Launch

LO: I will explore rational numbersusing fractions, decimals, & integers.

Exploring Rational Numbers-Fractions, Decimals and IntegersSimplify each expression.1. (–9)(–9) 2. 3. 4. Complete the sequence:

Explore

integer = perfect square²

√perfect root = integer Look for and describe the pattern of the highlighted numbers.

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.

Repeating decimal as approximationFirst-Use long division to find the repeating decimal that represents Calculator Exploration1. Take the number obtained by including only the first two digits after the decimal point, and multiply that by 13.2. Take the number obtained by including only the first four digits after the decimal point, and multiply that by 13.3. 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?

(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 + b a − b ab + 1

Use 0, ½, or 1 as a benchmark.

0 ½ 1

Lab-Fractions, Decimals, & Percents p28Explore and record rational numbers to complete the lab, then glue into notebook.

Think: What is ____ closest to 0? ½ ? 1? What is a benchmark for ____?

Skills & Modifications

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.

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 = __ = __ = 4 Positive squareroot of(–4)(–4) = (–4)2 = 16 = (–1)4–

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 .

Writing Math

BEFORE: Compare Rational Numbers Using a Common DenominatorMultiply the denominators to find a common _________________________.

5 6

7 10

Convert into equivalent fractions with a common _______________ = .

6 10 =

5 10 6 10

= 7 6 10 6

=

OR Compare Rational Numbers Using the Least Common Denominator/MultipleList __________________ of 3 and 5. The LCM is .

2 3

4 5

3; 3, 6, 9, 12, 15… 5; 5, 10, 15

“Whatever.”

“Whatever.”

2 3

= 4 3 5 3

=

NOW: Comparing Rational (Fractional) Numbers Using _______ Products

Compare using Cross Products 1x5 __ 2x21 2

2 5

2 3

3 4

Compare using __________________ 2x4 __ 3x3

2 9

-5 -5 1 5

2 9 4 4 3

5

OR Convert the fraction into decimal then compare Rational (Fractional) Numbers.

0.1 1 9

4. –0.80 – 4 5 _

1 4

1 3

8. 6.

1.

2.

3.

5.

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.

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 6The percent changes in population from Least to gReatest are

< < <

Justify your reasoning.12.

2.2 RM & 2.2 SR p73 #42-53even

13. (Class work)