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Back to Understand a rational number as a point on the number line

Rational Numbers as Points on the Number Line and Coordinate Plane

For number line problems, identify the unit and subdivision. For coordinate plane problems, name the quadrant before plotting or locating the point.

Grade 6·21 problems·~35 min·Common Core Math - Grade 6·standard·6-ns-c-6
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

On a number line from 0 to 2, where would you place the fraction 32\frac{3}{2}?

2.

A point is located at (3, 5) on a coordinate plane. In which quadrant is it?

3.

What is the opposite of 7 on the number line?

B

Fluency Practice

1.

On a number line, a point is located 2.5 units to the left of 0. What is the signed number for this point?

2.

What is the opposite of −23-\frac{2}{3}?

Number line from −3 to 1 subdivided into thirds, with integers labeled and no point marked
3.

On a number line subdivided into thirds, where is the point −53-\frac{5}{3}?

4.

If n=−5n = -5, what is −n-n?

5.

In which quadrant is the point (−4, 3)?

C

Varied Practice

1.

Which rational number is located between −2-2 and −1-1 on the number line?

2.

The opposite of −9-9 is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . This means −(−9)=‾-(-9) = \underline{\hspace{5em}}.

opposite of −9:
value of −(−9):
3.

Which statement about −n-n is always true?

Coordinate plane with quadrants labeled and point A at (3, −4) in Quadrant IV marked; x-axis highlighted as the axis of reflection
4.

The point (3,−4)(3, -4) is in Quadrant   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Its reflection across the x-axis is the point (  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ,   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ).

quadrant number:
x-coordinate of reflection:
y-coordinate of reflection:
5.

The point (−2, 5) is reflected across the y-axis. What are the coordinates of the reflected point?

D

Word Problems

Number line showing point P at −3/4 and point Q at 5/4 with an arrow indicating the distance between them
1.

A number line is subdivided into fourths. Point P is located at −34-\frac{3}{4} and point Q is located at 54\frac{5}{4}.

How far apart are points P and Q? (Count the fourths between them.)

Coordinate plane showing four points: A(3,4) in Quadrant I, B(−3,4) in Quadrant II, C(−3,−4) in Quadrant III, and D(3,−4) in Quadrant IV
2.

Points A(3, 4), B(−3, 4), C(−3, −4), and D(3, −4) are plotted on a coordinate plane.

1.

Which quadrant contains point C(−3, −4)?

2.

Complete the description.
The points have the same   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   -coordinate and opposite   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   -coordinates.
The transformation from A to B is a reflection across the   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   -axis.

shared coordinate:
opposite coordinate:
axis of reflection:
3.

A coordinate plane is used to map a garden. The origin (0, 0) is a birdbath. The rose bed is at (−2.5, 1.5).

What are the coordinates of the point that is the reflection of the rose bed across the x-axis?

E

Error Analysis

1.

Carlos evaluated −n-n when n=−7n = -7 and wrote: '−n=−7-n = -7 because there is a minus sign in front, so the answer must be negative.'

What error did Carlos make?

2.

Yuki was asked: 'What is the reflection of the point (3,4)(3, 4) across the x-axis?' She answered: '(−3,4)(−3, 4) — I change the x-coordinate because I''m reflecting across the x-axis.'

What error did Yuki make?

F

Challenge / Extension

1.

Point P is at (−3/2, 2) on the coordinate plane.

What are the coordinates of the point that results from reflecting P first across the y-axis and then across the x-axis?

2.

Explain why −(−(−4))=−4-(-(-4)) = -4. Use the meaning of 'opposite' in your explanation.

0 of 21 answered