A focused Grade 7 learning session for Rational Number Operations in Extended Contexts using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving rational number operations in extended contexts.
Rational Number Operations in Extended Contexts 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 rational number operations in extended contexts 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 Rational Number Operations in Extended Contexts, 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 rational number operations in extended contexts.
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.
A scuba diver descends at a rate of \(-1.5\) meters per second. How long does it take to reach a depth of \(-18\) meters from the surface?
Answer B: \(12\) seconds
Time \(=\) distance \(\div\) rate. The diver descends \(18\) meters at \(1.5\) m/s: \(18\div1.5=12\) seconds.
An ocean temperature is changing at a rate of -0.3°C per hour. If the current temperature is 12°C, what will the temperature be after 5 hours?
Answer A: 10.5°C
Temperature change \(= -0.3 \times 5 = -1.5°\)C. New temperature \(= 12 + (-1.5) = 10.5°\)C.
Maria's bank account has a balance of \($85.50\). She withdraws \($12.75\) twice in one week. What is her new balance?
Answer A: \($59.00\)
Two withdrawals: \(-$12.75 - $12.75 = -$25.50\). New balance: \($85.50 - $25.50 = $59.00\).
A football team gains 15 yards on first down, loses 4 yards on second down, then gains 8 yards on third down. What is the net yardage change for this series?
Answer A: \(19\) yards
Net change \(= 15 - 4 + 8 = 19\) yards.
A hiker is at an elevation of \(1,450\) feet. She climbs up \(325\) feet, then descends \(180\) feet. What is her final elevation?
Answer A: \(1,595\) feet
Final elevation \(= 1,450 + 325 - 180 = 1,595\) feet.
A swimmer completes laps in \(\frac{3}{4}\) minute during the first 9 minutes. Then her pace slows and she takes \(\frac{7}{8}\) minute per lap for the next 7 minutes. How many total laps does she complete?
Answer A: \(20\) laps
First 9 minutes: \(9 \div \frac{3}{4} = 12\) laps. Next 7 minutes: \(7 \div \frac{7}{8} = 8\) laps. Total: \(12 + 8 = 20\) laps.
A recipe calls for \(\frac{2}{3}\) cup of sugar and \(\frac{3}{4}\) cup of flour. If you make 2 batches, then use \(\frac{1}{2}\) of that total sugar for a second dessert, how much sugar remains?
Answer A: \(\frac{2}{3}\) cups
Total sugar for 2 batches \(= 2 \times \frac{2}{3} = \frac{4}{3}\) cups. Sugar used for second dessert \(= \frac{1}{2} \times \frac{4}{3} = \frac{2}{3}\) cups. Remaining \(= \frac{4}{3} - \frac{2}{3} = \frac{2}{3}\) cups.
A business loses \($450\) in the first quarter. In the second quarter, the loss is reduced by half. In the third quarter, the company breaks even (no profit or loss). What is the net change across all three quarters?
Answer B: Loss of \($675\)
Q1 loss: \(-$450\). Q2 loss: \(-$225\) (half of Q1). Q3: \($0\) (break even). Net: \(-$450 - $225 + 0 = -$675\).
A temperature reading shows -5°F in the morning. By afternoon, the temperature increases by 18°F. What is the afternoon temperature?
Answer B: 13°F
Afternoon temperature \(= -5 + 18 = 13°\)F.
A car's fuel tank is at \(\frac{3}{4}\) capacity. After a drive, \(\frac{1}{4}\) of the tank is used. What fraction of the tank remains?
Answer B: \(\frac{1}{2}\)
Remaining \(= \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\) tank.
A stock price drops by \($2.50\) on Monday, rises by \($1.75\) on Tuesday, and drops by \($0.85\) on Wednesday. What is the net change?
Answer A: \(-$1.60\)
Net change \(= -$2.50 + $1.75 - $0.85 = -$1.60\).
