The temperature dropped 2.5°F each hour for \(4\) hours. What was the total change in temperature?
- A -10°F
- B -6.5°F
- C 6.5°F
- D 10°F
Check answer and explanation
Answer A: -10°F
A drop of 2.5°F is \(-2.5\). Over \(4\) hours: \(4\times(-2.5)=-10°\)F.
CH03-08 lesson
Solving Real-World Problems with Rational Numbers Learning Activity
A focused Grade 7 learning session for Solving Real-World Problems with Rational Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
- 18
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of solving real-world problems with rational numbers using models, equations, and test-style reasoning.
Student goal: I can solve problems involving solving real-world problems with rational numbers.
Helpful first:
Converting Rational Numbers to Decimals
Learn the Idea
Solving Real-World Problems with Rational Numbers 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 solving real-world problems with rational numbers using models, equations, and test-style reasoning.
See the Math
| 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.
Follow a Worked Example
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 Solving Real-World Problems with Rational Numbers, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
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.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving solving real-world problems with rational numbers.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsA diver descends \(3.5\) meters below sea level each minute. After \(6\) minutes, what is the diver's depth relative to sea level?
- A \(-21\) m
- B \(-10.5\) m
- C \(10.5\) m
- D \(21\) m
Check answer and explanation
Answer A: \(-21\) m
Each descent of \(3.5\) m is negative: \(-3.5 \times 6 = -21\) m.
guided
1 questionMaria has a bank account balance of \($145.50\). She withdraws \($28.75\), then deposits \($52.25\). What is her new balance?
- A \($116.75\)
- B \($118.75\)
- C \($169.00\)
- D \($226.50\)
Check answer and explanation
Answer C: \($169.00\)
\(145.50 - 28.75 + 52.25 = 116.75 + 52.25 = 169.00\) dollars.
practice
5 questionsA football team loses \(7\) yards on one play and gains \(13\) yards on the next. What is the net change in yards?
- A \(-20\) yards
- B \(-6\) yards
- C \(6\) yards
- D \(20\) yards
Check answer and explanation
Answer C: \(6\) yards
Loss of \(7\) yards is \(-7\); gain of \(13\) is \(+13\): \(-7 + 13 = 6\) yards.
A recipe calls for \(\frac{3}{4}\) cup of sugar. If you are making \(\frac{1}{2}\) of the recipe, how much sugar do you need?
- A \(\frac{3}{8}\) cup
- B \(\frac{1}{2}\) cup
- C \(\frac{5}{4}\) cups
- D \(1\frac{1}{2}\) cups
Check answer and explanation
Answer A: \(\frac{3}{8}\) cup
Multiply: \(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\) cup.
The temperature at 6 AM was -8°C. It rose by 3.5°C by 9 AM. What was the temperature at 9 AM?
- A -11.5°C
- B -4.5°C
- C 4.5°C
- D 11.5°C
Check answer and explanation
Answer B: -4.5°C
\(-8 + 3.5 = -4.5°\)C.
An elevator starts at the 5th floor, goes down 8 floors, then up 6 floors. On which floor does it end?
- A Floor \(-3\)
- B Floor \(1\)
- C Floor \(3\)
- D Floor \(19\)
Check answer and explanation
Answer C: Floor \(3\)
Start at 5, go down 8: \(5 - 8 = -3\) (basement). Then up 6: \(-3 + 6 = 3\).
A store gives a discount of \(\frac{1}{5}\) off the original price of \($60\). How much does the item cost after the discount?
- A \($12\)
- B \($36\)
- C \($48\)
- D \($72\)
Check answer and explanation
Answer C: \($48\)
Discount: \(\frac{1}{5} \times 60 = 12\). Price: \(60 - 12 = 48\) dollars.
exit
3 questionsOver \(5\) weeks, an account loses \($12.50\) per week. What is the total change in the account balance?
- A \(-$62.50\)
- B \(-$7.50\)
- C \($7.50\)
- D \($62.50\)
Check answer and explanation
Answer A: \(-$62.50\)
Loss of \($12.50\) per week for \(5\) weeks: \(-12.50 \times 5 = -62.50\) dollars.
A runner's time improves by \(2.4\) seconds each month for \(3\) months. What is the total improvement?
- A \(2.4\) seconds
- B \(7.2\) seconds
- C \(5.4\) seconds
- D \(7.8\) seconds
Check answer and explanation
Answer B: \(7.2\) seconds
Improvement of \(2.4\) sec/month \(\times\) \(3\) months \(= 7.2\) seconds total.
A bakery divides \(\frac{5}{8}\) pound of flour equally among \(4\) batches. How much flour is in each batch?
- A \(\frac{5}{32}\) pound
- B \(\frac{5}{12}\) pound
- C \(\frac{1}{8}\) pound
- D \(\frac{5}{4}\) pounds
Check answer and explanation
Answer A: \(\frac{5}{32}\) pound
Divide: \(\frac{5}{8} \div 4 = \frac{5}{8} \times \frac{1}{4} = \frac{5}{32}\) pound.
