CCSS.Math.Content.HSG-GPE.B.6
The Standard
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use endpoint coordinates and a given ratio to locate a point between them. They treat each coordinate separately and apply the ratio in the correct direction.
What Mastery Looks Like
- Given two endpoints and a ratio, students calculate the correct coordinates of the dividing point. They verify the result lies between the endpoints and matches the stated direction and ratio.
Common Misconceptions
- Students often reverse the endpoint weights or divide by only one part of the ratio. Some find the midpoint regardless of the ratio. Others calculate the change in coordinates correctly but forget to add it to the starting point.
How to Assess It
- Exit ticket: Given A(2, -1) and B(12, 9), find P so that AP:PB = 3:2. Verify that P lies three-fifths of the way from A to B.
Lesson moves
Ways to Teach It
Mark two endpoints on a floor grid, then place a marker at a given fractional distance along the segment.
Ask students to explain why a point dividing AB in a 3:1 ratio lies closer to B than A.
Give pairs of endpoint cards and ratio cards, then award points for correct coordinates and a valid check.
Use a map route between two locations and find where a rest stop should go for a stated distance ratio.
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Printable HSG-GPE.B.6 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-GPE.B.6, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.7.NS.A.3
Partitioning a coordinate segment in a ratio requires adding, multiplying, and dividing rational coordinates and ratio parts accurately.
- CCSS.Math.Content.7.RP.A.2
Partitioning a segment uses ratio reasoning to compare the two smaller lengths and translate that ratio into coordinate changes.
- CCSS.Math.Content.HSN-VM.A.2
Partitioning a directed segment uses the coordinate differences between endpoints as a scaled displacement to locate the new point.
Keep exploring
Related Standards
- CCSS.Math.Content.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
- CCSS.Math.Content.6.NS.C.6c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational nu...
- CCSS.Math.Content.3.NF.A.2b
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint ...
- CCSS.Math.Content.3.NF.A.3a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
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