1. How do you write expressions with exponents to help solve problems? For example, would you rather be paid $4 which doubles daily for four days or accept $50 as total payment for a job?

2. In this lesson you will learn how to write a numerical expression using exponents by interpreting a specific problem or situation.

3. Let’s Review Numerical expressions are mathematical phrases containing numbers and operations. 13 – (2 x 4)

4. When finding the value of an expression, we need to follow the Order of Operations. 1st P Parentheses 2 nd E Exponents 3 rd M Multiply or D Divide from left to right 4 th A Add or S Subtract from left to right

5. Let’s Review Exponents tell us how many times to use the base as a factor. 5 2 = 5 x 5 = 25

6. A Common Mistake Not reading the problem carefully or misinterpreting the situation. Not looking at the reasonableness of an answer.

7. Let’s Review Core Lesson Would you rather be paid $4 which doubles daily for four days or accept $50 as total payment for a job? What do we know? What do we want to know? Paid $4 that doubles everyday for 4 days or paid $50 total Which pays more?

8. Let’s Review Core Lesson Let’s take a look at our earnings for each day. Day 1Day 2Day 3Day 4 $4$4 x 2$4 x 2 x 2$4 x 2 x 2 x 2

9. Let’s Review Core Lesson The numerical expression which would give us the total would be $4 + ($4 x 2) + ($4 x 2 2 ) + ($4 x 2 3 ) $4 + ($4 x 2) + ($4 x 2 x 2) + ($4 x 2 x 2 x 2)

10. Let’s Review Core Lesson $4 + ($4 x 2) + ($4 x 2 2 ) + ($4 x 2 3 ) $4 + ($4 x 2) + $4 + + + $16 $8 $32 $20 + $40 $60 ($4 x 4)+ ($4 x 8)

11. Let’s Review Core Lesson So, which is more profitable? $50 or $4 which doubles each day for 4 days?

12. In this lesson you have learned how to write a numerical expression using exponents by interpreting a specific problem.

13. Let’s Review Guided Practice If you are to be paid $4 which doubles daily each day, how much money would you make on day 10? (Hint: Take a look at the pattern.) Day Expression $ 1 4 4 2 4 2 8 3 4 2 2 16 4 4 2 3 32 5 6 7 8 9 10

14. Let’s Review Extension Activities A population of 50 rabbits triples every two months. Write a numerical expression using exponents that shows what the population of rabbits will be in 6 months.

15. Let’s Review Extension Activities A population of 50 rabbits triples every two months. Write a numerical expression that could be used to show how many months it would take for there to be over 4000 rabbits.

16. Let’s Review Quick Quiz A group of 20 bacteria triples in size everyday. What numerical expression shows the number of bacteria on day three? What numerical expression shows the total number of bacteria at the end of day three?