01 · DISCOVER
Before you begin
Enter your name and school email to save your learning. You’ll explore Proportional Relationships in Tables and then practice 12 questions with feedback.
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can you recognize a constant rate in a table and use it to solve problems?
02 · DISCOVER
Why this math matters
A class orders tickets costing $5 each. Can you predict the cost of 7 tickets from a table?
Tables are useful for shopping, pay rates, travel, and science measurements.
03 · DISCOVER
Build the mathematical foundation
A proportional table has the same output divided by input for every nonzero input. The equation has the form y = kx.
Before continuing, recall how multiplication and division are inverse operations and how two equivalent ratios represent the same relationship.
04 · BUILD YOUR FOUNDATION
Words mathematicians use
Ratio: an ordered comparison. Rate: a ratio involving different units. Unit rate: amount for exactly one unit. Proportional: two quantities connected by a fixed multiplier.
05 · BUILD YOUR FOUNDATION
Explore the relationship
Study the matching inputs and outputs, then explain the multiplicative pattern.
| Input | Output |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 4 | 20 |
Try creating one more matching pair in your notes.
Explore the math visually
Compare one unit with multiple units. Identify the multiplier and explain what remains constant.
06 · BUILD YOUR FOUNDATION
Input
Identify the independent quantity.
Identify the independent quantity.
x07 · INVESTIGATE
Output
Identify the quantity that depends on x.
Identify the quantity that depends on x.
y08 · INVESTIGATE
Compare
Calculate y ÷ x in each row.
Calculate y ÷ x in each row.
k09 · INVESTIGATE
Watch the problem solved, step by step
A class orders tickets costing $5 each. Can you predict the cost of 7 tickets from a table?
- List (tickets, cost): (1, 5), (2, 10), (4, 20).
- Divide cost by tickets: 5/1 = 10/2 = 20/4 = 5.
- Multiply 7 tickets by $5 per ticket.
- The total for 7 tickets is $35.
| Input | Output |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 4 | 20 |
Reasonableness check: Compare your answer with the original quantities and units.
10 · APPLY
Choose your strategy
Try the next three questions. Explain why your operation makes sense before selecting an answer. Use a hint if necessary.
11 · APPLY
Apply your understanding
Work through the independent questions. Pause to calculate, sketch a table or graph, and use feedback to correct misconceptions.
12 · APPLY
Connect and explain
Essential question: How does proportional relationships in tables help you understand real-world quantities?
Write a short explanation, include one example outside school, and identify how you would check your answer. Submit your results when complete.
INDEPENDENT PRACTICE · 1 OF 12
Does the table (1,4), (2,8), (4,16) show a proportional relationship?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 2 OF 12
What is y when x=5 and k=3?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 3 OF 12
Which pair belongs in y=2.5x?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 4 OF 12
For (2,7), (4,14), (6,21), what is k?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 5 OF 12
Which table is NOT proportional?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 6 OF 12
A table doubles both x and y. What stays constant?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 7 OF 12
For x = 1, 3, 6 and y = 5, 15, 30, what is k?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide y by x.
INDEPENDENT PRACTICE · 8 OF 12
A proportional table has k = 2.5. What is y when x = 8?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Use y = kx.
INDEPENDENT PRACTICE · 9 OF 12
Which table is not proportional?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Test y ÷ x in each row.
INDEPENDENT PRACTICE · 10 OF 12
If (4, 14) is in a proportional table, what is y when x = 10?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
First find 14 ÷ 4.
INDEPENDENT PRACTICE · 11 OF 12
Why can the row (0, 0) fit any proportional table?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Use y = kx with x = 0.
INDEPENDENT PRACTICE · 12 OF 12
In a proportional table, what stays constant?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Return to the vocabulary and three main ideas if needed.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.