Fishtank Learning

6th Grade Math
Unit 4: Rational Numbers
Lesson 5

Objective

Find and position integers and rational numbers on the number line.

Anchor Problems - Problem 1

Graph the number $${\frac{3}{10}}$$ and its opposite on the number line.

Number line from -1 to 1 with 0 centered, showing 0 and 1/10 marked.

Guiding Questions

What do the denominator and numerator of a fraction represent? How can you use that to help you graph $${{\frac{3}{10}}}$$?
Create a scale on the number line and label it. What is the length of each segment?
How far away is $${{\frac{3}{10}}}$$ and $$-{{\frac{3}{10}}}$$ from $$0$$?
Is $$-\frac{5}{10}$$ to the right or left of $$-{{\frac{3}{10}}}$$? Why?

Notes

Use this problem to introduce the term rational number. Rational numbers include whole numbers, 0, integers, and all other numbers that can be written in the form $$\frac{a}{b}$$, given $$b \neq 0$$. Every rational number can be located on the number line.
Students know how to segment a number line into fractional segments from third grade (3.NF.2) and most recently will have worked with fractional line plots in fifth grade (5.MD.2). Use this Anchor Problem as an opportunity to reengage students with these concepts, extended to include negative values. Ensure the value is placed in a location that demonstrates an appropriate level of precision (MP.6).

Anchor Problems - Problem 2

Point $$A$$ is shown on the number line below.

Number line with point A between -2 and -1, closer to -1.

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.

Guiding Questions

Is point $$A$$ located to the left or right of $${{{-2}}}$$? Does that make it greater than or less than $${{{-2}}}$$?
How far from 0 is point $$A$$? In which direction?
Consider the opposite of point $$A$$. Between which two whole numbers is the opposite of point $$A$$ located?
Name a number between $${{{-1}}}$$ and $${{{-2}}}$$. Where would that number be located on the number line?
Name a number less than $${{{-2}}}$$. Where would that number be located on the number line?
How would you communicate the correct answer to either Adan or Serena that would help them understand the error they made (MP.3)?

Notes

Watch a video analysis of this Anchor Problem in the Unit Launch, Big Idea 1, Step 2 starting at 3:14.

Anchor Problems - Problem 3

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.

Number line from -1 to 1 with arrows indicating direction.

b. Explain what 0 represents in your situation.

Anchor Problems - Problem 4

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?

Problem Set

View Problem Set

Target Task

Use the number line below to answer the questions that follow.

Number line showing points P and Q, with P between -2 and -1 and Q between 0 and 1.

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.