MathGrade 10ages 15–16
📉 Line versus curve
A graph that goes up and to the right can look "linear" just because it's rising, even when the amount it climbs keeps getting bigger and the line is actually curving.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- Linear growth adds the same amount at every step.
- In a linear table the gaps between neighbouring rows are identical.
- In quadratic growth the gaps themselves grow, which is why the graph curves upward.
- Both graphs can rise. Only one of them rises at a steady rate.
The mistake most kids make here
Thinking any rising graph is a straight line.
Try one question
Which kind of growth draws a straight line?
Which growth
- the same addition every step
- an addition that grows every step
- any growth at all
Answer
the same addition every step — That's it. The same step and the same climb, again and again.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say how to spot linear growth in a table.
How to help at home
The word "linear" describes a very specific kind of rising: the same amount added at every step. Anything that rises by a growing amount each step is curving, even if it never goes down.
Build two savings tables together: one where you add 5 shekels every week (linear), and one where the weekly amount added itself grows — say 2, then 4, then 8 (not linear). Ask which one, plotted as points, would sit on a perfectly straight line.
If your child calls both graphs "a straight line" just because both go up, say: "both rise, but only one adds the same amount every single step. Check the gaps between each week's total — if the gaps are all equal, it's a straight line. If the gaps themselves grow, the line bends upward."
A sign they've got it: given a table of numbers, they check the differences between consecutive rows before looking at the graph at all, and predict correctly whether it will be straight or curved.
Questions parents ask
- Why does my child think every rising graph is a straight line?
- Rising and "straight" get bundled together visually, especially on a small graph. The real test isn't whether it rises, but whether it rises by the same amount at every step — that's what makes it linear.
- How can I tell linear growth from quadratic growth in a table?
- Look at the differences between consecutive values. If those differences stay exactly the same, the growth is linear. If the differences themselves keep growing, the growth is quadratic, and the graph curves upward.
- Can a quadratic graph ever look like it's rising steadily at first?
- Yes — early on, the growing gaps can be small and easy to miss, which is exactly why checking the actual differences in a table is more reliable than eyeballing the shape.
- How does Maya teach linear versus quadratic growth?
- Maya has the child compute the differences between consecutive values in a table before ever looking at the graph, so the distinction is built on the numbers rather than on how a curve happens to look.
No card needed. The first lesson is free.
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