Patterns
This linear pattern has a constant repeated pattern and no rate of change.
What is a horizontal line/constant line/line with no slope?
The equation for a constant graph is this.
What is y=c?
Complete the data table for c=15 for a horizontal line graph.
x=1, 2, 4, 6
What is y=15, 15, 15, and 15?
What is 4 seconds?
Identify the Reasoning in this CER.
A hand's distance from the hinge affects the force needed to push open a door. The closer a hand is to the hinge, the harder it is to push open. At a distance of 0.25 meters it takes 60 newtons but a distance of 0.5 meters takes 30 newtons of force. Since the smaller distance takes more force, it follows that the closer a hand is to the hinge, the harder it is to push open.
What is "Since the smaller distance takes more force, it follows that the closer a hand is to the hinge, the harder it is to push open"?
This pattern has a constant, non-zero rate of change.
What is a proportional pattern?
The equation for a proportional graph is this.
What is y=cx?
Complete the data table for a proportional graph when c=15 for x=1, 2, 4, 6.
What is y=15, 30, 60, and 90?
Predict the force needed for a distance of 3 meters knowing that Force=30/distance.
What is 10 Newtons?
Identify the claim in this CER.
A hand's distance from the hinge affects the force needed to push open a door. The closer a hand is to the hinge, the harder it is to push open. At a distance of 0.25 meters it takes 60 newtons but a distance of 0.5 meters takes 30 newtons of force. Since the smaller distance takes more force, it follows that the closer a hand is to the hinge, the harder it is to push open.
What is "The closer a hand is to the hinge, the harder it is to push open"?
When graphed on both sides of the y axis, this curve is shaped like a U.
What is a quadratic curve/parabola?
The equation for a quadratic pattern is this.
What is y=cx2?
Complete the data table for a quadratic curve when c=15 and x=1, 2, 4, 6.
What is y=15, 60, 240, and 540?
Predict the amount of ink used to make a 100m line if the rate of change is 14mL/m for a proportional graph.
What is 1400mL?
When you compare and contrast the rate of change between horizontal lines and inversely proportional graphs, you'll notice this.
What are horizontal lines have a constant rate of change while inversely proportional curves do not?
This curve is shaped like a crooked C.
What is inversely proportional?
The equation for inversely proportional pattern is this.
What is y=c/x?
Complete the data table of an inversely proportional curve when c=15 and x=1, 2, 4, 6.
What is y=15, 7.5, 3.75, and 2.5?
Predict the Time of one swing of a flagpole knowing that time=30/frequency and the frequency is 2Hz.
What is 15 seconds?
Provide reasoning for this claim and evidence. "The angle of the swing does not affect the time it takes for a pendulum to complete 1 complete swing. At starting angles of 50, 60, and 150, it took the pendulum 5 seconds to complete one swing."
What is "since three different data points at different angles took the same amount of time, it follows that the angle of the swing does not affect the time it takes for the pendulum to complete one swing"?
The difference between a quadratic curve and an inversely proportional curve is that inversely proportional curve has these at the x and y axes.
What are horizontal and vertical asymptotes?
The difference between proportional and inversely proportional relationships with c is this.
What is proportional multiplies by c while inversely proportional divides by c?
Compare and contrast all four graph patterns when c=20 for x=1 and 2 and name 1 similarity and 1 difference.
What is x=1 y=20 for all graphs and x=2 yields different values for all graphs (y=20, 30, 80, and 10)?
Predict the distance a ball is dropped (m) at a time of 4 seconds knowing that distance=20*time2.
What is 320m?
Write a CER using evidence from the graph to describe how pen A is different than pen B.
What is "Pen A uses more ink per meter than pen B. At 1 m, pen A uses 25mL of ink while pen B uses 17mL of ink. Since pen B uses 17 mL while pen A uses 25 mL to write a 1m line, it follows that pen A uses more ink per meter than pen B"?