8/12/2019 Growth Pattern Investigation

1/11

!"#$ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '"($ &&&&&&&&&& )$* &&&&&

Growth Pattern Investigation

Big Ideas:1. Students will be able to model real-world situations using algebraic expressions and equations.2. Students will be able to identify a variable as a convenient way for mathematicians to

generalize situations.

Outline of investigation:

Day 1

! Introduce the concept of a growth pattern with squares or blocks! Students use the first two terms in a growth pattern to create subsequent terms! Students will use algebra to generalize their pattern(s)

! Advanced students will create equivalent expressions to represent the patterns! Students will create their own growth pattern and use algebra to generalize itDay 2!

Students will explore, using manipulatives, several growth patterns that involve real-worldsituations.! Students will create their own situation (ideally one that is relevant and interesting to them)

that can be modeled using a growth pattern.

Day 3

! Students will present their growth patterns using posters, powerpoint, or other media.Lessons:

Day 1

! Warm-up! Draw the following pattern on the board

Term 1 Term 2

! Ask students to draw the next term in the growth pattern. There are several differentoptions. It might help to have students use colored pencils to show where the new

squares are in their pattern.

! Students share responses. Many responses will be incorrect. Work as a class todecide which patterns are growth patterns and why.

8/12/2019 Growth Pattern Investigation

2/11

!"#$ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '"($ &&&&&&&&&& )$* &&&&&

! Independent or Partner Work: Students will work independently or in pairs to complete thegrowth pattern worksheet for at least two of the growth patterns found during the warm-

up. (Note that the middle pattern shown above is quadratic and is quite difficult!) You maywant to show how to use the worksheet with a simple growth pattern before the students

work on their own.! Independent assignment or homework: Students should complete one section of the growth

pattern worksheet for a pattern that they create. Students should have their patternapproved by teacher or classmate for validity before completing this assignment.

Day 2

! Set up six stations with manipulatives corresponding to the problems in the growth patternpacket. Students will rotation stations, completing each worksheet as they go.

! When finished, students will work independently to create their own situation that follows agrowth pattern. Students will create a worksheet for other students to complete, or present

their pattern in another manner, like a powerpoint presentation or a poster.

Day 3

!Students will present projects!

8/12/2019 Growth Pattern Investigation

3/11

!"#$ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '"($ &&&&&&&&&& )$* &&&&&

Name(s) ______________________________ Date ___________ Per______

Growth Pattern Worksheet

1) Draw the first 4 terms of the pattern.

2) Describe in words how the pattern is

growing.

3) SKETCH the 20

th

term.

4) How many tiles will be in the 20th

term?Show your thinking.

5) How many tiles will be in the 100th

term?

Show your thinking,

6) Write an expression to represent the number

of tiles in the nth term.

1) Draw the first 4 terms of the pattern.

2) Describe in words how the pattern is

growing.

3) SKETCH the 20

th

term.

4) How many tiles will be in the 20th

term?Show your thinking.

5) How many tiles will be in the 100th

term?

Show your thinking,

6) Write an expression to represent the number

of tiles in the nth term.

8/12/2019 Growth Pattern Investigation

4/11

!"#$ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '"($ &&&&&&&&&& )$* &&&&&

1) Draw the first 4 terms of the pattern.

2) Describe in words how the pattern isgrowing.

3) SKETCH the 20thterm.

4) How many tiles will be in the 20th

term?

Show your thinking.

5) How many tiles will be in the 100thterm?Show your thinking,

6) Write an expression to represent the numberof tiles in the nth term.

1) Draw the first 4 terms of the pattern.

2) Describe in words how the pattern isgrowing.

3) SKETCH the 20thterm.

4) How many tiles will be in the 20th

term?

Show your thinking.

5) How many tiles will be in the 100thterm?Show your thinking,

6) Write an expression to represent the numberof tiles in the nth term.

8/12/2019 Growth Pattern Investigation

5/11

!"#$ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '"($ &&&&&&&&&& )$* &&&&&

!"#$%#&'() +#"&,

+,* " -*"./"(0,1 2"*(34 5($26"10$78 .". 08 2/((01- (,-$(6$* 9,(8 ,: $;/09"($*"9 (*0"1-9$8 901$ 2$*8,1 ?"1 80( "( $"?6 80.$ ,: (6$ (*0"1-9$=

@= A1 (6$ 82"?$ B$9,C4 01D$8(0-"($ 6,C #"13 2$,29$ ?"1 80( "( ("B9$8 #".$ ,: @ (*0"1-9$4 E

(*0"1-9$84 F (*0"1-9$84 G (*0"1-9$84 $(?= H$$2 C,**-"10I$ 3,/* C,*