Topics
1. Integers
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United States of America
Grade 7

Investigation: Life-size number line

Lesson
Practice
Overview
Activity
Reflection

Investigate absolute value with a life-size number line.

Objectives
  • To understand what absolute value is.
  • To visualize how to add and subtract integers.
  • To visualize how to find the opposite of a number.
Materials
  • Tape (any tape that is not see-through)
  • Paper
  • Pen or pencil
  • Colored marker

Life-size number line

Create your number line
Start by creating your life-size number line. Lay a piece of tape on the floor that is about 15 \text{ feet} long.
Along the piece of tape, place a vertical piece of tape every 5 \text{ inches}. Label the vertical pieces of tape with the numbers -18 to 18, making sure that 0 is in the center of the line.
Complete the following steps and answer the corresponding questions with a partner.

One person stand at the spot labeled -5 and the other person stand at the spot labeled 5.

What do you notice? Examine the distance from zero that you are standing.

Each person pick a direction and move 3 marks in that direction.

What number are you standing at now? How can you represent this through addition or subtraction of integers? What is the distance from zero of the number you are currently standing at? Is it the same for both of you? Why or why not?

Pick a direction and move 5 marks in that direction.

What number are you standing at now? How can you represent all of the moves you have made so far through addition or subtraction of integers? What is the opposite of the number you are standing at now? How do you know?

Walk the amount of steps required to represent the opposite you have just found.

Where did you end up? Where are you standing with regard to your partner? Why is this?
Investigate
Consider the following questions after you have completed the above.
1.
Move along your number line to model the following problems, then solve them and write down your answers: -7 + 7 + 3, -4 + 0, -2 -1, -9 - 5 -3, 1 - (-6), -14 + (-3), 8+ (-5).
2.
Is there any way you can rewrite the last two problems from the previous question using different signs? Explain your answer.
3.
Work with your partner to create three more of your own problems similar to those you just worked through in the first question. Use the number line to find the answers.

Answer the questions below after you have completed the activity.

Discussion
1.
Define what absolute value means in your opinion. Use the number line that you created as a reference.

Outcomes

7.NS.A.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.1.A

Describe situations in which opposite quantities combine to make 0.

7.NS.A.1.B

Understand p+q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.A.1.C

Understand subtraction of rational numbers as adding the additive inverse, p-q=p+(-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

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