Algebra 1 Unit 2: All Patterns

Warm-Up State the next term in each sequence or pattern:

1. 4, 11, 18, ______

2. 4a, 8a, 16a, 32a, _________

3. , , , , …

Warm-Up State the next term in each sequence or pattern:

1. 4, 11, 18, ______

2. 4a, 8a, 16a, 32a, _________

3.

, , , , …

x

x

x

x

x

x

x

x

x

x

Algebra 1 Unit 2: All Patterns

Student Notes – Patterns

Develop a table and a pattern rule for the representation:

1. A) Find the perimeter for the first three trains and write this in the table.

B) Write a function rule that could be used to find the perimeter of the nth train. _________________

C) What is the perimeter of the 10th train? ______________

2. Scatterplot:

Determine the y-value when: A. The x-value is 12:

B. The x-value is 20:

Function rule: _____________________ C. What will the x-value be when the y-value is -61?

3. Sequence:

18, 23, 28, 33

Function Rule: __________________

Train 1 Train 3 Train 2

Table:

Table:

Table:

Algebra 1 Unit 2: All Patterns

If n represents a number’s position in a sequence, write the first 5 terms described by each expression. 4. 3 4n � 5. ( 1.5) 2n n � �

6. A train is moving at a constant rate of speed. The table below shows how far it travels in a given number of minutes. Use the information in the table to determine how many miles the train will travel in 45 minutes and write a function rule.

Time in Minutes 5 10 15 20 45

Distance in Miles 5.75 11.5 17.25 23

7. Given the function rule 6 2y n � , what would be the term number if it took 110 blocks to build the pattern?

8. The figures to the right have a repeating pattern. Which shows the 34th figure in this pattern?

9. John delivers newspapers every morning in his neighborhood. He gets paid based on the number of hours, x, that he works.  This table reflects John’s pay scale.

Number of Hours Worked Wages

1 $10

2 $18

3 $26

4 $34 Which equation represents the number of dollars, w, he will be paid for doing x hours of work? A 2 8w x � B 10 8w x � C 34 8w x � D 2 8w x �

A. B. C. D.

Function Rule: ________________

Algebra 1 Unit 2: All Patterns

0 1 2 3 4 5 6 70

1.2

2.4

3.6

4.8

6

x

y

Height of Stack

# of DVDs

Exit Slip A Kendra wants to stack her DVD cases on her TV shelf, and wants to know how many cases she can stack on the shelf. the Record your data in the table below.

B Write two ordered pairs for data in your table, and explain what each ordered pair means.

Ordered Pair: _________ Means: ________________________________________ Ordered Pair: _________ Means: ________________________________________

C Create a scatterplot of your data on the grid below.

D Using information contained in either your table or your scatterplot, predict the height of a stack that contains:

6 DVDs _________ 10 DVDs _________ 100 DVDs _________

E What if you are told that a stack of DVDs is 30 cm high? How many DVD cases would you expect to find in the

stack? Explain how you got your answer.

Number of DVDs: ______ Explain: ___________________________________________________________

# of DVDs Height of Stack (cm) 0 1 1.2 cm 2 3 4 n

Algebra I - Unit 2: Topic 1 –All Patterns Practice – All Patterns No Textbook Correlation Name ______________________________________ Date ____________________ Period _____

If n represents a number’s position in a sequence, write the first 5 terms described by each expression.

1. 2 7n �

Find the term number when it takes 103 blocks to build.

2. ( 6) 2n n � �

Match each sequence with its rule on the right.

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

4. 6, 9, 14, 21, 30

5. 6, 7, 8, 9, 10

A x + 5

B x – 5

C x2 + 5

Answer the following questions. 6. A special sequence is called the Fibonacci sequence. It is named after Leonardo Fibonacci from Italy who

presented it in 1201. This sequence is very intriguing because the numbers in the sequence are often found in nature. The first six terms of the sequences are listed below. Give the next six terms of the sequence.

1, 1, 2, 3, 5, 8 … 

7. Pam needs to make a tower of soup cans as a display in a supermarket. Each layer of the tower will be in the shape of a rectangle as shown. The length and width of each layer will be one less than the layer below it.

A. How many cans will be needed for the fourth layer?

B. What is the total number of cans needed for an 8-layer tower?

8. Sara planted rows of tulips in her garden, as shown in the table. Which expression best shows the number of tulips per row, r.

Row Number Number of Tulips

1 3

2 6

3 9

4 12

Top Layer

Second Layer

Third Layer

A. 3 – r B. r + 3 C. 3 D. 3r

A. 3 – r B. r + 3 C. 3 D. 3r

Algebra I - Unit 2: Topic 1 –All Patterns 9. The pattern of squares below continues indefinitely. More squares are added with each step, n.

Which expression can be used to determine the number of squares in the nth step?

A 2n – 1 B 3n C n2 - n + 1 D n2

10. A geometry class was exploring the sum of the interior angles, S, of polygons as compared to the number of sides, n, that the polygon has. They recorded their data in the table below. Complete the table, and state the function rule.

Function Rule: ________________________

11. The figures to the right have a repeating pattern. Which shows the 57th figure in this pattern?

12. A pattern of equations is shown at the right. Which statement best describes this pattern of equations?

A When the percent is tripled and the other number is divided by 3, the answer is 24.3.

B When the percent is tripled and the other number is tripled, the answer is 24.3.

C When the percent is increased by 3 and the other number is divided by 3, the answer is 24.3.

D When the percent is increased by 2 and the other number is subtracted by 81, the answer is 24.3.

n S 3 180 4 360 5 540 6 720 7 8 9 10

1% of 2430 = 24.3

3% of 810 = 24.3

9% of 270 = 24.3

27% of 90 = 24.3

81% of 30 = 24.3

243% of 10 = 24.3

A B C D

Algebra I - Unit 2: Topic 1 –All Patterns

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Hours Worked

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Earnings (dollars)

13. The table below indicates a linear relationship between x and y.

x y

2 5

4 9

6 13

12 25 Which equation would generate the values in this table? A 3y x � B 3 1y x � C 2 1y x � D 7y x �

14. Roberto earns $7.00 an hour working at a grocery store. If he works 20 hours each week, which of these graphs best represents Roberto’s earnings?

A C

B D

Algebra I - Unit 2: Topic 1 –All Patterns

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Servings

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15. The table below lists the amount of calories for each of the different servings of one bag of potato chips.

Number of Servings (n) Calories (c)

2 300 4 600 6 900 8 1,200

Which of the following graphs best represents the data in the table?

A C

B D

16. The chart below shows the average number of points per game for the five starting players on the boys’ basketball

team.

A Player Points B Player Points C Player Points D Player Points Jim 16.5 Jim 17.5 Jim 16.5 Jim 17.3 John 6.0 John 6.0 John 6.0 John 6.0 Tim 22.5 Tim 22.5 Tim 23.0 Tim 23.3 Chris 10.5 Chris 11.0 Chris 10.5 Chris 11.3 Mike 18.0 Mike 20.0 Mike 19.0 Mike 18.8