2.1+Adding+on+a+Number+Line

04-04-09 Eva v. V.

Essential Question: How can I add integers?
2.1 Adding on a Number Line ←←←←← ←←← -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7
 * A. Write the addition sentence illustrated by each figure. **
 * 1. **

-3 + -4 = -7 **2.** →→→→→  ←←←←  -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6

-3 + (+4) = +1 →→→→→→→→→→→→→→ ←←←←←← -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7
 * 3. **

-4 + (+11) = +7

→→→→→ -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8
 * 4. ←←←←←←←←← **

+5 + -8 = -3


 * B. Illustrate each addition problem on a number line, and give the answer. **

→→→→→→→→→→ ←←←←←←← -6 -5 -4 -3 -2 -1 ** 0 **1 2 3 4 5 6 7 8 9
 * 1. –5 + (+8) = +3 **

←←←←← ←←←←←← -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9
 * 2. –4 + -3 = -7 **

→→→→→→→→→→→→→ ←←←←← ←←← -5 -4 -3 -2 -1 **0 ** 1 2 3 4 5 6 7 8 9
 * 3. –2 + -3 + (+10) = +5 **

→→→→→→→→→→→→→ ←←←←←←← -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9 10
 * C. When you add two integers, does the order of the numbers make a difference? Illustrate your answer by showing each of these pairs of sums on a number line. **
 * 1. –5 + (+10) and +10 + -5 **

←←←←←← →→→→→→→→→→→→ -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9 10

←←←←←←←←← ←←←←←← -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9 10
 * 2. –4 + -6 and –6 + -4 **

←←←←←← ←←←←←←←←← -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9 10

←←←←←←←←← →→→→→→→→→ -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8
 * 3. +8 + -8 and –8 + (+8) **

→→→→→→→→→→→→ ←←←←←←←←←←←← -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8

←←←←←←←← →→→→→→→ -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7
 * 4. +6 + -7 and –7 + (+6) **

→→→→→→→→→ ←←←←←←←←←← -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7

= Follow – Up = 0 + 200 + -150 = +50 0 + 100 + -100 = 0 0 + -50 + -100 + (+250) = +100 →→→ ←←← -5 -4 -3 -2 -1 **0** 1 2 3 4 5
 * 1. You can think of the scoring in MathMania as follows: When a team answers a question correctly, a positive integer is added to their score. When a team answers a question incorrectly, a negative integer is added to their score. For each of the following situations, write an addition sentence that will give the team’s score. Assume each team starts with 0 points. **
 * a. The Brainiacs answer a 200-point question correctly and a 150-point question incorrectly. **
 * b. The Aliens answer a 100-point question correctly and a 100-point question incorrectly. **
 * c. The Prodigies answer a 50-point question incorrectly, a 100-point question incorrectly, and a 250-point question correctly. **
 * 2. Illustrate each addition problem on a number line and give the answer. **
 * a. –2 + (+2) = 0 **

←←←←←←←←← →→→→→→→→→ -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8
 * b. +8 + -8 = 0 **

→ ← -3 -2 -1 **0** 1 2 3
 * c. –1 + (+1) = 0 **

When you add opposites the answer will always be zero, because you’re adding the same values from opposite sides. So if you have the problem, +2 + -2, it equals 0, because you have 2, but then you add –2, leaving you with 0. You have a value, but then you add or take away that same value, which always leaves you with zero.
 * 3. What happens when you add opposites? Explain how you know your answer is correct. **