1. 4.1 Writing Equations to Describe Patterns Math

2. The Banquet A banquet has small square tables that seat 1 person on each side. The tables can be pushed together to form longer tables. Sketch the next 2 tables in the pattern. What stays the same in each arrangement? What changes? Work with a partner to determine the number of people at 6 tables? 10 tables? 25 tables? Can you figure this out without sketching the tables?

3. The Landscaper… A landscape designer uses wooden boards as edging for the plots in a herb garden. The number of boards (b), is related to the number of plots (p). This relationship can be represented in different ways: –Using pictures –Using a table of values –Using an equation

4. The Landscaper cont’d… 1 plot2 plots3 plots Picture Number of Plots (p) Number of Boards (b) 1 2 3 4 Table of Values +1 +3 As the number of plots increases by 1, the number of boards increases by 3. Repeated addition of 3 is the same as multiplication by 3.

5. How can we get the equation? Number of Plots (p) Number of Boards (b) 14 27 310 413 +1 +3 As the number of plots increases by 1, the number of boards increases by 3. Repeated addition of 3 is the same as multiplication by 3. So, does this equation work? Why or why not? What can we do to make this equation work? Let’s take a look!

6. Let’s Check our Equations… Number of Plots (p) Number of Boards (b) b = 3p 143(1) = 273(2) = 3103(3) = 4133(4) = Does this equation work for all plots? How can we check? These are the number we want. These are the number we get with our first equation. What can we do? Equation

7. Let’s try another one! An airplane is cruising at a height of 10 000 m. It descends to land. This table shows the height of the plane every minute after it began its descent. Time (t minutes) Height (h metres) 010 000 19 700 29 400 39 100 48 800 1.Write an expression for the height in terms of the time since the plane began it’s descent. 2.Write an equation that relates the height of the plane to the time since it began its descent. 3.What is the height of the plane after 15 min? 4.How long after beginning its descent does the plane land?

8. Airplane cont’d… Time (t minutes) Height (h metres) Height in Terms of Time 010 000 19 700 29 400 39 100 48 800 +1 -300 1.Write an expression for the height in terms of the time since the plane began it’s descent. 2. Write an equation that relates the height of the plane to the time since it began its descent.

9. Airplane cont’d… 3.What is the height of the plane after 15 min? 4. How long after beginning its descent does the plane land? What do we know about the plane’s height when it lands? Always substitute into brackets! What does 15 represent, height or time?

10. The Cab Ride Kelly’s Cabs advertises the cost of their cab rides as follows: Fixed Cost $3.60 + $1.50 per kilometre 1.Write an expression for the fare in terms of the fixed cost and the cost per kilometre. 2.Write an equation that relates the fare to the distance covered. 3.What is the fare for an 11-km ride?

11. Assignment Required Questions: Page 159-160 Questions 4-9, 11, 13,17 Enrichment questions: –Pg. 162: #19, 20, 21