Changes over Equal Intervals

5 min

Narrative

This Warm-up allows students to practice writing equivalent expressions. It prepares students to use this skill as they work with complex expressions arising from linear and exponential functions in this lesson.

Student Task

For each given expression, write an equivalent expression with as few terms as possible.

  1. 7p−3+2(p+1)7p -3+ 2(p +1)
  2. [4(n+1)+10]−4(n+1)[4(n+1)+10] - 4(n+1)
  3. 95⋅92⋅9x9^5 \boldcdot 9^2\boldcdot 9^x
  4. 24n2n\frac {2^{4n}}{2^n}

Sample Response

  1. 9p−19p-1
  2. 10
  3. 97+x9^{7+x}
  4. 23n2^{3n}
Activity Synthesis (Teacher Notes)

Invite students to share how they manipulated the expressions. If not already mentioned in students' explanations, bring up how arithmetic properties of operations (distributive, commutative) and properties of exponents come into play in writing equivalent expressions.

Standards
Building On
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
  • 8.EE.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <em>For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.</em>
  • 8.EE.A.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <span>For example, <span class="math">\(3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27\)</span>.</span>

10 min

20 min