Activity One: Who S the Farthest from Zero?

73 - Integers

Number, operation, and quantitative reasoning. The student will Lesson develop understanding of integers and represent and compare quantities Focus using integers. TI-73 Explorer™ graphing calculator TI-Navigator™ Materials Numline Application Student Activity sheets Integer Activity Center settings This lesson is designed for whole group, partners and individual Grouping groupings. Prior knowledge of whole numbers. In lower grades, students may have connected negative integers, in appropriate ways, to informal knowledge Prerequisite derived from everyday experiences, such as, below-zero winter Knowledge temperatures or lost yards on football plays. They should extend these and Skills initial understandings of integers. Positive and negative integers should be seen as useful for noting relative changes or values. Students will be able to develop number sense for negative rational numbers. Connect the model, number word, and number using a variety Overview of of representations, including the number line. Learn to compare and order the lesson integers, encourage students to use a number line before ordering them and be able to use integers to represent real-life situations. Suggested Activity 1: 50-55 minutes Time Activity 2:

Activity One: Who’s the farthest from zero? Part I (A) 1. Distribute Student Activity I sheet.

2. Open TI- Navigator and Start Class

3. Have students log into NavNet

4. Introduce this activity with the focus on opposites. Start with concepts such as; save (spend), above (below), height (depth). Discuss how negative numbers are like owing money. Quick Poll (open response) “Which is better owing $6 or $5?” “Withdrawal $116 from an ATM machine” “opposite of 15” “opposite of -11”

TI MathForward™ 1 © 2010 Texas Instruments Incorporated 5. Then have students continue to explore words that are used to identify positive and negative numbers in the real world. Quick Poll (open response) Explore the following the negative and positive values of 8: Identify the integer used which will represent each situation. a temperature drop of 8 degrees Celsius (-8) a depth of 8 m (-8) a growth of 8 in (+8) a time 8 years ago (-8) a gain of 8 yards (+8)

Part I (B) 6. Students will then use to explore integers on a number line. Have the students set the following values to Ω and æ. List A: Ω -8, -3, -1, 0, 2, 7 æ 0, 0, 0, 0, 0, 0 Tech Tip Dimensions must match or will get an error message. ERR: DIM MISMATCH

7. Press  select 1:  and press  Turn select on by highlighting on and press  Press  and select scatter plot  press  X list: L1 (1) Y list: L2(2) Mark: (select the large point)

8. Press  and values accordingly. Xmin= -12 Xmax= 12 Xscl=1 Ymin=-0.2 Ymax=0.2 Yscl=0.1

Tech Tip: Use the Screen Shot option on Navigator to view how students are setting up their Lists, Stat Plot, Window settings, etc.

10. Have students then press  to view the of values. This will show the students other values and how their values compare.

Tech Tip: You may want students to () to adjust the scale of the table to .5 or another value for students to visualize and compare rational values as negatives. *Students may want to turn the calculator on its side to view the table. This creates a number line with negatives on the left and positives on the right.

11. Repeat this activity with 2 more sets of values and have the students record them on the student activity sheet. List B: Ω -10, 5, -3, 0, -2, 6 æ 0, 0, 0, 0, 0, 0

List C: Ω -3, -2, -1, 0, 2, 3 æ 0, 0, 0, 0, 0, 0

Quick Poll What do you think would happen if x-values were all zero and the y-values were integers? How would you plot a point in the center “the origin?”

Part I (A) Quick Poll Questions: Exploring the meaning of positive and negative values: 1. “Which is better owing $6 or $5?” $5 2. “Withdrawal $116 from an ATM machine” -166 3. “opposite of 15” -15 4. “opposite of -11” 11 Explore the following the negative and positive values of 8: 5. a temperature drop of 8 degrees Celsius (-8) 6. a depth of 8 m (-8) 7. a growth of 8 in (+8) 8. a time 8 years ago (-8) 9. a gain of 8 yards (+8) 10. “Which is greater a negative or a positive value?” positive value

Part I (B) Exploring integers on a number line. 1. Press to explore integers on a number line. Set the following values to Ω and æ. Ω -8, -3, -1, 0, 2, 7 æ 0, 0, 0, 0, 0, 0

2. Press  select  1 and press 1 Turn select on by highlighting on and press  Press  and select scatter plot  press  X list: L1 Y list: L2 Mark: (select the large point)

3. Press  and values accordingly. Xmin= -12 Xmax= 12 Xscl=1 Ymin=-0.2 Ymax=0.2 Yscl=0.1 TI MathForward™ 4 © 2010 Texas Instruments Incorporated 4. Press  then press and using the and  to look at the values. Then record the integers on numberlines below.

5. Press  to view the of values. This will show you other integer values and how your graphed values compare.

List A: Ω X= ______

æ Y= ______

List B: Ω X= ______

æ Y= ______

List C: Ω X= ______

æ Y= ______

6. What do you think would happen if x-values were all zero and the y-values were integers? Answer: The students should discover that the values would be on the vertical axis. **possibly discuss what the y-axis may represent in the real world (thermometer)

7. How would you plot a point in the center “the origin?” Answer: (0,0) the origin

8. Explain why 0 > -81 is incorrect? Answer: -81 is further on the left of the number line. Values more left are less.

TI MathForward™ 5 © 2010 Texas Instruments Incorporated 9. How do you tell which of 2 negative integers is the greatest value? Answer: The value more on the right of a number line is the integer with the greatest value.

Part I: Write the corresponding integer to the following real world scenarios.

1. 120 feet below sea level -120 9. 24° above zero 24 4 units to the left of -10 on the 2. A gain of 9 yards +9 10. -14 number line. 3. A withdrawal of $35 -35 11. A deposit of $65 +65 One hundred eleven feet above sea 4. A growth of 4 inches +4 12. +111 level 5. A pay cut of $3000 -3000 13. $25 late fee -25 6. 9° below zero -9 14. A gain of 9 points +9 7. A loss of $150 -150 15. 9 units to the right of -7 +2 8. Stock Market went up 141 pts today +141 16. A loss of $14,500 on an investment -14,500

Place in order starting with the least or smallest integer. Then graph the values on the number line.

17. -6, -8, 10 -8, -6, 10

18. 0, -3, -5, 2 -5, -3, 0, 2

19. 4, -3, 7, 3, -10 -10, -3, 3, 4, 7

Place in the following integers in order from least to greatest.

20. -25, 25, 21, 29, 16, -16, -26, -36 -36, -26, -25, -16, 16, 21, 25, 29

21. -42, 20, -60, -50, 4, 40, 49, 47, 27, -23, -43 -60, -50, -43, -42, -23, 4, 20, 27, 40, 47, 49

Use the appropriate inequality sign (< or >) to identify the greater integer.

22. 16 > -18 -10 < 2 4 > -14

23. -17 < -12 -3 < 0 0 > -49

24. 25 > -30 26 > -26 19 > 7

1. Group students into pairs. 2. Handout to the students a set of integer cards. These set of cards are of positive and negative integers, as well as, real world scenarios. Shuffle the cards. The dealer then should deal the cards out evenly between players. Each player then selects a card and holds a “face-off” comparing who is farthest from zero.

3. The player farthest from zero wins both cards. Once all cards have been played the player with the most cards wins.

4. Finally, both players are to place their cards in order from smallest to largest.

1. Distribute the Activity II student sheet.

2. Open Navigator and Start Class

3. Have students log in to NavNet

4. Launch Activity Center in Navigator

5. Select contribute Number line in Activity Center and click on Configure.

6. Fill out the configuration dialog box.

a. Specify a value or expression to be displayed on the device For example: Mark +4 (see chart for other values on page 10)

Tech Tip Number of marks allows you to restrict the number of vectors or points the students can submit.

Select Mark points only for this activity. *draw vectors is also another option that could be used on this activity if you wanted to introduce the understanding of addition or subtraction of integers.

TI MathForward™ 9 © 2010 Texas Instruments Incorporated 7. Set up the number line as you would like the students to start with on the calculator by defining the minimum value and maximum value shown, the step size they will move by and the tic marks that will be displayed.

Tech Tip

Be sure to set the Number line values appropriately for the value/expression entered.

8. Click on Start Activity

9. Students chose Activity Center from the TI-Navigator Home screen.

10. The Activity Center will open.

Tech Tip For each question start a new Activity.

Students then mark their points using their arrow keys left and right. To read the values on the number line press  to select line. Press  to mark their point. Then press  to send their answer.

11. Student data will appear on the teacher computer.

1. Mark -5

2. Mark +7

3. Mark the value 3 units to the left of zero. (-3)

4. Mark the value 4 units to the right of zero. (+4)

5. Mark the value 9 units to the right of -5. (+4)

6. Mark the value 10 units to the right of 0. (+10)

7. Mark the value 5 units to the left of +3. (-2)

8. Mark the value 4 units to the right of -10. (-6)

9. Mark the value 4 units to the right of -2 and then, 6 units to the left of that value. (-4)

10. Mark the value 7 units to the left of 0 and then, 8 units to the right of that value. (+1)

11. Mark the value 10 units to the left of +4 and then, 5 units to the left of that value. Then, right 12 units. (+1)

12. Mark the value 2 units to the right of -6 and then, 8 units to the left of that value. Then, right 17 units. (+5)

Activity III: Independent practice activity

Part I (A) Quick Poll Questions: Exploring the meaning of positive and negative values: 1. “Which is better owing $6 or $5?” 2. “Withdrawal $116 from an ATM machine” 3. “opposite of 15” 4. “opposite of -11” Explore the following the negative and positive values of 8: 5. a temperature drop of 8 degrees Celsius 6. a depth of 8 m 7. a growth of 8 in 8. a time 8 years ago 9. a gain of 8 yards 10. “Which is greater a negative or a positive value?”

Part I (B) Exploring integers on a number line. 1. Press to explore integers on a number line. Set the following values to Ω and æ. Ω -8, -3, -1, 0, 2, 7 æ 0, 0, 0, 0, 0, 0

2. Press  select  1 and press 1 Turn select on by highlighting on and press  Press  and select scatter plot  press  X list: L1 Y list: L2 Mark: (select the large point)

3. Press  and values accordingly. Xmin= -12 Xmax= 12 Xscl=1 Ymin=-0.2 Ymax=0.2 Yscl=0.1 TI MathForward™ 12 © 2010 Texas Instruments Incorporated 4. Press  then press and using the and  to look at the values. Then record the integers on numberlines below.

5. Press  to view the of values. This will show you other integer values and how your graphed values compare.

List A: Ω X= ______

æ Y= ______

List B: Ω X= ______

æ Y= ______

List C: Ω X= ______

æ Y= ______

6. What do you think would happen if x-values were all zero and the y-values were integers?

7. How would you plot a point in the center “the origin?”

8. Explain why 0 > -81 is incorrect?

For each question the teacher will start a new Activity. Then ask you to answer the question using your calculator and the marking the answer.

To answer the following questions: Move using your arrow keys left and right. To read the values on the number line press  to select line. Press  to mark your point. Then press  to send your answer.

1. Mark -5

2. Mark +7

3. Mark the value 3 units to the left of zero.

4. Mark the value 4 units to the right of zero.

5. Mark the value 9 units to the right of -5.

6. Mark the value 10 units to the right of 0.

7. Mark the value 5 units to the left of +3.

8. Mark the value 4 units to the right of -10.

9. Mark the value 4 units to the right of -2 and then, 6 units to the left of that value.

10. Mark the value 7 units to the left of 0 and then, 8 units to the right of that value.

11. Mark the value 10 units to the left of +4 and then, 5 units to the left of that value. Then, right 12 units.

12. Mark the value 2 units to the right of -6 and then, 8 units to the left of that value. Then, right 17 units.

Part I: Write the corresponding integer to the following real world scenarios.

1. 120 feet below sea level 9. 24° above zero 4 units to the left of -10 on the 2. A gain of 9 yards 10. number line. 3. A withdrawal of $35 11. A deposit of $65 One hundred eleven feet above sea 4. A growth of 4 inches 12. level 5. A pay cut of $3000 13. $25 late fee 6. 9° below zero 14. A gain of 9 points 7. A loss of $150 15. 9 units to the right of -7 8. Stock Market went up 141 pts today 16. A loss of $14,500 on an investment

Place in order starting with the least or smallest integer. Then graph the values on the number line.

17. -6, -8, 10

18. 0, -3, -5, 2

19. 4, -3, 7, 3, -10

Place in the following integers in order from least to greatest.

20. -25, 25, 21, 29, 16, -16, -26, -36

21. -42, 20, -60, -50, 4, 40, 49, 47, 27, -23, -43

Use the appropriate inequality sign (< or >) to identify the greater integer.

22. 16 -18 -10 2 4 -14

23. -17 -12 -3 0 0 -49

24. 25 -30 26 -26 19 7

Earned $3 walking the -1 -2/3 neighbor’s dog.

A temperature 4 drop of 5 1/2 degrees.

.75 -8 9

The Stock Market went down 10 -11 .12 points

-16 17 -18

A growth of -19 20 feet. -21

-2.2 23 24

28 -2.05 .99

$1.25 $2.29 9/10

2/7 -7/12 -1/3

.42 cent wage -.36 .41 increase

-.43 -.44 4/5

1/6 -.47 48

*Intentionally left blank to make more cards.