6th Grade Math

327 core topics + 11 prerequisite topics taught as needed · approximately 95 hours of instruction including spaced review

How the course runs

An adaptive diagnostic (up to 40 questions) places the student on the course's knowledge graph - topics already known are credited, and instruction begins exactly at the learning frontier. Every topic is taught with a worked-example lesson and auto-graded practice; a topic is mastered at 75%+ and then maintained through spaced reviews on an expanding schedule. Mixed checks follow every 6 lessons; each unit ends with a 12-item quiz, and course-wide assessments appear at 25%, 50%, 75%, and 100% mastery. Prerequisite gaps below the course are detected and taught rather than skipped, so completion certifies the whole tower, not just the top.

Core curriculum

Arithmetic Foundations · 7 topics

Adding & Subtracting Whole Numbers [E]	Multi-digit addition and subtraction.
Multiplication [E]	Multiplying whole numbers.
Division [E]	Dividing whole numbers.
Order of Operations [M]	Parentheses first, then multiplication/division, then addition/subtraction.
Negative Numbers: Adding & Subtracting [M]	Working with numbers below zero on the number line.
Negative Numbers: Multiplying & Dividing [M]	Sign rules for products and quotients.
Exponents [M]	Repeated multiplication in shorthand.

Fractions · 7 topics

Equivalent Fractions [M]	Different fractions can name the same amount.
Simplifying Fractions [M]	Reducing a fraction to lowest terms.
Adding Fractions (Like Denominators) [M]	Same-denominator addition.
Adding Fractions (Unlike Denominators) [M]	Rewrite over a common denominator first.
Multiplying Fractions [M]	Multiply straight across.
Dividing Fractions [M]	Multiply by the reciprocal.
Mixed Numbers & Improper Fractions [M]	Converting between forms.

Decimals, Percents & Ratios · 5 topics

Decimal Addition & Subtraction [M]	Line up the decimal points.
Fractions ↔ Decimals [M]	Converting between the two notations.
Percent of a Number [M]	Percent means per hundred.
Percent Increase & Decrease [M]	Applying a percent change to a quantity.
Ratios & Proportions [M]	Two quantities that scale together.

Expressions & Equations · 3 topics

Evaluating Expressions [M]	Substituting a value for a variable.
Combining Like Terms [M]	Adding the coefficients of matching variable parts.
One-Step Equations [M]	Undoing a single operation.

Elementary Math Skills · 10 topics

Place Value & Comparing [E]	Each digit's position multiplies its value by ten.
Rounding & Estimation [E]	Look one digit to the right: 5 or more rounds up.
Multi-Digit Multiplication [E]	Split by place value, multiply each part, add.
Long Division [M]	Divide, multiply, subtract, bring down - repeat.
Time & Elapsed Time [E]	Count up to the next hour, then keep going.
Money Problems [E]	Money is decimals with two places - line up the point.
Units & Measurement [E]	Bigger unit → multiply; smaller unit → divide.
Perimeter & Area of Rectangles [E]	Perimeter walks around; area covers.
Reading Graphs & Tables [E]	Read the values first; the math is the easy part.
Multi-Step Word Problems [M]	One sentence at a time: what do I know, what changes, what's asked?

Ratios, Data & Geometry (Middle School) · 12 topics

GCF & LCM [E]	Greatest common factor and least common multiple.
Prime Factorization [E]	Every whole number is a unique product of primes.
Absolute Value & Distance [E]	Absolute value is distance from zero.
Unit Rates [E]	Per-one comparisons: dollars per item, miles per hour.
Ratio Tables & Equivalent Ratios [E]	Scaling both parts of a ratio keeps it equivalent.
Area: Triangles & Trapezoids [E]	Half of base times height - and its trapezoid cousin.
Area of Composite Figures [E]	Split odd shapes into rectangles and triangles.
Volume: Rectangular Prisms [E]	Length × width × height, fractional edges included.
Surface Area & Nets [E]	Unfold the box: surface area is the area of its net.
Mean, Median & Range [E]	Three ways to summarize a data set with one number.
Reading Data Displays [E]	Pulling answers out of dot plots, tables, and bar graphs.
Probability Basics [E]	Favorable outcomes over total outcomes.

Grade 5: Fraction Operations in Depth · 12 topics

Rewriting with Common Denominators [E]	Before unlike fractions can meet, rename them with the same-size pieces.
Adding Unlike Fractions in Context [M]	Rename to a common denominator, then add the numerators - story or not.
Subtracting Unlike Fractions in Context [M]	How much more, how much left - common denominator first, then subtract tops.
Estimating Sums with Benchmark Fractions [M]	Round each fraction to 0, 1/2, or 1 before computing - the estimate polices the answer.
Fraction × Fraction with Area Models [M]	Columns for one fraction, rows for the other - the overlap is the product.
Fraction of an Amount [M]	“Of” means multiply: divide by the bottom, multiply by the top.
Multiplication as Scaling [M]	Compare the factor to 1 - that alone says whether the product grows or shrinks.
Dividing a Unit Fraction by a Whole Number [M]	Splitting 1/b into n equal shares makes pieces n times smaller: 1/(b × n).
Dividing a Whole by a Unit Fraction [M]	n ÷ 1/b asks how many 1/b-size pieces fit in n - every whole holds b of them.
Mixed Numbers with Unlike Denominators [M]	Handle wholes and parts separately - but give the parts a common denominator first.
Multiplying Mixed Numbers [M]	Convert each mixed number to an improper fraction, then multiply straight across.
Multi-Step Fraction Word Problems [H]	Chain the moves: combine the fractions first, then compare to the whole.

Grade 5: Patterns, Expressions & Data · 12 topics

Nested Grouping Symbols [E]	Work from the innermost parentheses outward.
Comparing Expressions [E]	Parentheses can make the same numbers give a bigger or smaller value.
Writing Expressions from Words [E]	Turn a phrase into symbols - parentheses show what happens first.
Interpreting Expressions [E]	See what an expression says without grinding out the arithmetic.
Rules & Input-Output Tables [E]	Apply a two-step rule forward - or undo it backward.
Generating Number Patterns [E]	Follow the rule step by step to grow the pattern.
Comparing Two Patterns [M]	Line up matching terms and see how the two rules relate.
Ordered Pairs from Patterns [M]	Pair matching terms as (x, y) points ready to plot.
Reading Points in Real-World Graphs [E]	A point (x, y) tells a story: x of one thing, y of another.
Classifying Triangles [E]	Name triangles by their sides or by their angles.
The Quadrilateral Hierarchy [M]	Categories nest: a square is a rectangle is a parallelogram.
Multi-Step Conversion Problems [M]	Convert to one unit first, then finish the problem.

Grade 6: Rational Numbers & the Coordinate Plane · 12 topics

Opposites in Context [E]	Every number has a mirror twin on the other side of zero.
Absolute Value in Context [E]	Absolute value answers 'how far from zero?' - order answers 'which is greater?'
Comparing & Ordering Rational Numbers [E]	Smaller means farther left on the number line - even below zero.
Rational Numbers on the Number Line [E]	Fractions and decimals claim exact spots between the integers.
Plotting in All Four Quadrants [E]	Negative coordinates open up the other three quadrants.
Reflections Across the Axes [E]	Reflecting a point just flips the sign of one coordinate.
Distances on the Coordinate Plane [M]	Same x or same y: subtract and take the absolute value.
Rectangles on the Coordinate Plane [M]	Coordinates give the side lengths; perimeter and area follow.
Dividing Fractions: Word Problems [M]	'How many of this size fit?' is a division by a fraction.
Decimal Operations in Context [E]	Money problems are decimal arithmetic with two places, always.
Dividing Decimals in Context [M]	Slide both decimal points until the divisor is whole, then divide.
Percent of a Quantity: Parts & Wholes [M]	Percent problems run in three directions: find the part, the percent, or the whole.

Grade 5: Volume & Measurement Applications · 12 topics

The Volume Formula V = l × w × h [E]	Multiply the three edge lengths - no more counting cubes one by one.
Base Area × Height: Thinking in Layers [E]	A prism is a stack of identical layers, so volume is base area times height.
Volume Word Problems [M]	Spot the three dimensions hiding in a story, then multiply them.
Finding a Missing Dimension [M]	Divide the volume by the dimensions you know to uncover the one you don't.
Comparing Volumes [E]	Compute each volume, then subtract to see how far apart they are.
Volume of Composite Solids [M]	Split an L- or step-shaped solid into two prisms and add their volumes.
Volume by Subtraction [M]	When a piece is carved away, find the whole, find the hole, and subtract.
Packing Problems: How Many Fit? [M]	Count how many fit along each edge, then multiply the three counts.
Liquid Volume: Liters & Milliliters [E]	Convert between liters and milliliters to solve pouring and filling stories.
Mass Word Problems: Grams & Kilograms [E]	Turn kilograms into grams before adding, subtracting, or scaling masses.
Cubic Centimeters Meet Milliliters [M]	One cubic centimeter holds exactly one milliliter - volume becomes capacity.
Multi-Step Measurement Problems [H]	Chain a volume computation with a unit conversion to finish a real task.

Grade 5: Multi-Step Word Problems · 12 topics

Adding Up the Shopping Cart [M]	Multiply each price by its count, then add the lines like a receipt.
Unit Prices [M]	Divide the total by the count to find the price of just one.
Making Change [M]	Total the purchase first, then subtract it from what was handed over.
Budgets: Spending & Saving [M]	Track what goes out against what you started with - and what still fits.
Two-Step Whole-Number Problems [M]	Do the sentences in order: build the total first, then adjust it.
Equal Shares or Equal Groups? [E]	The same division answers two different questions - know which one you asked.
What the Remainder Means [M]	Round up, drop, or report the leftover - the story decides, not the arithmetic.
Recipe Problems: Add, Then Multiply [M]	Combine the fraction amounts for one batch, then scale up by the number of batches.
Fraction of a Group, Then One More Step [M]	Find the fraction of the group first - then answer what the story actually asks.
Mixing Decimals & Fractions [H]	Friendly numbers let fractions and decimals share one problem - take the fraction first.
Choosing the Operation [M]	Match the story's action to the right operation before touching the numbers.
Multi-Step Problem Marathon [H]	Three or more moves in one story - plan the steps before computing any of them.

Grade 6: Equations & Inequalities in Context · 12 topics

Writing Addition & Subtraction Equations [E]	Turn a join-or-separate story into a one-step equation.
Writing Multiplication & Division Equations [E]	Equal-groups and fair-share stories become px = q or x ÷ p = q.
Solving Add & Subtract Equations in Context [E]	Undo one addition or subtraction to answer the story's question.
Solving Multiply & Divide Equations in Context [E]	Undo one multiplication or division to find the missing amount.
Is It a Solution? [E]	Substitute a value for the variable and see if both sides agree.
Money Equations [M]	One-step equations where the amounts are dollars and cents.
Evaluating Expressions in Context [E]	Substitute a number for the variable and follow the order of operations.
Dependent & Independent Variables [E]	Which quantity drives the relationship, and which one responds?
Using Two-Variable Equations [E]	Feed the independent variable into a rule to get the dependent one.
Writing Inequalities from Constraints [E]	Translate 'at least', 'more than', 'at most', 'fewer than' into symbols.
Graphing Inequalities on a Number Line [E]	Open or closed circle, shaded left or right - read and draw both ways.
Boundary Values of an Inequality [E]	Find the smallest or greatest whole number an inequality allows.

Grade 6: Ratios, Rates & Statistical Thinking · 13 topics

Equivalent Ratios in Context [E]	Scale both parts of a ratio by the same number to keep it equivalent.
Solving Problems with Ratio Tables [M]	Extend a ratio table by scaling a known row up or down.
Unit Rate as a Tool [M]	Divide to a per-one rate, then multiply back up to answer.
Unit Pricing & the Better Buy [M]	Reduce each option to price per unit, then the smaller one wins.
Finding a Part or the Whole from a Ratio [M]	One share of the ratio unlocks every part and the total.
Percent as a Rate per 100 [E]	A percent is just a ratio scaled to a denominator of 100.
Finding a Percent of a Number [M]	Percent of a number = (percent ÷ 100) × the number.
Recognizing a Statistical Question [E]	A statistical question anticipates variety in its answers.
Mean, Median & Mode [M]	Three single-number summaries of the 'center' of a data set.
The Mean as a Fair Share & Balance Point [M]	The mean is what everyone gets when totals are shared out evenly.
Range: Measuring Spread [E]	Range is the distance from the smallest value to the largest.
Interquartile Range [M]	The IQR is the spread of the middle half of the data.
Describing the Shape of a Distribution [E]	Read a distribution's shape: symmetric, skewed, or uniform.

6th Grade Math - Mastery II · 15 topics

Dividing Fractions by Fractions [M]	Dividing by a fraction means multiplying by its reciprocal.
Whole-Number Exponents [M]	An exponent counts how many times the base is used as a factor.
Order of Operations with Exponents [M]	Exponents come before multiplication, which comes before addition.
Writing Algebraic Expressions [M]	Turn each phrase into an operation, watching the order words imply.
Combining Like Terms [M]	Add the coefficients of the x-terms; add the plain numbers separately.
The Distributive Property [M]	Multiply the outside factor by each term inside the parentheses.
Factoring Out the Greatest Common Factor [M]	Pull the largest shared factor to the front of the parentheses.
Identifying Equivalent Expressions [M]	Two expressions are equivalent if they agree for every value of x.
Volume with Fractional Edge Lengths [M]	Volume is length × width × height, even when the edges are fractions.
Converting Units with Ratios [M]	A conversion is a rate: multiply by how many small units fill one big one.
Mean Absolute Deviation [M]	MAD is the average distance of the data values from their mean.
Choosing the Better Measure of Center [M]	Use the median when an outlier would drag the mean; otherwise the mean.
Mean from a Frequency Table [M]	Multiply each value by its frequency, add, then divide by the count.
Reading a Box Plot [M]	The box marks Q1, median, and Q3; the whiskers reach the extremes.
Reasoning on a Double Number Line [M]	Scale both rows of the double number line by the same factor.

6th Grade Math - Mastery III · 34 topics

Unit Rates with Fractions [H]	Divide a fraction distance by a fraction time to get a per-one rate.
Working with Fractional Rates [H]	Multiply a per-one fraction rate up, or divide a total back down.
Setting Up Percent Equations [H]	Every percent problem is (percent as a decimal) × whole = part.
Solving Percent Problems with Equations [H]	Undo the multiplication in a percent equation to find the unknown.
Multi-Step Percent Problems [H]	Percents of the same whole add to 100, so the leftover group is 100 minus the rest.
LCM Word Problems [H]	Repeating events line up again at the least common multiple.
GCF Word Problems [H]	The greatest number of identical groups is the GCF of the counts.
GCF or LCM? Choosing the Tool [H]	Splitting into groups points to GCF; waiting for events to line up points to LCM.
Rewriting a Sum with the GCF [H]	Pull the GCF out of both addends: a + b = GCF x (sum of what is left).
Ordering Signed Numbers in Context [H]	Least means farthest left on the number line, not smallest digits.
Comparing Values and Absolute Values [H]	A number can be smaller in value yet larger in absolute value.
Grid Distances: Walking the Blocks [H]	Along the streets, distance is the across-change plus the up-change.
Right Triangles on the Coordinate Plane [H]	Coordinate differences give the legs; the area is half their product.
Distances Created by Reflections [H]	A point and its axis reflection sit twice the coordinate's distance apart.
Matching Nets to Solids [M]	Count and name a net's shapes to see which solid it folds into.
Surface Area of a Triangular Prism [H]	Two triangle ends plus three rectangles, one for each triangle side.
Surface Area Problems in Context [H]	Real surface-area problems drop faces or add a cost step.
Reading a Histogram [H]	Each bar counts the values falling in one interval of equal width.
Interpreting a Histogram [H]	Use interval counts to find the mode interval, percents, and the median's home.
Finding the Equation Behind a Table [H]	Test a candidate rule against every row - one row is never enough.
Extending a Two-Variable Table [H]	Recover the rule from the filled rows, then apply it to the new row.
Testing Solutions of an Inequality [H]	Substitute the value and check the comparison, watching the boundary.
Inequalities Below Zero [H]	Below zero, 'colder' and 'lower' move AWAY from zero on the number line.
Missing Exponents & Bases [H]	Work a power backward: keep multiplying the base until the target appears.
Comparing Powers [H]	Evaluate each power before comparing - a bigger base does not always win.
Edges from Areas and Volumes [H]	Undo s squared or s cubed by asking which number was multiplied by itself.
Powers of Ten [M]	10 to the k is a 1 followed by k zeros; multiplying appends the zeros.
Comparing Rates [H]	Convert each traveler to a per-one rate, then compare the rates.
Percents from Benchmarks [H]	Snap a percent to 10%, 5%, and 1% chunks and add the pieces.
Polygon Areas by Decomposition [H]	Cut a grid polygon into rectangles and right triangles, then add or subtract.
Multi-Step Unit Conversions [H]	Chain the conversion rates one hop at a time, then finish the question.
Volume Stories with Fractional Edges [H]	Use V = lwh forward for filling, backward for a missing edge, and count small cubes by volume.
Zero Pairs: Changes that Cancel [M]	A quantity and its opposite add to zero, so spot the pair that cancels first.
Exponents and Parentheses [H]	Parentheses decide what gets raised: the whole group, or just one base.

6th Grade - Ratios, Rates & Percent (Mastery) · 38 topics

Multi-Step Ratio Word Problems [H]	Find the multiplier that scales the ratio, then read off any part.
Ratio Tables with a Missing Entry [H]	Every row shares one ratio; scale a full row to fill the blank.
Splitting a Total by a Ratio [H]	Add the ratio parts, divide the total into that many shares, hand them out.
Three-Term Ratios [H]	A three-part ratio scales exactly like a two-part one: one multiplier.
Part-to-Part and Part-to-Whole [H]	A part-to-part ratio a : b hides a part-to-whole fraction a / (a + b).
Ratios in Simplest Form [H]	Divide both terms by their greatest common factor to reach lowest terms.
Equivalent Ratios on a Double Number Line [H]	Whatever factor moves one row of a double number line, moves the other.
Which Ratio Is Stronger? [H]	Give both ratios a common term, or compare their unit rates, then decide.
Multi-Step Unit-Rate Problems [H]	Reduce to a per-one rate, then multiply by whatever amount is asked.
Comparing Unit Rates [H]	Turn each into a per-one rate; the larger per-one value is faster.
From a Unit Rate to a Big Total [H]	Multiply the per-one rate by the total count to scale all the way up.
Filling a Rate Table [H]	Find the constant per-one rate from a full row, then extend it.
Best Value Among Three Sizes [H]	Divide price by quantity for each; the smallest per-item price wins.
Distance = Speed x Time [H]	At a constant speed, distance is speed multiplied by time.
Time = Distance / Speed [H]	To find the time, divide the distance by the constant speed.
Speed = Distance / Time [H]	Speed is the distance covered divided by the time it took.
Multi-Leg Trips at Constant Speed [H]	Find each leg's distance with speed x time, then add the legs.
Comparing Two Travelers [H]	Find each traveler's distance, then subtract (or add) as the story asks.
Percent of a Quantity [H]	Percent of a number = (percent / 100) x the number.
Finding the Whole from a Part [H]	If a part is p% of the whole, the whole is the part divided by p/100.
What Percent Is This? [H]	Percent = (part / whole) x 100.
Percent Remaining [H]	The listed percents plus the leftover make a full 100 percent.
Sale Price after a Discount [H]	A p% discount leaves (100 - p)% of the price; multiply to get the sale.
Adding Sales Tax [H]	Tax is a percent of the price; the total is price plus that tax.
Figuring a Tip [H]	A tip is a percent of the bill; add it on, then split if needed.
Percent Increase in Context [H]	Increase = p% of the start; the new amount is start plus that increase.
Percent Decrease in Context [H]	Decrease = p% of the start; the new amount is start minus that decrease.
Markup and Selling Price [H]	Markup is a percent of the cost added on to set the selling price.
Discount, Then Tax [H]	Take the discount first, then charge tax on the discounted price.
Scaling a Recipe Up [H]	Find how many times bigger the batch is, then scale every ingredient.
Scaling a Recipe Down [H]	Making a fraction of a recipe multiplies every ingredient by that fraction.
A Missing Ingredient by Ratio [H]	Keep the recipe's ratio: scale the known ingredient to find the other.
Map Scale: Real Distance [H]	Multiply the map length by how many real units one map unit stands for.
Map Scale: Distance on the Map [H]	To go from real distance back to the map, divide by the scale.
Converting Length by Ratio [H]	A conversion is a rate: multiply to go to smaller units, divide to go up.
Converting Capacity and Weight [H]	Use the per-one conversion rate; multiply going down, divide going up.
Two-Step Unit Conversions [H]	Convert one step at a time: big to middle, then middle to small.
Converting the Units in a Rate [H]	Change a rate's time unit by multiplying or dividing by the conversion.

6th Grade - Number System, Expressions & Equations (Mastery) · 37 topics

Servings from What Is Left [H]	Take away what is used first, then divide the rest by one serving.
Finishing the Leftover Piece [H]	Divide to find the leftover, then subtract it from one whole piece.
Unit Price from a Fractional Weight [H]	Divide the cost by the fractional weight to get the price per pound.
Comparing Servings from Two Pots [H]	Divide each pot by its own bowl size, then subtract the two counts.
A Missing Length from an Area [H]	Area equals length times width, so length is area divided by width.
Identical Bags with Nothing Left Over [H]	The most equal groups with no remainder is the GCF of the two counts.
When Two Schedules Line Up [H]	Two repeating events coincide again after the LCM of their periods.
Tiling a Floor with the Largest Square [H]	The largest square tile that fits with no cuts has side equal to the GCF.
Matching Packages Evenly [H]	The smallest equal total is the LCM of the two pack sizes.
Temperature Spread Across Cities [H]	Order the signed values, then subtract the lowest from the highest.
Vertical Distance with Signed Heights [H]	Distance is the absolute value of the difference of the two elevations.
How Deep Is the Deepest Debt? [H]	Distance from zero is absolute value; compare the sizes, not the signs.
Counting Values Past a Threshold [H]	A number is less than the cutoff if it lies to its left on the line.
Farthest from Zero [H]	Farthest from zero means largest absolute value, sign aside.
Rectangle from Two Corners [H]	A side length is the absolute difference of the matching coordinates.
Total Distance of a Grid Walk [H]	Each straight leg is an absolute difference; add the legs for the total.
Sizing a Rectangle from Three Corners [H]	Two corners share a coordinate; their gaps give the two side lengths.
Comparing Two Segment Lengths [H]	Measure each axis-aligned segment, then subtract the two lengths.
Grouping Symbols and a Power [H]	Do the parentheses, then the power, then multiply, then add or subtract.
Powers, Multiplication, and Division Together [H]	After the power, multiply and divide left to right before adding.
Evaluating Over a Fraction Bar [H]	Finish the whole grouped top, including the power, before dividing.
Squares and Cubes in Area and Volume [H]	A square's area is the side squared; a cube's volume is the edge cubed.
Order of Operations in a Story [H]	Translate the words to k times a square, minus what is removed.
Perimeter as an Expression [H]	Add all the side expressions, then combine the x-terms and the numbers.
Combining Like Terms in Two Variables [H]	Group the x-terms, the y-terms, and the plain numbers separately.
Writing Expressions with Parentheses [H]	When a whole sum or difference is acted on, wrap it in parentheses.
Write It, Then Evaluate It [H]	Turn the words into an expression, then substitute the given number.
Modeling a Cost with an Expression [H]	A per-unit charge multiplies the variable; a one-time fee is added once.
Distributing Over Three Terms [H]	The outside factor multiplies every term inside, one by one.
Distribute, Then Combine [H]	First distribute each factor, then collect like terms into one.
Factoring the GCF from Three Terms [H]	Pull the largest number that divides all three terms to the front.
Distributive Property for Mental Math [H]	Split a number into friendly parts, multiply each, then add.
Two-Step Cost Equations [H]	Subtract the one-time fee first, then divide by the per-unit rate.
Two-Step Savings Equations [H]	Subtract what is already saved, then divide by the weekly amount.
Budget Inequalities: The Most You Can Buy [H]	Spend the fee first, then see how many whole items the rest buys.
Goal Inequalities: The Fewest You Need [H]	Find how much more is needed, divide, then round up to a whole step.
A Fraction of the Whole Is Known [H]	A fraction of the whole equals the part, so divide the part by the fraction.

6th Grade - Statistics & Data Displays (Mastery) · 38 topics

The Attribute a Question Measures [H]	A statistical question measures one attribute that varies across a group.
The Population a Question Studies [H]	The population is the whole group of individuals the data describe.
Leveling Data to a Fair Share [H]	Redistributing data to an equal amount produces the mean.
Recovering a Missing Value from the Mean [H]	The values must total mean times count; subtract to find a missing one.
The Score Needed to Reach a Target Mean [H]	The needed value is the target total minus the sum already earned.
How the Mean Shifts When a Value Is Added [H]	Rebuild the total with the new value, then divide by the new count.
Combining the Means of Two Groups [H]	Add both groups' totals, then divide by the combined count.
The Balance Point and a Missing Value [H]	Total distance below the mean must equal total distance above it.
The Median of an Even Number of Values [H]	With an even count the median is the mean of the two middle values.
The Median from a Dot Plot [H]	Count dots inward from both ends to the middle position of the data.
One Mode, Two Modes, or None [H]	The mode is the most frequent value; ties give two modes, all-different none.
The Mode from a Dot Plot [H]	The mode is the value with the tallest stack of dots.
A Missing Value from the Range [H]	Range is maximum minus minimum; add the range to the minimum to recover a top value.
The Quartiles of a Data Set [H]	Q1 is the median of the lower half; Q3 is the median of the upper half.
The Five-Number Summary [H]	The summary lists minimum, Q1, median, Q3, and maximum in order.
The IQR from a Raw Data List [H]	The IQR is Q3 minus Q1, the spread of the middle half of the data.
Choosing a Resistant Measure of Spread [H]	The IQR ignores the extremes, so an outlier barely moves it.
Counting Values in a Dot Plot [H]	Add the dots on the side of the threshold the question asks about.
The Mean from a Dot Plot [H]	Add every value (each dot counts once) and divide by the number of dots.
The Range from a Dot Plot [H]	Subtract the smallest value with a dot from the largest value with a dot.
The Shape of a Dot Plot [H]	Read symmetry, skew, or uniformity from where the dots pile up.
The MAD from a Dot Plot [H]	Average the distances of the dots from the mean.
Combining Two Intervals of a Histogram [H]	Add the frequencies (bar heights) of the two named intervals.
Counting Below a Boundary in a Histogram [H]	Add the frequencies of every interval that lies below the boundary.
Locating the Median in a Histogram [H]	Add frequencies from the left until you pass the middle data position.
The Total Count in a Histogram [H]	The total number of values is the sum of every bar's frequency.
Relative Frequency of an Interval [H]	Relative frequency is an interval's count divided by the total count.
The Percent of Data in a Box-Plot Region [H]	Quartiles cut the data into four groups of about 25% each.
Counting Values in a Box-Plot Region [H]	Multiply the total count by the fraction of data the region holds.
Comparing Two Box Plots [H]	Compute each plot's median, IQR, or range, then compare the numbers.
The Most Spread-Out Quarter of a Box Plot [H]	The longest section covers the quarter of data with the widest spread.
The Length of a Whisker [H]	A whisker's length is the distance from a quartile to that extreme.
Removing an Outlier and Recomputing the Mean [H]	Drop the far-off value, then average the values that remain.
Outliers: Mean versus Median [H]	The mean uses every value, so an outlier moves it more than the median.
Skew from the Mean-Median Gap [H]	The mean is pulled toward the tail, so mean above median means right skew.
Naming Features of a Distribution [H]	Clusters, gaps, peaks, and outliers name where data gather or stand apart.
Pairing a Center with the Right Spread [H]	Median goes with IQR for skewed data; mean goes with MAD for symmetric data.
Reading Spread from the MAD [H]	A larger MAD means the values sit farther from the mean on average.

6th Grade - Geometry & Measurement (Mastery) · 36 topics

Area of a Parallelogram [H]	A parallelogram's area is base times its perpendicular height.
A Missing Dimension of a Parallelogram [H]	Divide the area by the known dimension to recover the other one.
Base Times Height, Not the Slant Side [H]	Area uses the perpendicular height, never the length of the slanted side.
A Missing Base or Height of a Triangle [H]	From area = half base times height, double the area then divide.
Area of a Triangle with Fractional Dimensions [H]	The half-base-times-height rule holds when the lengths are fractions.
Area of a Trapezoid [H]	Average the two parallel bases, then multiply by the height.
A Missing Base of a Trapezoid [H]	Undo the trapezoid formula: from the area, back out the unknown base.
Trapezoid Area with Fractional Bases [H]	Add the fractional bases, halve the sum, then multiply by the height.
Choosing the Right Lengths for a Triangle's Area [H]	Area is one half the base times the perpendicular height to that base.
Composite Area: a Rectangle Plus a Triangle [H]	Decompose into a rectangle and a triangle, find each area, then add.
Area of a Border or Frame [H]	Subtract the inner opening's area from the outer rectangle's area.
Area of an L-Shaped Region [H]	Split the L into two non-overlapping rectangles and add their areas.
A Rectangle with a Triangle Removed [H]	Subtract the cut triangle's area from the whole rectangle's area.
Area of a Three-Rectangle Staircase [H]	Find the area of each step rectangle, then add all three together.
Perimeter of a Rectangle on the Plane [H]	Find each side length by subtracting coordinates, then add all sides.
Perimeter of a Polygon on the Plane [H]	Add the length of every side, each found from a coordinate difference.
Area of a Parallelogram on the Plane [H]	Read the horizontal base and the vertical height from the coordinates.
Area of a Trapezoid on the Plane [H]	The bases are the two horizontal sides; the height is their vertical gap.
Area on a Grid, Then a Cost [H]	Find the rectangle's area from its vertices, then multiply by the price.
Surface Area of a Cube [H]	A cube has six identical square faces, so its surface area is 6 s squared.
Surface Area of a Rectangular Prism from a Net [H]	Add the areas of the three pairs of faces: 2lw + 2lh + 2wh.
Total Area of a Net [H]	The net's area is the sum of the areas of all of its rectangles.
Surface Area of a Square Pyramid from a Net [H]	Add the square base to four triangular faces: s squared plus 4 half s l.
Matching the Faces in a Net [H]	Each face of a box is a rectangle made from two of the three edge lengths.
Faces, Edges, and Vertices of Prisms and Pyramids [H]	Count a solid's faces, edges, and vertices from the shape of its base.
Volume with Three Fractional Edges [H]	Volume is length times width times height, even for three fractions.
Volume with Mixed-Number Edges [H]	Rewrite mixed-number edges as improper fractions, then multiply.
Counting Unit-Fraction Cubes in a Prism [H]	Count how many unit-fraction cubes fit along each edge, then multiply.
A Missing Edge from the Volume [H]	Divide the volume by the product of the two known edges.
Comparing the Volumes of Two Prisms [H]	Compute both volumes as exact products, then compare the two numbers.
Carpeting a Room: Area Then Cost [H]	Find the floor area, then multiply by the cost per square foot.
Painting the Walls Around a Door [H]	Add the four wall areas, then subtract the door opening.
Packing Boxes into a Crate [H]	Count how many boxes fit along each edge, then multiply the three counts.
Filling a Tank to a Given Depth [H]	The water forms a prism: base times the water depth, not the full height.
Tiling a Floor: Counting Tiles and Cost [H]	Count tiles along each side, multiply for the total, then times the price.
Fencing a Garden: Perimeter Then Cost [H]	Find the perimeter for the fence length, then multiply by the price.

Prerequisite material - taught automatically when the diagnostic finds gaps

Math Kangaroo: Pre-Écolier & Écolier · 2 topics

Counting Pictures & Objects	Careful counting beats fast counting.
Sides & Corners	Shapes hide multiplication; cuts make one more piece.

Grade 5: Decimals, Volume & the Coordinate Plane · 7 topics

Powers of 10 & Patterns	Each power of ten shifts every digit one place.
Multiplying Decimals	Multiply as whole numbers, then place the decimal.
Dividing Decimals	Divide, keeping the decimal point lined up.
Volume by Unit Cubes	Volume counts the unit cubes that fill a solid.
Coordinate Plane (First Quadrant)	(x, y): right then up from the origin.
Converting Measurement Units	Multiply or divide by the conversion factor.
Order of Operations with Grouping	Parentheses first, then multiply/divide, then add/subtract.

Grade 4: Multi-Digit Operations & Place Value · 2 topics

What the Remainder Means	The story, not the arithmetic, decides what to do with a remainder.
Division Stories with Remainders	Divide, then round up, drop, or report the leftover - as the story asks.

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