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Understanding Integers

N.FL.07.07 Solve problems involving operations with integers.

N.FL.07.08 Add, subtract, multiply, and divide positive and negative rational numbers fluently.*

N.FL.07.09 Estimate results of computations with rational numbers.

Unwrapping the GLCE’s:

Concepts (what students need to know):

• Absolute value

• Rules for adding, subtracting, multiplying and dividing integers

• Multiplicative inverse/reciprocal

Skills (what students need to be able to do):

• Fluently add, subtract, multiply and divide positive and negative rational numbers

• Solve contextual problems with integers

Prior Knowledge:

• Students should have mastered basic facts in all operations.

• Students should understand order of operations.

Big Ideas:

1. Absolute value is the distance a number is from zero on number line.

2. The sign of an integer determines how rules of operations are applied to a given situation.

3. Addition & subtraction, and multiplication & division are opposites of each other.

Essential Questions:

1. What is absolute value?

2. What is an integer?

3. How does the sign of a number impact the four operations?

4. How can integers be used to solve real world problems?

Pre-Assessment Questions:

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PreAssessment Answers:

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Answer: B

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Answer: A

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Answer: A

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Answer: B

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Answer: A

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Answer: C

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Answer: C

INSTRUCTIONAL ACTIVITIES & LESSON PLANS:

Introductory Activity:

Human Number Line: Give each student an index card with an integer on it. These should range from -100 to 100, randomly. Students should arrange themselves in order from least to greatest. This activity should be done without talking.

Integer/Absolute Value PowerPoint:

See attached slides for example or use one at:



Students can take notes or just view as teacher explains.

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Intro examples:

Example 1 Write an integer for the situation.

a 10-yard loss

The integer is –10.

Example 2 Write an integer for the situation.

5( above normal

The integer is +5.

Examples Compare Two Integers

Replace each with , or = to make a true sentence. Use the integers graphed on the number line below.

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Example 3 5 –3

5 is greater than –3, since it lies to the right of –3. Write 5 > –3.

Example 4 –6 –2

–6 is less than –2, since it lies to the left of –2. Write –6 < –2.

Example 5 Order Integers

WEATHER The table below shows the record low temperatures for selected states. Order these temperatures from least to greatest.

|State |AZ |

= 7 Simplify.

The average low temperature for the week was 7(F.

Independent practice:

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For a review of multiplying and dividing integers, students can follow the steps online at:



Post Assessment Items:

For each of the following, write an expression to describe the situation, then solve:

1.A team gains 8 yards on one play, then loses 5 yards on the next.

2. A scuba diver dives 125 feet. Later, she rises 46 feet.

3.You get on an elevator in the basement of a building, which is one floor below ground level. The elevator goes up 7 floors.

4.The temperature outside is -2° F. The temperature drops by 9°.

5.On Mercury, the temperatures range from 805° F during the day to -275° at night. Find the drop in temperature from day to night.

6.For every 1 kilometer increase in altitude, the temperature drops 7°C. Find the temperature change for a 5 kilometer altitude increase.

7.Draw a number line. Graph 2 numbers on your number line which have the same absolute value.

8. Give an example of a number that is not an integer.

Post assessment key:

1.A team gains 8 yards on one play, then loses 5 yards on the next. 8 + -5 = 3 The team has a net gain of 3 yards.

2.A scuba diver dives 125 feet. Later, she rises 46 feet. -125 + 46 = -79 The diver is now 79 feet below the surface.

3.You get on an elevator in the basement of a building, which is one floor below ground level. The elevator goes up 7 floors. -1 + 7 = 6 You are now on the 6th floor.

4.The temperature outside is -2° F. The temperature drops by 9°. -2 + – 9 = -11 The temperature drops 11 degrees.

5.On Mercury, the temperatures range from 805° F during the day to -275° at night. Find the drop in temperature from day to night. 805 - -275 = 1080 The temperature dropped 1080°.

6.For every 1 kilometer increase in altitude, the temperature drops 7°C. Find the temperature change for a 5 kilometer altitude increase. -7 * 5 = -35° or a drop of 35°

7.Most people lose 100-200 hairs per day. If you were to lose 150 hairs per day for 10 days, what would be the change in the numbers of hairs you have? -150 * 10 = -1500 hairs or 1500 hairs lost

8.Draw a number line. Graph 2 numbers on your number line which have the same absolute value.

-2 0 2

9. Give an example of a number that is not an integer. ½, .75

RESOURCES:









United Streaming videos:

The Zany World of Basic Math, Module 1: Integers and Addition

The Zany World of Basic Math, Module 2: Subtracting Integers

The Zany World of Basic Math, Module 3: Multiplying Integers

The Zany World of Basic Math, Module 4: Dividing Integers

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