Warm Up What rule could be used to create the pattern 9, 18, 27, 36, 45, 54,….?

Generate Numerical Patterns Alignment Lesson

Find Day 81, “Catching Fish” Sam and Terri went fishing every day after school this week. Sam caught 2 fish each day. Terri caught 4 fish each day. How many fish did they each have after each of the five days? Make a chart and a graph to represent the number of fish that Sam and Terri caught. How might we create a chart to organize the amount of fish Sam and Terri caught?

Draw and Complete this chart! Days Sam’s Total Number of Fish Terri’s Total Number of Fish 1 2 3 4 5

Sam’s Total Number of Fish Terri’s Total Number of Fish Days Sam’s Total Number of Fish Terri’s Total Number of Fish 1 2 4 8 3 6 12 16 5 10 20

Math Talk: What patterns do you notice in your data table? Did you realize?...... Since Terri caught 4 fish each day and Sam caught 2 fish each day, the total number of fish Terri caught was always greater than Sam’s. Terri’s total number of fish was always twice as much as Sam’s. On Day 0, both Sam and Terri had no fish because it was the day before they went fishing (on Day 1). Both Terri and Sam went fishing each day. Sam’s total number of fish increased by 2 each day. Terri’s total number of fish increased by 4 each day.

Find Day 81, “Graph Paper” How might you set up a graph to show the relationships between the two patterns? A line graph should be used to compare the two patterns because they both represent growing patterns that change over time. Both patterns are linear patterns (that increase by a constant amount) and will create straight lines when graphed. What information will go on the x-axis? “Days” is the independent variable and should be placed on the x-axis.

Find Day 81, “Graph Paper” What information will go on the y-axis? “Total Number of Fish” is the dependent variable and should be placed on the y-axis. We will have two lines graphed on the same graph (one representing Sam’s fish, one representing Terri’s fish) so that the relationships between the two patterns can be easily compared.

Create your graphs to represent the relationships between the numbers of fish caught by Sam and Terri. Once we have finished, we will have student leaders to share the graphs they created with the class. Explain the information shown in your graph. How do the two lines compare? How do the rates of increase compare? Sam only catches 2 fish every day, so his total number of fish increases at a slower rate than Terri’s. Will the lines continue to get further apart? Why or why not? Will the lines ever intersect? Write an expression to represent the total number of fish Terri has and the total number of fish Sam has. Terri – 4n, Sam – 2n (n represents the number of days)

Day 81, “Hamburger Prices” Work in pairs to complete the activity. Once you have completed your charts, graphs, and the relationship between the costs of hamburgers at the two restaurants, we will discuss. Explain the information shown in your graph. How does the cost of 5 burgers compare at the two restaurants? How do the two lines compare? How do the rates of increase compare? Will the lines continue to get further apart? Why or why not? Will the lines ever intersect? Write an expression to represent the cost of Matthew’s burgers and the cost of Kylie’s burgers. Matthew – 0.50n, Kylie – 0.40n (n represents the number of burgers)

Homework Day 81, “Mowing Loans”