Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 2
Math
Unit 5
10th Grade
Lesson 2 of 15
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Partition horizontal and vertical line segments into equal proportions on a number line.
The core standards covered in this lesson
G.GPE.B.6 — Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
The foundational standards covered in this lesson
6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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
Partitioning a Segment by Jennifer Wilson is made available on Easing the Hurry Syndrome. Accessed March 12, 2017, 5:16 p.m..
$$A$$ 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.
$$C$$ 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Point $$C$$ at $${-1}$$ marks $${{2\over3}}$$ of the distance between point $$A$$ at $${-4}$$ and point $$D$$. What is the location of point $$D$$?
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 $$R$$?
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.
Lesson 1
Lesson 3
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
G.GPE.B.7
G.GPE.B.6
Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.
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Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular lines.
G.GPE.B.5 G.SRT.C.8
Describe and apply the slope criteria for parallel lines.
G.GPE.B.5
Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
G.GPE.B.4
Algebraically verify midsegment, median, and parallel line relationships in triangles.
G.CO.C.10 G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11 G.GPE.B.4
Topic C: Area and Perimeter On and Off the Coordinate Plane
Calculate and justify the area and perimeter of polygons and composite shapes off the coordinate plane.
Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
Calculate and justify composite and irregular areas on the coordinate plane.
G.GPE.B.7 N.Q.A.3
Describe how the area changes when a figure is scaled.
Solve area applications by creating and solving quadratic equations.
A.CED.A.1
Describe a polygon on the coordinate plane using a system of inequalities.
A.CED.A.3 G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12 G.GPE.B.4 G.GPE.B.7
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