. Draw geometric objects with specified surface area and volume. MA8:6b 3. Use coordinate geometry to examine 4. Make and test conjectures and solve 4. Use Cartesian, navigational, polar and
properties such as side lengths and become 5. Investigate the relationship among the special geometric shapes, such as regular problems involving relationships such as spherical systems to represent and analyze
fluent with the vocabulary for classifying angles, side lengths, perimeter and areas polygons or those with pairs of parallel or congruence and similarity for various 2- geometric situations and solve problems.
angles and triangles. MA8:6c and volumes of similar objects. MA8:6d perpendicular sides and solve problems and 3-dimensional figures. MA12:6b MA12:6a, e
5. Use coordinate graphing to locate points 6. Use coordinate geometry to examine involving congruence, similarity, and 5. Deduce properties of figures from given 5. Represent translations, reflections,
and represent and examine the properties special geometric shapes such as regular transformations. MA8:6d assumptions and develop an understanding rotations and dilations of plane figures
of geometric shapes. MA8:6b polygons or those with pairs of parallel or 4. Use visual tools such as networks and of an axiomatic system through geometric using sketches, coordinates, vectors,
perpendicular sides. geometric models to represent numerical investigations, the formulation of function notation and matrices and use
MA8:6c and algebraic relationships. MA8:6f arguments and construction of proofs. these representations to solve real-world
MA12:6c problems and examine the effects of
6. Use Cartesian coordinates and appropriate transformations and their compositions.
computer software to investigate and MA12:6a, f, e
analyze geometric situations, relationships
and transformations. MA12:6a
CDGoals\Bk 9-12\Chp2\Scope & Seq #6.doc 06/21/02 VI - 2