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:

- Express the value as an integer to a rational power. (Claim 1)
- Explain why each expression has that value. (Claim 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.

- Sketch the graph of the function using the information given in questions a - d
- 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