Number Foundations Checkpoint
A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes the number skills from the first unit. Expect integers, fractions, ratios, unit rates, and percents in the same set, just like they appear in real math work. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Review integers, fractions, ratios, and percents
- Choose efficient strategies across number topics
- Build readiness for algebraic reasoning
Worked example
Problem. A jacket costs 80 dollars and is 25% off. What is the sale price?
- Find 25% of 80. Since 25% is 1/4, 1/4 of 80 is 20.
- Subtract the discount from the original price.
- 80 - 20 = 60, so the sale price is 60 dollars.
- Connect the calculation back to Number Foundations Checkpoint so the method, not just the arithmetic, is clear.
Answer: 60
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Compute -9 + 14.
Show solution
- The signs are different.
- 14 - 9 = 5, and the positive number has the larger distance from zero.
Answer: 5
2. Compute 6 - 15.
Show solution
- Rewrite as 6 + -15.
- 15 is farther from zero, so the answer is negative.
- 15 - 6 = 9.
Answer: -9
3. Which fraction is equivalent to 9/12?
Choices: 3/4 · 4/3 · 1/3 · 9/4
Show solution
- Divide 9 and 12 by 3.
- 9/12 simplifies to 3/4.
Answer: 3/4
4. Compute 1/4 + 3/8.
Show solution
- Rewrite 1/4 as 2/8.
- 2/8 + 3/8 = 5/8.
Answer: 5/8
5. A car travels 210 miles in 3 hours. What is the speed in miles per hour?
Show solution
- Divide miles by hours.
- 210 divided by 3 is 70.
Answer: 70
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