Module 3 lessons 5 & 6 merged

Module 3 Lesson 5 & 6 Merged.notebook

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January 22, 2015

Jan 294:20 PM

Problem Set Lesson 3


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January 22, 2015

Jan 294:21 PM


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January 22, 2015

Jan 294:20 PM

Problem Set Lesson 4


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January 22, 2015

Jan 294:24 PM


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January 22, 2015

Jan 294:24 PM


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January 22, 2015

Aug 265:45 PM

MODULE 3 Rational NumbersTopic A: Understanding Positive and Negative Lesson 5: The Opposite of a Number’s Opposite Student Outcomes§ Students understand that, for instance, the opposite of ‐5 is denoted –(‐5) and is equal to 5. In general, they know that the opposite of the opposite is the original number; e.g., ‐(‐a) = a

§ Students locate and position opposite numbers on a number line.


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January 22, 2015

Nov 172:29 PM

Example 1: The Opposite of an Opposite of a Number

What is the opposite of the opposite of 8? How can we illustrate this number on a number line?

a. What number is 8 units to the right of 0?

b. How can you illustrate locating the opposite of 8 on this number line?

What is the opposite of 8?

c. Use the same process to locate the opposite of ‐8. What is the opposite of ‐8?

d. The opposite of an opposite of a number is .


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January 22, 2015

Nov 172:29 PM

A “” symbol means “the opposite of a number.”

(5) = 5

Since the opposite of 5 is negative 5, and the opposite of negative 5 is positive 5, then ‐(‐5) = 5.

§ What is the opposite of negative six?

§ What is the opposite of the opposite of 10?

§ How would you write the opposite of the opposite of 12?

§ What does a “” symbol mean?

§ What is the opposite of the opposite of a debit of $12?

§ In general, the opposite of the opposite of a number is the original number; e.g., ‐(‐a) = a.


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January 22, 2015

Nov 172:29 PM

Exercise

Complete the table using the cards in your group.


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January 22, 2015

Nov 172:29 PM

1. Write the opposite of the opposite of ‐10 as an equation.

2. In general, the opposite of the opposite of a number is the ___________

3. Provide a real‐world example of this rule. Show your work.


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January 22, 2015

Aug 268:21 PM

Closing

Please take out your exit ticket for Lesson 5, close your binder, and complete the exit ticket. This will be collected.

§ What is the opposite of an opposite of a number? Support your answer with an example.

ú The opposite of an opposite of a number is the original number. The opposite of the opposite of negative 6 is negative 6 because the opposite of ‐6 is 6. The opposite of 6 is ‐6.

§ What is the relationship between the location of a nonzero number on the number line and the location of its opposite on the number line?

ú A number and its opposite are located the same distance from 0 on a number line but on opposite sides of 0.


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January 22, 2015

Jan 227:26 AM

MODULE 3 Rational NumbersTopic A: Understanding Positive and Negative

Lesson 6: Rational Numbers on the Number LineStudent Outcomes§ Students use number lines that extend in both directions and use 0 and 1 to locate integers and rational numbers on the number line. Students know that the sign of a nonzero rational number is positive or negative, depending on whether the number is greater than zero (positive) or less than zero (negative), and use an appropriate scale when graphing rational numbers on the number line.

§ Students know that the opposites of rational numbers are similar to the opposites of integers. Students know that two rational numbers have opposite signs if they are on different sides of zero, and that they have the same sign if they are on the same side of zero on the number line.


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January 22, 2015

Jan 227:26 AM

What is a rational number?

A rational number is a number that can be written as a fraction. (The denominator cannot

be zero.)Integers, Whole Numbers, Some Decimals

Decimals are rational when:~it terminates (ends)

~it repeats with a pattern


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January 22, 2015

Jan 227:28 AM

So what about a number like Pi?Pi does not terminate and

it never repeats or develops a pattern. What do we call it?

Irrational number and are written with a symbol


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January 22, 2015

Jan 227:29 AM

Locate and graph the number and its opposite on a number line.

Example 1: Graphing Rational Numbers


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January 22, 2015

Jan 227:29 AM

Use what you know about the points, and its opposite, to graph both points on the number line below. The

fraction, , is located between which two consecutive integers? Explain your reasoning.

Exercise 1:

On the number line, each segment will have an equal length of . In the fraction ,

the numerator is and the denominator is . The fraction is located

between and .

0

Explanation:


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January 22, 2015

Jan 227:29 AM

Example 2: Rational Numbers and the Real World

The water level of a lake rose 1.25 feet after it rained. Answer the questions below using the diagram below.

a. Write a rational number to represent the situation.

b. What two integers is 1.25 between on a number line?

c. Write the length of each segment on the number line as a decimal and a fraction.

d. What will be the water level after it rained? Graph the point on the number line.

e. After two weeks of rain, the water level of the lake is the opposite of the water level before it rained. What will be the new water level? Graph the point on the number line. Explain how you got your answer.

f. State a rational number that is not an integer whose value is less than 1.25, and describe its location between two consecutive integers on the number line.


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January 22, 2015

Jan 227:30 AM

Closing

Please take out your exit ticket for Lesson 6, close your binder, and complete the exit ticket. This will be collected.

Module 3 lessons 5 & 6 merged

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