Unit Plan 35 (Grade 8 Math): Number System & Exponents Spiral—Fluency & Sense-Making
8th graders strengthen number sense by classifying rational and irrational numbers, applying exponent rules, and mastering scientific notation. They approximate square roots, simplify powers, and interpret real-world quantities with precise scale and unit reasoning.
Focus: Polish fluency with irrational approximations, integer exponents, and scientific notation in real contexts.
Grade Level: 8
Subject Area: Mathematics (Number System • Expressions & Equations • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This spiral week tightens the number sense that powers Grade 8 algebra and science: classifying numbers as rational or irrational, approximating and placing irrational numbers, simplifying with integer exponent rules (including zero and negative exponents), and using scientific notation to describe and operate on very large and very small quantities. Emphasis: clean structure, units, order-of-magnitude reasoning, and reasonableness in real contexts.
Essential Questions
- What makes a number rational or irrational, and how can I approximate an irrational on the number line with confidence?
- How do the properties of exponents keep my algebra neat and consistent across positive, zero, and negative powers?
- When is scientific notation the right tool, and how do I compare and compute with it while keeping track of scale and units?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Classify numbers as rational (terminating or repeating decimals; ratios of integers) or irrational; convert simple repeating decimals to fractions and explain why the decimal form repeats.
- Approximate square roots and other irrationals to a stated precision; locate/compare them on the number line and justify the estimate.
- Apply integer exponent rules (product, quotient, power, zero, negative exponents) to simplify expressions and evaluate numerical powers; connect to equivalence and patterns.
- Write numbers in scientific notation, convert to standard form, compare magnitudes, and perform operations (multiply/divide/add/subtract) with attention to units and significant scale.
- Use order-of-magnitude and reasonableness checks to judge whether results make sense in context.
Standards Alignment — CCSS Grade 8
- 8.NS.1: Know that every number has a decimal expansion; rational numbers have repeating or terminating decimals; convert a repeating decimal to a rational number.
- 8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers; locate them on a number line; estimate the value of expressions.
- 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- 8.EE.2: Use square and cube roots to solve x^2 = p and x^3 = q; evaluate square and cube roots of small perfect powers and approximate others.
- 8.EE.3: Use scientific notation to express very large/small numbers; compare quantities using powers of 10.
- 8.EE.4: Perform operations with numbers in scientific notation and interpret results in context (including measurement units).
Success Criteria — Student Language
- I can tell if a number is rational or irrational and explain why.
- I can estimate an irrational number (like sqrt(17)) and show where it goes on a number line.
- I can simplify with exponents using rules like a^m * a^n = a^(m+n), a^0 = 1, and a^(-n) = 1/(a^n).
- I can write numbers in scientific notation and convert back; I can compare how big they are.
- I can calculate with scientific notation and check if my answer makes sense with units and order of magnitude.