Integers Introduction — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
Adding -3 to 5 means jumping right three times because three is a counting number.
Corrected: Adding -3 to 5 means jumping left three times because the integer is negative.
Negative integers always move you left, so 5 plus -3 lands on 2.
2. Fix the sentence:
The sum 6 plus -6 equals 12 since adding any two integers always grows the total.
Corrected: The sum 6 plus -6 equals 0 because opposites cancel each other completely.
Adding opposites returns you to your starting jump point, which is zero.
3. Fix the sentence:
An arrow showing -4 should point to the right toward larger positive integers.
Corrected: An arrow showing -4 should point to the left toward smaller negative integers.
Conventionally, negative arrows face left because the number line decreases that direction.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Drawing -2 plus -3 on a number line, you end at -5.
Both negatives push you leftward, so total motion equals -2 plus -3 equaling -5.
2. Starting at -1 and moving 4 right lands on 3.
From -1, moving 4 right means -1 plus 4, which equals 3.
3. The opposite of 0 is 0 because zero has no sign.
Since 0 has no positive or negative side, its opposite is itself.
4. Adding 8 and -8 on a number line gives 0.
Equal magnitudes with opposite signs always sum to zero.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe how to use arrows to model 3 plus -7 on a number line.
Sample answer: Draw an arrow 3 units right from zero, then a 7-unit arrow left from there. The endpoint, -4, is the answer.
Sequential arrows visualize sums by combining direction and magnitude correctly.
2. Why does -5 plus 5 always equal zero on a number line?
Sample answer: Moving 5 left then 5 right brings you back to start. The opposites perfectly cancel each other.
Pairs of opposite integers always combine to zero by definition.