Students explore measurements of geometric figures in two-and three-dimensions, finding area, surface area, and volume in mathematical and real-world problems.
In Unit 7, sixth graders explore measurements in geometric space in both two-dimensional and three-dimensional figures. Throughout previous grade levels, students have been composing and decomposing geometric figures. In sixth grade, students apply those concepts of composition and decomposition to new and familiar shapes to formulate properties and formulas for finding area (MP.7). By understanding the area of rectangular arrays and using regularity in repeated reasoning, students are able to determine the area of parallelograms, triangles, and other polygons that are formed from these shapes (MP.8). Students also re-engage in major work of the grade in a few ways. They use their knowledge of the coordinate plane and absolute value to represent and measure polygons in a four-quadrant plane, they write equations to represent volume of rectangular prisms with fractional side lengths, and they write and evaluate numerical expressions to represent the surface area of prisms and pyramids.
In fifth grade, students explored volume as a measurement of a three-dimensional solid with whole-number side lengths. In this unit, students will reinvestigate how to find volume when packing solids now with fractional unit cubes. They will rely on their skills of working with fractions from fifth grade and earlier in their sixth-grade year.
Throughout the geometry standards in sixth grade through eighth grade, students will encounter increasingly complex and multi-part geometric measurement problems, culminating in eighth grade with standard 8.G.9. Learning how to make sense of these complex problems, determine solution pathways, and organize information will be important skills for students to have as the demands and rigor levels increase (MP.1).
Pacing: 19 instructional days (17 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
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face
height
right triangle
parallelogram
polygon
composition
decomposition
trapezoid
base
acute triangle
obtuse triangle
prism
unit cube
edge
vertex
pyramid
polyhedron
net
volume
surface area
area
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6.G.A.1
Find the area of parallelograms.
6.G.A.1
Find the area of right triangles.
6.G.A.1
Find the area of acute triangles using height and base.
6.G.A.1
Find the area of any triangle using height and base.
6.G.A.1
Find the area of polygons using composition and decomposition.
6.G.A.1
Solve real-world and mathematical problems involving area of polygons.
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 1).
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 2).
6.G.A.1
6.G.A.3
Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.
6.G.A.2
Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
6.G.A.2
Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
6.G.A.2
Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
6.G.A.2
Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.
6.G.A.4
Describe features of and identify nets that match prisms and pyramids.
6.G.A.4
Create nets and use them to find surface area of three-dimensional figures.
6.G.A.4
Find the surface area of three-dimensional figures with and without nets.
6.G.A.2
6.G.A.4
Find surface area and volume in real-world problems.
Key: Major Cluster Supporting Cluster Additional Cluster
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