Claim 1

Target A (HSN.RN.A): Extend the properties of exponents to rational exponents.

The students below wrote two different expressions, both of which have the same value.

Student A:                                                                  Student B:

                                                   

  1. Express the value as an integer to a rational power. (Claim 1)
  2. Explain why each expression has that value. (Claim 3)
  3. Write your own expression for that value. Your expression should include (Claim 1)


Claim 1

Target C (HSN.Q.A.1): Reason quantitatively and use units to solve problems. (Claims 1, 2, 3, 4)

Sadie is buying a new car. She is trying to decide between two models that she likes. Her parents told her they just went on a trip where they filled their car with gas before they left and drove 378 miles, using ¾ of the tank. The tank holds 12 gallons of gas. Sadie’s cousin, Nanette, has a car that uses 6 liters of gas to go 100 km. If you were Sadie which car would you buy if she is looking for an environmentally friendly car and why?

Adapted from:

https://www.illustrativemathematics.org/content-standards/HSN/Q/A/1/tasks/930, accessed on 6/20/17, is licensed by Illustrative Mathematics under CC BY 4.0


Claim 1

Target K (HSF.IF.A):  Understand the concept of a function and use function notation. (Claims 1,3,4)

You put a yam in the oven. After 45 minutes, you take it out. Let f(t)be the temperature of the yam t minutes after you placed it in the oven.

In (a)–(d), explain the meaning of the statement in everyday language.

  1. f(0)%3D65

  1. f(5)<f(10)

  1. f(40)%3Df(45)%3D160°F

  1. f(45)>f(60)

  1. Sketch the graph of the functionf(t) using the information given in questions a - d
  2. Estimate the temperature of the yam after 20 minutes.

Adapted from:

https://www.illustrativemathematics.org/content-standards/HSF/IF/A/2/tasks/625, accessed on 6/20/17, is licensed by Illustrative Mathematics under CC BY 4.0


Compiled June 19-23 at AERO Summer Institute by Dan Ladbrook, Sonal Novick, and Jon Lind