Alg1 Lesson 4.2: Multiplicative Patterns

Lesson 4.2: Multiplicative

Patterns

Obj: 12C, 12D: I can convert a given representation
of a geometric sequence to another representation
of the geometric sequence.

EQ: How do I write formulas given a sequence?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Hotspot

Click on the cat's ears.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Multiple Choice

Choose the correct answer.

• A.

• B.

• C.

• D.

Part 1: Comparing Arithmetic
and Geometric Sequences

Drag and Drop

Sequence 1: 167, 172, 177, 182, , ,

​

Placeholder

, ​

Placeholder

, ​

Placeholder

, …

Sequence 2: 2, 10, 50, 250, , ,

​

Placeholder

, ​

Placeholder

, 31,250, …

Drag these tiles and drop them in the correct blank above

192

6,250

197

187

1,250

500

182

Drag and Drop

Sequence 1: 167, 172, 177, 182, , .

Sequence 2: 2, 10, 50, 250, , ,

Both sequences are ​ increasing. In sequence 1, the terms increase ​

Placeholder

and steadily because the next term is 5 ​

Placeholder

the previous term. The terms in sequence 2 get much bigger much ​

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than sequence 1, because in sequence 2 the next term is the previous term ​

Placeholder

5.

Because sequence 1 has a ​

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rate of change, it is an arithmetic sequence. Sequence 2 is not an arithmetic sequence.

Drag these tiles and drop them in the correct blank above

added to

slowly

faster

multiplied by

linear

constant

slower

quickly

Dropdown

Sequence 3: 72, 24, 8, 8/3, 8/9, 8/27,...

Sequence 4: 1.9, 0.5, −0.9, −2.3, −3.7, −5.1, …

The terms in sequence 3 can be found by ​

Select answer

the previous term by ​

Select answer

, and the terms in sequence 4 can be found by ​

Select answer

​

Select answer

.

Part 2: Modeling Pizza Night

with Sequence Formulas

Eating Habits

Two friends, Freddy and Harry, each have their own 8-slice pizza, but they
eat their pizza differently. “Slow and Steady” Freddy eats one slice of pizza
at a time. “Half Some More” Harry takes half a pizza at first, then every time
he goes for more pizza, he takes half as much as he had the previous time.

Reorder

How many slices are in Freddy’s pizza the 2nd time he reaches for a slice? What about the 4th time? How many slices are in Harry’s pizza the 2nd and 4th times he reaches for a slice? Put your answers in that order.

• 7

• 5

• 4

• 1

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

Will Harry ever finish the pizza?

• Yes

• No

Multiple Choice

If you wrote Freddy's remaining pizza as a sequence, what kind would it be?

• Arithmetic

• Geometric

• Quadratic

Multiple Choice

If you wrote Harry's remaining pizza as a sequence, what kind would it be?

• Arithmetic

• Geometric

• Quadratic

Poll

Who's eating habit is more common?

• Harry's

• Freddy's

Multiple Choice

The sequence formula for Freddy is ...

• F(n) = -n + 9

• F(n) = n - 8

• F(n) = 8(0.5)^(n-1)

• F(n) = 8(2)^n

Multiple Choice

The sequence formula fo Harry is...

• F(n) = -n + 9

• F(n) = n - 8

• F(n) = 8(0.5)^(n-1)

• F(n) = 8(2)^n

Geometric Sequences

A geometric sequence is a sequence of
numbers where each term is found by
multiplying the previous term by a fixed
value. The fixed value is called the
common ratio.

Part 3: Investigating Fractal

Patterns

d) Use your table of values to write a
sequence formula for the number of new
branches in any stage.

Does the number of new branches at each stage
form a geometric sequence? How do you know?

b) Does the number of black triangles in each stage form a geometric
sequence? How do you know?

a) Look for a pattern. How can you determine the length of a single line segment in stage 5?

c) Write a sequence formula for the length of single line
segments for any stage of the Koch curve.

Drag and Drop

Tree Fractals, Sierpinski Triangle, and Koch Snowflake all involve ​

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patterns, or ​

Placeholder

sequences.

Drag these tiles and drop them in the correct blank above

multiplicative

geometric

factorial

additive

arithmetic

quadratic

Drag and Drop

Tree Fractals, Sierpinski Triangle, and Koch Snowflake all have different common ratios. Also, all of these investigations involve ​

Placeholder

values, but in the ​

Placeholder

, each segment was ​

Placeholder

as
long as the segments in the previous stage.

Drag these tiles and drop them in the correct blank above

factorial

additive

arithmetic

quadratic

increasing

Koch Snowflake

Tree Fractals

Sierpinski Triangle

1/3

-3

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.