Topic: Geometry |
Common Core Mathematics 6-8 |
| Cluster Solve real-world and mathematical problems involving area, surface
area, and volume. |
| | Grade 6 |
| | | 6.G.1. | Find the area of right triangles, other triangles, special quadrilaterals,
and polygons by composing into rectangles or decomposing into
triangles and other shapes; apply these techniques in the context of
solving real-world and mathematical problems. |
| Cluster Use properties of operations to generate equivalent expressions. |
| | Grade 7 |
| | | 7.EE.2. | Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the quantities
in it are related. For example, a + 0.05a = 1.05a means that “increase by
5%” is the same as “multiply by 1.05.” |
| Cluster Draw, construct, and describe geometrical figures and describe the
relationships between them. |
| | Grade 7 |
| | | 7.G.1. | Solve problems involving scale drawings of geometric figures,
including computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale. |
| | | 7.G.2. | Draw (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no
triangle. |
| | | 7.G.3. | Describe the two-dimensional figures that result from slicing threedimensional
figures, as in plane sections of right rectangular prisms
and right rectangular pyramids. |
| Cluster Solve real-life and mathematical problems involving angle measure,
area, surface area, and volume. |
| | Grade 7 |
| | | 7.G.4. | Know the formulas for the area and circumference of a circle and use
them to solve problems; give an informal derivation of the relationship
between the circumference and area of a circle. |
| | | 7.G.5. | Use facts about supplementary, complementary, vertical, and adjacent
angles in a multi-step problem to write and solve simple equations for
an unknown angle in a figure. |
| | | 7.G.6. | Solve real-world and mathematical problems involving area, volume
and surface area of two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms. |
| Cluster Understand congruence and similarity using physical models, transparencies,
or geometry software. |
| | Grade 8 |
| | | 8.G.1. | Verify experimentally the properties of rotations, reflections, and
translations:
a. Lines are taken to lines, and line segments to line segments of the
same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines. |
| | | 8.G.2. | Understand that a two-dimensional figure is congruent to another if
the second can be obtained from the first by a sequence of rotations,
reflections, and translations; given two congruent figures, describe a
sequence that exhibits the congruence between them. |
| | | 8.G.3. | Describe the effect of dilations, translations, rotations, and reflections
on two-dimensional figures using coordinates. |
| | | 8.G.4. | Understand that a two-dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar twodimensional
figures, describe a sequence that exhibits the similarity
between them. |
| | | 8.G.5. | Use informal arguments to establish facts about the angle sum and
exterior angle of triangles, about the angles created when parallel lines
are cut by a transversal, and the angle-angle criterion for similarity of
triangles. For example, arrange three copies of the same triangle so that
the sum of the three angles appears to form a line, and give an argument
in terms of transversals why this is so. |
| Cluster Understand and apply the Pythagorean Theorem. |
| | Grade 8 |
| | | 8.G.6. | Explain a proof of the Pythagorean Theorem and its converse. |
| | | 8.G.7. | Apply the Pythagorean Theorem to determine unknown side lengths
in right triangles in real-world and mathematical problems in two and
three dimensions. |
| | | 8.G.8. | Apply the Pythagorean Theorem to find the distance between two
points in a coordinate system. |
| Cluster Solve real-world and mathematical problems involving volume of
cylinders, cones, and spheres. |
| | Grade 8 |
| | | 8.G.9. | Know the formulas for the volumes of cones, cylinders, and spheres
and use them to solve real-world and mathematical problems. |