8th Grade Task: Hexagon Puzzle

8th Grade Task: Hexagon Puzzle

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.EE.C.7
Solve linear equations in one variable.
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.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe...
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.
GLE 0806.5.2
Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
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.
SPI 0806.5.3
Generalize the relationship between two sets of data using scatterplots and lines of best fit.
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.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 of an...
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...
TSS.Math.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 example, in a...
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Essential and guiding questions: 

The key understandings that students should come to in the discussion of this task and questions you can ask in the whole group setting to support arrival at these key understandings.
Key understanding:

  • Are all of these expressions equivalent? How do we know? What would be the perimeter of the 9th figure? 100th figure?
  • Discuss different students’ approaches to solving the different models.
  • There may be several paths to form a relationship but if they all simplify to the same equation then they must be equal.
  • What property can we use to justify our findings? Reflexive property of equality y=y 4n+2=4n+2

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….

  • Could you write a table of values of number of shapes compared to the perimeter of the figure? This may give you insight into the equation.
  • How does equation A relate to the linear model of y=mx+b?
Extension suggestions: 

If students finish early….

  • If I added a fifth shape would any of the equations model that relationship.
  • What if I put together triangles with each side being one unit. How many different equations could you write to model that relationship?