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)
• At least one negative exponent
• At least two terms, neither of which has the same base

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 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. Sketch the graph of the function 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