A focused Grade 7 learning session for Percent Error: How Close Are Your Estimates? using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving percent error: how close are your estimates?.
Percent Error: How Close Are Your Estimates? is part of Grade 7 Percents and Financial Literacy. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of percent error: how close are your estimates? 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 Percent Error: How Close Are Your Estimates?, 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 percent error: how close are your estimates?.
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.
Jonah estimated the length of a pencil to be \(7\) inches, but the actual length is \(8\) inches. What is the percent error?
Answer D: \(12.5\%\)
Percent error \(=\frac{|\text{estimate}-\text{actual}|}{|\text{actual}|}\times100\%=\frac{|7-8|}{8}\times100\%=12.5\%\).
Maria guessed that a book weighs \(2\) pounds, but it actually weighs \(2.5\) pounds. What is the percent error?
Answer D: \(20\%\)
Percent error \(=\frac{|2-2.5|}{2.5}\times100\%=\frac{0.5}{2.5}\times100\%=20\%\).
A student estimated a room to be \(12\) meters wide, but the actual width is \(10\) meters. What is the percent error?
Answer D: \(20\%\)
Percent error \(=\frac{|12-10|}{10}\times100\%=\frac{2}{10}\times100\%=20\%\).
Leo predicted that he would run a race in \(45\) seconds, but he actually completed it in \(50\) seconds. What is the percent error in his prediction?
Answer D: \(10\%\)
Percent error \(=\frac{|45-50|}{50}\times100\%=\frac{5}{50}\times100\%=10\%\).
A baker estimated \(120\) cups of flour were needed, but the recipe actually required \(100\) cups. What is the percent error?
Answer D: \(20\%\)
Percent error \(=\frac{|120-100|}{100}\times100\%=\frac{20}{100}\times100\%=20\%\).
An estimate of \(42\) meters has a percent error of \(16.7\%\) compared to the actual distance. What was the actual distance?
Answer D: \(50\) meters
If percent error is \(16.7\%\), then \(\frac{|42-\text{actual}|}{|\text{actual}|}\times100\%=16.7\%\). Testing \(50\): \(\frac{|42-50|}{50}\times100\%=16\%\approx 16.7\%\).
What is the percent error for the height estimate?
Answer C: \(8.3\%\)
Percent error \(=\frac{|66-72|}{72}\times100\%=\frac{6}{72}\times100\%=8.3\%\).
A shopkeeper estimated \(240\) customers would visit on a day, but only \(200\) actually came. What is the percent error?
Answer D: \(20\%\)
Percent error \(=\frac{|240-200|}{200}\times100\%=\frac{40}{200}\times100\%=20\%\).
A student estimated the population of a city to be \(500,000\), but the actual population is \(450,000\). What is the percent error?
Answer D: \(11.1\%\)
Percent error \(=\frac{|500000-450000|}{450000}\times100\%=\frac{50000}{450000}\times100\%\approx 11.1\%\).
A scout estimated that a hiking trail is \(7.5\) miles long, but the actual length is \(8.25\) miles. What is the percent error?
Answer D: \(9.1\%\)
Percent error \(=\frac{|7.5-8.25|}{8.25}\times100\%=\frac{0.75}{8.25}\times100\%\approx 9.1\%\).
A student predicted she would solve \(28\) math problems correctly, but she actually solved \(32\) correctly. What is the percent error in her prediction?
Answer D: \(12.5\%\)
Percent error \(=\frac{|28-32|}{32}\times100\%=\frac{4}{32}\times100\%=12.5\%\).
