Maryland Math 8.GR.B.4

8.GR.B.4 is a cluster heading. These are the individual standards under it.

• 8.GR.B.4.a

  Use diagrams, examples, or informal reasoning to explain the Pythagorean Theorem and why it applies to all right triangles.

• 8.GR.B.4.b

  Use the converse of the Pythagorean Theorem to determine whether a set of three side lengths forms a right triangle, and extend this reasoning to identify wheth...

01

What Students Need to Do

Use a diagram to explain why the squares on a right triangle’s shorter sides add to the square on its longest side. Compare squared side lengths to tell whether a triangle is right, acute, or obtuse.

02

What Mastery Looks Like

Students can explain why rearranging the same four right triangles shows the rule works for any right triangle. They classify sides 3, 4, and 6 as obtuse because 6² is greater than 3² + 4².

03

Common Misconceptions

Students may square the sides before identifying the longest one, or reverse the acute and obtuse comparisons. They may also classify three lengths without checking whether they can form a triangle.

04

How to Assess It

Exit ticket: Draw two arrangements of four identical right triangles in a square, and label the uncovered areas to explain the right-triangle rule. Then classify sides 3, 4, and 6 by comparing squares.

1. 01

   Cut four 3-by-4 right triangles and rearrange them in a 7-by-7 square to uncover 5-by-5, then 3-by-3 and 4-by-4 squares.

2. 02

   Ask: Why do both arrangements leave the same uncovered area, and would that reasoning work for any right triangle?

3. 03

   Sort cards labeled 3, 4, 5; 4, 5, 6; and 3, 4, 6 into right, acute, and obtuse using squared lengths.

4. 04

   Mark a 3-foot, 4-foot, 5-foot triangle with masking tape on the floor and check its right angle against a sheet of paper.

• 8.GR.B.5

  Apply the Pythagorean Theorem to solve problems in context.

• 7.GR.B.4.c

  Interpret and justify solutions in context by comparing different geometric representations, estimating or checking for reasonableness, and explaining how the r...