HOMESCHOOL AND DISTANCE LEARNING
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3: Math

Unit 1

Unit 1: Numbers

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Students identify and record the zero and negative exponent rules (a^0 = 1 and a^{-n} = 1/a^n) and solve practice problems on the Negative & Zero Exponents activity page. In Activities 2 and 3, students apply the Product of Powers rule (a^m × a^n = a^{m+n}) and the Quotient of Powers rule (a^m ÷ a^n = a^{m-n}), including worked examples that add/subtract exponents and then convert negative results to reciprocals. Activities 4–6 require students to apply Power of a Power, Power of a Product (and Power of a Quotient in the answer key), and to produce exponent form and numerical answers on mixed-review problems.
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Students calculate and interpret positive and negative integer exponents (e.g., using the calculator to evaluate 2^5 = 32 and entering negative exponents such as 2^(−3) to get 0.125 and relate it to 1/2^3). Students solve problems that require applying exponent rules, such as simplifying (2^3)^2 and multiplying like bases (3^4 · 3^2) on quizzes and activity pages. Real-world problems and exercises ask students to generate and evaluate exponential expressions (e.g., 3 × 2^4 and several problems finding squares, cubes, and their roots).
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Students encounter tasks that require working with integer exponents on the Review Quiz and answer key: problems ask students to simplify 3^x × 3^4, evaluate (2)^4, use 2^n in an exponential growth formula, and compute side length and area expressions involving 2^3. The materials also include expressions with fractional/root notation (16^(1/3), √ expressions) and at least one reference to a negative exponent in an answer (e.g., 5^{-2} = 1/25), so students practice evaluating and simplifying exponential expressions in assessment items.
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Students multiply and divide expressions in scientific notation and are instructed to add exponents when multiplying and subtract exponents when dividing (e.g., (3 × 10^4) × (6 × 10^3) and (6 × 10^8) ÷ (2 × 10^3)). Students convert negative exponents to standard decimals (e.g., 1.2 × 10^-4 → 0.00012) and convert between standard form and 10^n notation by moving the decimal point. Multiple activity pages and worked examples require students to perform these exponent operations with base 10 in a variety of problems and word contexts.
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The Parent Plan explicitly lists the skill "Know and apply the properties of integer exponents to generate equivalent numerical expressions." Students convert decimals to scientific notation in Phase 1 (e.g., 0.0000042 → 4.2 × 10^-6) and work with given values in scientific notation (1.2 × 10^8 and 9.5 × 10^7) to compare and find differences. In Phase 3 students evaluate and use integer exponents in growth models (N = 2^t, compute 2^6 and 2^10, and compare 3^4).
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The Parent Plan and student-facing introduction explicitly state that students should "use the rules for exponents (powers) to rewrite and simplify expressions" and even give the example 3^2 × 3^-5 = 3^-3 = 1/3^3 = 1/27. Multiple student problems require applying exponent properties: Problem 9 (5^3 × 5^2), Problem 10 (4^5 ÷ 4^3), Problem 11 (reciprocal of 3^-2), the bacteria growth problem using exponent addition, and other test items such as 3^4 × 3^2, 2^6 ÷ 2^3, and simplifying 4^-2. The answer keys convert negative exponents to fractional form (e.g., 4^-2 = 1/16) and demonstrate adding and subtracting exponents and combining bases in scientific notation.
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The Parent Plan explicitly lists "Know and apply the properties of integer exponents to generate equivalent numerical expressions" as a targeted skill. In Task 3 students are given a fuel-cell energy amount written as 7 × 10^2 kWh and are instructed to convert this scientific-notation expression to a whole number (700 kWh). The Parent Plan and wrap-up also state students "perform operations with numbers expressed in scientific notation" and "use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities."
Unit 2

Unit 2: Proportions

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The Skills Review and its answer key include items that ask students to work with integer exponents: converting 5,600,000 to 5.6 × 10^6 and multiplying (3 × 10^7) × (2 × 10^3) with the result given as 6 × 10^6. The review also contains an exponent-simplification problem (answer key shows manipulating powers such as (2^3 × 2^2) ÷ 2^4 = 2^1 = 2), so students practice product/quotient rules for integer exponents and operations with powers of 10.
Unit 3

Unit 3: Expressions

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Students are asked to simplify multiplication of variables and are given the explicit hint x · x = x^2 in Activity 3, prompting them to write repeated factors as powers (e.g., problems and answer keys showing 3x^2y, 3a^2b). Several activities require students to multiply coefficients and combine like terms, producing expressions with exponents (Activity 3, Activity 4, and Activity 6 include x^2, a^2, q^2, etc.). Student tasks ask them to simplify products such as 3a · 3a · b · 2c into 18a^2bc, so students practice converting repeated multiplication into exponent notation in context.
Unit 9

Unit 9: Semester Exams

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Students complete Activity 3 "Exponent Escape Room," where they evaluate expressions that use exponent rules: 5^0, 2^3, 3^4 · 3^2 (product of powers with same base), (2^1)^2 (power of a power), and (4·5)^2 (power of a product). Students also answer a True/False item about 2^1 · 3^1 = 6^1 and must explain why bases must match to combine exponents, and they evaluate combined expressions such as (3^3)^2 + 3^3.
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Students are asked to simplify expressions that require exponent rules: problem 8 asks them to simplify 6.9 × 10^2 (use of a power of 10), problem 9 asks them to simplify 5^1 × 5^2 (product rule for same base), and problem 10 asks them to simplify 8^4 ÷ 8^2 (quotient rule for same base). The answer key provides simplified results for these problems, indicating students are expected to generate equivalent numerical expressions using those properties.