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–5 –4 –3 –2 –1 0 1 2 3 4 5. What do you notice about the mid-point of opposites? . Find the distance from zero. 2. |3| = . 1. |–3| = . –3 is 3 units from 0, so |–3| = . 3 is 3 units from 0, so | 3| = .

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What do you notice about the mid-point of opposites?

Find the distance from zero.

2. |3| =

1. |–3| =

–3 is 3 units from 0, so |–3| = .3 is 3 units from 0, so | 3| = .

Therefore 3 has exactly two absolute values: _____ and _____

How would you represent the combining of opposites?

Use the number line to model what happens when you combine an integer to its opposite.

Note: Two numbers that have the sum of zero are _____________________ inverses.

NS.7.a

Comparing and Ordering Integers

Integers & Absolute Value

integer, opposite, absolute value, perfect square roots = integers

Absolute value of a number is:

The distance, how many units, from _________.

“The absolute value of –4” is written as | |.

Opposites (4 and ___) have the same absolute value, 4.

An integer’s |absolute value| is its ______________ from 0 on a number line.

Distances on the Number Line

On the number line above, the numbers a and b are the same distance from 0. What is a + b ? Explain how you know.

When might evaluating absolute values be of use as a consumer?

Activity: Absolute Value War

Card game similar to the playing card game War. Only difference is that the red playing cards are │positive integers│, black cards are │negative integers│.

• Absolute Value War Rules
• Deal out cards evenly.
• All players simultaneously turn over a card and the greatest absolute value wins all the cards tuned up.
• If two or more players tie for highest there is a war - everyone plays their next card face-down and then turns up a third card. This continues until one of the face-up cards is greater than all the others, and then that player wins all the cards in a war.
• Note that all players take part in a war, not only the ones who had the highest cards.
• The game goes on until when the teacher calls time.
• The winner is the player with the greatest absolute value sum.

If you were to play this game again, what rule modifications would you make?

Now:

Order of Operations = GEMDAS:

1st Grouping Symbols (Parentheses), {[brackets]}, /fraction bars̶ ̶ ,

√ radical square root sign │absolute value sign │

2ndExponents

3rdMultiply and Divide from left to right ---.

4thAdd and Subtract from left to right ---.

Good Education Makes Doing Algebra Simple

Comparing Freezing Points

1.

Ocean water freezes at about −1.9∘C.

Fresh water freezes at 0∘C.

Antifreeze, a liquid used in the radiators of cars, freezes at −37∘C.

2.

Imagine that the temperature has dropped to the freezing point for ocean water. How many degrees more must the temperature drop for the antifreeze to turn solid? Explain.

Evaluating Absolute Value Expressions

Tip: 1st Evaluate the problems inside the Grouping

sign⃒absolute values bars⃒. THEN remove the bars and simplify.

3. |17 – 6|

4. |5 + 1| + |8 – 6|

5. |–8| + |–5|

Negative sign outside of the absolute value bar? Yes! Evaluate using GEMDAS, THEN simplify.

6. -|17 – 6|

7. -|5 + 1| + |8 – 6|

8. -|–8| + |–5|

Integers and absolute value real-world applications.

9. Initial sales price of \$85 Wholesale product cost of \$53

profit = |\$85 – \$53|

The total net profit earned would be _________.

10. On Monday the average temperature was -10 ̊ F. On Tuesday it was -15 ̊ F. On Wednesday it was -13 ̊ F. Thursday it was -1 ̊ F. Write the temperatures as an inequality of coldest to warmest.

11. Use absolute value to calculate the temperature range.

|warmest | + | coldest| = temperature ____________

12. Amelia has been flying her airplane all day fighting wildfires in Death Valley. She fuels up near Badwater, which is 282 feet below sea level, and is working to contain a brush fire on top of Telescope Peak that has an elevation of 11,049 feet. Use integers to represent the elevation, to the nearest hundred foot, of each Death Valley location.

13. Use absolute value to calculate the change of elevation between Badwater and Telescope Peak.

HW 1.3 RMp3 & p16 # 16-18 even, 22, 26