MathGrade 8ages 13–14
🔁 What happens when the input grows
A child can be great at plugging numbers into a formula and still think that's the only thing a function is allowed to be, not one of several ways to describe it.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- A function ties each input to one output.
- The same input must always give the same output, otherwise the machine cannot be relied on.
- A function can be a table, a graph or a rule in words — not only a formula.
- Two different inputs are allowed to give the same output.
The mistake most kids make here
Thinking a function has to be a tidy formula.
Try one question
The machine doubles and adds 1. What comes out for 4?
Put in 4
- 8
- 9
- 5
Answer
9 — That's it. Both steps happened, in the order written.
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 what comes out when 4 goes into a machine that doubles and adds one.
How to help at home
The core idea of a function — every input gets exactly one output — is simple, but children often narrow it to "a formula you compute", which makes tables, graphs, and word rules feel like a different, unrelated topic.
Play "number machine": you pick a secret rule (like "double it, then add one"), and your child calls out numbers while you call back the results, without revealing the rule. Ask them to guess the rule from the pattern of inputs and outputs.
When your child insists a function "has to" be a formula, say: "the machine is still a function even before you know the rule — it's a function because every number you put in gives back exactly one result, every time." A table of the inputs and outputs you've already played is proof.
A sign they've got it: given a table of number pairs with no formula in sight, they can say whether it could be a function just by checking that no input repeats with two different outputs.
Questions parents ask
- Why does my child think a function has to be a formula?
- Early practice with functions is usually formula-heavy, so the formula becomes the definition in their head instead of one example of it. Tables, graphs, and rules in words all count too, as long as each input gives one output.
- What's the actual rule for something to be a function?
- Every input has to produce exactly one output, and the same input always gives the same output. Two different inputs are allowed to share an output — that part doesn't break anything.
- How can I check if a table is a function without a formula?
- Look down the input column for any repeats. If the same input ever appears with two different outputs, it's not a function. If every input appears with just one output, it is — no formula needed.
- How does Maya teach what a function is?
- Maya plays a number-machine guessing game before introducing any formula, so the child meets the input-output idea directly instead of learning it as a rule about equations.
No card needed. The first lesson is free.
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