Study Guide — 8.NS.A.2
Use rational approximations of irrational numbers to compare the size…
Extend number sense to integers, rationals, and absolute value on the number line.
What this standard means
- Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
- Apply use rational approximations of irrational numbers to compare the size… with models and explanation
- Operates with integers and rationals accurately
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Use a number line for addition of signed numbers 2. Convert between fractions, decimals, and percents 3. Plot and compare rational numbers
_See printable PDF for diagram._
Common mistakes
- Subtracting integers in the wrong direction
- Absolute value sign errors
- Incorrect placement of negatives on the number line
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for 8.NS.A.2.
- [ ] Operates with integers and rationals accurately
- [ ] Uses absolute value correctly
- [ ] Explains reasoning with a number line or diagram
Materials for this standard
- Practice Problems — 20 printable sets (computational and word problems)
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors