Choose the clearest way to show a pattern.
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.
Success criteria
- 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 we use connecting tables, graphs & equations to solve problems?
02 · LEARN & EXPLORE
Real-world challenge
A proportional table has (1,4), (2,8), (3,12). Connect its representations.
First make a prediction, then learn a mathematical strategy for checking it.
Move between raw values and visual trends.
Use one representation to check another.
03 · LEARN & EXPLORE
Build the core concept
The table, graph, and equation y = 4x all represent the same constant rate of four.
Think about which quantity is input, which is output, and what their units mean.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
A way of showing a mathematical idea.
A relationship described in words.
Values organized in rows and columns.
A symbolic statement of equality.
A visual display of ordered pairs.
Matching the same relationship.
05 · LEARN & EXPLORE
Explore the structure
A proportional table has (1,4), (2,8), (3,12). Connect its representations.
Represent the known quantities in a table, equation, number line, or graph. Identify what remains constant.
Explore the math visually
1input units
2input units
3input units
4input units
Compare one unit with multiple units. Identify the multiplier and explain what remains constant.
Find y ÷ x.
Find the coefficient of x.
Find rise ÷ run.
06 · LEARN & EXPLORE
Divide
Find y ÷ x.
1Notice what quantities, values, or representations are given.
2Use Divide to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Start with this foundation.
Find y ÷ x.
table07 · LEARN & EXPLORE
Read
Find the coefficient of x.
1Notice what quantities, values, or representations are given.
2Use Read to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Build on the first idea.
Find the coefficient of x.
equation08 · LEARN & EXPLORE
Measure
Find rise ÷ run.
1Notice what quantities, values, or representations are given.
2Use Measure to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Connect everything with the final idea.
Find rise ÷ run.
graph09 · LEARN & EXPLORE
Worked solution with reasoning
- Divide output by input: 4/1 = 8/2 = 12/3 = 4.
- Write the equation y = 4x.
- Plot (0,0), (1,4), (2,8), (3,12).
- The straight line through the origin confirms proportionality.
10 · LEARN & EXPLORE
Choose the steps; use a hint if needed.
The next three problems remove some of the support. Identify what is known, select the right strategy, calculate carefully, and check the units or representation.
11 · LEARN & EXPLORE
Now complete the work independently.
Complete six questions without following a worked model. Hints remain available when you truly need them, and feedback will explain every answer.
Interactive practice tip: Use a quick sketch, table, or graph to test each answer. After selecting an answer, read the explanation and revisit your model if necessary.
12 · LEARN & EXPLORE
Explain and apply
Explain the mathematical strategy used in this lesson and describe how it would help in a different everyday situation. Give a reasonableness check.
INDEPENDENT PRACTICE · 1 OF 12
For table (1,6),(2,12), what equation matches?
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
Graph through (0,0),(4,20). Constant rate?
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 table matches y=3x?
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
What must all three representations share?
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
For y=2.5x, which graph point fits?
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 graph crosses y-axis at 3. Is it y=kx?
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
Which table matches y = 3x?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply every x by 3.
INDEPENDENT PRACTICE · 8 OF 12
A graph passes through (0,0) and (5,20). Which equation matches?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Find 20 ÷ 5.
INDEPENDENT PRACTICE · 9 OF 12
Which verbal rule matches y = 0.6x?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Read multiplication by 0.6.
INDEPENDENT PRACTICE · 10 OF 12
A table has k = 7/2. Which graph point must be included?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Use y = 7/2 × x.
INDEPENDENT PRACTICE · 11 OF 12
What feature should agree in a matching table, graph, and equation?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Focus on the mathematical relationship.
INDEPENDENT PRACTICE · 12 OF 12
Which equation matches a unit rate of 4?
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
Reflect on your learning: Which problem best shows what you learned? What strategy helped, and what would you still like to practice? Explain your answer to a partner or write it on paper before submitting.
Check your work and submit your first-attempt score to your teacher.