1. Lesson 3.1.3 – Teacher Notes Standard:
8.F.1, 8.F.2, 8.F.3, 8.F.4 Functions with a heavy emphasis on rules, graphs, and tables.
Chapter 8 - Further practice identifying functions, (linear and non-linear)
Chapters 4 – Additional practice on rate of change and comparing representations
Chapter 7 - Continue with comparing representations
Lesson Focus:
Students expand their knowledge of multiple representations by creating a table, rule, and graph of data. Refrain from giving the official mathematical term of “slope” and “y-intercept”. This section of the text is building the conceptual understanding of the formula. The mathematical terms will come in a later chapter. When teaching problems 3-19 and 3-20, do not hand out calculators to students. This problem is best completed as a whole group, direct instruction, and using the CPM Student eTool found in the eBook. (3-18, 3-19, 3-20)
I can represent a function in a table or graph.
I can generate a function rule from a graph or table.
I can recognize a function form a table or graph.
Calculator: No
Literacy/Teaching Strategy: Peer Check (Whole lesson)

2. Bell Work

3. In the last two lessons, you examined several patterns
In the last two lessons, you examined several patterns. You learned how to represent the patterns in a table and with a rule. For the next few days, you will learn a powerful new way to represent a pattern and make predictions. As you work with your team today, use these focus questions to help direct your discussion: What is the rule? How can you represent the pattern?

4. 3-18.
On the Lesson Resource Page provided by your teacher, find the “Big C’s” pattern shown bellow. Figures 1, 2, and 3.
Draw Figure 0 and Figure 4 on the grid provided on the resource page.

5. On the resource page or using the 3-18 Student eTool (CPM), represent the number of tiles in each figure with:
• An x → y table.
• An algebraic rule.
• A graph.
c. How many tiles will be in Figure 5? Justify your answer in at least two different ways.
d. What will Figure 100 look like? How many tiles will it have? How can you be sure?

6. 3-19. Use graphing paper or the 3-19 to 3-22 Student eTool  to analyze the pattern further and make predictions.
Graph the information from your x → y table for problem 3‑18.  What do you notice?
Find another x → y pair that you think belongs in your table.  Plot the point on your graph.  Does it look correct?  How can you tell? 
Imagine that you made up 20 new x → y pairs.  Where do you think their points would lie if you added them to the graph? 

7. On the same graph that contains the data points, graph the algebraic equation for the pattern from problem 3-18.
What do you notice? Why did that happen?
Charles wonders about connecting the points of the “Big C’s” data. When the points are connected with an unbroken line or curve, the graph is called continuous. If the graph of the tile pattern is continuous, what does that suggest about the tile pattern? Explain.
Jessica prefers to keep the graph of the tile-pattern data as separate points. This is called a discrete graph. Why might a discrete graph be appropriate for this data?

8. Extra Practice 1.

9. 3.

10. 5.

13. 8.

14. 9.