Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

C.D.1e

Explain graphically and analytically the relationship between the average rate of change and the instantaneous rate of change.

Example Problems

What is the average rate of change of

z(x) = |x|

over the interval

[-4, 3]

?

What is the average rate of change of

r(x) = 3^{x}

over the interval

[0, 2]

?

What is the average rate of change of

g(x) = 7 - 8x

over the interval

[3, 10]

?

Khan Academy Resources

Average rate of change review Average rate of change of polynomials Average rate of change word problems Average rate of change: graphs & tables Introduction to average rate of change Worked example: average rate of change from graph Worked example: average rate of change from table Sign of average rate of change of polynomials Average rate of change word problem: graph Finding average rate of change of polynomials Average rate of change word problem: table

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