Exponential functions – Grade 9 math lesson

Lesson 17 of 17 in the Grade 9 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 9 (ages 14–15)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “Why does an exponential function always overtake a linear one in the end?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Confusing linear and exponential tables. Check differences (linear) and ratios (exponential).
Using the percentage as the factor (5% growth as b = 5). 5% growth means b = 1.05.

Tip for home: Talk about how savings or populations grow over time.

What your child will learn

Learning goal: recognize, write and solve exponential functions and models.

Success looks like

I can tell linear and exponential relationships apart.
I can write an exponential model.
I can solve simple exponential equations.

Key words

exponential function: y = a·bˣ
growth factor: the number multiplied each step
decay: decreasing by a constant factor
logarithm: the exponent needed to reach a number

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Fold a sheet of paper in half again and again and record how many layers you get.

The big ideas (for the adult)

An exponential function has the form y = a·bˣ: the starting value a is multiplied by the factor b each time x goes up by 1.

If b > 1 it shows growth; if 0 < b < 1 it shows decay. Linear functions add the same amount; exponential functions multiply by the same amount.

Logarithms undo exponents: if 2ˣ = 32, then x = log₂ 32 = 5.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

Algebra 1: Exponential Growth and Decay Practice TestGraded instantly

All Grade 9 math lessons and tests · Math Department

More Grade 9 math lessons

Curriculum

Common Core State Standards HSF.LE.A.1.b: “Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.”

Common Core State Standards HSF.LE.A.1.a: “Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.