Pattern+Graphing

Open the first file below.

Fill out the T-Chart for each of the six functions. Determine the rate of change between the steps of each function; in other words what each step goes up by. Determine value of the zero step for each function. (Step 1 minus the rate of change) Graph steps 0 through five.

The value for step N is determined by (Rate of change/what it goes up by) x N + (value of step zero)

If y = the value of the step and m = what each step goes up by and b = the value of step zero, then y = mx + b

Graph each function from the T-Chart

Open this file to follow the presentation.



We started a “Pattern Graphing” activity on Science Notebook page 17. Graphs are used to interpret scientific data and is a step in scientific inquiry/the scientific method. Students will be drawing six T-Charts on page 17 as shown. Students then look at the series of three changing patterns to start filling out the T-Chart. Students count the squares in the first pattern (Step 1) and write the number of squares to the right of the “1” in the T-Chart <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Students then count the squares in the second pattern (Step 2) and write the number of squares to the right of the “2” in the T-Chart. <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Students repeat the process for the third step. <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Students then use dots to draw pattern 1(dots are faster to draw than squares). Then they add dots to turn it into pattern two. Then they add dots to turn it into pattern 3. Now they can add more dots to make a Step 4. Then they should record the number to the right of the 4 in the T-Chart. They should then add dots to make Step 5. This number should also be entered into the T-Chart. <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">At this point students have figured out what each step “goes up by.” <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Next, students have to run the pattern backwards to figure out the number in Step 0. <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Figuring out “Step N”, where N could be any step, is done using "what the pattern goes up by" and the "number at step zero." <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">So the value at “Step N” is found by multiplying N by the number the pattern goes up by and adding “Step 0.” <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">For example the value at Step N is 3(N) + 1 <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">Now 10 or any number can be substituted in for N and the value of the step can be calculated. <span style="color: #1f497d; font-family: Calibri,sans-serif; font-size: 11pt;">This experientially derives the equation of a line which is y = mx + b