Write true or false. If the example is true, write a conclusion that shows the relationship of the

sets of numbers.

1.

2.

3.

4. Real Number System

5.

6.

c

Name_____________________ Write a Conclusion Activity 40

Irrational

Numbers

Locate the lists of rational and irrational numbers on the number lines.

1. Plot 31 and 2π on the number line. Which is less? Explain.

2. Plot π and 15 on the number line. Which is greater? Explain.

3. Plot 99 on the number line.

4. Plot 71 on the number line.

5. Plot 201 and 14.431… on the number line.

c

Name_____________________ Approximating Irrational Numbers Activity 48

–3 7

–1 1

9 10

–1

14 15

Use the TEST MENU on your calculator to compare the numbers. Write true or false for each.

1. 10

9

5

4−> __________ 2.

2

1

4

1−<− __________

3. 4

1

2

1> __________ 4.

4

1

8

3−<− __________

5. 85.0 7

6−>− __________ 6.

7

4

5

3

2

1<+ __________

7. 100

1

8

1−>− __________ 8. 100 2.2 −>− __________

9. 16

13

8

1

4

3>+ __________ 10.

32

2

16

1= __________

The table shows the average high and low temperatures during January in degrees Celsius for

several cities in Canada.

Canadian Average High and Low Temperatures in January

City High Low

Yellowknife –22.7 –30.9

Québec –7.9 –17.6

Montréal –5.7 –14.7

Ottawa –6.1 –15.3

Toronto –2.1 –10.5

Winnipeg –12.7 –22.8

Vancouver 6.1 0.7

http://www.statcan.gc.ca

Use the table to answer the questions.

11. Which city had the lowest average temperature? _______________________

12. Order the average low temperatures from lowest to highest.

___________________________________________________________________________

13. Order the average high temperature from highest to lowest.

___________________________________________________________________________

14. Which city had the greatest range between the highest and lowest temperature?

City:___________________ What was the range? Range:__________________

c

Name_____________________ Compare and Order Rational Numbers Activity 69

90. Use the Slope Formula to Find the Slope

Group: Whole Class/Pairs

Materials: Use the Slope Formula to Find the Slope cards, coordinate planes, TI-Graphing Calculator, paper and

pencil, ruler

Issue a TI-Graphing Calculator, and a set of the Use the Slope Formula to Find the Slope cards, a ruler, and 12 cut

out coordinate planes to each pair. Instruct pairs to place the cards face down in a stack. Student A displays a

card and finds the slope of the line through the pairs of points using the slope formula12

12

x x

y y

−

−

. Student B plots

the points on a blank coordinate plane. Student B uses a ruler to draw a line through the points touching the

edges of the graph on each side. Student B then draws a slope triangle using the slope ratio run

riseto find the

slope. Pairs compare the slopes found using the slope formula and the slope ratio. Have students make

observations about the slopes and the different methods used. Continue in the same manner with students

alternating roles of using the slope formula and plotting points on the line using the rise over run ratio.

Card 1

(–1, 3), (4, –1)

Card 2

(–2, 1), (6, 3)

Card 3

(–4, 2), (3, 1)

Card 4

(1, 4), (3, 4)

Card 5

(–2, 0), (2, –1)

Card 6

(2, 3), (4, 6)

Card 7

(2, 4), (2, 0)

Card 8

(5, –3), (1, –7)

Card 9

(1, 3), (–6, –2)

Card 10

(3, 1), (8, 1)

Card 11

(–2, 2), (–3, –6)

Card 12

(–6, 1), (3, –3)

Activity 90

Use the Slope Formula to Find the Slope Cards

Activity 90

Use the Slope Formula to Find the Slope Cards

Make a Graph

Write an Equation

Complete a Table

Activity 109

Situations and Solutions Cards

109. Situations and Solutions

Group: Whole Class/ Three

Materials: TI-Graphing Calculator, Situations and Solutions cards, paper and pencils

Issue the TI-Graphing Calculator to each student. Display a Situations and Solutions card one at a time, on the

overhead projector or document camera. Pause to give students time to represent the displayed situation.

Issue a graph card, an equation card, and a table card to each group. Explain that these cards are label cards

which are to be passed to the right to a different group member after each situation is displayed. All group

members will complete 2 tables, 2 graphs, and write 2 equations. Distribute to each group, 6 small index cards

to write the equations on, 6 cut out graphs to show a graph of a line that represents the situation, and 6 table

cut outs to generate tables of values that are related to each situation. Begin by having each group member

take a label card. Then group members select the appropriate representation that corresponds with h/her

card. (table cut out, index card, or graph cut out.) The teacher displays a card. Group members write the

appropriate representation for the displayed card. After ample time, display another card. Group members

pass label cards to the right. Continue until all problems have been completed. Instruct students to write 1

question that can be answered from each problem. Some questions that can be asked include:

� How much will Clarence earn for working 3 hours? ($48.50)

� What is the cost of a large pizza with 3 toppings at Mia’s Pizza? ($20.25)

� If the shoes Krystina is saving for cost $75, how many weeks will it take her to save this amount? (10 weeks)

� What is the charge for a newspaper ad with 145 words? ($64)

� If Leonard earned $172, how many hours did he work? (16 hours)

� What is the temperature in Dallas after the 6th day? (33⁰F)

Have students share their questions with the class.

Activity 109

Situations and Solutions Cards

109. Proportional and Non-Proportional Pairs

Group: Whole Class/Four

Materials: TI-Graphing Calculator, Proportional and Non-Proportional Pairs cards, paper and pencil

Issue the Proportional and Non-Proportional Pairs cards to each group and a TI-Graphing Calculator to each

student. Header cards are placed side-by-side. Tell students that they will determine which set of ordered pairs

and tables represent proportional and non-proportional relationships. Remind students that proportionality can

be tested in tables and in ordered pairs by using the ratiox

y. Point out that students can check for

proportionality on the calculator by inputting the ratio as a fraction by pressing ALPHA Y=, #1 ENTER ( x

y ). The

ratio can also be input by pressing y ÷ x ENTER. Instruct each group member to write a ratio from the table to

test for proportionality. The student that displays the card chooses the first pair of values in the table. The group

members to the right of this student select pairs from the table ordered pairs in sequence. For example, a

student displays a card and writes a ratio for the first pair of values in the table. The student to the right of this

student, chooses the second pair of values in the table, the next student chooses the third pair of values and so

on. After students complete the task, have them write a statement about their observations. Write the following

questions on the board:

� How do you test for proportionality in tables and ordered pairs?

� Which tables or ordered pairs could you check for proportionality by just looking at the values? Why?

(If a table or ordered pairs had the values (0, 0), then the relationship is proportional.)

Invite volunteers to read statements aloud. Discuss which tables and ordered pairs students pairs placed

underneath the header cards.

1

(–2, –1.6), (2, 1.6), (4, 3.2), (5, 4)

2

x y

10 139

83 6

0 –1

–2 –29

3

x –5 0.2 1 2

y –33 1.32 6.6 13.2

4

x y

–2 4

–1 2

3 –6

4 –8

5

(–5, –0.75),(–2, –0.3), (6, 0.9), (8, 1.2)

6

x 5 10 12 15

y 29 62 75.2 95

7

x y

2 28

4 56

6 84

8 112

8

x 5 8 10 12

y 63 99 123 147

Activity 130

Proportional and Non- Proportional Pairs Cards

Proportional Non-Proportional

9

x y

–2 4

–1 2

3 –6

4 –8

10

(–2, –27), (–1, –14), (0, 12), (2, 25)

11

x y

–2 0.4

1 5.8

3 9.4

5 13

12

x 6 8 10 14

y –1.1 –0.8 –0.5 0.1

x y

–6 9

1 –1.5

8 –12

12 –18

13

14

x 29.5 31 36.6 37

y 232 248 292.8 296

15

(–2, –26), (–1, –13), (0, 0), (2, 26)

16

x y

0 –1

1 1.5

2 4

3 6.5

Activity 130

Proportional and Non- Proportional Pairs Cards

Use the STAT key on the calculator to find the slope and the y-intercept. Then write equations

in the form y = mx + b.

1.

Equation:__________________________

(–2, –7) and (3, 8)

2.

Equation:__________________________

(0, 3) and (2, –5)

3.

Equation:__________________________

x –2 –1 1 2

y –11.5 –6.5 3.5 8.5

4.

Equation:__________________________

x y

–1 –1

2 –10

1 –7

5.

Equation:__________________________

x y

–2 11

–3 9

–4 7

6.

Equation:__________________________

(3, 5) and (6, 6)

7.

Equation:__________________________

(–5, –4) and (15, 0)

8.

Equation:__________________________

x –4 –2 4 8

y 2 2.5 4 5

c

Name_____________________ Writing Equations in the Form y = mx + b on the Calculator Activity 152

Find the area of the shaded squares.

1.

_______________ m2

2.

_______________ in.2

3.

_______________ cm2

4.

_______________ cm2

5.

_______________ in.2

6.

_______________ ft2

c

Name_____________________ Find the Area of the Shaded Squares Activity 167

225 m2

12 m

6 in.

8 in.

25 cm2

16 cm2

5 in.

144 in.2

15 ft

625 ft2

100 cm2

26 cm

Convert the relations to the other representations.

1. Is the relation a function? ________Explain.

Ordered pairs: ____________________________________________

x y

2. Is the relation a function? ________Explain.

Ordered pairs: ____________________________________________

x y

c

Name_____________________ Convert the Relations Activity 139

–1

0

1

2

5

10

7

Preserves Congruence

Does Not Preserve Congruence

1

(x, y) → (x + 3 , y – 6)

2

(x, y) → (–y, –x)

3

(x, y) → (x, –y)

4

(x, y) → (x – 5, y – 5)

5

(x, y) → (x + 1, y – 4)

6

(x, y) → (1.5x, 1.5y)

7

(x, y) → (x + 1, y – 2)

8

(x, y) → (y, –x)

Activity 250

Which Examples Preserve Congruence Cards

9

(x, y) → (0.2x, 0.2y)

10

(x, y) → (y, x)

11

(x, y) → (�

�x, �

�y)

12

(x, y) → (x + 2 , y – 6)

13

(x, y) → (�

�x, �

�y)

14

(x, y) → (x – 3 , y)

15

(x, y) → (3x, 3y)

16

(x, y) → (x – 4 , y + 5)

17

(x, y) → (x – 3, –y)

18

(x, y) → (�

�x, �

�y)

Activity 250

Which Examples Preserve Congruence Cards

176. Is it Right?

Group: Three

Materials: Is it Right cards, TI-Graphing Calculator, paper and pencil

Issue Is it Right cards and the TI-Graphing Calculator to each student. Issue the 3 Calculator Option cards to

each group. The converse of the Pythagorean Theorem states that if a, b, and c, are the lengths of the sides of

a triangle, and a2 + b2 = c2, then the triangle is a right triangle. There are many ways students can test to see if

the three sides form a right triangle on the calculator. Familiarize students with the following options:

Given that a = 11.9, b = 12, and c = 16.9. Let the two shorter sides be a and b. Let the longest side be c.

Option 1 TEST MENU

On the HOME SCREEN of the calculator. Input the values for a, b, and c as follows:

11.92 + 122, 2ND MATH #1, 16.92 ENTER. If the result is 1, the statement is true and this is a right triangle. If

the result is 0, the statement is false, and this is not a right triangle.

Option 2 SQUARE ROOT KEY

Press 2ND x2. Input 11.92 + 122 → ENTER. 22 12 + 11.9 If the result is 16.9, the statement is true and this is

a right triangle. If the result is not 16.9, this is not a right triangle.

Option 2 SQUARES on HOME SCREEN

On the HOME SCREEN input 11.92 + 122, ENTER, (find the square root of the result) press 2ND x2, input

285.61, ENTER. 61.285

Begin by having each student selecting a calculator option card. The card assigned to a student identifies the

calculator option they will use to complete the task. Students exchange cards on each turn. Make sure

students order the numbers on the cards from least to greatest to distinguish between sides a, b, and c. Side

lengths cards are placed face down in a stack. Group members take turns displaying a card. When a card is

displayed, group members used the assigned methods to state whether or not the three given numbers could

represent the lengths of the sides of a right triangle. After a decision is made, have students write __, __, and

__ form a right triangle or __, __, and __ do not form a right triangle. Students proceed in the same manner,

exchanging option cards each time a new card is displayed. Have students share answers in a class discussion.

Follow the instructions on your index card and find the Mean Absolute Deviation of the data.

1. The table shows the total rushing yards from 10 teams in the National Football League.

Teams 1 2 3 4 5 6 7 8 9 10

Rushing Yards 1,052 1,076 1,452 1,030 1,449 1,020 1,150 1,075 982 1,040

Absolute Deviation

Mean: ________________________________ MAD: ________________________________

Interpret the MAD in words. _____________________________________________________

2. The table shows the number of stories in the tallest buildings in the United States.

Buildings 1 2 3 4 5 6 7 8

Number of Stories 110 102 55 75 57 76 72 60

Absolute Deviation

Mean: ________________________________ MAD: ________________________________

Interpret the MAD in words. _____________________________________________________

3. The table shows the fuel economy in miles per gallon of 8 top selling Ford car models.

Cars 1 2 3 4 5 6 7 8

Fuel Economy (mi/gal) 28 25 32 42 37 18 21 36

Absolute Deviation

Mean: ________________________________ MAD: ________________________________

Interpret the MAD in words. _______________________________

Name_____________________ Find the Mean Absolute Deviation on the Calculator Activity 271