Proportional
A student says the pairs (2,8) and (4,16) are proportional.
👉 Do you agree or disagree? Explain.
Agree, the ratio is 4.
A student says the constant of proportionality for (3,12) is 9.
👉 Is the student correct? Explain.
No, it is 4 (12/3)
A graph passes through (0,0).
👉 Does this guarantee it is proportional? Explain.
No it must also be a straight line.
A table shows x=2 → y=8.
A student says k = 6.
👉 Is this correct? Explain.
No, k=4
A student says k tells how x changes.
👉 Is this correct?
No, it tells how y changes per 1 x
(5,15), (10,30), (15,50)
👉 A student says this is proportional. Do you agree?
No the last ratio is different.
A student finds k = 20 ÷ 4 = 5
👉 What does this mean in context?
y increases by 5 per 1 x
A line goes through (0,0) and (2,10).
👉 A student says k = 12. Explain error.
k=5, not 12.
x: 2, 4, 6
y: 6, 12, 18
👉 Predict y at x=8 and explain
24
A student says any pattern is proportional.
👉 Explain why this is wrong.
Ratios must be constant.
(6,18), (12,36), (18,60)
👉 A student says proportional. Do you agree?
No
k = 7
👉 A student says y = x + 7.
👉 Is this correct?
No it should be y=7x
A graph goes through (3,15).
👉 A student says k = 15. Explain.
Must divide and k=5
A table has changing ratios
👉 A student says still proportional
👉 Explain error
Ratios must match
Why must proportional relationships have a constant ratio?
That defines proportional.
A table increases, but ratios change
👉 Is it proportional? Justify
No, ratios must be constant.
k = 5
👉 Explain what this means in a real-world situation
5 per 1 unit
Graph: (0,0), (3,15)
👉 A student predicts y = 45 at x=8
👉 Is this correct? Explain
No it is 40
Explain how to check proportional from a table
Divide y / x
“All straight lines are proportional”
👉 Agree/disagree
Disagree
Create a real-world example of a proportional relationship and explain why it is proportional.
Answers may vary.
Explain how you can find the constant of proportionality using a table of values.
Divide y by x
Explain how a graph shows that a relationship is proportional.
Straight line through the origin
Explain why a table with changing ratios cannot represent a proportional relationship.
Ratios must be constant
Explain how tables, graphs, and equations all represent the same proportional relationship.
They all show the same constant ratio