Guided Lab Shell / Logic reasoning

Fraction Forge

Fraction Forge becomes a guided simulation lab where learners make predictions, act, revise, transfer, and produce evidence.

Playable World missions

Pick one mission. Follow the guide. Submit evidence.

Twenty certified missions span fair sharing, fraction operations, rational expressions, limits, and fractional exponents.

K-2 · Guided Lab Shell · released

Share the cookies

Give two friends equal cookie shares and check fairness

Share the cookiesShow my choice

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K-2 · Guided Lab Shell

Share the pizza

Distribute four equal pizza slices across four friends

Share the pizzaCheck all four shares

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3-5 · Guided Lab Shell · released

Two builds, one half

Build one half with two different partitions

Two builds, one halfTest my idea

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3-5 · Guided Lab Shell

Two builds, one third

Build 1/3 and 2/6, then compare their shaded lengths

Two builds, one thirdTest my idea

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3-5 · Guided Lab Shell

Quarters and halves

Build 2/4 beside 1/2 and test equivalence

Quarters and halvesTest my idea

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3-5 · Guided Lab Shell

Which is bigger: 1/3 or 1/4?

Compare one third with one fourth using a shared whole

Which is bigger: 1/3 or 1/4?Test my idea

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3-5 · Guided Lab Shell

Unit fraction lineup

Order 1/2, 1/3, 1/4, and 1/5 from largest to smallest

Unit fraction lineupCheck the order

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3-5 · Guided Lab Shell

Add one to the top and bottom?

Build one half, then add one to the top and the bottom

Add one to the top and bottom?Test my idea

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3-5 · Guided Lab Shell

Are these fifths?

Decide whether 2 of 5 unequal pieces make 2/5

Are these fifths?Line it up with equal fifths

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3-5 · Guided Lab Shell

Whose piece is bigger?

Compare 1/2 of a small bar with 1/4 of a bar three times as long

Whose piece is bigger?Measure both pieces

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3-5 · Guided Lab Shell

Two names, one amount?

Build 1/2 and 3/6 and test whether two names mean two amounts

Two names, one amount?Test my idea

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3-5 · Guided Lab Shell

Where does 3/4 go?

Decide whether 3/4 has a place on a 0-to-2 number line, then find it

Where does 3/4 go?Cut 0 to 1 into equal jumps

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3-5 · Guided Lab Shell

Add the tops and the bottoms?

Build 1/2 + 1/4 beside 2/6, the add-the-tops-and-bottoms answer

Add the tops and the bottoms?Test my idea

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6-8 · Guided Lab Shell · released

Equivalence via splitting

Split one half into fourths without moving its shaded edge

Equivalence via splittingLock it in and run

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6-8 · Guided Lab Shell

Compare 2/3 vs 3/5

Compare 2/3 and 3/5 using exact cross-products

Compare 2/3 vs 3/5Check the cross-products

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6-8 · Guided Lab Shell

Adding fractions: 1/4 + 1/3

Rename 1/4 and 1/3 in twelfths before combining

Adding fractions: 1/4 + 1/3Combine the twelfths

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6-8 · Guided Lab Shell

Fraction times fraction

Overlay 2/3 and 3/4 on a three-by-four area model

Fraction times fractionReveal the overlap

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6-8 · Guided Lab Shell

Beyond the unit: 7/4

Count seven fourth-size pieces across two unit bars

Beyond the unit: 7/4Join the two unit bars

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6-8 · Guided Lab Shell

Mixed numbers and improper fractions

Re-read five third-size pieces across two unit bars

Mixed numbers and improper fractionsJoin the two unit bars

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6-8 · Guided Lab Shell

The add-1-to-top-and-bottom trap

Test whether adding one to numerator and denominator preserves value

The add-1-to-top-and-bottom trapTest the tempting move

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6-8 · Guided Lab Shell

Does multiplying make it bigger?

Predict 1/2 × 1/3 against 1/3, then take half of the shaded third

Does multiplying make it bigger?Take half of the shaded third

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6-8 · Guided Lab Shell

How many halves fit?

Predict 4 ÷ 1/2, then cut four wholes into halves and count

How many halves fit?Cut and count

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9-12 · Guided Lab Shell · released

Scaling equivalence: proof and boundary

Generalize a visible split into a nonzero scaling argument

Scaling equivalence: proof and boundaryLock it in and run

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9-12 · Guided Lab Shell

Rational expression equivalence

Probe a rational expression and its simplified form at allowed and excluded inputs

Rational expression equivalenceProbe an x-value

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9-12 · Guided Lab Shell

The cancel-term trap

Find a numerical counterexample to canceling additive terms

The cancel-term trapTest an x-value

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9-12 · Guided Lab Shell

The square-root-2 chase

Squeeze square root of two between neighboring rational bounds

The square-root-2 chaseChoose a precision

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9-12 · Guided Lab Shell

Iterate to the limit

Iterate the geometric series and track its exact remainder

Iterate to the limitAdd the next term

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9-12 · Guided Lab Shell

The exponent bar

Compare a fractional exponent with division and test the inverse power

The exponent barChoose an x-value

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