Fishtank Learning

6th Grade Math
Unit 7: Geometry
Lesson 16

Objective

Find the surface area of three-dimensional figures with and without nets.

Anchor Problems - Problem 1

A rectangular prism is shown below.

a. Write a numerical expression, using the dimensions, that represents the surface area of the prism.

b. Evaluate your expression to find the surface area in square units.

Guiding Questions

How many different rectangular faces are there in the prism? How many copies of each one are there?
What are the dimensions of the front rectangular face? The back?
What are the dimensions of the right side rectangular face? The left side?
What are the dimensions of the bottom rectangular face? The top?
How can you put all of these pieces together to write a numerical expression?
What is a general expression, in terms of length, width, and height, for finding the surface area of a rectangular prism?

Notes

If helpful, show a net of the prism in order to highlight the pairs of identical faces.
In writing a numerical expression, use the structure of the prism and properties of operations to guide students towards a form similar to: $$SA=2(6\times10)+2(6\times5)+2(5\times10)$$. This will support them in seeing/understanding a general form of $$SA=2lw+2lh+2hw$$ for a rectangular prism.

Anchor Problems - Problem 2

Find the surface area of the isoceles triangular prism below.

Guiding Questions

How many faces are there on the triangular prism? What shapes are they?
Are there any faces that have the same area?
What values will you use to find the area of the triangle?
What numerical expression can you use to represent the surface area?

Notes

A common error is representing the surface area as $$ 3(7\times12)+\frac{1}{2} (4\times6) $$ which assumes an equilateral triangle. If this appears in class, discuss why it is incorrect and how to adjust the numerical expression.

Anchor Problems - Problem 3

A square pyramid is shown.

Maya writes the expression $$4{\left ({1\over2}\cdot 12 \cdot 15\right ) + 12^2}$$ to represent the surface area of the pyramid. Is Maya’s expression correct? Explain why or why not.

Problem Set

View Problem Set

Target Task

A cube is shown below.

a. Write a numerical expression that represents the surface area of the cube, and then use it to find the value of the surface area in square inches.

b. How does your numerical expression change if one of the side lengths of the cube becomes 10 inches? Write and evaluate a new numerical expression to represent the surface area of the new prism.