Curriculum / Math / 6th Grade / Unit 4: Rational Numbers / Lesson 5
Math
Unit 4
6th Grade
Lesson 5 of 13
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Find and position integers and rational numbers on the number line.
The core standards covered in this lesson
6.NS.C.6.C — 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 numbers on a coordinate plane.
The foundational standards covered in this lesson
3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.
4.NF.C.6 — Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students do not need to have a formal definition of rational numbers, particularly as it relates to terminating or repeating decimals; they will learn more about this in seventh grade NS standards on The Number System. The focus for sixth-grade understanding is extending their understanding beyond integers to include locating positive and negative fractions and simple decimals on the number line.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Graph the number $${\frac{3}{10}}$$ and its opposite on the number line.
Point $$A$$ is shown on the number line below.
Adan says that point $$A$$ is located at $${-2\frac{3}{4}}$$. Serena says that point $$A$$ is located at $${-1\frac{1}{4}}$$.
Do you agree with either Adan or Serena? Explain your reasoning.
Your school is located exactly$${\frac{2}{5}}$$ of a mile directly north of your home. A post office is located the same distance from your home in the opposite direction.
a. Show the locations of your home, your school, and the post office on the number line.
b. Explain what 0 represents in your situation.
Jakhil says he’s thinking of two numbers. They are 12.8 units apart on the number line, and they are opposites. What are the two numbers?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the number line below to answer the questions that follow.
a. At what value is point $$P$$ located?
b. At what value is point $$Q$$ located?
c. Plot and label point $$R$$ at $$-1\frac{1}{3}$$ on the number line.
d. Plot and label point $$S$$ at $$\frac{2}{3}$$ on the number line.
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 4
Lesson 6
Topic A: Understanding Positive and Negative Rational Numbers
Extend the number line to include negative numbers. Define integers.
6.NS.C.6 6.NS.C.6.C
Use positive and negative numbers to represent real-world contexts, including money and temperature.
6.NS.C.5
Use positive and negative numbers to represent real-world contexts, including elevation.
Define opposites and label opposites on a number line. Recognize that zero is its own opposite.
6.NS.C.6.A 6.NS.C.6.B
6.NS.C.6.C
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Topic B: Order and Absolute Value
Order integers and rational numbers. Explain reasoning behind order using a number line.
6.NS.C.6.C 6.NS.C.7.A
Compare and interpret the order of rational numbers for real-word contexts.
Write and interpret inequalities to compare rational numbers in real-world and mathematical problems.
6.NS.C.7.A 6.NS.C.7.B
Define absolute value as the distance from zero on a number line.
6.NS.C.7.C
Model magnitude and distance in real-life situations using order and absolute value.
6.NS.C.7.C 6.NS.C.7.D
Topic C: Rational Numbers in the Coordinate Plane
Use ordered pairs to name locations on a coordinate plane. Understand the structure of the coordinate plane.
6.NS.C.6.B 6.NS.C.6.C
Reflect points across axes and determine the impact of reflections on the signs of ordered pairs.
6.NS.C.6.B
Calculate vertical and horizontal distances on a coordinate plane using absolute value in real-world and mathematical problems.
6.NS.C.7.C 6.NS.C.8
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