A focused Grade 7 learning session for Integers and Their Opposites using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving integers and their opposites.
Integers and Their Opposites is part of Grade 7 The Number System. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of integers and their opposites using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Integers and Their Opposites, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving integers and their opposites.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the opposite of \(-15\)?
Answer A: \(15\) (correct)
The opposite of a number reverses its sign. The opposite of \(-15\) is \(15\). Note: the absolute value \(|-15| = 15\) looks the same but represents distance, not the additive inverse.
What is \(|-7|\)?
Answer D: \(7\) (correct; distance is always non-negative)
The absolute value of any number is its distance from zero, which is always non-negative. \(|-7| = 7\).
Marcus walks \(12\) meters east. To return to his starting point, he must walk \(12\) meters west. Which number represents his westward walk?
Answer A: \(-12\) (opposite direction)
If east is positive, then west is negative. Walking \(12\) meters west is represented by \(-12\).
A bank account starts with a credit of $50. After a debit of $50, what is the account balance?
Answer D: \($0\) (correct; opposites sum to zero)
The credit of \(+50\) and debit of \(-50\) are opposites and sum to zero. This demonstrates the additive inverse property: \(50 + (-50) = 0\).
What is \((-9) + 9\)?
Answer C: \(0\) (opposites sum to zero)
Opposites sum to zero: \(a + (-a) = 0\).
Temperature drops \(20\) degrees from \(10\) degrees. Express the drop (change) as a signed number.
Answer D: \(-20\) (correct; drop is negative change)
A decrease or drop is represented by a negative number. A \(20\)-degree drop is \(-20\).
What is the opposite of the opposite of \(11\)?
Answer D: \(11\)
The opposite of \(11\) is \(-11\). The opposite of \(-11\) is \(11\). So the opposite of the opposite returns you to the original number.
A scuba diver descends \(40\) feet below sea level. Which integer represents this depth?
Answer D: \(-40\) (correct; below is negative)
Descending (going down) below sea level is represented by a negative number. A descent of \(40\) feet is \(-40\).
A stock loses \(15\) points. Express this as a signed number.
Answer A: \(-15\) (correct; loss is negative)
A loss is represented by a negative number. A loss of \(15\) points is \(-15\).
What is the opposite of \(0\)?
Answer C: \(0\)
Zero is its own opposite. The opposite of \(0\) is \(0\), since \(0 = -0\).
A bank account has a balance of \(-$75\) (overdrawn). To bring it to zero, you must deposit:
Answer A: \($75\)
To cancel out a debt of \(-75\), you must add \(+75\). Their sum is zero: \(-75 + 75 = 0\).
