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3. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING LESSON GOALS  Perform addition, subtraction, multiplication, and division on rational numbers. (Q.2.a)  Perform computations and write numerical expressions with squares and square roots of positive, rational numbers. (Q.2.b)  Perform computations and write numerical expressions with cubes and cube roots of rational numbers. (Q.2.c)  Determine when a numerical expression is undefined. (Q.2.d)  Solve one-step or multi-step arithmetic, real world problems involving the four operations with rational numbers, including those involving scientific notation. (Q.2.e) 3

4. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 4 WORKING WITH THE CONTENT Think & Work Alone Think, Pair, Share Cooperative Learning In Small Groups Reflect On Your Own Learning

5. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 5  Write the definition of a rational number and give several examples in different forms.  Write the definition of an irrational number and give several examples.  What would you say that having “number sense” means?  Why do you think it is important for us to have “number sense” and know how to compute with rational numbers? IN YOUR OWN WORDS…

6. Using the TI-30XS MultiView Calculator Calculating with Irrational Numbers 6

7. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 7 IS IT POSSIBLE…  To ever have a fully accurate answer when calculating with irrational numbers?  With repeating decimals?  With terminating decimals?

8. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING COMPUTING WITH RATIONAL NUMBERS Key Concepts  Factors and Multiples  Properties of Numbers  Order of Operations and Undefined Expression  Exponential Notation  Rules of Exponents  Scientific Notation  Percents as Decimals and Fractions  Percent of a Number  Percent as a Proportion  Discounts  Simple Interest

9. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING FIND THE VALUE OF THE FOLLOWING ARITHMETIC EXPRESSION. 8 × 5 ÷ 10 + 50 ÷ 5 × (3 – 1) 2

10. PRE-INSTITUTE ASSIGNMENT REVIEW Identify Your Top 3 Questions 10

11. COMPUTING WITH SQUARES, SQUARE ROOTS, CUBES, AND CUBE ROOTS What do we need to know? 11

12. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 12 GED ASSESSMENT TARGETS AND KEY CONCEPTS Perform computations and write numerical expressions with squares and square roots of positive, rational numbers. (Q.2.b) Perform computations and write numerical expressions with cubes and cube roots of rational numbers. (Q.2.c) Lesson Key Concepts Square Roots and Cube Roots Approximating Square and Cube Roots Radicals and Rational Exponents

13. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING CONCEPT BACKGROUND What are inverse operations? What are some examples of inverse operations?

14. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING KEY TERMS TO KNOW  Exponent  Square  Square root  Radical  Cube  Cube root

15. USING THE TI-30XS MULTIVIEW CALCULATOR Perfect Squares, Cubes, and their Roots 15

16. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING PONDER THESE QUESTIONS EVEN ROOTS Would a perfect square ever have more than one square root? ODD ROOTS Would a perfect cube ever have more than one cube root? 16

17. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING CALCULATING SQUARE & CUBE ROOTS When would a square or cube root need to be rounded off?

18. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Calculate these cube roots to the nearest hundredth. 3 √7 ≈ ? 3 √32 ≈ ? 3 √63 ≈ ? 3 √120 ≈ ? YOUR TURN

19. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING CALCULATING & SIMPLIFYING RADICALS CALCULATING ROOTS Calculate the square root of 90 to the nearest hundredth. SIMPLIFYING ROOTS Simplify the square root of 90. 19

20. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING WHAT ARE “LIKE” RADICALS? Radicals that have the same index are considered to be like radicals. ⁿ√a and ⁿ√b are like radicals Why?

21. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING PROPERTIES FOR LIKE RADICALS Multiplication Property for Like Radicals ⁿ√a x ⁿ√b = ⁿ√ab Example: √5 x √4 = √20 Division Property for Like Radicals ⁿ√a ÷ ⁿ√b = ⁿ√a÷b, where b≠0 Example: √20 ÷ √2 = √10

22. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING YOUR TURN 3 √2880 3 √60 Simplify and then calculate to the nearest hundredth.

23. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING SIMPLIFY THIS EXPRESSION AND JUSTIFY EACH STEP. 23 (√9 × 3 √729) (√3 × √27)

24. LET’S TRY WHAT WE HAVE LEARNED! 25-Minutes to Complete Assignment 24

25. REFLECTIONS OF LEARNING 25

26. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING REFLECTING ON OUR LEARNING … 1. Thinking about this entire lesson, as well as, the pre-institute assignment, what key concepts do you feel you still need to work on? 2. What key concepts do you feel that you know very well and could explain to your colleagues? 3. What more could you do to study the key concepts that you identified in the first question?

27. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 27 ONE OF MY FAVORITE QUOTES!