Mathematics
Grade 10
15 min
Lengths of segments on number lines: Set 1
Lengths of segments on number lines: Set 1
What you'll learn
- Solve one-step addition and subtraction word problems with whole numbers up to 10,000 with 80% accuracy.
- Apply addition and subtraction to solve two-step word problems involving whole numbers up to 10,000, showing their work with clear steps.
- Explain the reasoning behind choosing addition or subtraction to solve a word problem, using complete sentences and math vocabulary (e.g., sum, difference, total).
- Identify the key information (numbers and what the problem is asking) needed to solve an addition or subtraction word problem.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Define a line segment and its endpoints on a number line.
State and apply the Ruler Postulate to find the length of a segment.
Calculate the length of a segment on a number line using the coordinates of its endpoints.
Use the Segment Addition Postulate to find the length of a segment composed of smaller, collinear segments.
Determine the coordinate of an unknown endpoint given the other endpoint and the segment length.
Solve algebraic problems involving segment lengths and the Segment Addition Postulate.
Define and identify congruent segments on a number line.
How does a GPS calculate the straight-line distance between two locations? 🗺️ It all starts with the fundamental concept of measuring a segment on a simple number line!
This tutorial will cover t...
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Key Concepts & Vocabulary
TermDefinitionExample
Number LineA line on which numbers are marked at regular intervals, used to represent and order real numbers. Each point on the line corresponds to a unique number.A ruler is a physical representation of a number line.
CoordinateThe number that corresponds to a specific point on a number line.On a number line, if point P is at the number -5, the coordinate of P is -5.
Line SegmentA part of a line that consists of two endpoints and all the points between them. A segment is named by its endpoints.The segment with endpoints A and B is denoted as \(\overline{AB}\).
Length of a SegmentThe distance between the two endpoints of a segment. Length is always a positive value.The length of \(\overline{AB}\) is denoted as \(AB\). If A is at 2 and B is at 7, then \(AB = 5\).
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Core Formulas
Ruler Postulate (Distance on a Number Line)
For any two points A and B on a number line with coordinates \(x_1\) and \(x_2\) respectively, the length of \(\overline{AB}\) is given by the formula: \(AB = |x_2 - x_1|\)
Use this formula to find the distance between any two points on a number line. The absolute value ensures the result is always non-negative, as distance cannot be negative.
Segment Addition Postulate
If point B is between points A and C, then \(AB + BC = AC\).
This postulate applies only to collinear points. It states that the lengths of two adjacent segments add up to the length of the total segment they form.
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Challenging
Points P, Q, and R are collinear. The length of PQ is 12 and the length of QR is 7. What are the possible lengths for segment PR?
A.19 only
B.5 only
C.19 and 5
D.12 and 7
Challenging
On a number line, points A, B, and C are collinear with B between A and C. If AB = 2x + y, BC = x - y, and AC = 30, what is the value of x?
A.10
B.15
C.20
D.Cannot be determined
Challenging
The coordinate of point M is -4. The length of segment MN is given by the algebraic expression |2k + 6|. Which expression represents the possible coordinates of point N?
A.-4 + 2k + 6 and -4 - 2k - 6
B.-4 ± (2k + 6)
C.-4 ± |2k + 6|
D.2k + 2 and -2k - 10
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Frequently asked questions
What grade level is "Lengths of segments on number lines: Set 1"?
Lengths of segments on number lines: Set 1 is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Lengths of segments on number lines: Set 1?
You'll be able to: Solve one-step addition and subtraction word problems with whole numbers up to 10,000 with 80% accuracy; Apply addition and subtraction to solve two-step word problems involving whole numbers up to 10,000, showing their work….
Is "Lengths of segments on number lines: Set 1" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Lengths of segments on number lines: Set 1?
This lesson includes 45 practice questions across multiple difficulty levels, each with instant feedback and explanations.