Polygons and Algebraic Relationships

Lesson 2

Math

Unit 5

10th Grade

Lesson 2 of 15

Objective


Partition horizontal and vertical line segments into equal proportions on a number line.

Common Core Standards


Core Standards

  • G.GPE.B.6 — Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Foundational Standards

  • 6.RP.A.1
  • 6.RP.A.2
  • 6.RP.A.3

Criteria for Success


  1. Describe that partitioning a line segment proportionally means that you are dividing a line segment according to a particular ratio.
  2. Describe that to partition a line segment, you need three of the four components of where you begin, where you end, ratio of partitioning, and where the partition is in order to divide a line segment. 
  3. Describe that dividing a line segment proportionally can be done on or off a coordinate plane through dilations if you have a benchmark set of proportions. 
  4. Describe that partitioning a line segment into halves can be done on or off a coordinate plane through constructions. 
  5. Identify a line segment as vertical or horizontal based on the coordinates of the endpoints of that line segment. 
  6. Develop a process for partitioning a horizontal or vertical line segment with just the coordinates and without plotting on a coordinate plane.
  7. Name a coordinate that is a certain proportion away from one of the endpoints in a vertical or horizontal line. Verify this distance algebraically. 

Tips for Teachers


  • This lesson connects to Unit 3 Lessons 4 and 6 because it continues the idea of dividing a line segment into equal pieces. We are now focusing on the division of a line segment on the number line and coordinate plane rather than using constructions off the number line. 
  • The website, "Partition a Line Segment" by Cobb Virtual Academy may be helpful to fully understand the Anchor Problems.
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Anchor Problems

25-30 minutes


Problem 1

A $${32}$$-foot long piece of wood is cut to divide the wood into a ratio of $${3:5}$$. Which of the following locations could you cut the wood to create this ratio? (Choose all that apply.) 

A. $${12}$$ feet from one end of the wood

B. $${20}$$ feet from one end of the wood

C. $${10{2\over3}}$$ feet from each end of the wood

D. Divide the wood into $${6{2\over5}}$$ feet pieces

E. $$3$$ feet from one end of the wood

Guiding Questions

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References

Easing the Hurry Syndrome Partitioning a Segment

Partitioning a Segment by Jennifer Wilson is made available on Easing the Hurry Syndrome. Accessed March 12, 2017, 5:16 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

$$A$$ is at $${-4}$$ and $$B$$ is at $${10}$$. Find the point $$T$$, so that $$T$$ partitions the segment $$\overline {AB}$$ into a $${3:4}$$ ratio.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Easing the Hurry Syndrome Partitioning a Segment

Partitioning a Segment by Jennifer Wilson is made available on Easing the Hurry Syndrome. Accessed March 12, 2017, 5:16 p.m..

Problem 3

$$C$$ is at $${(1,-10)}$$  and $$R$$ is at $${(1,-2)}$$

a.  Find the point $$L$$, so that $$L$$ partitions the segment into a $${1:2}$$ ratio.
b.  Write a formula for partitioning a line segment into a certain ratio. 

Guiding Questions

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Target Task

5-10 minutes


Problem 1

Point $$C$$ at $${-1}$$ marks $${{2\over3}}$$ of the distance between point $$A$$ at $${-4}$$ and point $$D$$. What is the location of point $$D$$?

Problem 2

Point $$L$$ is at $$7$$ and point $$R$$ is at $${-5}$$. Where are two locations where point $$Q$$ is located if it is $${{3\over4}}$$ of the distance between $$L$$ and $$R$$? How far is each of these points from $$R$$?

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.

  • Include problems with line segments on the number line. 
  • Include problems with vertical and horizontal line segments on the coordinate plane. 
  • Include problems where students must find the missing endpoint given one endpoint and the location of a point that partitions the line segment in a given ratio.

Next

Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.

Lesson 3
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Lesson Map

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

Topic A: Distance on the Coordinate Plane

Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments

Topic C: Area and Perimeter On and Off the Coordinate Plane

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