Directed Numbers

UK Secondary (7-11)

Life-Size Number Line (Investigation)

Lesson

- To understand absolute value is distance from zero.
- To visualise how to add and subtract integers.
- To visualise how to find an additive inverse of a number.
- To practise with adjacent signs.

- Masking Tape (or any tape that is not clear)
- Paper
- Pen
- Marker

- Lay down a piece of tape on the floor approximately $4.5$4.5 metres ($15$15 feet) long.
- Along the piece of tape place a vertical piece of tape every $12$12 centimetres ($5$5 inches).
- Determine the placement of each number from $-18$−18 to $18$18 on the number line you have created on the floor. Write the correct number on the vertical piece of tape. Make sure to place $0$0 in the center. Make the piece of tape indicating $0$0 be a little larger than all of the others.

With a partner answer the following questions.

- One person stand at the spot labeled $-5$−5 and the other person stand at the spot labeled $5$5. What do you notice? Examine the distance from zero that you are standing.
- Each person pick a direction and move $3$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$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 additive inverse of the number you are standing at now? How do you know.
- Walk the amount of steps required to represent the additive inverse you have just found. Where did you end up? Where are you standing with regard to your partner? Why is this?
- Move along your number line to model the following problems. Write down the answer you find to each.
- $-7+7+3$−7+7+3
- $-4+0$−4+0
- $-2-1$−2−1
- $-9-5-3$−9−5−3
- $1-(-6)$1−(−6)
- $-14+(-3)$−14+(−3)
- $8+(-5)$8+(−5)

- Is there any way you can rewrite the last two problems using different signs? Explain your answer.
- Work with your partner to create more of your own problems similar to those you just solved in number 8. Use the number line to find the answer.