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Meaning and calculation of area of nonrectangles
Meaning and calculation of surface area using
nets
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Meaning and calculation of volume
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Angle relationships in figures
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Pythagorean Theorem
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Cross sections of 3D solids
6th Grade: Area of triangles and special
quadrilaterals; volume of rectangular prisms; surface
area using nets
7th Grade: Area and circumference of circles; volume
and SA of composite figures; scale drawings; crosssections; angle relationships
8th Grade: Volume of cones, cylinders, spheres;
transformations; Pythagorean Theorem; congruent
and similar figures; angle relationships
NCTM Box Problem on Illuminations
GSP simulation
Simulation including graph
Table for 22: Real-World Geometry Problem
MSU Virtual Manipulatives for finding area
Start with a 1x2 rectangle. Find the area.
Then consider a 2x4 rectangle. How have the sides
changed? How has the area changed?
Find the area of a 3x6 rectangle.
How have the sides changed?
How has the area changed?
Make a table to try a few more of these, following the
same pattern.
What might explain this pattern?
What if you tried this with rectangular prisms
and volume?
s
2s
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GSP simulation of laying out slices of a circle
to find its area
Learning activities from Annenberg
Online animations of unfolding cubes and rectangular prisms
Find all 11 nets of a cube on the handout
The diagram shows a prism constructed from two
rectangular prisms.
Draw the net for the solid and mark the lengths.
Calculate the surface area of the solid.
Build one if you like.
Will the other nets make a closed solid?
Unfolding a cylinder
Huge Chrome Cylinder Box Unfolding
Sugar cubes and boxes
at your table
Annenberg Learner - Surface Area and Volume
5.MD.3 Recognize volume as an attribute of solid figures and
understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to
have “one cubic unit” of volume, and can be used to measure
volume.
b. A solid figure which can be packed without gaps or overlaps
using n unit cubes is said to have a volume of n cubic units.
5.MD.4 Measure volumes by counting
unit cubes, using cubic cm, cubic in,
cubic ft, and improvised units.
5.MD.5 Relate volume to the operations of multiplication and
addition and solve real world and mathematical problems
involving volume.
a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show
that the volume is the same as would be found by multiplying
the edge lengths, equivalently by multiplying the height by
the area of the base. Represent three-fold whole-number
products as volumes, e.g., to represent the associative
property of multiplication.
b. Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular
prisms to find volumes of right rectangular prisms with
whole-number edge lengths in the context of solving real
world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures
composed of two non-overlapping right rectangular prisms
by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
Illuminations - Interactive Simulation of Volume
Generate possible dimensions for other toy
chests that have a volume of 5400 square
inches. Here is one:
12” high by 15” deep by 30” wide
9 x 15 x 30 = 4050
Each toy chest will be covered felt. Will the
same amount of felt be needed for each chest
regardless of the dimensions, since they all
have the same volume?
First, work through these problems.
How much practice with 1a and 2a is needed?
Would you give 1b/c and 2b as separate
problems and not provide the formulas?
How much support is needed to do 1b/c and
2b?
The diagram shows a prism constructed from two
rectangular prisms.
Draw the net for the solid and mark the lengths.
Calculate the surface area of the solid and its volume.
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First, work through these problems.
Remembering that percent increase is in 7th
grade, where would these problems fit in the
curriculum?
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Where would this problem fit in the
curriculum?
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Doing it with clay on YouTube
Linear Pair
Vertical Angles
Exterior Angle of a Triangle 1
Exterior Angle of a Triangle 2
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Parallel lines cut by a transversal
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Exterior angles of a triangle
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Two reflections equal a rotation
Explore a rotation
Do you have a proof you like?
Proof by rearrangement
Distance between two points in the plane
AB2 + AC2 = CB2
4 + 36 = CB2
40 = CB2
6.32 = CB
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Re-teaching the whole class
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Based on weekly formative assessments
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During individual or small group practice time