8.7.B
The Standard
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students unfold each solid mentally or with a net, then connect each face or curved section to an area calculation. They find lateral and total area, choose the needed measurements, and report answers in square units.
What Mastery Looks Like
- A student can identify the bases and lateral parts of each solid and explain where every term in an area formula comes from. Given dimensions or a context, the student calculates accurately, includes square units, and rounds only when directed.
Common Misconceptions
- Students often include the bases in lateral area or leave them out of total area. They may use πr² for a cylinder's curved side instead of 2πrh. On triangular prisms, they may omit a rectangle or use a triangle's side length as its height.
How to Assess It
- Give an exit ticket: “A closed cylinder has radius 3 cm and height 5 cm. Find its lateral and total area in terms of π, and label each part of your calculation.”
Lesson moves
Ways to Teach It
Give pairs a cereal box, triangular prism net, and can; measure dimensions, sketch each net, then calculate lateral and total area.
Ask students to explain why a cylinder's lateral area is circumference times height, using an unwrapped paper label in their explanation.
Run a card sort matching solid diagrams, dimensions, surface area expressions, and answers; include cards with common errors as distractors.
Have students compare two soup can sizes by calculating label paper and total metal needed, then decide which design uses less material.
Keep exploring
Related Standards
- 5.4.G
use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V...
- 8.7.A
solve problems involving the volume of cylinders, cones, and spheres
- 7.9.A
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
- 7.9.D
solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining...
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