Download Common Core Learning Standards GRADE 7 Mathematics

Common Core Learning Standards
GRADE 7 Mathematics
GEOMETRY
Common Core Learning
Standards
Draw construct, and describe
geometrical figures and describe the
relationships between them.
Concepts
scale
drawings
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.
Embedded Skills
Compute the actual length of a figure from a scale
drawing.
Compute the actual area of a figure from a scale
drawing.
Apply a scale from one drawing to create a second
scale for that drawing.
Solve problems involving scale drawings of
geometric figures.
Vocabulary
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scale drawing
area
lengths
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?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II. Use the figure below .
10 ft.
6 ft.
9 ft.
15 ft.
What is the scale factor for the parallelograms?
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?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Draw construct, and describe
geometrical figures and describe the
relationships between them.
Drawing
geometric
shapes
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.
Embedded Skills
Vocabulary
a.Construct a triangle (freehand, with ruler and
protractor, and technology) given three angle
measures.
b.Construct a triangle (freehand, with ruler and
protractor, and technology) given three side
measures.
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°).
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e.Describe when side measures determine a unique
triangle (a+b>c) or no triangle (a+b ≤ c)
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triangle
inequality
theorem
triangle angle
sum theorem
geometric
figures
uniquely
defined
triangle
ambiguously
defined
triangle
nonexistent
triangle
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 measure of the three interior angles of a triangle are 57°, 62°, and 61°. Describe the location of each side with respect to the
measures of the opposite interior angle by drawing the triangle. Describe the location of each side with respect to the measures of the
opposite interior angle by drawing the triangle.
III.(b/e) Manipulate three pieces of pasta with varying lengths to determine if a triangle can be formed.
IV.(a) Draw any triangle on a piece of paper. Tear off the triangles three angles. Arrange the angles so that they are adjacent angles. What do
you notice about the sum of these three angles?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Draw construct, and describe
geometrical figures and describe the
relationships between them.
slicing threedimensional
figures
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.
Embedded Skills
Define two-dimensional figures that result from
slicing a right rectangular prism.
Define two-dimensional figures that result from
slicing a right rectangular pyramid.
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.
Vocabulary
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Slice
twodimensional
figures
pyramid
rectangular
prism
cylinder
triangular
pyramid
cube
cone
SAMPLE TASKS
Use the figures below to answer questions I and II.
I.
Identify the two dimensional faces that make up a:
 Right rectangular prism
 Circular cylinder
 cone
 Cube
 Triangular pyramid
 Right triangular prism
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II. Find 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
 Triangular pyramid
 Right triangular prism
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve real-life and mathematical
problems involving angle measure,
area, surface area, and volume.
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.
Concepts
Embedded Skills
Circumference Derive the relationship between the circumference
and area of a circle. (A = Cr/2…..Area of a circle =
and area of
half the circumference times the radius ) Example:
circles
C = 16π find the area.
Solve problems utilizing the circumference of a
circle formula.
Vocabulary
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Circle
Circumference
Area
Diameter
Radius
Solve problems utilizing the area of a circle formula.
SAMPLE TASKS
I.
The circumference of a circular pond is 942 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 long 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?
PART B: What happens to the circumference of the garden if the area is doubled?
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.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Solve real-life and mathematical
problems involving angle measure,
area, surface area, and volume.
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.
Embedded Skills
Define supplementary, complementary, vertical,
and adjacent angles.
Solve for an unknown angle in a figure utilizing
definitions of supplementary, complementary,
vertical, and adjacent angles.
Vocabulary
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vertical angles
Supplementary
Complementary
adjacent angles
SAMPLE TASKS
C
D
B
F
A
E
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.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
E.) If <BFA is 40°, what is the measure of <DFE? Explain how you found the measure.
C
2y°
A
y°
B
D
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.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve real-life and mathematical
problems involving angle measure,
area, surface area, and volume.
Concepts
Embedded Skills
Area, volume, Solve area, volume, and surface area problems of
and surface two- and three-dimensional objects from real world
situations.
area of
figures
7.G.6.
Solve real-world and mathematical problems
involving area, volume and surface area of twoand three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and
right prisms.
Vocabulary
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Area
Volume
surface area
two- and
threedimensional
figures
SAMPLE TASKS
I.
Error Analysis
Explain the mistake made below. What is the correct surface area?
SA = (2 + 2 + 2 + 2)(5)+4
SA = (8)(5) + 4
SA = 40 + 4
SA = 44 in2
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
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?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.