MathTabla Labs

See the curriculum, then pick the model.

MathTabla Labs are now organized as learning progressions: repeated addition, area models, box methods, manipulatives, and traditional scaffolds all connect instead of living as one-off prototypes.

Build the area Explore the map

Live lab gallery

Curriculum paths

Start with the math idea

Each path shows the representation ladder: concrete model, visual structure, organized method, then the traditional scaffold.

Path

Repeated addition → area → box → algorithm

Multiplication progression

A KISS ladder for multiplication: start with grouped quantities, move into rectangles, then compress the same partial products into box and symbolic scaffolds.

Repeated addition with rodsUse Cuisenaire® rods or base-ten chains to make “groups of” visible before notation.
Next
Base-ten area modelWhole-number multiplication as a decomposed rectangle.Ready
Algebra tile binomialsBinomial products as area with x², x, and unit tiles.Ready
Traditional scaffoldUse the same partial products after the structure is understood.
Planned

Path

Reverse area → regroup → quotient

Division progression

Division should feel like running the rectangle backward: start with the area, keep one side fixed, and discover the missing side.

Reverse base-ten rectangleBuild 84 ÷ 7 by regrouping tens and ones against the known side.Ready
Division layout languageName target area, side rail, quotient rail, and regrouping regions.Prototype
Partial quotient bridgeConnect the visual decomposition to chunking and partial quotients.
Planned
Traditional scaffoldMove to algorithmic division once the reverse-area logic is stable.
Planned

Path

Tiles → box → a·c → symbolic factoring

Factoring progression

Factoring is multiplication in reverse, so the UX should separate the manipulative model from the box method and later symbolic cases.

Factor with algebra tilesRecover side lengths from a completed tile rectangle.
Next
Box method factoringSplit the middle term, fill the box, and read factors from rails.Ready
a > 1 factoringIntroduce a·c decomposition after the box structure is familiar.
Planned
Traditional factoring scaffoldFade the visual support into symbolic factoring choices.
Planned

Path

Length model → common unit → add → reduce

Fraction common-unit progression

Fractions need a representation ladder too: rods for magnitude, organizers for common units, then symbolic addition and simplification.

Fractions as rod lengthsChoose a whole, compare parts, and feel equivalent lengths.Prototype
Common denominator organizerRace denominator rows to find the first shared unit.Ready
Composable organizer V2Break common-unit work into smaller engines: race, scale, add, reduce, convert.Ready
Traditional fraction scaffoldMove from common-unit visuals into symbolic operations.
Planned

Manipulative families

Then choose the representation

Families are reusable engines. A family can power several curriculum tasks without turning one page into a three-headed prototype dragon.

Whole-number structure

Base-ten blocks

The concrete engine for place value, area multiplication, reverse-area division, regrouping, and eventually base-ten chains.

place valueareadivisionregrouping

Base-Ten Area Model Base-Ten Division

Next: Build the base-ten chain / repeated-addition bridge.

Polynomial area model

Algebra tiles

A manipulative family for multiplying binomials, combining like terms, and later factoring trinomials without stuffing it all into one page.

binomial productslike termsfactoringbox bridge

Quadratic Factoring Box Base-Ten Division Layout Playground

Next: Split the current tile playground into focused multiplication and factoring pages.

Length relationships

Cuisenaire® rods

The representation for repeated addition, fraction magnitude, equivalent lengths, and systems/comparison work.

repeated additionfractionsequivalencesystems

Systems with Cuisenaire® rods Algebra Tiles

Next: Create the multiplication/repeated-addition rod path.

Common-unit engine

Fraction organizers

A curriculum family for denominator races, scale factors, equivalent fractions, adding, reducing, and mixed-number conversion.

common denominatorscale factorsadditionreduction

Fractions with Cuisenaire® rods Fraction Graphic Organizer

Next: Promote V2 as the canonical activity and retire the old MVP to workshop when ready.

Current activity pages

Ready-to-open experiences

These are the concrete pages available now. Some will eventually move under focused curriculum-path routes.

New

Forward rectangle lab

Base-Ten Area Model

Build 22 x 21 with base-ten blocks, move the same partial products into the box method, then run the rectangle backward for division.

Build the area

Division

Reverse rectangle lab

Base-Ten Division

Start with 84 as eight tens and four ones, use the known 7-side, and discover the missing quotient through regrouping.

Try 84 divided by 7

Recovered

Prototype rebuild

Quadratic Factoring Box

Split the middle term, build the factoring box, and move the shared factors into the row and column rails. This is the recovered CAMT prototype rebuilt for the web.

Factor the box

Sketch

Layout sketch tool

Base-Ten Division Layout Playground

Drag labels, rails, regions, tens, and ones into a rough division setup, then copy the JSON snapshot so the real model can match it.

Sketch the layout

Demo

Equation systems lab

Systems with Cuisenaire® rods

Use Cuisenaire® rods to compare two relationships, align unknowns, and see where the equations balance. It is really systems of equations made tangible.

Solve with rods

MVP

Common unit lab

Fraction Graphic Organizer

Race denominator rows to find the first shared unit, move the landing groups into scale factors, then build equivalent fractions before adding.

Find the common unit

New

Area model lab

Algebra Tiles

Set the factors, build the product grid, click-count every tile, then watch the middle terms combine into the trinomial. This is the hands-on algebra playground.

Build a trinomial

Workshop shelf

Useful prototypes, clearly labeled

These stay accessible for development and review, but they no longer compete with the student-facing curriculum paths.

Forward rectangle lab

Base-Ten Multiplication Scene

Set the two factor sides, fill the rectangle with hundreds, tens, and ones, then read the product — rebuilt on the new LabDraggable scene.

Rod fraction lab

Fractions with Cuisenaire® rods

Build fraction sums with Cuisenaire® rods instead of flat bars alone: choose a whole, compare rod lengths, and make equivalent pieces snap into meaning.

Composable common unit lab

Fraction Graphic Organizer V2

Work the same common-unit organizer through smaller engines: denominator race, scale-factor mapping, common-unit addition, reduction, and mixed-number conversion.

Cuisenaire® rods are referenced descriptively. MathTabla is not affiliated with or endorsed by the trademark owner. Legal notices