AC9M7A05 • Year 7 Maths • Algebra • Learn
generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane.
We are learning to generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane.
A growing pattern connects a stage number x with a quantity y. Constant additive growth produces a linear rule whose coefficient is the growth per stage.
Build a value table, calculate first differences and use one ordered pair to determine the constant term; write and plot each pair in x-then-y order.
A pattern of separate stages is discrete even when its plotted points align. Verify the rule against every known stage before using it to predict a later stage.
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 1
Final answer: y=3x+1
Check: At discrete stage 3 the rule gives 10 tiles.
Example 2
Final answer: (0,−1), (1,1), (2,3), (3,5)
Check: Each first difference is 2 when x rises by 1.
Example 3
Problem: A growing pattern follows y=3x+1. Generate values for x=0,1,2,3, plot the ordered pairs mentally or on paper, and explain what 3 and 1 mean.
Final answer: The points are (0,1), (1,4), (2,7), (3,10). The 3 is the increase in y for each increase of 1 in x; the 1 is the starting value when x=0.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: Find the rule through (1,4),(2,7),(3,10), then predict stage 20.
Final answer: The first difference is 3, so y=3x+b; using (1,4) gives the constant term b=1, hence y=3x+1 and discrete stage 20 has y=3(20)+1=61.
Check: The complete model for “Find the rule through (1,4),(2,7),(3,10), then predict stage 20.” shows The first difference is 3, so y=3x+b; using (1,4) gives the constant term b=1, hence y=3x+1 and discrete stage 20 has y=3(20)+1=61.
Common mistake: Growth number used as complete rule.
Correction: Include the starting/fixed component.
Common mistake: x and y coordinates reversed.
Correction: Plot input first, output second.
Common mistake: Discrete points joined automatically.
Correction: Only join if intermediate inputs are meaningful.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Continue the pattern 5, 8, 11, __ by using its first difference.
Answer: 14.
Hint: Add the constant first difference.
Why: Using the method “Add the constant first difference.” gives 14.
2. For y=4x+2, find y when x=3.
Answer: 14.
Hint: Substitute x=3.
Why: Using the method “Substitute x=3.” gives 14.
3. Write the ordered pair for x=2 and y=7.
Answer: (2,7).
Hint: Write x before y when you record the ordered pair.
Why: Using the method “Ordered pairs place x first.” gives (2,7).
4. For y=3x−2, list y when x=0,1,2.
Answer: −2, 1, 4.
Hint: Apply the rule to each input.
Why: Using the method “Apply the rule to each input.” gives −2, 1, 4.
5. A pattern has 6 tiles at stage 1 and grows by 4. Find its rule.
Answer: y=4x+2.
Hint: Use 6=4(1)+b.
Why: Using the method “Use 6=4(1)+b.” gives y=4x+2.
6. Do (1,5),(2,8),(3,11) fit y=3x+2?
Answer: Yes. Substitution gives 3(1)+2=5, 3(2)+2=8 and 3(3)+2=11, so all three ordered pairs satisfy the rule.
Hint: Substitute each x and compare y.
Why: The reasoning for “Do (1,5),(2,8),(3,11) fit y=3x+2?” is complete because Yes. Substitution gives 3(1)+2=5, 3(2)+2=8 and 3(3)+2=11, so all three ordered pairs satisfy the rule.
7. Explain the constant term 5 in y=2x+5.
Answer: The constant 5 is the output when x=0, because y=2(0)+5=5; graphically it is the vertical-axis intercept.
Hint: Set x equal to zero.
Why: The reasoning for “Explain the constant term 5 in y=2x+5.” is complete because The constant 5 is the output when x=0, because y=2(0)+5=5; graphically it is the vertical-axis intercept.
8. For the discrete rule y=5x−1, which whole-number stage first exceeds 30?
Answer: A short table gives stage 6: y=5(6)−1=29 and stage 7: y=5(7)−1=34; because the discrete stages are whole numbers, stage 7 is the first output above 30.
Hint: Test stages 6 and 7 in a short value table.
Why: The complete model for “For the discrete rule y=5x−1, which whole-number stage first exceeds 30?” shows A short table gives stage 6: y=5(6)−1=29 and stage 7: y=5(7)−1=34; because the discrete stages are whole numbers, stage 7 is the first output above 30.
9. Find the rule through (1,4),(2,7),(3,10), then predict stage 20.
Answer: The first difference is 3, so y=3x+b; using (1,4) gives the constant term b=1, hence y=3x+1 and discrete stage 20 has y=3(20)+1=61.
Hint: Use the first difference to find the coefficient, then the constant term.
Why: The complete model for “Find the rule through (1,4),(2,7),(3,10), then predict stage 20.” shows The first difference is 3, so y=3x+b; using (1,4) gives the constant term b=1, hence y=3x+1 and discrete stage 20 has y=3(20)+1=61.
10. A growing pattern follows y=3x+1. Generate values for x=0,1,2,3, plot the ordered pairs mentally or on paper, and explain what 3 and 1 mean.
Answer: The points are (0,1), (1,4), (2,7), (3,10). The 3 is the increase in y for each increase of 1 in x; the 1 is the starting value when x=0.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Content description: generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane.
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Math Antics — Connect inputs, a rule and outputs before creating a table and plotting a relationship.
As you watch: Why must a function give only one output for each input?
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Try it: Use the rule y = 2x + 1 to make a table for x = 0 to 4, plot the pairs and describe the pattern.
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Mapped skill: generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7A05 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7A05 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-LIN-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M7A05 — Growing Patterns, Tables and Cartesian Graphs
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