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Discover apps people built on Collabby by chatting. Run them, then remix to make them yours.
Complex Numbers & the Complex Plane
Plot points on the complex plane and discover how multiplication rotates by adding angles and multiplying magnitudes, then draw regular polygons with powers.
Arithmetic & Geometric Sequences
Explore how terms grow using common differences and ratios, then pair the two sequences to discover a sum formula.
Sorting by Color and Shape
Color, shape, and use guide you as you drop matching items into the sparkling basket to build a group.
Conditional Probability and Bayes
Add a condition and watch the denominator shrink out of 100, then trace the probability tree backward to see whether a positive test really means disease.
Repeated and Circular Permutations
Rearrange items by hand to compare permutations with repetition, circular permutations, and permutations with repeated letters, and see how the counting rule changes.
Pascal's Triangle and the Binomial Theorem
Tap cells in Pascal's triangle to see that the entries, the right-and-down lattice paths, and the coefficients of (a+b)ⁿ are all the same combinations.
Combinations nCr
List every possible selection, divide permutations by r! to strip out order, and see the symmetry of choosing r versus leaving out the rest.
Counting and Permutations
Fill the spots one by one, multiplying the choices that remain, and count the leaves of the tree diagram to confirm the multiplication rule and n!.
Limits of Sequences and Infinite Series
Change the common ratio to see where convergence, divergence, and oscillation part ways, and find when an infinite geometric series still adds up to a finite sum.
Two-Digit Multiplication
Split two-digit numbers into tens and ones to see the four part-products, and find out why the second line of long multiplication shifts a place.
Order of the Day
Read the sun's position and sky color to tell morning, day, evening, and night apart, then put the day in order.
Parts and Wholes
Fill the missing piece and join the halves to figure out the whole picture from just a part.
Comparing Sizes
Pick from aligned objects to compare big and small, long and short, then tap them in size order.
Counting Fun
Tap objects one by one to count them, fill the basket to match a number, and compare which side has more.
Colors & Shapes
Tap big color dots to paint pictures, then compare colors and shapes to find the matching twin and the missing piece in repeating patterns.
Multiplying Fractions
Cut an area model across and down, count the overlapping squares, and see why multiplying fractions gives a smaller answer.
Multiplying and Dividing Decimals
Drop the decimal point, multiply, then put it back by counting the decimal places to discover the rules for multiplying and dividing decimals.
Long Division
Divide, multiply, subtract, and bring down to see where each quotient digit sits and how big a remainder can get.
Carrying and Borrowing
Change the two numbers and watch when the ones place forces you to carry or borrow, then solve problems column by column.
Probability
Put red and blue balls in the bag to name the chance in words and as 0, 1/2, or 1, then compare two bags on the same scale.
Big Numbers
Tap nine place-value slots to build huge numbers and skip-count to see which digits change as you add or subtract.
Units of Length
Read millimeter ticks by placing objects on a 20cm ruler, then see one length as mm, cm, m, and km to pick the unit that fits best.
Dividing Fractions
Count with bar models how many times a fraction fits, then multiply by the reciprocal to divide fractions.
Function Rules
Feed numbers into the rule box to find △=○×a+b, and use tables and expressions to see how two quantities correspond.
Counting Outcomes
Pair tops with bottoms in a grid and arrange number cards to count outcomes by the multiplication principle and n×(n−1).
Order of Operations
Clear parentheses and ×÷ first, watching an expression shrink one step at a time to learn the order of operations.
Simplifying Fractions
Divide fraction bars by common factors to see the size stay the same, then use the greatest common factor to reach the simplest form in one step.
Weight and Capacity
Stack 1kg, 100g, 1L, and 100mL blocks to see that 1kg=1000g and 1L=1000mL, then convert mixed units.
Mixed and Improper Fractions
Slice and group pizzas to see how an improper fraction like 7/3 turns into the mixed number 2 1/3.
Elapsed Time
Move the hands of two analog clocks to see how start time plus elapsed time gives the end time, then test it in a quiz.
Rounding and Estimation
Slide numbers along a number line to see how rounding up, rounding down, and rounding to the nearest differ.
Ratio and Proportion
Mix blue and yellow to build the ratio a:b, then discover how multiplying both parts gives equivalent ratios with the same value.
Percentages
Color 100 squares to link percentages with fractions and decimals, and use bar models to find discounted prices.
Exponent Rules
Change the base and exponent to count factors and see why aᵐ×aⁿ adds exponents while (aᵐ)ⁿ multiplies them, then test it on division and powers.
Array Multiplication
Place dots in rows and columns to link multiplication with repeated addition, then rotate the array to see the total stay the same.
Bar Models
Draw numbers as bars to compare part and whole, find the difference between two amounts, and work out the missing ? in word problems.
Ten Frames
Fill a ten frame with dots to see how many more make 10, then turn 8+5 into 10+3 to add.
Scientific Notation
Change the coefficient a and exponent n in a×10ⁿ to watch the decimal point shift, and write huge or tiny quantities like the speed of light in scientific notation.
Probability
Spin spinners and roll dice to watch the experimental probability close in on the theoretical one, and count the outcomes behind each two-dice sum.
Multiplication Formulas & Area Model
Slice a square into parts to see (a+b)² and (a+b)(a−b) as areas, then use the algebraic identities to find values.
Quadratic Equations · Factoring & Discriminant
Set two roots, expand (x−r₁)(x−r₂)=0 and watch the discriminant b²−4ac tell how many real roots meet the parabola's x-intercepts.
Saltwater Concentration (Dilution & Evaporation)
Set the concentration (%) of a salt solution, then add water or let it evaporate to see how the unchanging mass of salt determines the new percentage.
Square Roots & Irrationals (√ on the Number Line)
Build square roots from the area of a square and locate them between two integers on the number line to understand irrational numbers.
Prime Factors, GCD & LCM
Break numbers down into prime factors and compare the exponents to work out the greatest common divisor and the least common multiple.
Linear Inequalities & Number Lines
Solve linear inequalities step by step and mark the solution set on a number line (●/○), seeing how dividing by a negative flips the inequality sign.
Algebra Tiles (Expanding & Factoring)
Expand and factor (x+a)(x+b) by arranging rectangular tiles until their areas match.
Outcomes & Probability
Roll two dice and flip coins to count outcomes with the multiplication rule and tree diagrams, then read off the probability of each sum out of 36.
Fun with Integers
Jump along the number line to master addition and subtraction of integers, then apply sign rules to multiplication and division.