1-01 Live
Add to and Take from Word Problems
Visualize addition and subtraction within 20 using an interactive frog jumping along a number line.
K-5 CCSS 1.OA.A.1CCSS 1.OA.C.5
Launch Game → K-12 Math Spectrum · CCSS Aligned
K-12 Interactive Math Tools & Virtual Manipulatives
A comprehensive catalog of 161 interactive math tools with 17 live bilingual games featuring real-world challenges and instant step-by-step feedback. Categorized by grade (K through 12) and mathematical domain.
Total Tools: 161
🌟 Live Interactive Games: 17
Grade Spectrum: K – 12
Native Vue · Real Challenges
🌟 Live Interactive Math Games
The following tools are fully published with native bilingual components, real challenges, instant step-by-step reasoning, and zero third-party iframes.
1-06 Live
Telling Time to the Hour and Half Hour
Move between hour and half-hour times while the analog hands and digital display update together.
K-5 CCSS 1.MD.B.3
Launch Game → 1-07 Live
Sort and Compare Three Categories
Change three category counts, read the matching bar chart, and answer how many or how many more.
K-5 CCSS 1.MD.C.4
Launch Game → 1-08A Live
Defining Shape Attributes
Rotate, resize, and recolor shapes while the sides and corners that define each name remain visible.
K-5 CCSS 1.G.A.1
Launch Game → 1-08C Live
Halves and Fourths of Circles and Rectangles
Partition circles and rectangles into halves or fourths and connect each equal share to its fraction name.
K-5 CCSS 1.G.A.3
Launch Game → 2-08B Live
Rows, Columns, and Rectangular Arrays
Tile a rectangle with equal squares, change its rows and columns, and connect counting to repeated addition.
K-5 CCSS 2.G.A.2
Launch Game → 2-08C Live
Halves, Thirds, and Fourths of Shapes
Make halves, thirds, and fourths in different arrangements and use equal area to name every share.
K-5 CCSS 2.G.A.3
Launch Game → 3-05 Live
Equivalent Fractions and Fraction Comparison
Generate equivalent fractions and compare fraction sizes using equal-length bars built from the same whole.
K-5 CCSS 3.NF.A.3
Launch Game → 5-11 Live
Fraction Line Plots and Operations
Plot fraction measurements on a number line and use fraction operations to solve real-world problems.
K-5 CCSS 5.MD.B.2
Launch Game → 5-12 Live
Unit Cubes, Volume Formulas, and Composite Solids
Pack unit cubes into 3D rectangular prisms, connect V = l × w × h with V = B × h, and calculate composite solid volumes.
K-5 CCSS 5.MD.C.3CCSS 5.MD.C.4
Launch Game → 6-09D Live
Nets and Surface Area of Solids
Explore nets and surface area of solids with a responsive visual model that connects each action to a mathematical relationship and explanation.
6-8 CCSS 6.G.A.4
Launch Game → 7-02 Live
Discounts, Tax, and Percent Change
Adjust original price, discount, and tax to explore multistep proportional relationships and real-world billing.
6-8 CCSS 7.RP.A.3
Launch Game → 7-07A Live
Two-Dimensional Cross Sections of Three-Dimensional Figures
Explore two-dimensional cross sections of three-dimensional figures with a responsive visual model that connects each action to a mathematical relationship and explanation.
6-8 CCSS 7.G.A.3
Launch Game → 8-05 Live
Systems of Linear Equations
Solve two linear equations graphically and explain what the intersection means in context.
6-8 CCSS 8.EE.C.8
Launch Game → 8-09C Live
Volumes of Cylinders, Cones, and Spheres
Explore volumes of cylinders, cones, and spheres with a responsive visual model that connects each action to a mathematical relationship and explanation.
6-8 CCSS 8.G.C.9
Launch Game → 9-04 Live
Linear Relations, Lines, and Systems
Connect equations, graphs, and intersections across Algebra I and Integrated Math I.
9-12 CCSS HSA-REI.C.5CCSS HSA-REI.C.6
Launch Game → K-05 Live
Number Bonds and Make Ten
Split numbers within 10, find complements to 10, and build addition and subtraction fluency within 5.
K-5 CCSS K.OA.A.3CCSS K.OA.A.4
Launch Game → Curriculum Spectrum
Browse Tools by Grade
From early number sense in Kindergarten to fractions in elementary, and systems of equations in middle/high school.
K
Kindergarten
Counting, cardinality, number comparisons, basic addition/subtraction, and 2D/3D shapes.
10 modules (1 live)
K-01 Design
Counting Sequences and Writing Numbers Counting and Cardinality
K-02 Design
One-to-One Correspondence and Cardinality Counting and Cardinality
K-03 Design
Comparing Quantities and Numerals Counting and Cardinality
K-04 Design
Joining, Adding To, Separating, and Taking Away Operations and Early Algebraic Thinking
K-05 Live
Number Bonds and Make Ten Operations and Algebraic Thinking
K-06 Design
Teen Numbers as One Ten and Some Ones Base-Ten Foundations
K-07 Design
Describing and Comparing Measurable Attributes Measurement and Data
K-08 Design
Sorting, Counting, and Ordering Categories Measurement and Data
K-09 Design
Two-Dimensional and Three-Dimensional Shapes Geometry
K-10 Design
Drawing, Building, and Composing Shapes Geometry
Grade 1
Grade 1
Addition/subtraction within 20, place value tens and ones, telling time, and shape partitions.
10 modules (5 live)
1-01 Live
Add to and Take from Word Problems Operations and Algebraic Thinking
1-02 Design
Operation Properties, Inverse Operations, and Equations Operations and Algebraic Thinking
1-03 Design
Counting to 120, Tens and Ones, and Comparing Numbers Base Ten and Two-Digit Numbers
1-04 Design
Addition Within 100 and Multiples of Ten Base Ten and Two-Digit Numbers
1-05 Design
Ordering Lengths and Measuring with Nonstandard Units Measurement and Data
1-06 Live
Telling Time to the Hour and Half Hour Measurement and Data
1-07 Live
Sort and Compare Three Categories Measurement and Data
1-08A Live
Defining Shape Attributes Geometry
1-08B Design
Composing and Decomposing 2D and 3D Shapes Geometry
1-08C Live
Halves and Fourths of Circles and Rectangles Geometry
Grade 2
Grade 2
Addition/subtraction within 100, arrays and repeated addition, length measurement, and equal shares.
10 modules (2 live)
2-01 Design
One-Step and Two-Step Problems Within 100 Operations and Algebraic Thinking
2-02 Design
Odd and Even Numbers with Rectangular Arrays Operations and Algebraic Thinking
2-03 Design
Place Value and Three-Digit Numbers to 1,000 Base Ten and Multi-Digit Numbers
2-04 Design
Addition and Subtraction Within 1,000 Base Ten and Multi-Digit Numbers
2-05 Design
Standard Length Units, Estimation, and Number-Line Distance Measurement, Time, Money, and Data
2-06 Design
Telling Time and Working with Dollars and Cents Measurement, Time, Money, and Data
2-07 Design
Line Plots, Picture Graphs, and Bar Graphs Measurement, Time, Money, and Data
2-08A Design
Identifying and Drawing Shapes by Their Attributes Geometry
2-08B Live
Rows, Columns, and Rectangular Arrays Geometry
2-08C Live
Halves, Thirds, and Fourths of Shapes Geometry
Grade 3
Grade 3
Multiplication & division concepts, unit fractions on a number line, area models, and perimeter.
11 modules (1 live)
3-01 Design
Multiplication and Division Models and Facts Multiplication, Division, and Arithmetic
3-02 Design
Two-Step Problems and Arithmetic Patterns Multiplication, Division, and Arithmetic
3-03 Design
Rounding and Arithmetic Within 1,000 Base-Ten Operations
3-04 Design
Unit Fractions, Fractions, and the Number Line Fractions
3-05 Live
Equivalent Fractions and Fraction Comparison Fractions
3-06 Design
Elapsed Time, Mass, and Liquid Volume Measurement and Data
3-07 Design
Scaled Graphs and Fraction Line Plots Measurement and Data
3-08 Design
Area Units, Arrays, and the Distributive Property Measurement and Data
3-09 Design
Perimeter, Area, and Unknown Side Lengths Measurement and Data
3-10A Design
Classifying Quadrilaterals and Other 2D Shapes Geometry
3-10B Design
Equal Areas and Unit Fractions Geometry
Grade 4
Grade 4
Multi-digit multiplication, equivalent fractions, line plots, angles, and 2D classification.
16 modules
4-01 Design
Multiplicative Comparison and Multistep Problems Operations and Algebraic Thinking
4-02 Design
Factors, Multiples, Prime Numbers, and Patterns Operations and Algebraic Thinking
4-03 Design
Place Value, Comparison, and Rounding to One Million Base Ten and Multi-Digit Numbers
4-04 Design
Standard Algorithms for Multi-Digit Addition and Subtraction Base Ten and Multi-Digit Numbers
4-05 Design
Multi-Digit Multiplication and One-Digit Division Base Ten and Multi-Digit Numbers
4-06 Design
Equivalent Fractions and Fraction Comparison Fractions and Decimals
4-07 Design
Fraction Decomposition and Like-Denominator Operations Fractions and Decimals
4-08 Design
Multiplying a Fraction by a Whole Number Fractions and Decimals
4-09 Design
Tenths and Hundredths as Fractions and Decimals Fractions and Decimals
4-10 Design
Measurement Conversions Within One System Measurement and Data
4-11 Design
Area and Perimeter Formulas with Unknown Sides Measurement and Data
4-12 Design
Line Plots with Fractional Units Measurement and Data
4-13 Design
Angle Measurement and Angle Addition Measurement and Data
4-14 Design
Points, Lines, Rays, Angles, Parallel, and Perpendicular Lines Geometry
4-15 Design
Classifying Triangles and Quadrilaterals Geometry
4-16 Design
Lines of Symmetry Geometry
Grade 5
Grade 5
Fraction operations, 3D unit cubes and volume formulas, coordinate planes, and line plots.
14 modules (2 live)
5-01 Design
Parentheses and Writing and Interpreting Expressions Operations and Algebraic Thinking
5-02 Design
Two-Rule Patterns and Coordinate Relationships Operations and Algebraic Thinking
5-03 Design
Powers of Ten and Decimal Place Value Base Ten and Operations
5-04 Design
Multi-Digit Multiplication and Two-Digit Division Base Ten and Operations
5-05 Design
Decimal Operations Through Hundredths Base Ten and Operations
5-06 Design
Adding and Subtracting Unlike Fractions and Mixed Numbers Fractions
5-07 Design
Fractions as Division Fractions
5-08 Design
Fraction Multiplication, Area Models, and Scaling Fractions
5-09 Design
Division with Unit Fractions Fractions
5-10 Design
Multistep Measurement Conversions Measurement, Data, and Volume
5-11 Live
Fraction Line Plots and Operations Measurement and Data
5-12 Live
Unit Cubes, Volume Formulas, and Composite Solids Measurement and Data
5-13 Design
First-Quadrant Coordinates and Real-World Problems Geometry
5-14 Design
The Hierarchy of Two-Dimensional Shapes Geometry
Grades 6-8
Middle School (Grades 6–8)
Ratios, proportions, negative numbers, linear systems, Pythagorean theorem, and statistics.
38 modules (5 live)
6-01 Design
Ratios, Rates, Unit Rates, and Multiple Representations Ratios, Rates, and Percents
6-02 Design
Finding the Whole from a Percent and Converting Rates Ratios, Rates, and Percents
6-03 Design
Dividing Fractions by Fractions The Number System
6-04 Design
Division, Decimal Operations, GCF, and LCM The Number System
6-05 Design
Positive and Negative Rational Numbers The Number System
6-06 Design
Variables, Terms, and Equivalent Expressions Expressions, Equations, and Inequalities
6-07 Design
One-Step Equations and One-Variable Inequalities Expressions, Equations, and Inequalities
6-08 Design
Independent and Dependent Variables Expressions, Equations, and Inequalities
6-09A Design
Area of Triangles and Polygons Geometry
6-09B Design
Volume with Fractional Edge Lengths Geometry
6-09C Design
Coordinate Polygons and Side Lengths Geometry
6-09D Live
Nets and Surface Area of Solids Geometry
6-10 Design
Statistical Questions, Distributions, Center, and Variability Statistics
7-01 Design
Unit Rates, Proportional Constants, and y = kx Proportional Relationships
7-02 Live
Discounts, Tax, and Percent Change Ratios and Proportional Relationships
7-03 Design
Rational Number Operations and Decimal Forms The Number System
7-04 Design
Rewriting Linear Expressions and Multistep Algebra Expressions, Equations, and Inequalities
7-05 Design
Linear Equations and Inequality Solution Sets Expressions, Equations, and Inequalities
7-06 Design
Scale Drawings and Triangle Construction Geometry
7-07A Live
Two-Dimensional Cross Sections of Three-Dimensional Figures Geometry
7-07B Design
Pi, Circumference, and Area of Circles Geometry
7-07C Design
Supplementary, Complementary, Vertical, and Adjacent Angles Geometry
7-07D Design
Area, Surface Area, and Volume of Composite Figures Geometry
7-08 Design
Random Samples and Population Inference Statistics and Probability
7-09 Design
Comparing Centers and Variability of Two Populations Statistics and Probability
7-10 Design
Theoretical and Experimental Probability Statistics and Probability
8-01 Design
Irrational Numbers and Rational Approximations The Number System
8-02 Design
Integer Exponents, Radicals, and Scientific Notation Exponents and Radicals
8-03 Design
Proportions, Slope, and Linear Equations Equations and Systems
8-04 Design
Three Solution Types for Linear Equations Equations and Systems
8-05 Live
Systems of Linear Equations Equations and Systems
8-06 Design
Functions in Tables, Graphs, Equations, and Words Functions
8-07 Design
Linear Functions, Rate of Change, and Initial Value Functions
8-08 Design
Transformations, Congruence, and Similarity Geometry
8-09A Design
Parallel Lines, Transversals, and Triangle Angles Geometry
8-09B Design
The Pythagorean Theorem and Coordinate Distance Geometry
8-09C Live
Volumes of Cylinders, Cones, and Spheres Geometry
8-10 Design
Scatter Plots, Lines of Fit, and Two-Way Tables Statistics
Grades 9-12
High School (Grades 9–12)
Algebra I, Integrated Math, linear relations, quadratic functions, and geometric modeling.
52 modules (1 live)
9-01 Design
Quantities, Units, and Mathematical Modeling Algebra I
9-02 Design
Expression Structure and Equivalent Forms Algebra I
9-03 Design
Linear Equations, Inequalities, and Rearranging Formulas Algebra I
9-04 Live
Linear Relations, Lines, and Systems Algebra I
9-05 Design
Function Domain, Range, and Multiple Representations Algebra I
9-06 Design
Linear Function Models Algebra I
9-07 Design
Exponential Growth and Decay Algebra I
9-08 Design
Quadratic Equations and Functions Algebra I
9-09 Design
Polynomial Operations, Zeros, and Factors Algebra I
9-10 Design
Univariate and Bivariate Data and Correlation Algebra I
9-11 Design
The Mathematical Modeling Cycle Algebra I
10-01 Design
Transformations in the Coordinate Plane Geometry
10-02 Design
Congruence and Triangle Criteria Geometry
10-03 Design
Geometric Theorems and Proof Geometry
10-04 Design
Compass and Straightedge Constructions Geometry
10-05 Design
Similarity and Proportionality Theorems Geometry
10-06 Design
Right Triangles and Trigonometric Ratios Geometry
10-07 Design
Circle Theorems, Arc Length, and Sector Area Geometry
10-08 Design
Coordinate Proofs, Lines, Circles, and Parabolas Geometry
10-09 Design
Area, Surface Area, Volume, and Dimensional Relationships Geometry
10-10 Design
Geometric Modeling Geometry
10-11 Design
Conditional Probability and Probability Rules Geometry
11-01 Design
Rational Exponents and Radicals Algebra II
11-02 Design
Complex Numbers and Quadratic Equations Algebra II
11-03 Design
Polynomial Theorems, Identities, and Zeros Algebra II
11-04 Design
Rational and Radical Expressions Algebra II
11-05 Design
Nonlinear Equations and Systems Algebra II
11-06 Design
Global Features of Functions Algebra II
11-07 Design
Function Transformations, Composition, and Inverses Algebra II
11-08 Design
Function Models and Growth Comparisons Algebra II
11-09 Design
Arithmetic and Geometric Sequences and Finite Series Algebra II
11-10 Design
The Unit Circle, Periodic Models, and Trigonometric Identities Algebra II
11-11 Design
Sampling, Experiments, and Statistical Inference Algebra II
11-12 Design
Conditional Probability, Expected Value, and Decisions Algebra II
12-A1 Design
Polynomial and Rational Functions Precalculus
12-A2 Design
Exponential and Logarithmic Functions Precalculus
12-A3 Design
Trigonometric and Polar Functions Precalculus
12-A4 Design
Parametric Equations, Vectors, Matrices, and Representations Precalculus
12-B1 Design
Limits and Continuity Calculus
12-B2 Design
The Definition of the Derivative and Differentiation Rules Calculus
12-B3 Design
Applications of Derivatives Calculus
12-B4 Design
Integrals, Accumulated Change, and Applications Calculus
12-B5 Design
Differential Equations and Growth Models Calculus
12-B6 Design
AP Calculus BC Extensions Calculus
12-C1 Design
Statistical Questions, Data Collection, and One-Variable Data Statistics
12-C2 Design
Probability, Random Variables, and Probability Distributions Statistics
12-C3 Design
Inference for Categorical Data: Proportions Statistics
12-C4 Design
Inference for Quantitative Data: Means Statistics
12-C5 Design
Regression Analysis and Choosing an Inference Method Statistics
12-D1 Design
Data Science Advanced Mathematics Pathways
12-D2 Design
Discrete Mathematics Advanced Mathematics Pathways
12-D3 Design
Financial Algebra Advanced Mathematics Pathways
Subject Domains
Browse Tools by Mathematical Domain
Cross-grade progression across fundamental math concepts for targeted conceptual practice.
Operations & Algebraic Thinking
28 toolsAddition, subtraction, multiplication, division, patterns, arrays, and word problem models.
1-01 · Add to and Take from Word Problems 1-02 · Operation Properties, Inverse Operations, and Equations 1-04 · Addition Within 100 and Multiples of Ten 2-01 · One-Step and Two-Step Problems Within 100 2-02 · Odd and Even Numbers with Rectangular Arrays 2-04 · Addition and Subtraction Within 1,000 3-01 · Multiplication and Division Models and Facts 3-02 · Two-Step Problems and Arithmetic Patterns
+20 more
Number & Operations in Base Ten
15 toolsPlace value, counting, multi-digit operations, and powers of ten.
1-03 · Counting to 120, Tens and Ones, and Comparing Numbers 1-04 · Addition Within 100 and Multiples of Ten 2-03 · Place Value and Three-Digit Numbers to 1,000 2-04 · Addition and Subtraction Within 1,000 3-03 · Rounding and Arithmetic Within 1,000 4-03 · Place Value, Comparison, and Rounding to One Million 4-04 · Standard Algorithms for Multi-Digit Addition and Subtraction 4-05 · Multi-Digit Multiplication and One-Digit Division
+7 more
Fractions & Decimals
18 toolsUnit fractions, equivalent fraction bars, fraction arithmetic, and decimal place values.
1-08C · Halves and Fourths of Circles and Rectangles 2-08C · Halves, Thirds, and Fourths of Shapes 3-04 · Unit Fractions, Fractions, and the Number Line 3-05 · Equivalent Fractions and Fraction Comparison 3-07 · Scaled Graphs and Fraction Line Plots 3-10B · Equal Areas and Unit Fractions 4-06 · Equivalent Fractions and Fraction Comparison 4-07 · Fraction Decomposition and Like-Denominator Operations
+10 more
Measurement, Data & Volume
19 toolsTime, money, bar graphs, line plots, 3D unit cubes, and volume formulas.
1-05 · Ordering Lengths and Measuring with Nonstandard Units 1-06 · Telling Time to the Hour and Half Hour 1-07 · Sort and Compare Three Categories 2-05 · Standard Length Units, Estimation, and Number-Line Distance 2-06 · Telling Time and Working with Dollars and Cents 2-07 · Line Plots, Picture Graphs, and Bar Graphs 3-06 · Elapsed Time, Mass, and Liquid Volume 3-07 · Scaled Graphs and Fraction Line Plots
+11 more
Geometry & Spatial Reasoning
31 tools2D/3D shapes, perimeter, area tiling, angles, coordinate planes, and Pythagorean proofs.
1-08A · Defining Shape Attributes 1-08B · Composing and Decomposing 2D and 3D Shapes 1-08C · Halves and Fourths of Circles and Rectangles 2-08A · Identifying and Drawing Shapes by Their Attributes 2-08B · Rows, Columns, and Rectangular Arrays 2-08C · Halves, Thirds, and Fourths of Shapes 3-10A · Classifying Quadrilaterals and Other 2D Shapes 3-10B · Equal Areas and Unit Fractions
+23 more
Eight Mathematical Practice Standards
Shared pedagogical principles guiding the interaction design of every tool in this catalog.
P-01
Make sense of problems and persevere in solving them
Break a problem into knowns, unknowns, and constraints, then keep trying viable steps.
P-02
Reason abstractly and quantitatively
Move between concrete quantities and the symbols that represent them.
P-03
Construct viable arguments and critique reasoning
Justify conclusions with evidence and evaluate the reasoning of others.
P-04
Model with mathematics
Represent real situations with diagrams, equations, and models.
P-05
Use appropriate tools strategically
Choose and use the right tool — number line, model, or diagram — for the task.
P-06
Attend to precision
Communicate clearly with accurate units, labels, and definitions.
P-07
Look for and make use of structure
Notice patterns and structure to simplify and generalize.
P-08
Look for and express regularity in repeated reasoning
Spot repetition to build shortcuts and general methods.
Frequently Asked Questions
What is the Inquiry AI K-12 Math Tool Catalog?
A structured catalog of 161 math manipulatives and concept labs spanning Kindergarten through Grade 12. Every tool aligns with Common Core standards to transform abstract equations and theorems into interactive visual models.
Are these virtual math manipulatives and games free to use?
Yes. All live interactive tools run directly in modern web browsers with zero downloads, zero logins, zero sign-ups, and zero ads.
What is the difference between Live Interactive Games and Reference Prototypes?
Live games (such as Frog Number Line Jumps, Telling Time, Fraction Line Plots, and 3D Unit Cubes) are built natively with responsive Vue components featuring real-world challenge modes, step-by-step reasoning, and touch/keyboard accessibility. Prototypes serve as interactive references and are progressively upgraded to native tools.
How do these tools support classroom instruction and home practice?
Each tool detail page provides a complete 10-point pedagogical guide, covering target grade levels, learning goals, step-by-step directions, focus observations, common misconceptions, prerequisite skills, and actionable tips for educators and parents.