Learn together
Pictures, prompts, and step checks stay visible.
A separate learning space · working name
Math should feel like someone is teaching you.
Start with a picture, work one manageable step at a time, and let the help fade when you are ready. Released pilot practice now spans Kindergarten foundations through Grade 12 goal-directed pathways.
Try with a hint
The model stays, but help waits until you ask.
Show what I know
No hints. This becomes one piece of independent evidence.
kindergarten
Kindergarten foundations
Count, compare, sort, measure, and reason with shapes using friendly concrete models.
Sort by one attribute
Notice one shared attribute and use it to make a group.
Count a small group
Count each object once and tell how many are in the group.
Count all the way to 10
Keep one count word matched to each object in a larger group.
Match a set to its numeral
Represent how many objects are in a set with a written numeral, including zero.
Which group has more?
Compare two visible groups as more, fewer, or equal.
One more or one less
Connect the next or previous number to a change of one object.
Keep counting from here
Continue the count sequence without starting over at one.
Find the missing part
See a whole as two parts and find a missing part.
Put two groups together
Use objects or drawings to solve a small joining or taking-away story.
Take some away
Use objects or drawings to solve a small joining or taking-away story.
Compare length or height
Describe and compare a visible length, height, or capacity.
Count a sorted category
Classify visible objects and count how many are in a named category.
Name the shape
Recognize a shape even when its size or orientation changes.
Count sides and corners
Describe shapes using sides, corners, faces, edges, and curved surfaces.
Build a larger shape
Put simple shapes together to make a new shape.
Build teen numbers
Read teen numbers as one group of ten and some extra ones.
grade 1
Grade 1 paths
Build flexible operations, place value, time, measurement, data, and equal-share reasoning.
Add within 10
Join or separate small quantities accurately.
Subtract within 10
Join or separate small quantities accurately.
Add within 20
Use number relationships and make-ten thinking within 20.
Subtract within 20
Use number relationships and make-ten thinking within 20.
Find the unknown in a story
Represent adding to, putting together, taking from, and comparing with an unknown in different positions.
Add three small groups
Combine or separate quantities while keeping track of each part.
Is the equation true?
Treat the equal sign as a claim that both sides have the same value.
Find the missing number
Use the relationship between addition and subtraction to find an unknown.
Make a ten to add
Break apart an addend to make a friendly ten.
Continue toward 120
Continue a number sequence and connect numerals to quantities beyond 20.
Compare two-digit numbers
Compare tens first, then ones when the tens match.
Ten more or ten less
Change the tens while preserving the ones.
Add a one-digit number
Combine tens and ones, composing a new ten when needed.
Subtract groups of ten
Use the value of tens to subtract without counting every one.
Measure with equal units
Place equal-size units end to end with no gaps or overlaps.
Tell time to the half hour
Connect analog clock hands with hour and half-hour digital times.
Read a picture graph
Read category counts in a picture graph where each picture represents one vote.
Which attribute defines it?
Separate defining attributes such as sides from non-defining attributes such as color.
Halves and fourths
Split circles and rectangles into two or four equal parts and name the shares.
grade 2
Grade 2 workshop
Work through hundreds, regrouping, story problems, arrays, measurement, money, data, and geometry.
Tens and ones
Interpret each digit in a two-digit number as tens or ones.
Add by place value
Align tens and ones and add each place.
Subtract by place value
Align tens and ones and subtract each place.
Regroup when adding
Bundle 10 ones into a new ten while adding.
Decompose a ten
Trade one ten for 10 ones when the top ones are too small.
Odd or even?
Pair objects to decide whether every object has a partner.
Count an array
Use repeated addition to find the total in rows and columns.
Hundreds, tens, and ones
Read a hundred as ten tens and locate the value of every digit.
Write expanded form
Move among numerals, number names, base-ten models, and expanded form.
Compare three-digit numbers
Move among numerals, number names, base-ten models, and expanded form.
Skip-count by 5, 10, or 100
Continue sequences that grow by equal groups.
Ten or one hundred more or less
Use the relationship among ones, tens, and hundreds to change a number mentally.
Solve a two-step story
Represent a story, choose operations, and track what each step finds.
Read a ruler
Read a length from a zero-aligned ruler and compare measurements.
Tell time to five minutes
Use minute marks and the hour hand together.
Count coin values
Use coin values and skip-counting to find a total amount.
Read a bar graph
Use a data display to answer category and comparison questions.
Classify shapes by attributes
Use sides, angles, faces, and other defining attributes to classify shapes.
Equal shares of rectangles
Partition rectangles into equal rows, columns, halves, thirds, or fourths.
grade 3
Grade 3 multiplication bridge
Connect equal groups to multiplication and division, then build fractions, area, perimeter, elapsed time, and scaled-data reasoning.
Multiply equal rows
Connect equal groups and arrays to a multiplication equation.
Share an array equally
Interpret division as the size or number of equal groups.
Use a related fact
Use commutative and inverse relationships instead of isolated memorization.
Choose multiplication or division
Represent equal-group situations and decide which operation answers the question.
Name one equal part
Treat one equal part of a whole as a unit fraction.
Locate a fraction on a number line
Build fractions by iterating equal unit lengths from zero.
Find an equivalent fraction
Explain equivalence by matching the same amount with different equal partitions.
Compare like-denominator fractions
Compare how many equal parts are selected when the whole and denominator match.
Find rectangle area
Connect rows of unit squares, multiplication, and rectangle area.
Find rectangle perimeter
Add every outside side length without confusing perimeter with area.
Find elapsed minutes
Measure the duration between two times using friendly intervals.
Read a scaled bar graph
Use the stated scale before comparing category values.
grade 4
Grade 4 fraction workshop
Use multiplicative comparisons, multi-digit arithmetic, equivalent fractions, decimals, angles, conversions, and shape properties.
Compare multiplicatively
Distinguish “times as many” from additive comparison.
Find factor pairs
Use rectangular factor pairs to analyze whole numbers through 100.
Round a multi-digit number
Use the neighboring multiples and midpoint instead of a memorized digit trick.
Multiply by place value
Decompose a multi-digit factor and combine partial products.
Divide and interpret a remainder
Use place value and equal groups to find a quotient and remainder.
Scale an equivalent fraction
Multiply numerator and denominator by the same nonzero whole number.
Compare unlike fractions
Compare fractions referring to the same whole using a benchmark or common denominator.
Add and subtract like-denominator fractions
Join or separate same-size fractional parts and preserve the denominator.
Multiply a fraction by a whole number
Interpret repeated copies of a fraction as multiplication.
Connect fractions and decimals
Move between decimal notation and fractions with denominator 10 or 100.
Compare decimals to hundredths
Compare place values only when both quantities refer to the same whole.
Convert within one measurement system
Use a known multiplicative relationship between like measurement units.
Measure an angle
Treat angle measure as the amount of turn between two rays.
Classify lines and shapes
Use parallel, perpendicular, and angle properties to classify a figure.
Read a fractional line plot
Use a line plot whose scale is partitioned into equal fractional units.
grade 5
Grade 5 pre-algebra bridge
Build expressions, decimal and fraction operations, volume, coordinate reasoning, patterns, and shape hierarchies.
Evaluate grouped expressions
Evaluate the innermost grouped calculation before applying outside operations.
Compare two patterns
Generate corresponding terms and describe a relationship between two rules.
Shift by powers of ten
Explain how a digit value changes by a factor of ten from one place to the next.
Round a decimal
Use neighboring decimal benchmarks and place value to round to a requested place.
Multiply multi-digit numbers
Combine place-value partial products accurately.
Divide by a two-digit divisor
Estimate and verify quotients using multiplication.
Add and subtract decimals
Align equal place values before combining decimal quantities.
Multiply decimals
Use whole-number products and reason about decimal place value.
Add unlike-denominator fractions
Rename fractions with a common denominator before combining them.
Solve a fraction story
Model fractions referring to the same whole and check reasonableness.
Interpret a fraction as division
Connect sharing whole numbers to numerator divided by denominator.
Multiply fractions
Multiply numerators and denominators while tracking the size of the result.
Divide with a unit fraction
Use how many fractional units fit and the inverse relationship with multiplication.
Find prism volume
Connect layers of unit cubes to length times width times height.
Locate a coordinate point
Read horizontal x-distance before vertical y-distance.
Use a shape hierarchy
Recognize that a figure can belong to every category whose properties it satisfies.
grade 6
Grade 6 ratios and variables
Develop ratios, signed numbers, fraction division, variables, geometry, and statistical distributions.
Describe a ratio
Describe how two quantities compare using an ordered pair of multiplicities.
Complete a ratio table
Scale both quantities by the same factor and organize equivalent pairs.
Find a unit rate
Divide both quantities to find an amount for one unit.
Find a percent of a quantity
Connect percent, fractions with denominator 100, and multiplication.
Divide fractions
Interpret fraction division through measurement and reciprocal multiplication.
Find a GCF or LCM
Analyze factor and multiple structure without relying on isolated lists.
Compare signed numbers
Use position and context to compare positive and negative quantities.
Interpret absolute value
Separate a number's direction from its distance to zero.
Plot in four quadrants
Interpret signs as horizontal and vertical directions from the origin.
Evaluate whole-number exponents
Interpret an exponent as repeated multiplication of equal factors.
Evaluate a variable expression
Substitute a value while preserving grouping and operation order.
Solve a one-step equation
Use inverse operations while maintaining equality.
Represent an inequality
Connect a boundary, strictness, and direction to infinitely many solutions.
Find polygon area
Split triangles and quadrilaterals into familiar area models.
Reason about prisms
Connect nets and layers to surface area and rectangular-prism volume.
Describe a distribution
Use center, variability, and shape together to describe numerical data.
grade 7
Grade 7 proportional reasoning
Apply proportions and rational arithmetic to equations, geometry, sampling, and probability.
Find a rate with fractions
Divide fractional quantities to express an amount per one unit.
Identify a proportional relationship
Check for a constant ratio and a graph through the origin.
Write a proportional equation
Use the constant of proportionality in an equation of the form y = kx.
Solve a percent-change problem
Use the original quantity as the percent-change reference.
Add and subtract signed numbers
Model direction and distance while combining signed quantities.
Multiply and divide signed numbers
Use sign relationships and magnitude separately.
Rewrite an expression
Use distribution and combining like terms without changing value.
Solve a multi-step equation
Undo distribution and combine like terms while preserving equality.
Solve an inequality
Reverse the comparison only when multiplying or dividing by a negative.
Use a scale drawing
Apply a scale factor consistently to corresponding lengths.
Find circle measures
Distinguish radius, diameter, circumference, and area.
Use angle relationships
Use complementary, supplementary, vertical, and adjacent relationships.
Solve a solid-measure problem
Choose and apply the measure appropriate to a three-dimensional situation.
Reason from a sample
Judge whether a sample can represent a population and interpret its estimate cautiously.
Find a simple probability
Compare favorable equally likely outcomes with all possible outcomes.
Find a compound probability
Use organized lists or trees to count multistage outcomes.
grade 8
Grade 8 linear foundations
Unify equations, functions, exponents, transformations, Pythagorean reasoning, solids, and bivariate data.
Locate an irrational number
Use nearby perfect squares to place an irrational value on the number line.
Evaluate a root
Connect roots to inverse exponent relationships.
Apply exponent laws
Combine equal bases by operating on exponents and interpret negative exponents.
Compute with scientific notation
Separate coefficients from powers of ten and normalize the result.
Find slope
Compare vertical change with horizontal change between two points.
Write a line equation
Represent a constant rate and initial value with y = mx + b.
Solve a linear equation
Expand, collect terms, and preserve equivalence to isolate the variable.
Count equation solutions
Simplify both sides to see whether the variable remains or a true/false statement results.
Solve a linear system
Find the ordered pair that satisfies both equations.
Is it a function?
Require every input to have exactly one output.
Compare two functions
Extract and compare rate of change or initial value from tables and equations.
Classify a function
Check whether equal input changes produce equal output changes.
Transform a point
Track coordinates under translations, reflections, and rotations.
Reason about similarity
Distinguish rigid motions from dilations and compare corresponding measures.
Use the Pythagorean theorem
Relate the square on the hypotenuse to the squares on the legs.
Find round-solid volume
Choose the correct round-solid structure and distinguish linear from cubic measures.
Interpret a scatterplot
Describe direction, form, and strength without treating association as causation.
grade 9
Grade 9 Algebra I pathway
Model constraints and functions, compare growth, operate on polynomials, factor quadratics, and interpret their graphs.
Rearrange a formula
Use inverse operations to rewrite a formula for a named variable.
Build a linear model
Translate a situation into a linear expression and interpret its parameters.
Solve a linear inequality
Preserve equivalence while isolating a variable and reversing the sign when required.
Eliminate a variable
Combine equivalent equations so one variable cancels, then check the ordered pair.
Model two constraints
Create and solve two simultaneous constraints, then interpret the viable solution.
Evaluate function notation
Treat function notation as a named input-output rule rather than multiplication.
Choose a meaningful domain
Restrict inputs to values that make sense for the modeled quantity.
Find average rate of change
Compare output change with input change over a specified interval.
Write an arithmetic sequence rule
Connect a common difference to explicit and recursive sequence rules.
Evaluate exponential growth
Interpret initial value and growth factor in an exponential model.
Compare linear and exponential growth
Use equal differences or equal ratios to identify and compare model families.
Read polynomial structure
Read a polynomial as a structured expression before operating on it.
Add polynomials
Combine only terms with matching variable parts and exponents.
Multiply polynomial expressions
Distribute every term and combine like powers without losing signs.
Factor out a common factor
Reverse distribution by removing the greatest shared factor.
Factor a monic quadratic
Find two integers whose product and sum match the quadratic coefficients.
Connect factors and zeros
Use the zero-product property to connect factors, solutions, and intercepts.
Read a quadratic graph
Connect quadratic form to the graph’s vertex, symmetry, and direction.
grade 10
Grade 10 Geometry pathway
Build proof, congruence, similarity, trigonometry, coordinate geometry, circles, and solid measurement.
Use segment addition
Use betweenness and addition to connect two adjacent lengths with the complete segment.
Reason with a transversal
Distinguish congruent angle pairs from supplementary same-side pairs.
Find a missing triangle angle
Connect the three interior angles of a triangle to a total of 180 degrees.
Choose a congruence criterion
Decide whether marked side and angle information proves SSS, SAS, ASA, AAS, or HL.
Choose a valid proof reason
Select a precise justification for a step rather than relying on appearance.
Find a polygon angle sum
Use a triangulation from one vertex to explain the interior-angle sum formula.
Dilate a coordinate point
Multiply both coordinates by the same scale factor and interpret the image point.
Find a corresponding side
Match corresponding sides before applying one common scale factor.
Name a trigonometric ratio
Identify opposite, adjacent, and hypotenuse relative to a marked acute angle.
Find a side with trigonometry
Choose the ratio that connects the known side to the requested side.
Find coordinate distance
Treat horizontal and vertical changes as legs of a right triangle.
Find a segment midpoint
Find the coordinate halfway between each pair of endpoint coordinates.
Write a perpendicular line
Use a negative reciprocal slope and verify that the new line passes through the given point.
Find an arc length
Use the central-angle fraction of a full circle to scale its circumference.
Find an inscribed angle
Recognize that an inscribed angle measures half its intercepted arc.
Read a circle equation
Interpret signed binomials and the squared radius in standard circle form.
Find a solid volume
Use dimensions and the appropriate cylinder or cone formula while preserving exact pi.
Scale the volume of a solid
Cube a linear scale factor because three independent dimensions are changing.
grade 11
Grade 11 Algebra II pathway
Extend functions, polynomial and rational structure, complex numbers, sequences, probability, and data models.
Transform a function graph
Connect changes inside and outside function notation to horizontal and vertical graph changes.
Predict polynomial end behavior
Use the parity of the degree and sign of the leading term to predict both ends of a polynomial graph.
Find polynomial zeros
Read every linear factor as a zero and retain all real solutions.
Use the Remainder Theorem
Recognize that dividing by x minus a leaves remainder p of a.
Add complex numbers
Treat real parts and imaginary parts as separate like-term groups.
Multiply complex numbers
Distribute complex factors and replace i squared with negative one before combining terms.
Find complex quadratic roots
Interpret a negative radicand with i and keep both square-root branches.
Recognize a polynomial identity
Match expanded and factored structures by distribution rather than surface resemblance.
Simplify a rational expression
Cancel common factors while retaining excluded domain values.
Solve a rational equation
Clear denominators, solve the resulting equation, and reject values outside the original domain.
Solve a radical equation
Square only after isolating the radical and verify the result in the original equation.
Find an inverse function
Exchange input and output, then solve for the new output.
Compose two functions
Use the inner output as the outer input without combining unrelated rules.
Solve an exponential equation
Rewrite compatible bases or apply the inverse relationship between exponents and logarithms.
Evaluate a geometric sequence
Use an initial term and common ratio in an explicit geometric sequence rule.
Find a conditional probability
Use only the conditioned group as the denominator and count its overlap with the target event.
Use the probability addition rule
Add two event probabilities and subtract their shared intersection once.
Interpret a model residual
Compute observed minus predicted and interpret the sign as above or below the model.
grade 12
Grade 12 advanced pathways
Choose among precalculus, statistics, calculus readiness, financial modeling, and matrix applications.
Convert degrees and radians
Use a half-turn as the anchor relating 180 degrees and pi radians.
Read a unit-circle coordinate
Use reference angles and quadrant signs to identify exact coordinates.
Read a sinusoidal model
Read vertical scale and center from a periodic function rule or graph.
Use a trigonometric identity
Use sine squared plus cosine squared equals one and select the sign from the quadrant.
Find vector components
Subtract initial coordinates from terminal coordinates in a fixed order.
Add vectors by components
Add corresponding components while preserving magnitude-and-direction meaning.
Standardize a data value
Subtract the mean and divide by the standard deviation with attention to sign.
Use a normal-distribution benchmark
Connect one, two, and three standard deviations with the empirical-rule proportions.
Estimate probability by simulation
Divide simulated successes by total trials and distinguish an estimate from a guarantee.
Interpret a confidence interval
Describe a plausible range for a population parameter without assigning probability to a fixed parameter.
Explain random assignment
Separate random sampling for generalization from random assignment for treatment comparison.
Critique a statistical claim
Match the strength of a conclusion to sampling, assignment, measurement, and possible confounders.
Find average rate of change
Compute output change over input change and interpret it over an interval.
Estimate a limit from a table
Track values approaching from both sides without requiring the function value at the point.
Differentiate a power function
Multiply by the exponent and reduce the exponent by one.
Approximate accumulation
Multiply each rate by its interval width and sum the signed contributions.
Model compound growth
Distinguish principal, periodic rate, number of periods, and accumulated value.
Apply a matrix transformation
Multiply each matrix row by the vector column and interpret the new vector.