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How do I teach math online?

Teaching math online works when the student can do the math with you — not just watch you work through it. In practice that means three things a video call plus a screen share can't give you: virtual manipulatives the student can drag and arrange on a shared canvas (number rods for early numeracy, fraction bars and circles for fraction sense, number lines and shapes for the geometric side), a way to write real math notation live during the lesson (a symbols palette so a fraction reads as a fraction and an angle reads as an angle, without stopping the lesson to Google how to type a square root), and a way to reach the practice the student needs — an interactive worksheet, a Desmos graph, a Khan Academy problem set — inside the lesson rather than in a link the student opens and drifts away from. The tools that make the difference between "we chatted about math for 30 minutes" and "we did math together" are almost always these three, plus (for younger learners) an engagement layer that keeps them past the fifteen-minute mark.

Why teaching math online is harder than teaching English or reading

The gap online math tutors hit is not that math is harder to teach remotely than reading is — plenty of teachers do both — it's that math has a physicality that generic web conferencing was never built to carry. In an in-person math lesson you routinely reach for something: a set of Cuisenaire rods to compare 3 + 7 against 10, a fraction wall to show that 2/4 is the same size as 1/2, a hundred-square to walk through place value, a pencil to write "x² + 3x − 4 = 0" without stopping to explain what the "²" is supposed to look like. On a video call, all of that lives on the teacher's side of the screen and the student watches. On a shared Google Doc it can move to a text box but not manipulate as a physical thing. The three problems below are the ones every math tutor eventually names, in some form.

  1. The manipulatives problem. Elementary and middle-school math is taught concretely before it's taught abstractly — you show a fraction by cutting a circle into quarters before you write 1/4 on a page. Manipulatives are how that works: physical objects the student picks up, moves, and compares. Online, the student is on the other side of a webcam. Either the student has their own physical set (parents almost never have Cuisenaire rods lying around), or they're watching you work — which is not the same thing.
  2. The notation problem. Real math has symbols keyboards don't. A student who wants to write "√25" in a Google Doc has to remember Alt-codes or paste from a page of glyphs. A fraction typed as "1/2" in a text box does not read as a fraction — it reads as one over two. Multi-digit exponents, angle marks, the plus-or-minus sign, an inequality that isn't ≤ or ≥ — every one of these is a small paper cut that slows the lesson down and makes the whiteboard look like a chat window instead of a page of math.
  3. The practice problem. Math is learned by doing problems, not by watching problems get done. In person, that means a worksheet on the desk. Online, that either means a PDF the student can't write on (bad), a PDF you send after the lesson (worse, because you're not there when they get stuck), or an interactive site the student opens in their own browser (a distraction risk with younger students, an accountability risk with older ones). None of these keep the student inside the shared lesson space.

An online math workflow that actually works has an answer to each of the three — not the same answer as in-person tutoring, but an answer that produces the same instructional move. The rest of this page walks through what those answers look like, and where Koala Go's math tools fit.

Solving the manipulatives problem: virtual manipulatives on the shared whiteboard

The move that closes the manipulatives gap is a set of manipulatives the teacher can place on the shared whiteboard and the student can drag, snap, and count in real time. On Koala Go, these live in a Math Tools panel inside the Whiteboard Library, available to every paid tutor (tier-gated by tool, not restricted to enterprise). The four kinds that do most of the work:

  • Cuisenaire-style number rods (Pro tier). Ten coloured rods, one unit through ten units long, that you drop onto the whiteboard and rearrange. The primary use is number-sense and early-arithmetic: compare a "5" rod and a "3" rod against an "8" rod to build the "5 + 3 = 8" fact; stack a red and a blue "5" rod against a "10" to see the bond; line up two "4" rods against an "8" to introduce multiplication as repeated addition. Rods are Pro-tier — so any working tutor on Koala Pro or Platinum can drop them into a lesson. On Platinum, you additionally get a red-and-blue alternating fill (the classic "count the units" visual), a vertical placement mode (useful when a rod is doing double duty as a bar chart), and an "add all" one-click staircase of all ten rods, which is the fastest way to reset the canvas at the start of a new number-sense activity.
  • Number lines (Pro tier). Preset lines for 0–10, 0–20, 0–30, 0–100 (by 5s or by 10s), −10 to 0, −10 to 10, and a blank one you can label yourself. These cover most K-5 numeracy — counting on, skip-counting, negative-number introduction, rounding. On Platinum, a "make your own" builder lets you specify start, end, and step (say, 0 to 1 in tenths for decimal work, or 0 to 360 in thirties for angle work) so you're not limited to the presets when a student needs something specific.
  • Fraction bars and fraction circles (Platinum tier). Individual bar segments and pie-slices for denominators of a half through a twelfth (plus a sixteenth) — you place one piece at a time and build up a whole together. This is what makes "1/4 + 1/2 = 3/4" a visual fact rather than a rule to memorise: place a half bar next to a quarter bar next to a quarter bar and see the three-quarters shape. The pie-slice equivalents let you do the same work in a circle rather than a bar, which some students grasp more easily. Denominators skip from twelve to sixteen (there's no thirteenth/fourteenth/fifteenth piece) because those are the denominators that actually show up in elementary and middle-school fraction work.
  • 2D and 3D shapes (core set on Pro, full library on Platinum). A shape library you place and resize on the canvas. The core shapes are on Pro — square, rectangle, circle, equilateral triangle, straight lines and arrows, and the cube — which covers a lot of basic area, perimeter, and symmetry work. The fuller library is Platinum: most polygons (rhombus, parallelogram, trapezium, kite, pentagon, hexagon, octagon), the non-equilateral triangles (isosceles, scalene, right-angle), curved 2D shapes (oval, semicircle, sector), and almost all the 3D solids (cylinder, sphere, cone, prism, pyramid, cuboid, and the rest — the cube is the one 3D solid on Pro). So a Pro tutor can do basic shape work; a tutor who leans on the full geometry set, especially 3D solids for faces-edges-vertices, wants Platinum. On Platinum, a shape-labels toggle also turns automatic labels on so a placed rectangle shows its dimensions without you retyping them each time.

Each of these is a first-class object on the shared whiteboard, meaning the student can grab it, move it, and rearrange it in real time — the same as they'd move a physical rod on a desk. The teacher isn't demonstrating; the student is doing. That's the point. For deeper walk-throughs of two of the most-searched sub-workflows: teaching fractions online covers the Fraction Bars and Fraction Circles workflow, and teaching number sense online with virtual manipulatives covers the Number Rods and Number Lines workflow.

Solving the notation problem: a math symbols palette on the whiteboard

Real math needs symbols keyboards don't have. Koala Go's whiteboard ships a Math Symbols palette on paid tiers, sorted into the categories you actually reach for during a lesson. On Koala Pro you get the operations, comparison, and geometry set you'd use through elementary and middle school: the four operations and equals (+ − × ÷ =), the basic comparisons (< >), the fraction/ratio/percent group (/ : %), a square-root sign (√), a degree symbol (°), and round brackets. On Koala Platinum you additionally get the algebra, geometry, and powers set that shows up in later middle school and secondary work: not-equal and approximately-equal (≠ ≈), less-than-or-equal and greater-than-or-equal (≤ ≥), superscript powers (² ³ ⁿ), pi and infinity (π ∞), plus-or-minus (±), and the geometry markers (∠ △ ⊥ ∥). Square and curly brackets sit on Platinum as well.

Clicking a symbol on the palette drops it into whichever text box, sticky note, or new text box you'd rather type into — so you can build up "x² + 3x − 4 = 0" or "∠ABC = 90°" or "3/4 + 1/2 = ?" without stopping the lesson to look up an alt-code. That is the whole design goal of the palette: keep the tutor in the lesson, not in the search for a symbol. For the full walk-through — both places the palette lives, the six notation moves that carry most math tutoring, and what to do when a lesson needs something the palette can't write — see how do I write math equations and notation on an online whiteboard?

Honest limit: the palette is a symbols set, not a full equation editor. It won't stack a fraction bar horizontally the way LaTeX would, won't nest a radical inside another radical, and doesn't render live graphs. For tutors who work heavily in advanced algebra, calculus, or graph-heavy statistics, that gap is real, and the pattern most Koala tutors use is the palette for symbols plus the cobrowser (below) for a graphing tool like Desmos when a live graph is what the lesson needs. Where the whiteboard's math coverage sits in the broader landscape — versus dedicated whiteboard tools with equation editors and graph modes — is described in the best online whiteboards for tutoring comparison, which we don't repeat here.

Solving the practice problem: cobrowser and PDF upload

The practice problem — how the student actually does math during the lesson — has two well-worn solutions inside a virtual classroom, and Koala Go ships both.

  • PDF and PowerPoint upload onto the whiteboard (Pro tier). On Koala Pro, you upload a worksheet as a PDF or a slide deck and it becomes the lesson surface — both you and the student can annotate the same page in real time, using the same pen and shape tools you'd use on a blank board. That collapses the "here's a worksheet, we'll go through it together" workflow from a screenshare-and-narrate exercise into a real shared workspace. The uploaded material stays on the whiteboard between lessons, so next week's continuation opens with last week's marks still there.
  • Cobrowser for interactive practice sites. A cobrowser is a shared browser window inside the classroom — you open a page (Khan Academy, IXL, Desmos, ALEKS, GeoGebra, NRICH, a school district's own interactive maths portal) and both of you can click, type, and interact with the page live. Not screen sharing — actual shared control. That means a student doing a Desmos graph or a Khan Academy problem is doing it in the lesson room, and you can see exactly what they typed, why they got it wrong, and jump in without them switching windows. On Koala Free the cobrowser is capped at 10 minutes per session with a 20-minute cool-down; on Pro it's unlimited. See what is a cobrowser? for the mechanic in depth, and how do I give homework to online tutoring students? for the between-lesson-practice workflow that uses it.

The pattern most working online math tutors converge on is: manipulatives + notation + one uploaded worksheet for the shared work, plus the cobrowser for one specific practice tool the lesson needs. Not four different tabs, five bookmarks, and a screenshare — one classroom.

Keeping a younger math learner engaged past the fifteen-minute mark

K-2 and lower-elementary math has an engagement problem on top of the mechanical problems above. A five-year-old learning to bond numbers to ten doesn't have the attention budget for a webcam-and-screenshare setup, no matter how good the manipulatives are. This is where the engagement layer of a virtual classroom starts to matter — rewards for a completed activity, an avatar in a shared 3D space as a brain break between problems, points the student is playing for. On Koala Go, that layer runs through the Playground (a shared browser-based 3D world with avatars), the Gems reward system (teachers award 1–100 gems per student per action; students see them add up in real time and can spend them on avatar customisation), and streak/rewards on top. This is the same engagement layer described in depth in what is a gamified virtual classroom? — for a young-learner math lesson it does the same job it does for a young-learner phonics lesson, which is to give the student a reason to want to come back next week.

Two things worth naming honestly. First, the engagement layer helps most below age ten; above that, students want the maths and the manipulatives, not the avatar, and lean into the workflow-and-notation side of the classroom instead. Second, this is not a substitute for good math teaching — a well-run lesson without an engagement layer will out-perform a badly run lesson with one every time. The engagement layer is what makes the difference between "we lost her at minute twelve" and "she wanted to do one more."

What Koala Go actually is for math, specifically

Koala Go (the classroom we build) is a browser-based virtual classroom purpose-built for independent tutors and small teaching businesses. For a math tutor, here's what's on the platform right now, at which tier:

  • The shared whiteboard (Free tier and up) is the primary lesson surface. It ships the standard pen/shape/text/sticky-note controls and lets both teacher and student act on the same canvas.
  • PDF and PowerPoint upload onto the whiteboard is a Koala Pro feature ($25.99/month monthly, $21.99/month billed annually). Free-tier tutors can upload images but not PDF or PPT.
  • Math Tools panel inside the Whiteboard Library, with tier splits as described above: Number Rods, Number Lines, the core 2D/3D shapes (square, rectangle, circle, equilateral triangle, lines, cube), and the basic Math Symbols set on Pro; Fraction Bars, Fraction Circles, Number Roller, advanced Math Symbols, the full shape library (most polygons and the 3D solids), Shape Labels, red-and-blue rod fills, and the "make your own" number line on Platinum ($49.99/month monthly, $39.99/month billed annually). Enterprise/B2B tutors are treated as professional and never see Platinum locks.
  • Cobrowser for practice-site work is on every tier — capped at 10 minutes with a 20-minute cool-down on Free, unlimited on Pro.
  • Playground, avatars, and Gems — the engagement layer for younger math learners — is available across tiers; see the gamified virtual classroom explainer for how it fits together.
  • Scheduling, recording, and worldwide invoicing — the workflow layer that matters when a math tutor's practice grows past a handful of students — is Pro-and-up. See how to schedule online tutoring lessons and how to record online tutoring lessons for the specifics.

The Free tier is enough to try Koala Go with a student — the whiteboard, image uploads, a capped cobrowser session, and the Playground — but the Math Tools panel itself (Number Rods, Number Lines, Shapes, Fractions, Math Symbols) is gated behind Pro or Platinum, so Free is a trial surface rather than a math-tutoring day-to-day. Pro is where the tools most math tutors reach for daily land — Number Rods, Number Lines, the core shapes, the operations symbols, PDF upload, unlimited cobrowser. Platinum adds fractions, the algebra/geometry symbols, the full shape library (most polygons and the 3D solids), and the "make your own" number-line builder — the specific tools middle-school and early-secondary math work depends on.

Where Koala Go isn't the right pick for math

Two honest tradeoffs worth naming, so you know before you sign up:

  • Advanced STEM tutoring that lives on a full equation editor or live graphing. Koala Go's whiteboard math tools go deep on the elementary-and-middle-school side — manipulatives, notation, worksheets, practice sites. They stop short of a full LaTeX-style equation editor or a live graphing canvas of the kind a dedicated STEM whiteboard would ship. For late-secondary calculus or heavily graph-driven statistics tutoring where every lesson needs a live-plotted function, a dedicated STEM whiteboard (compared honestly in the best online whiteboards for tutoring) usually goes further on the whiteboard axis. What Koala tutors typically pair with the Math Tools palette for that gap is a cobrowser tab into Desmos or GeoGebra.
  • Whole-class delivery to a 25-student math class. Koala Go is calibrated for 1-on-1 and small-group tutoring — the free tier caps sessions at four students, and Pro lifts that cap for group teaching. It's not designed for a full school-class synchronous delivery of the kind Nearpod or Pear Deck are built for. For that shape of teaching, look at platforms built for whole-class lesson delivery.

Honest limits worth flagging that show up in real teaching regardless of subject: iPad works for lessons but is rougher than desktop for extended math work with heavy manipulatives; students in mainland China sometimes hit connection issues (we route through Hong Kong proxies but the Great Firewall is a moving target — see teaching students in mainland China for the workaround pattern); and the Playground itself is actively developed, with requested features (timers, group-select of objects) still on the roadmap rather than shipped today.

By age band: what actually works

Different age bands lean into different parts of the toolkit. A rough guide, matching what most tutors converge on after a few months:

  1. K–2 (ages 5–7): manipulatives + engagement layer. Number rods, number lines to twenty, pie-slice fractions, and the Playground / Gems reward layer between short activities. Sessions are 25–30 minutes with two or three activities inside them. Notation is minimal (mostly + − =); the manipulatives are what teach.
  2. Grades 3–5 (ages 8–10): manipulatives shifting to notation. Rods and number lines for multiplication and division facts, fraction bars for equivalent fractions, the operations palette to start writing equations. Cobrowser walk-throughs of Khan Academy or IXL start earning their keep here. Engagement layer still matters, but sessions can push to 40–45 minutes with the right pacing.
  3. Middle school (ages 11–13): notation-heavy, some manipulatives. The algebra symbol set (superscripts, ± , < ≤ > ≥, √, π, ∠), fraction bars for early ratio and proportion work, the number-roller for randomised practice problems, geometry shapes with labels. Cobrowser into Desmos for graph work or GeoGebra for angle work becomes standard.
  4. High school (ages 14–17) and adult learners: notation, practice, and worksheets. Uploaded PDF past-papers on the whiteboard, the algebra/geometry symbol set, cobrowser into subject-specific practice sites and graphing tools. Engagement layer is beside the point at this age band; the notation and workflow layers do the work. See how do I teach exam prep online? for the exam-focused version of this workflow (SAT, ACT, A-level maths, IB, GRE).

Related answers (and the math cluster we're building out)

This page is the top of a small hub — over the coming weeks we're publishing spokes on specific parts of the workflow. Existing neighbours that already cover an adjacent question:

If you'd like a walk-through of the setup for your subject mix and student ages, open Koala Go at classroom.teachwithkoala.com, or write to koala@teachwithkoala.com with a sentence about the shape of your math practice and we'll give you our honest read on the fit — including the parts where a dedicated STEM whiteboard would suit you better.

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