CCSS.Math.Content.HSA-SSE.B.3c
The standard
Use the properties of exponents to transform expressions for exponential functions.
Common Core State Standards for Mathematics · Write expressions in equivalent forms to solve problems
What this standard means
Students need to rewrite exponential expressions so the time unit or growth factor is clearer. They should use exponent rules to move between yearly, monthly, daily, doubled, halved, or other time scales without changing the function.
Mastery looks like explaining why two forms are equivalent and choosing the form that answers the question. Students often get stuck treating exponents like linear factors, such as dividing the base instead of taking a root. They also mix up growth rate and growth factor.
Ways to teach it
- Give pairs cards with expressions like 2(1.08)^t and ask them to rewrite each for monthly growth using exponent rules.
- Ask students to explain which form better answers, What is the monthly growth rate, 1.06^t or (1.06^(1/12))^(12t)?
- Use an exit ticket with one expression, 500(0.7)^t, asking students to rewrite it for half-year intervals.
- Show a savings account ad with annual interest and have students calculate the matching monthly growth factor.
Plan a lesson for CCSS.Math.Content.HSA-SSE.B.3c
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Related standards
- CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- CCSS.Math.Content.HSN-RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- CCSS.Math.Content.HSF-IF.C.8b
Use the properties of exponents to interpret expressions for exponential functions.
- CCSS.Math.Content.HSN-RN.A
Extend the properties of exponents to rational exponents.