Pythagorean Theorem and Volume

Lesson 12

Math

Unit 7

8th Grade

Lesson 12 of 16

Objective


Find the distance between points in the coordinate plane using the Pythagorean Theorem.

Common Core Standards


Core Standards

  • 8.G.B.8 — Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Foundational Standards

  • 6.G.A.3

Criteria for Success


  1. Use the Pythagorean Theorem to find diagonal lengths in the coordinate plane.
  2. Find the distance between two points in the coordinate plane with and without plotting the points. 

Tips for Teachers


  • Similar to Lesson 9, students discover ways that the Pythagorean Theorem can be a useful tool to determine measurements they could not find before. Given a diagonal line in a coordinate plane, students recognize how they can create a right triangle and apply the Pythagorean Theorem to find the length of the diagonal line (MP.7)

Lesson Materials

  • Calculators (1 per student)
  • Graph Paper (2-3 sheets per student)
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Anchor Problems

25-30 minutes


Problem 1

Three line segments are shown in the coordinate plane below. Order the line segments from shortest to longest. 

Guiding Questions

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Student Response

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Problem 2

A triangle is defined by the following vertices in the coordinate plane:

$${A: \space (-3,5)}$$$${B: \space (2,7)}$$$${C: \space (-3,-1)}$$

Find the perimeter of the triangle to the nearest tenth of a unit. You may use the grid below if needed.

Guiding Questions

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Student Response

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Problem 3

The line segments in the list below are defined by the pairs of coordinate points shown. 

$${\overline{AB}}$$: (1, 4) and (4, 7)
$${\overline{CD}}$$: (2, 2) and (5, 0)
$${\overline{EF}}$$: (6, 0) and (7, 4)
$${\overline{GH}}$$: (3, 4) and (9, 7)
$${\overline{IJ}}$$: (12, 1) and (7, 5)
$${\overline{KL}}$$: (1, 2) and (5, 4)

a.   Pick one pair of points. Plot the points on a coordinate grid and find the exact distance between the points. Describe how you find the distance.

b.   Pick another pair of points. Find the exact distance between the points without plotting them on a coordinate plane. You can check your answer on a coordinate plane afterward.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Line segment $${\overline{JK}}$$ is defined by the points $${J \space (-5,1)}$$ and $${K \space (-5,8)}$$. Line segment $${\overline{AB}}$$ is shown below. 

Which line segment is longer? 

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$  and $${x^3=p}$$.

Lesson 13
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

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