PowerPoint Presentation

Surface Area and Volume

Meaning and calculation of area of non-rectangles

Meaning and calculation of surface area using nets

Meaning and calculation of volume

Angle relationships in figures

Pythagorean Theorem

Cross sections of 3D solids

Learning Targets:

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; cross-sections; angle relationships

8th Grade: Volume of cones, cylinders, spheres; transformations; Pythagorean Theorem; congruent and similar figures; angle relationships

Common Core

NCTM Box Problem on Illuminations

GSP simulation

Simulation including graph

Table for 22: Real-World Geometry Problem

Basics for intervention

Area of rectangles

What do kids need to know in order to do a problem like that?

7

Area of rectangles

Area of parallelograms

MSU Virtual Manipulatives for finding area

Area of triangles

Area of trapezoids

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?

A little fun

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2s

GSP simulation of laying out slices of a circle to find its area

Dont forget circles

Learning activities from Annenberg

Online animations of unfolding cubes and rectangular prisms

Find all 11 nets of a cube on the handout

Nets and surface area

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.

Net of a pyramid

Build one if you like.

Will the other nets make a closed solid?

Unfolding a cylinder

Huge Chrome Cylinder Box Unfolding

Net of a cylinder

Sugar cubes and boxes at your table

Annenberg Learner - Surface Area and Volume

Finding 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 whole-number 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

Finding 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

Toy Chest

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?

Substituting values into formulas

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.

Recognize volume as additive

First, work through these problems.

Remembering that percent increase is in 7th grade, where would these problems fit in the curriculum?

Cereal Box and Toy Chest

Where would this problem fit in the curriculum?

Design a container

Volume of cylinders & pyramids

Doing it with clay on YouTube

Cross-sections

Angles

Linear Pair

Vertical Angles

Exterior Angle of a Triangle 1

Exterior Angle of a Triangle 2

Parallel lines cut by a transversal

More Angles

Exterior angles of a triangle

Two reflections equal a rotation

Explore a rotation

Transformations

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

Pythagorean Theorem

Re-teaching the whole class

Based on weekly formative assessments

During individual or small group practice time

Intervention approaches

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