# 8th Grade Task: Growth Patterns

8th Grade Task: Growth Patterns

### Standards & Objectives

Academic standards
CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
CCSS.Math.Content.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
CCSS.Math.Content.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
GLE 0806.3.5
Use slope to analyze situations and solve problems.
SPI 0806.1.2
Interpret a qualitative graph representing a contextual situation.
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.3.5
Determine the slope of a line from an equation, two given points, a table or a graph.
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
TSS.Math.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
TSS.Math.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
TSS.Math.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
TSS.Math.8.F.A.3
Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
TSS.Math.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description...
TSS.Math.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear...

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Essential and guiding questions:
• Why are the figures in Sets A and B called “Growth Patterns?” How do the figures in Sets A and B demonstrate growth?
• Which representation was more helpful in illustrating the nature of the pattern for the figures in Set A? (Set B?)
• Was the same representation more helpful when creating the expression for the nth figure in the pattern?

### Activity/Task Variations

Blooms taxonomy level:
Understanding
Differentiation suggestions:

If students can’t get started….
Assessing Questions

• What kind of pattern is illustrated by the numbers 1, 2, 3, 4, 5?
• If the top and bottom rows of the figures in Set A that each contain two square tiles were removed, describe the shapes that remain. What kind of pattern do these figures form?
• If the two tiles that stick out were removed from the first three figures of Set B, describe the shapes that remain. What kind of pattern do these figures form?

Advancing Questions

• Write a predictable pattern you are familiar with that contains numbers. Draw a graphical pattern to illustrate the numerical pattern you chose.
• Draw a set of rectangles that illustrate a pattern. Create a numerical sequence that illustrates the same pattern.
Extension suggestions:

If students finish early….
Assessing Questions

• Create a set of growth figures that illustrate a pattern. What characterizes the pattern you chose? Can you write an expression for number of tiles it will take to create the nth figure in your pattern?

Advancing Questions

• Given the expression n2 – 2n + 3 as representing the number of
• square tiles necessary to build the nth figure. Create the first four figures in a growth pattern that satisfies the given information.