Training module

Teaching functions with Desmos

Pagtuturo ng functions gamit ang Desmos

Use the free Desmos graphing calculator so learners predict, sketch and then verify graphs of linear, absolute value, quadratic, square root and cube root functions.

Time: 40 minutes
For: Grade 11 General Mathematics teachers (Term 1, Weeks 9–10)
Tools: Desmos

You will be able to

Set up a Desmos graph with sliders for the parameters of a function.
Design a predict–sketch–verify routine that keeps learners thinking before the technology answers.
Share a Desmos Classroom activity or a static link that works on low-end phones.

Module

Why Desmos

Desmos is a free, browser-based graphing calculator (desmos.com/calculator) that runs on most Android phones and needs no account. It renders equations instantly, so learners can test conjectures about how changing an equation changes its graph. It also works in a limited way without a connection once the page is loaded.

Set up a parameter explorer

f(x)=a|x-h|+k

g(x)=a(x-h)^2+k

r(x)=a\sqrt{x-h}+k

Type f(x)=a|x-h|+k. Desmos offers to add sliders for a, h and k; accept all three.
Set the slider ranges: a from -3 to 3 (step 0.5), h and k from -5 to 5 (step 1).
Add the point (h, k) so learners see the vertex move with the sliders.
Repeat with g(x)=a(x-h)^2+k and r(x)=a\sqrt{x-h}+k on the same graph; toggle visibility with the coloured circles.

The predict–sketch–verify routine

Explore

Technology should confirm thinking, not replace it. For every equation: learners predict the type of graph and the vertex or starting point, sketch it on paper or a mini whiteboard, and only then graph it in Desmos. Pairs compare their sketch to the screen and write one sentence explaining any difference.

Classroom logistics for one phone per group

One device per group of four; rotate the 'driver' every task.
Post equations on the board so the phone is used only for checking.
If data is scarce, load desmos.com/calculator once before class; the calculator keeps working while the tab stays open.
No internet at all? Project a screenshot set prepared in advance, or print the graphs as cards for a matching game.

Assessing with Desmos

Evaluate

Ask learners to produce an equation that matches a given screenshot (reverse engineering), or to find two different equations with the same vertex. Both tasks are harder than plotting and reveal whether they understand the parameters.

Try it

Build the three-function slider explorer above and save the link.
Write five equations in increasing difficulty for the predict–sketch–verify routine, including one square-root and one cube-root function.
Draft the sentence stems you will give learners for comparing their sketch to the Desmos graph.