Eighth Grade - MATH
3: Math
Unit 1: Numbers
Lesson 6
Scientific Notation
Students convert between standard form and scientific notation in multiple activities (examples: converting 45,000 to 4.5 × 10^4 and converting 2.3 × 10^-2 to 0.023). Students compare magnitudes by looking at exponents in the 'Comparing Large and Small Quantities' activity and use exponent comparison to order numbers (problems 7–13). Students apply scientific notation to real-world quantities (global population 8.1 × 10^9, distance to the Sun 1.5 × 10^8, virus size 5 × 10^-8) and perform operations (multiply/divide/add/subtract) with numbers in scientific notation in Activity 2 and Day 3 tasks.
Lesson 7
Arctic Marine Research
Students convert very small measurements (0.0000042 m and 0.0000065 m) into scientific notation (shown as 4.2 × 10^-6 and 6.5 × 10^-6) and determine which is larger. Students calculate how many times larger one measurement is than another (cod vs sponge) and compare cell densities given explicitly in scientific notation (1.2 × 10^8 vs 9.5 × 10^7). Students also compute differences and perform operations with numbers presented in scientific notation (difference given as 2.5 × 10^7).
Lesson 8
Unit 1 Test
Students are asked to convert large numbers to and from scientific notation (e.g., convert 450,000 into scientific notation; convert 3.2 × 10^4 into standard form; convert 5,600,000 into scientific notation). Students perform operations with numbers in scientific notation (e.g., multiply 2 × 10^2 × 3 × 10^5 and (4 × 10^3) × (2 × 10^4)) and solve contextual problems given in scientific notation (e.g., Earth–Moon distance 3.84 × 10^5 km and total weight from 1.5 × 10^-3 g × 1.2 × 10^4 grains). The Parent Plan explicitly describes estimating and comparing very large or very small quantities using examples like 3 × 10^8 and 7 × 10^9.
Final Project
Mars Station Test Mission
Students encounter scientific notation explicitly in Task 3 where each fuel cell is given as 7 × 10^2 kWh and are instructed to convert this to a whole number (700 kWh). Students then divide location energy shortfalls by this value to compute how many fuel cells are needed and compute storage area for those cells. The lesson's Skills section also explicitly lists using numbers in the form single digit × an integer power of 10 and interpreting scientific notation generated by technology.
Unit 2: Proportions
Lesson 4
Graphing Proportions
Students are asked to write and manipulate numbers in scientific notation on the Skills Review (e.g., convert 5,600,000 to 5.6 × 10^6 and compute products like (3 × 10^7) × (2 × 10^3)). The review includes a population-comparison item where numbers are given in scientific notation (3 × 10^6 and 9 × 10^7) and students compute how many times larger one is than the other, with the answer shown as 30 times larger. The answer key explicitly shows division of numbers in scientific notation to determine the factor between populations.
Unit 9: Semester Exams
Lesson 1
Numbers Review
Students practice scientific notation in Activity 4 by checking whether expressions (e.g., 7.32 × 10^3) are written correctly and by coloring items as correct or incorrect. Students classify numbers as rational or irrational and approximate square roots, which supports number-sense related to magnitude. Students also engage with identifying correct scientific notation form through the provided color-key tasks and self-checks.
Lesson 5
Semester Exam
Students are asked to simplify an expression written as a decimal times a power of ten (Problem 8: "Simplify: 6.9 x 10^2"). Students also work with exponents in several problems (e.g., 5^1 x 5^2 and 8^4 ÷ 8^2), so they practice manipulating powers of ten and exponent rules.
