Common Core Learning Standards

Common Core Learning Standards

GRADE 7 Mathematics

GEOMETRY

Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Draw construct, and describe geometrical figures and describe the relationships between them. / scale drawings / Compute the actual length of a figure from a scale drawing. / § Scale drawing
§ Area
§ Lengths
§ Geometric figures
Compute the actual area of a figure from a scale drawing.
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. / Given a scale drawing and scale, recreate the drawing using a different scale.
Solve problems involving scale drawings of geometric figures.
SAMPLE TASKS
I. The scale for the rectangle below is 1 cm to 3 ft.

3 cm
6 cm
PART A: Find the actual length and width of the rectangle.
PART B: What is the actual area of the rectangle?
II. Use the figure below .

10 ft.
6 ft.
9 ft. 15 ft.
The parallelogram at the right above was reduced by a scale factor of ______to create the parallelogram on the left above.
III.
The diagram below represents Bob’s living room.
Scale: 0.5 in. = 7 ft.
0.75 in.
1 in.
How much will it cost to carpet the room at $1.95 per square foot?
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Draw construct, and describe geometrical figures and describe the relationships between them. / Drawing geometric shapes / a. Construct a triangle (freehand, with ruler and protractor, and technology) given three angle measures. / § Triangle inequality Theorem
§ Triangle angle sum theorem
§ Geometric figures
§ Uniquely defined triangle
§ Ambiguously defined triangle
§ Nonexistent triangle
§ Congruent
§
b. Construct a triangle (freehand, with ruler and protractor, and technology) given three side measures.
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. / c. Construct a geometric shape given side lengths /angle measures.
d. Describe when angle measures determine a triangle (given angles equal 180°) or no triangle (given angles are greater or less than 180°).
e. Describe when side measures determine a unique triangle (a+b>c) or no triangle (a+b ≤ c)
SAMPLE TASKS
I.(b,c,e) Given the measurements of the segments below, can you form/create a triangle? Explain your reasoning.
3 in, 2.9 in, 5 in.
II.(a) The angles of triangle ABC are listed below:
°
°
°
Sketch this triangle, name the longest side and explain how you know this is the longest side. (Without measuring.)

III.(b/e) Manipulate three pieces of pasta with varying lengths to determine if a triangle can be formed.
(This is a sample task that could be used with students to explore the relationships between various sides of triangles)
IV.(d) Draw two triangles with congruent angles but different side lengths.
Explain how this is possible.
V.(e) Give three side measures that would not form a triangle. Explain why your sides do not form the triangle.
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Draw construct, and describe geometrical figures and describe the relationships between them. / slicing three-dimensional figures / Define two-dimensional figures that result from slicing a right rectangular prism. / § Slice
§ Two-dimensional figures
§ Pyramid
§ rectangular prism
§ Cylinder
§ Triangular pyramid
§ Cube
§ Cone
Define two-dimensional figures that result from slicing a right rectangular pyramid.
7.G.3.
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. / Define two-dimensional figures that result from slicing a triangular pyramid.
Define two-dimensional figures that result from slicing a cube.
Define two-dimensional figures that result from slicing a cylinder.
Define two-dimensional figures that results from slicing a cone.
SAMPLE TASKS
Use the figures below to complete the following task.

Name and draw the shape(s) of the cross section that will be formed by the intersecting (parallel and perpendicular) plane of the following:
· Right rectangular prism
· Circular cylinder
· Cone
· Cube
· Right triangular prism
· Square Pyramid
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / Circumference and area of circles / Derive the relationship between the circumference and area of a circle. (A = Cr/2…..Area of a circle = half the circumference times the radius ) Example: C = 16π find the area. / § Circle
§ Circumference
§ Area
§ Diameter
§ Radius
Solve problems utilizing the circumference of a circle formula.
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. / Solve problems utilizing the area of a circle formula.
SAMPLE TASKS
I. The circumference of a circular pond is ft. A model boat is moving directly across the pond along the diameter at a rate of 4 feet per second. How long does it take the boat to get to the other side?
PART A: Draw the pond and label what you know from the problem above.
PART B: What is the diameter of the pond?
PART C: How many seconds does it take the boat to get to the other side of the pond?
II. A circular garden has an area of 64π square yards.
PART A: What is the circumference of the garden (in terms of)?
PART B: What happens to the area of the garden if the circumference (found in Part A) is doubled?
(Leave all calculations in terms of )
III. A small silver dollar pancake served at restaurant has a circumference of 2π inches. A regular pancake has a circumference of 4π inches. Is the area of the regular pancake twice the area of the silver dollar pancake? Explain.
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / supplementary, complementary, vertical, and adjacent angles / Define supplementary, complementary, vertical, and adjacent angles. / § vertical angles
§ Supplementary
§ Complementary
§ adjacent angles
Solve for an unknown angle in a figure utilizing definitions of supplementary, complementary, vertical, and adjacent angles.
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.
SAMPLE TASKS

I. Using the diagram above:
A.) Name a pair of adjacent angles.
B.) Name a pair of vertical angles.
C.) Name a pair of complementary angles.
D.) Name a pair of supplementary angles.
E.) If <BFA is 40°, what is the measure of <DFE? Explain how you found the measure.

II.Use the diagram above.
PART A: Name the relationship between <ABC and <CBD.
PART B: Write an equation to find the value of y.
PART C: Solve your equation and find the measures of <ABC and <CBD.
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / Area, volume, and surface area of figures / Solve area, volume, and surface area problems of two- and three-dimensional objects from real world situations. / § Area
§ Volume
§ surface area
§ two- and three-dimensional figures
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.
SAMPLE TASKS
I. Domingo built a toy box 60 inches long, 24 inches wide, and 36 inches high. He has 1 quart of paint that covers about 87 square feet of surface. Does he have enough to paint the toy box? Explain your answer.

II. Sy is going to mail a glass ornament to his sister. He wants to use the box that will hold the greater volume of packing material.

Note: Figures are not drawn to scale.
Which box has the greater volume?