Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Clare has a summer job. She wants to save money to spend on the family vacation at the end of summer. She is going to save \$5 per week for each of the 10 weeks she is working.
Tyler also has a summer job, and he, too, would like to save money to spend on a family vacation. His aunt gives him \$1 to start saving, and Tyler decides to double the amount he saves each week.
Complete the table showing how much money each of them will have saved at the end of each week for the 10 weeks.
week
0
1
2
3
4
5
6
7
8
9
10
Clare
0
5
10
15
Tyler
1
2
4
8
1.3
Activity
Standards Alignment
Building On
Addressing
6.EE.1
Write and evaluate numerical expressions involving whole-number exponents.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Use the structure of an expression to identify ways to rewrite it. For example, see x4 — y4 as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t 1.01212t to reveal the approximate equivalent monhly interest rate if the annual rate is 15%.
