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Exploring Rational Numbers-Fractions, Decimals and Integers Simplify each expression . (–9)(–9) 2. 3. 4. Complete the sequence:. LO: I will explore rational numbers using fractions, decimals, & integers. Launch.

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## Launch

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1. Exploring Rational Numbers-Fractions, Decimals and Integers Simplify each expression. (–9)(–9) 2. 3. 4. Complete the sequence: LO: I will explore rational numbers using fractions, decimals, & integers. Launch

2. Look for and describe the pattern of the highlighted numbers. √perfect root = integer integer²= perfect square Explore

3. Complex Fractions Alison wants to make cookies for her son’s class. She is cutting a roll of chocolate cookie dough into pieces that are ¼ inch thick. If the roll is 15 inches long, how many cookies can she make? (HW) Rick runs 9/10 mile in 5 minutes. How many miles does he run in one minute? (HW) The Smiths have a car loan with an interest rate of 6½ %. Write the percent as a fraction in simplest form.

4. Repeating decimal as approximation • First-Use long division to find the repeating decimal that represents • Calculator Exploration • Take the number obtained by including only the first two digits after the decimal point, and multiply that by 13. • Take the number obtained by including only the first four digits after the decimal point, and multiply that by 13. • Take the number obtained by including only the first six digits after the decimal point, and multiply that by 13. • What do you notice about the product of 13 and decimal approximations of 29/13 as more and more digits are included after the decimal point?

5. (HW) Operations on the number line A number line is shown below. The numbers 0 and 1 are marked on the line, as are two other numbers a and b. • (HW) Which of the following numbers is negative? Choose all that apply. Explain your reasoning. • a − 1 a − 2 −b • a + ba − bab+ 1

6. Use 0, ½, or 1 as a benchmark. Think: What is ____ closest to 0? ½ ? 1? What is a benchmark for ____? 0 ½ 1 Lab-Fractions, Decimals, & Percents p28 Explore and record rational numbers to complete the lab, then glue into notebook.

7. A number that is multiplied by itself to form a product is a square root of that product. The radical symbol is used to represent square roots. For nonnegative numbers, the operations of squaring and finding a square root are inverse operations. In other words, for x ≥ 0, Positive real numbers have two square roots. The symbol is used to represent both square roots. A perfect square is a number whose positive square root is a whole number. Skills & Modifications

8. The principal square root of a number is the positive square root and is represented by . A negative square root is represented by – . 4  4 =__ =__ Positive square root of =4 = (–1)4 (–4)(–4) = (–4)2= 16 – Writing Math The small number to the left of the root is the index. In a square root, the index is understood to be 2. In other words, is the same as .

9. 2  3  4  3 5  3 7  6 10  6 5  10 6  10 = = = = BEFORE: Compare Rational Numbers Using a Common Denominator 5 6 7 10 Multiply the denominators to find a common _________________________. 6  10 = Convert into equivalent fractions with a common _______________ = . “Whatever.” OR Compare Rational Numbers Using the Least Common Denominator/Multiple 2 3 4 5 List __________________ of 3 and 5. The LCM is . 3; 3, 6, 9, 12, 15… 5; 5, 10, 15 “Whatever.”

10. NOW: Comparing Rational (Fractional) Numbers Using _______ Products 1 4 _ 2 9 2 9 4 5 1 2 2 5 1. 2. 3. 5. Compare using Cross Products 1x5 __ 2x2 2 3 3 4 Compare using __________________ 2x4 __ 3x3 3 5 4 4 4. –0.80 – OR Convert the fraction into decimal then compare Rational (Fractional) Numbers. 1 5 1 9 1 3 -5 -5 0.1 8. 6. 9. Suppose you and your friend shared two 12 inch pizzas, a mushroom pizza cut into 8 slices and a cheese pizza cut into 6 slices. If you ate 5 slices of the mushroom pizza and you friend ate 3 slices of the cheese pizza, explain who ate more pizza.

11. The percent changes in population from Least to gReatest are < < < • 10. The numbers , –3.4, 6.0, and –2.5 represent the percent changes in • populations for four states. List these numbers in order from least to greatest. 14 4 __ –4 –3 –2 –1 0 1 2 3 4 5 6 12. Justify your reasoning. 2.2 RM & 2.2 SR p73 #42-53even

12. 13. (Class work)