Course 1 Unit 5

Integers and the Coordinate Plane

Name: ___________________

Lesson 5-1: Integers and Graphingintegers – _______________________________________________________________

~ 1 ~

negative integers – _______________________________________________________

_______________________________________________________________________

positive integers – ________________________________________________________

________________________________________________________________________

Example 1:

Write an integer to represent the situation. Explain what zero would mean in each situation.

a 10-yard loss

Answer: Integer: _____

Zero: ___________________________

Example 2:

Write an integer to represent the situation. Explain what zero would mean in each situation.

4 inches of rain above normal

Answer: Integer: _____

Zero: ___________________________

Example 3:

Write an integer to represent the situation. Explain what zero would mean in each situation.

a $48 deposit into a savings account

Answer: Integer: _____

Zero: ___________________________

Got it?

Write an integer and the meaning of zero in each situation.

~ 2 ~

1) a gain of $2 a share

Answer: Integer: _____

Zero: ___________________________

2) 10 degrees below zero

Answer: Integer: _____

Zero: ___________________________

3) a withdrawal of $15 from your bank account

Answer: Integer: _____

Zero: ___________________________

For the next 4 Examples, draw the number line.

Example 4

Graph -7 on the number line.

Example 5

Graph the set of integers {-4, 2, -1} on a number line.

Example 6

Graph the set of integers {0, 2, -3}.

Got it?

For each problem, draw a number line and graph the integer sets. (0 does not have to be the center)

~ 3 ~

4) {-3, 0, -2}

5) {8, -6, -9, 5}

6) {2, -9, 0}

Example 7

Kendall and her dad played golf on four different days. The data set {-1,+1,-3,+2} shows Kendall’s scores in relation to par. Graph the scores. Explain the meaning of zero in this situation.

Zero is __________.

Got it?

7) The data set {+5, 0, -15, +20} shows the number of points Zeke scored on each hand at a card game. Graph the scores. Explain the meaning of zero.

Zero is __________.

Words that represent “Positive Integers” Words that represent “Negative Integers”

Guided Practice:

Write an integer for each situation. Explain the meaning of zero in each situation.

~ 4 ~

1.15-yard gain 2. Loss of 2 hours

Answer: Integer: _____ Answer: Integer: _____

Zero: _______________________ Zero: _______________________

Graph each integer or set of integers on a number line.

3. -2 4. {-1, 1, 0}

5. The data set {+5, 0, -15, +20} shows the number of points Delaney scored on each hand of a card game. Graph the score. Explain the meaning of zero.

Zero means _____________________.

6. Do you think zero is positive, negative or neither?

Lesson 5-2 Multiply Fractions and Whole Numbersabsolute value – __________________________________________________________

________________________________________________________________________

Absolute value is __________________________positive.

Absolute value is represented using two ____________________, like this |−7|.

Opposites - ______________________________________________________________

________________________________________________________________________

Example 1

Find the opposite of -5.

The opposite of -5 is ______.

Example 2

~ 5 ~

Find the opposite of the opposite of 4.

The opposite of the opposite of 4 is ______.

Got it?

1) What is the opposite of 3? ______

2) What is the opposite of the opposite of -2? ______

Example 3

Evaluate |−7|.

-7 is 7 units from 0 on the number line.

|−7| = ______

Example 4

Evaluate |5| + |−6|

|5| = ______

|−6| = ______

______ + ______ = ______

Example 5

Evaluate |−7+5|.

|−7+5| =______

______= ______¿¿

Got it?

3) |14| 4) |−9| + |3| 5) |−8+2|

Example 6

A seagull is flying 25 feet above sea level. Connor is diving 15 feet below sea level. What is the distance between Connor and the seagull?

To find the distance, add the absolute values.

|25| + |−15|

~ 6 ~

|25| =______

|−15| = ______

______ + ______ = ______ feet

Got it?

6) A game show contestant lost 15 points. He answered another questions incorrectly and lost another 15 points. How many total points has he lost?

Guided Practice:

1. What is the opposite of 0? 2. What is the opposite of the opposite of 6?

________ ________

3. |−5|= _________ 4. |20|−|−3|= _________

5. |−16|+|−12|=¿¿ 6. |2|+|−5|=¿¿

7. A game show contestant lost 15 points. He answered another question incorrectly and lost another 15 points. How many total points has he lost?

Lesson 5-3 Compare and Order IntegersComplete notes by drawing in all number lines.

Example 1:

Fill in the with <, >, or = to make a true sentence.

12 -4

~ 7 ~

If you graph 12 and -4 on the number line, which is further to the right? ________

So, _____ is greater than _____.

Got it?

1) -3 -5 2) -5 0 3) 6 -1

Example 2:

Adrian has a score of -4 on the Trueville Trivia Game. Ava’s score is -5. Write an inequality to compare the scores. Explain the meaning of the inequality.

_____ > ______

Since ______ is greater than ______, Adrian has a higher score than Ava.

Got it?

4) The temperature on Tuesday was 2℉ . The temperature on Wednesday was -2℉ . Write an inequality to compare the temperatures. Explain the meaning of the inequality.

Example 3:

Order the set {-9, 6, -3, 0} from least to greatest.

You can use a number line to help you:

So the order is ___________________.

Got it?

5) Order the set {-4, 3, 11, -25} from least to greatest.

Example 4

~ 8 ~

The table shows the lowest elevation for several continents. Order the elevation from least to greatest.

So the order would be ____________________________.

Got it?

6) The daily low temperatures in Kate’s hometown last week were 2℃, -9℃, -18℃, 3℃, 0℃, and -7 ℃. Order the temperatures from least to greatest.

Guided Practice:

Fill in each with a <, > or = to make the statement true.

1. 17 31 2. -6 -10 3. -83 -65

3. Andrew and his father are scuba diving -38 feet and Tackle Box Canyon has an elevation of -83 feet. Write an inequality to compare the depths. Which one has a greater depth?

4. How would “absolute value” change an inequality?

Lesson 5-4 Terminating and Repeating Decimalsrational number – ________________________________________________________

Every rational number can be written as a _________________________________ or

_____________________________________.

~ 9 ~

terminating decimal – _____________________________________________________

Example _____________

repeating decimal – _______________________________________________________

Example: ________________

bar notation – ___________________________________________________________

Example: ___________

Rational Number Repeating Decimal Terminating Decimal

Example 1:

Write 512 as a decimal.

Solve 5 ÷ 12.

~ 10 ~

The remainder will never be _____. So, 512 is equal to ______________…or _________.

Got it?

Write each fraction as a decimal.

1) 16=¿¿ 2)

89=¿¿ 3)

211

=¿¿

Example 2:

Write - 29 as a decimal.

The remainder will never be _____. So, 29 is equal to ______________…or _________.

Example 3:

Write - 2 23 as a decimal.

So - 2 23 = ________

Got it?

Write each fraction as a decimal.

~ 11 ~

4) −14

=¿¿ 5) - 56=¿¿ 6) -2

16=¿¿

Example 4:

Logan made 34 out of 44 free throws this season. To the nearest thousandth, what is his free-throw average?

Using a calculator type in 34 ÷ 44, then enter.

Round to the nearest thousandth.

34 ÷ 44 = ______

Got it?

7) Of nine students surveyed, four said they prefer exercising in the morning rather than in the evening. Express this fraction as a decimal. Use bar notation if necessary.

Guided Practice:

Write each fraction as a decimal. Use bar notation if necessary.

1. 79 = ________ 2.

1015 = ________

3. −2 56 = ________ 4. 1

59 = ________

5. What is the difference between a repeating and terminating decimal?

Lesson 5-5: Compare and Order Rational Numbers

~ 12 ~

Complete notes by drawing in all number lines.

Example 1:

Fill in the with <, >, or = to make a true statement.

-1.2 0.8

Draw a number line to compare.

Since ______ is to the left of ______, ______< ______.

Example 2:

-1.40 -1.25

Graph the decimals on a number line.

Since ______- is below ______, ______< -______.

Example 3:

- 38 -

516

1) Find the LCD

8: 8, 16, 24

16: 16, 32

2) Change the fractions to have the denominator of 16.

- 5

16 (stays the same)

- 38 x

22 = - ¿¿

3) Compare the numerators

¿¿ < ¿¿, so ¿¿ < ¿¿

~ 13 ~

Got it?

1) 3.1 -3.7 2) -4.5 -4.49

3) - 45 -

710 4)

916

1216

Example 4:

-0.51 - 8

15

Rewrite - 8

15 as a decimal.

- 8

15 = _______

_______> _______, so _______> _______

Example 5:

Order the set {-2.46, -22225 , -2

110} from least to greatest.

Write -22225 and -2

110 as decimals to the hundredths place.

-22225 = _______

-21

10 = _______

From least to greatest: _______, _______, _______

Got it?

5) -358 -3.625 6)

37 0.413

7) Order the set {-71320 , -7.78, -7

17100} from greatest to least.

~ 14 ~

Example 6

Mr. Plum’s science class is growing plants under different conditions. The table shows the difference from the average for some students’ plants. Order the difference from least to greatest.

The order would be: _____________________________________

So, ______, ______, ______, ______

Guided Practice:

Fill in each with <, > or = to make the statement true.

1. 9.7 -10.3 2. 58−3

8

3.−6.7−6 710 4.

−56

−0.94

Order these numbers from least to greatest.

5. {−3 13,3.3 ,−3 3

4,3.5} 6. {2.1,−2.1 ,2 1

11,−2}

7. Steve recorded these amounts in his checkbook. -$6.50, $7.00, -$6.75, and $7.75. Order these from least to greatest.

~ 15 ~

Lesson 5-6: The Coordinate Plane

quadrant – ______________________________________________________________

________________________________________________________________________

Example 1:

Identify the ordered pair that names point C.

Then identify the quadrant in which it is located.

Step 1: Start at the _________. Move right on the x-axis.

The coordinate of point C is 1¿¿_.

Step 2: Move up the y-axis. The y-coordinate is 1.

Point C is at (_____, ______) in Quadrant ______.

Example 2:

Identify the point located at (-112 , -1). Then identify the quadrant in which it is located.

Step 1: Start at the origin. Move left on the x-axis _______.

Step 2: Move down the y-axis _______.

Point B is located there in Quadrant _______.

Got it? ~ 16 ~

1) Identify the ordered pair that names point A. Then identify the quadrant in which it is

located.

2) Identify the point located at (1, -2). Then identify the quadrant in which it is located.

Reflections on the Coordinate Plane:

Just like a number line shows opposites….

…a coordinate plane shows opposites through reflections.

Example: (-4, 0) and (4, 0)

Example 3:

Name the ordered pair that is a reflection of (-3, 2) across the x-axis.

To reflect across the x-axis, keep the _______ x-coordinate and the ________________ y-coordinate.

So, (-3, 2) reflected across the x-axis is located at ___________.

Got it? Name the ordered pair that is a reflection of each point across the x-axis.3) (1, -4) 4) (-2, 5) 5) (-3, -1)

Example 4Xander is building a square fence. He places fence posts at the locations indicated on the grid. What is the location of the post that reflects (-4, 4) across the y-axis?

To reflect across the y-axis, keep the ___________

y-coordinate and the _____________ x-coordinate.

~ 17 ~

So, (-4, 4) reflected across the x-axis is ____________.

Got it? 6) Kendall also places a fence post at (-4, -4). What is the location of the post that reflects (-4, -4) over the y-axis?

Guided Practice:Identity the order pair that names each point or the name of each point. Then identify the quadrant in which it is located.

1. T 2.(−1 12,0) 3. (−2 ,2 1

2)

4. Refer to the diagram of the school.

a. What is located at the reflection of (-3, -4) across the y-axis?

What are the coordinates of this location?

b. What is located at the reflection of the science labs across the

x-axis? What are the coordinates of this location?

5. Looking back to the beginning of the lesson, if someone was heading North East, what quadrant was she heading towards?

~ 18 ~

Lesson 5 - 7 Graph on the Coordinate PlaneExample 1:

Graph point M at (-3, 5).

Each line represents 1 unit.

Start at the origin. Move along the x-axis first and then the y-axis.

\Example 2:

Graph point N at (-212 , -3

12).

Start at the origin and move along the x-axis and then the y-axis.

To plot a 12 point, place the point between the lines of the whole numbers.

~ 19 ~

Got it?

Graph and label each point on the coordinate plane.

1) P(-4, 4)

2) Q(0, -4)

3) R(-12 , -2

12)

4) S(4.5, 1)

Example 3:

Graph A(2,-4). Then graph the reflection across the x-axis.

Use the notation A’ to label the reflection of A.

Remember, to reflect across the x-axis, keep the same

x-coordinate and take the opposite of the y-coordinate.

So, A’ is ____________.

~ 20 ~

Example 4:

Graph B(-1.5, 3). Then graph its reflection across the y-axis.

Remember, to reflect across the y-axis, keep the same

y-coordinate and take the opposite of the x-coordinate.

So, B’ is ______________.

Got it?

5) Graph C(-1,-5).

Then graph its reflection across the x-axis.

6) Graph D(2, 312).

Then graph its reflection across the y-axis.

Example 5Mr. Martin is using a coordinate plane to design a logo. He graphs points at (2,4) and (2, -2). He reflects (2, -2) across the y-axis. Then he reflects the new point across the x-axis.

What figure is Mr. Martin using for his new logo?

Mr. Martin is making a ______________.

Got it?

~ 21 ~

7) Ms. Shaull is drawing a map of school. Her room is at (-3, 4) and the gym is (3, 4). The library is the reflection of (3, 4) across the x-axis. This point is then reflected across the y-axis to graph the office. What is the shape of the figure on the map?

Math Vocabulary Vocabulary Word

Book Definition Definition in my Words Picture or example to help me remember!

absolute value the distance between a number and zero on the number line

bar notation a bar placed over the digits that repeat

integer whole numbers: including positive numbers, negative numbers, and zero

negative integers

whole numbers that are less than zero

~ 22 ~

opposites numbers that are the same distance from zero in the opposite direction

positive integers whole numbers that are greater than zero

quadrants the four parts of the coordinate plane

rational numbers

numbers that can be written as fractions

repeating decimal

a decimal with one or more digits that repeat

terminating decimal

a decimal with a definite end

~ 23 ~