Math CC7/8 – April 6 Math Notebook: Things Needed Today (TNT): TwMM Pencil/Math Notebook/Calculators TwMM Math Notebook: Topic: Finding Patterns HW: TwMM p. 17 #4a-c, #27-31 or use copy of homework

What’s Happening Today? New Books – TwMM & BPW Warm Up – writing equations Lesson 1.3 – Finding Patterns

7 = -4(-1) +b next solve for b Warm Up Find the equation of a line with a slope = -4 and a coordinate point (-1 , 7) 2. Find the equation of a line with a slope = 1 and a coordinate point (6 , 3) 3. Using the coordinate point in #1 find the value of b in y = -4x + b Substitute the points into the equation y = mx + b 7 = -4(-1) +b next solve for b 7 = 4 +b -4 -4 b = 3 y = -4x + 3 Substitute the points into the equation y = mx + b 3 = 6(1) +b next solve for b 3 = 6 +b -6 -6 b = -3 y = x -3 7 = -4(-1) +b next solve for b 7 = 4 +b -4 -4 b = 3 y = -4x + 3

New Unit: Thinking with Mathematical Models

Question How can we predict if a pattern between variables will be linear or nonlinear?

Launch Video for Lesson 1.3 (In TwMM Inv. 1 file)

Skip 1.1 & 1.2

Use your Labsheet for this. Complete the table below on your labsheet to show the number of rods in trusses of different overall lengths.

1 rod 2 ft. = 7 rods 1 ft. = 3 rods Each additional ft. Equals 4 more rods 1 ft. = 3 rods

As the length increases by 1 ft., 4 rods are added

3 + 49 (4) = 199 rods for a 50 foot truss Table : Each increase of 1 ft. in length, is an increase of 4 rods Graph : It is a straight line, over 1 ft. and up 4 rods Each additional foot of truss length after the first foot requires 4 additional rods… So… 3 + 49 (4) = 199 rods for a 50 foot truss y = 4x – 1 y= 4(50) – 1 y = 200 -1 y= 199 rods for a 50 foot truss

3L comes from the length multiplied by 3 sides of the triangle N = 3L + L - 1 3L comes from the length multiplied by 3 sides of the triangle L is the length -1 comes from we know the first triangle only need 3 sides and every other triangle needs 4 rods. N = 3L + L – 1 N = 4L -1 Same as y = 4x - 1

Use your Labsheet for this. Complete the table below on your labsheet to show the number of rods in trusses of different overall lengths.

As the number of steps increases by 1, the number of rods increases by the next even number!

Table: The number of rods increases by 6, 8, 10 and so on Graph: it curves upward at an increasing rate 2 y = x + 3x 9 10 11 12 130 154 180 108 +6 +8 +10 +12 +14 +16 +18 +20 +22 +24 +26

Both patterns are increasing from left to right. The truss relationship is linear, so it has a straight line graph and a table with constant differences. The staircase relationship is nonlinear, so it has a curved graph and a table where the differences are not constant.

Skip D since we skipped 1.1 and 1.2