3rd Grade Math

296 core topics · approximately 87 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

Grade 3: Multiplication & Division · 20 topics

Multiplication as Equal Groups [E]	Equal groups combine by multiplying.
Multiplication with Arrays [E]	Rows times columns fills a rectangle.
Multiplication Facts within 100 [E]	Know the times-table facts by heart.
Commutative Property [E]	Order does not change a product.
Associative Property [E]	Group three factors any way - same product.
Distributive Property [M]	Split a factor, multiply the parts, add.
Division as Equal Sharing [E]	Split a total into equal shares.
Division Facts within 100 [E]	Recall the division facts fluently.
Multiplication & Division Fact Families [E]	One family, four related facts.
Missing Factors [E]	An unknown factor is a division in disguise.
Multiply by Multiples of 10 [E]	Use a known fact, then attach a zero.
Patterns in the Multiplication Table [E]	Each times-table climbs by a fixed step.
Two-Step Word Problems [M]	Two operations, one answer.
Order of Operations [M]	Multiply and divide before you add or subtract.
Multiply & Divide Within 100 Fluently [E]	Recall the times-table and its division facts quickly.
Unknown Number in an Equation [E]	Solve for the missing number in a × or ÷ equation.
Round to the Nearest 10 or 100 [E]	Round a number to the closest ten or hundred.
Add & Subtract Within 1000 Fluently [M]	Add and subtract three-digit numbers using place value.
Two-Step Word Problems (All Operations) [M]	Combine two of the four operations to reach an answer.
Estimate Sums by Rounding [E]	Round each number to the nearest ten, then add.

Grade 3: Fractions · 13 topics

Unit Fractions [E]	One equal part of a whole.
Fraction of a Whole [E]	Share a group into equal parts.
Fractions on a Number Line [E]	Fractions are points, spaced evenly.
Equivalent Fractions [M]	Different names for the same amount.
Fractions Equal to 1 [E]	A whole is all of its parts.
Whole Numbers as Fractions [E]	Every whole number is a fraction over 1.
Compare Fractions - Same Numerator [E]	Same top: fewer parts means bigger parts.
Compare Fractions - Same Denominator [E]	Same bottom: more parts means more.
Name the Shaded Fraction [E]	Shaded parts over total parts.
Order Simple Fractions [M]	Line fractions up smallest to largest.
Recognize Equivalent Fractions [E]	Spot a different fraction that names the same amount.
Compare a Fraction to One Half [E]	Decide whether a fraction is less than, equal to, or more than 1/2.
Fractions Greater Than 1 on a Number Line [M]	Locate a fraction past 1 by counting equal parts.

Grade 3: Measurement, Area, Perimeter & Data · 15 topics

Tell Time to the Minute [E]	Read the hour, then the minutes.
Elapsed Time (Minutes) [E]	Subtract start from end.
Liquid Volume & Mass [E]	Add and subtract grams and milliliters.
Area by Counting Unit Squares [E]	Area is the number of unit squares.
Area by Multiplication [E]	Area = length × width.
Perimeter of Polygons [E]	Perimeter is the distance all the way around.
Perimeter with a Missing Side [M]	Work backward from the perimeter.
Scaled Picture & Bar Graphs [E]	Multiply by the scale to read a graph.
Line Plots with Halves & Fourths [E]	Each X is one measurement.
Area of Composite Shapes [M]	Split, find each area, then add.
Choose Units of Mass & Volume [E]	Pick grams, kilograms, liters, or milliliters sensibly.
Area & the Distributive Property [M]	Split a rectangle, find each part's area, and add.
Perimeter of a Polygon [E]	Add every side length to find the distance around.
Elapsed Time Across the Hour [M]	Measure a time span that passes from one hour into the next.
Compare Scaled Graphs [E]	Use the scale to find how many more one category has.

3rd Grade Math - Depth · 42 topics

Multiplication Facts [M]	Recall products of numbers up to 10 times 10.
Multiply by 0 and 1 [M]	Know the special products with 0 and 1.
Multiply by 10 [M]	Multiply a number by ten quickly.
Division Facts [M]	Divide evenly using known multiplication facts.
Division as an Unknown Factor [M]	See division as finding a missing factor.
Commutative Property [M]	Swap the order of factors without changing the product.
Multiply Three Numbers [M]	Group factors in any way to multiply three numbers.
Break Apart to Multiply [M]	Split a fact into two easier facts.
Multiplication & Division Fact Families [M]	Use a known product to find a related quotient.
Multiplication Word Problems [M]	Solve a story about equal groups by multiplying.
Division Word Problems [M]	Share a total into equal groups by dividing.
Division: How Many Groups [M]	Find how many equal groups a total makes.
Arrays and Multiplication [M]	Multiply rows by columns to count an array.
Two-Step: Multiply Then Add [M]	Multiply equal groups, then add or subtract more.
Unit Fractions [M]	Name the fraction for one equal part.
Fractions of a Whole [M]	Write the fraction shown by shaded parts.
Fractions on a Number Line [M]	Locate a fraction between 0 and 1 on a number line.
Equivalent Fractions [M]	Find a fraction equal to another with a bigger denominator.
Compare Fractions: Same Denominator [M]	Compare fractions that share a denominator.
Compare Fractions: Same Numerator [M]	Compare fractions that share a numerator.
Fractions Equal to One Whole [M]	See that a fraction with equal top and bottom is one whole.
Fraction of a Set [M]	Find a unit fraction of a group of objects.
Area by Counting Squares [M]	Find area by counting unit squares.
Area of a Rectangle [M]	Use length times width to find area.
Perimeter of a Rectangle [M]	Add up all four sides of a rectangle.
Perimeter of a Polygon [M]	Add all the side lengths of a many-sided shape.
Find a Missing Side [M]	Use the perimeter to find an unknown side.
Area of Combined Rectangles [M]	Add the areas of two rectangles that form one shape.
Tell Time to the Minute [M]	Read the exact minutes on a clock.
Elapsed Time in Minutes [M]	Find how much time has passed.
Find the Start Time [M]	Work backward from an end time to a start time.
Round to the Nearest Ten [M]	Round a number to the closest ten.
Round to the Nearest Hundred [M]	Round a number to the closest hundred.
Estimate Sums by Rounding [M]	Round first, then add to estimate a total.
Add Within 1000 [M]	Add three-digit numbers fluently.
Subtract Within 1000 [M]	Subtract three-digit numbers fluently.
Two-Step Word Problems [M]	Solve a story needing two different operations.
Multiplicative Comparison [M]	Solve 'how many times as many' problems.
Add Mass and Liquid Volume [M]	Add measurements of mass or liquid volume.
Compare Mass and Volume [M]	Find the difference between two measurements.
Read a Scaled Graph [M]	Use a scale to read a bar or picture graph.
Compare on a Scaled Graph [M]	Find how many more using a graph's scale.

3rd Grade Math - Deep II · 60 topics

Twos Facts [M]	Know the 2 times table by heart.
Threes Facts [M]	Know the 3 times table by heart.
Fours Facts [M]	Know the 4 times table by heart.
Sixes Facts [M]	Know the 6 times table by heart.
Sevens Facts [M]	Know the 7 times table by heart.
Eights Facts [M]	Know the 8 times table by heart.
Nines Facts [M]	Know the 9 times table by heart.
Square Facts [M]	Multiply a number by itself.
Divide by 2 [M]	Divide numbers evenly by 2.
Divide by 5 [M]	Divide numbers evenly by 5.
Divide by 10 [M]	Divide numbers evenly by 10.
Multiply Three Factors [M]	Multiply three numbers together.
Double Twice to Multiply by 4 [M]	Use doubling to multiply by four.
Missing Dividend [M]	Find the number being divided.
Does It Divide Evenly? [M]	Tell whether one number splits evenly by another.
Times as Many [M]	Solve a 'times as many' comparison.
Sharing Word Problem [M]	Share a total equally into groups.
Array Word Problem [M]	Multiply rows by columns in a story.
Multiply Then Add [M]	Do a multiplication, then add more.
Divide Then Subtract [M]	Do a division, then take some away.
Two-Step Money Problem [M]	Multiply a cost, then find the change.
Is the Answer Reasonable? [M]	Judge whether an answer makes sense.
Find the Rule of a Pattern [M]	Find how much a pattern grows each step.
Continue a Number Pattern [M]	Add the pattern's step to find the next term.
Even Products Pattern [M]	See why some times tables give only even answers.
Break Apart a Fact [M]	Split one factor to make a fact easier.
Add Three Numbers Within 1000 [M]	Add three three-digit numbers.
Subtract Across Zeros [M]	Subtract when the top number has zeros.
Estimate a Difference [M]	Round to tens, then subtract to estimate.
Name a Fraction at a Point [M]	Read the fraction where a point sits.
Equivalent Fractions on a Number Line [M]	See equal fractions at the same point.
Write an Equivalent Fraction [M]	Build an equal fraction by scaling both parts.
Missing Number in Equal Fractions [M]	Find the denominator that keeps fractions equal.
Compare Fractions with a Symbol [M]	Choose >, <, or = for two fractions.
Compare to One Half [M]	Compare a fraction against one half.
Whole Number as a Fraction [M]	Write a whole number over one.
Write One as a Fraction [M]	Show one whole using equal parts.
Order Fractions, Same Denominator [M]	Find the largest of like-denominator fractions.
Find the Whole from a Unit Fraction [M]	Rebuild the whole from one equal part.
Find a Missing Side from Area [M]	Divide area by one side to get the other.
Area Word Problem [M]	Find area from a length and width in a story.
Area of a Square [M]	Multiply a square's side by itself.
Compare Areas [M]	Find which rectangle covers more space.
Perimeter of a Square [M]	Add up a square's four equal sides.
Perimeter of a Triangle [M]	Add the three sides of a triangle.
Find a Side from Perimeter [M]	Work backward from a rectangle's perimeter.
Perimeter Word Problem [M]	Find the distance around a rectangle in a story.
Elapsed Time in Hours and Minutes [M]	Add hours and minutes to a start time.
Find the End Time [M]	Add minutes to find a later time.
Time Word Problem [M]	Use minutes to solve a schedule story.
Mass Word Problem [M]	Add or subtract masses in grams.
Liquid Volume Word Problem [M]	Add liquid volumes in milliliters.
Mass with Equal Groups [M]	Multiply to find a total mass.
Volume with Equal Groups [M]	Multiply to find a total volume.
Total on a Picture Graph [M]	Use the key to total a scaled picture graph.
Total on a Bar Graph [M]	Add the values shown on a scaled bar graph.
Two-Step Graph Problem [M]	Find a difference on a scaled graph.
Difference on a Line Plot [M]	Compare two stacks of marks on a line plot.
Read a Frequency Table [M]	Find a count in a frequency table.
Classify Quadrilaterals [M]	Name a quadrilateral from its properties.

3rd Grade - Multiplication, Division & Problem Solving (Deep) · 48 topics

Equal Groups in a Picture [H]	Find the total when a picture shows equal groups.
Match a Picture to a Number Sentence [H]	Choose the number sentence that matches a picture of equal groups.
Repeated Addition as Multiplication [H]	Find the total of a sum whose addends are all the same.
Multiply with Jumps on a Number Line [H]	Read a product from equal jumps drawn on a number line.
Missing Row or Column of an Array [H]	Find the missing number of rows or number in each row of an array.
Share a Picture Equally [H]	Divide a pictured total into a given number of equal shares.
Measure Out Equal Bags [H]	Find how many equal groups of a given size a pictured total makes.
Divide with Jumps on a Number Line [H]	Use equal hops on a number line to find a quotient or a hop size.
Choose the Division Sentence [H]	Pick the number sentence that matches a sharing or grouping story.
Use a Multiplication Fact to Divide [H]	Name the multiplication fact that answers a division question.
Unknown Factor in a Story [H]	Solve a story written as a multiplication with one factor unknown.
Fives Facts [H]	Know the five times table by heart.
Divide by 3 [H]	Divide a number evenly by 3.
Divide by 4 [H]	Divide a number evenly by 4.
Divide by 6 [H]	Divide a number evenly by 6.
Divide by 7 [H]	Divide a number evenly by 7.
Divide by 8 [H]	Divide a number evenly by 8.
Divide by 9 [H]	Divide a number evenly by 9.
Turnaround Facts [H]	Use the fact that the order of two factors does not change the product.
Group Three Factors [H]	Multiply three factors by grouping two of them first.
Missing Part of a Break Apart [H]	Complete a product that has been broken into two easier products.
Multiply by Nine Using Tens [H]	Multiply by nine by taking one group away from ten groups.
Name the Property Used [H]	Identify which multiplication property makes an equation true.
Use a Basic Fact to Multiply by Tens [H]	Multiply a one-digit number by a multiple of ten using a basic fact.
Missing Factor with Multiples of Ten [H]	Find the missing factor when a product is a multiple of ten.
Divide a Multiple of Ten [H]	Divide a multiple of ten by a one-digit number or by another multiple of ten.
Multiples of Ten Word Problem [H]	Solve a story that multiplies by a multiple of ten.
Add Then Divide [H]	Solve a two-step story that combines amounts and then shares them equally.
Subtract Then Multiply [H]	Solve a two-step story that takes some away and then multiplies.
Two-Step Problem from a Table [H]	Use a table of givens to multiply and then add or subtract.
Choose the Number Sentence [H]	Pick the number sentence that matches a two-step story.
Groups of Groups [H]	Multiply three amounts that are nested inside one another.
Write an Equation with a Letter [H]	Choose the equation that uses a letter for the unknown amount in a story.
Find the Letter in a Division Equation [H]	Solve a division equation in which a letter stands for one number.
Find the Letter in an Addition Equation [H]	Solve an addition or subtraction equation within 1000 that uses a letter.
Estimate a Product [H]	Round a factor and multiply to estimate a product.
Check an Answer with an Estimate [H]	Use an estimate to judge whether an answer is reasonable.
Complete an Input-Output Table [H]	Use the rule of an input-output table to fill in a missing output.
Find the Rule of a Table [H]	Name the multiply or divide rule that a table follows.
Compare Two Patterns in a Chart [H]	Extend and compare two growing patterns shown in the same chart.
Round to the Nearest Ten on a Number Line [H]	Use a number line to round a number to the nearest ten.
Round to the Nearest Hundred on a Number Line [H]	Use a number line to round a number to the nearest hundred.
Which Number Rounds to This? [H]	Decide which numbers round to a given ten or hundred.
Rounding in a Story [H]	Round a number in a story to the nearest ten or hundred.
Add Within 1000 in a Story [H]	Add two or three three-digit amounts to answer a story question.
Subtract Within 1000 in a Story [H]	Subtract three-digit amounts to answer a story question.
Missing Part Within 1000 [H]	Find the missing part of a whole within 1000.
Compare Amounts on a Bar Graph [H]	Compare bars in the hundreds on a bar graph.

3rd Grade - Fractions, Area, Perimeter & Data (Deep) · 48 topics

Steps on a Fraction Number Line [H]	Name the fraction that one or two equal steps on a number line stand for.
Unit Pieces in Whole Amounts [H]	Count how many unit-fraction pieces fill a given number of wholes.
Build a Fraction from Unit Pieces [H]	Write the fraction made by a number of equal pieces of one whole.
Compare Only Within the Same Whole [H]	Recognize that two fractions can be compared only when the wholes match.
Read a Fraction from a Number Line [H]	Name the fraction shown by a point drawn on a partitioned number line.
Missing Label on a Number Line [H]	Fill in the fraction label missing from one tick of a number line.
Compare Two Points on a Number Line [H]	Decide which of two points on a number line is the larger fraction.
Steps to a Whole Number [H]	Count the unit-fraction steps between whole numbers on a number line.
Rename a Point in Bigger or Smaller Parts [H]	Write the fraction at a point using a different size of equal part.
Split Each Part [H]	Find the new fraction when every equal part of a model is split or joined.
Halves, Fourths, and Eighths [H]	Change a fraction into an equal number of smaller or larger equal parts.
Which Model Shows an Equal Fraction [H]	Pick the fraction equal to the one shown by a part-whole model.
Fraction That Equals a Whole Number [H]	Name the whole number equal to a fraction whose parts fill exact wholes.
A Whole Number Written in Equal Parts [H]	Write a whole number as a fraction using a given size of equal part.
Compare a Fraction to a Whole Number [H]	Decide whether a fraction is less than, equal to, or greater than a whole number.
Order Fractions with the Same Numerator [H]	Order fractions that share a numerator by the size of their parts.
Who Had More? [H]	Compare fractions of the same whole to answer a sharing story.
Make the Comparison True [H]	Choose the number that makes a fraction comparison statement true.
Count Unit Squares Row by Row [H]	Find area by counting equal rows of unit squares.
Choose the Unit for Area [H]	Choose a square unit when measuring area and a length unit when measuring around.
Area with a Corner Removed [H]	Find the area left after a rectangular corner is removed from a rectangle.
Missing Part of a Rectilinear Area [H]	Find one piece of a rectilinear area from the total and the other pieces.
Which Split Shows the Same Area [H]	Identify the two-rectangle split whose partial areas match a rectangle's area.
Missing Length in a Split Rectangle [H]	Find an unknown width inside a rectangle split into two partial areas.
Tiles That Cover a Floor [H]	Use the area of a rectangle to count unit tiles needed to cover it.
Different Rectangles, Same Area [H]	Find another pair of side lengths that gives a rectangle the same area.
Perimeter of a Regular Polygon [H]	Multiply the side length by the number of sides to get a regular polygon's perimeter.
Side Length of a Regular Polygon [H]	Divide a regular polygon's perimeter by its number of sides to find one side.
Missing Side of a Many-Sided Shape [H]	Find an unknown side of a polygon from its perimeter and the known sides.
Same Perimeter, Different Area [H]	Compare the areas of rectangles that share the same perimeter.
Same Area, Different Perimeter [H]	Compare the perimeters of rectangles that share the same area.
Perimeter Two-Step Problem [H]	Use a rectangle's perimeter inside a problem with a second step.
Perimeter of a Square from Its Area [H]	Find a square's perimeter from its area by first finding the side length.
Minutes Past the Hour on a Clock [H]	Read a clock face to the exact minute past the hour.
Minutes Until the Next Hour [H]	Find how many minutes are left from a clock time until the next hour.
Elapsed Time on a Number Line [H]	Measure a time interval by counting equal jumps on a time number line.
Which Activity Took Longer [H]	Compare time intervals by working out how long each one lasted.
Kilograms and Grams [H]	Change kilograms into grams and use them in a mass problem.
Liters and Milliliters [H]	Change liters into milliliters and use them in a liquid volume problem.
Read a Measuring Scale [H]	Read a liquid volume from a scale whose marks are not all labeled.
Share a Mass Equally [H]	Divide a total mass in grams into equal parts.
Two-Step Liquid Volume Problem [H]	Solve a liquid volume story that needs two steps.
How Many Symbols to Draw [H]	Use a picture graph key to find how many symbols stand for an amount.
Which Row Shows the Most [H]	Compare rows of a scaled picture graph using its key.
Missing Value from a Graph Total [H]	Find a missing category value from a scaled graph and the grand total.
Total Measurements on a Line Plot [H]	Count all the marks on a line plot marked in halves or fourths.
Marks at the Longest Length [H]	Find how many measurements sit at the largest or smallest value of a line plot.
Measurements Longer Than a Length [H]	Count the line plot marks past a given measurement.

3rd Grade - Multiplication, Fractions & Measurement (Deep) · 50 topics

A Gap in a Skip Count [H]	A skip count grows by the same amount at every step.
One More Group, One Less Group [H]	A fact you know gives the next fact by adding or taking one group.
Double It or Halve It [H]	Doubling one factor doubles the product; halving it halves the product.
Split a Fact into a Fives Part [H]	A hard fact splits into a fives fact plus a small leftover fact.
Which Product Is More? [H]	Products can be compared without working every one of them out.
Reading the Times Table [H]	A cell of the times table is the row number times the column number.
Is That Number in the Count? [H]	A number is in a count only when it splits into equal groups exactly.
The Missing Divider [H]	A missing divisor is found with the matching multiplication fact.
Dividing by One and by Itself [H]	Sharing among one keeps the whole; sharing among itself gives one each.
Working Backwards Two Steps [H]	Undo each step in the opposite order to find the number you started with.
What Is the Story Asking For? [H]	A sharing story hides the group size; a grouping story hides the count.
True or Not True? [H]	An equal sign promises that both sides name the very same amount.
Which Sign Belongs? [H]	The sign that fits is the one that makes both sides the same amount.
A Letter for the Unknown [H]	A letter names the unknown so a two-step story becomes one equation.
Take Some Away, Then Share [H]	Find what is left first, then split that leftover into equal parts.
Fill the Rows, Then Take Some Off [H]	Equal rows give the total; the story then takes part of that total away.
Gather Them Up, Then Share [H]	Equal packs make a total, and the total is then split equally again.
Which Step Comes First? [H]	A two-step problem hides a first question that must be answered first.
A Doubling Chain [H]	In a doubling chain each number is twice the one before it.
Counting Back by the Same Amount [H]	A count-back pattern drops by the same amount at every step.
What Is Always True About a Count? [H]	A pattern rule must hold for every number in the count, not just one.
Rounding a Halfway Number [H]	A number exactly halfway between rounds up to the larger benchmark.
Which Numbers Land Here? [H]	Each benchmark collects a band of numbers that lie nearest to it.
Check It the Opposite Way [H]	The opposite operation undoes a calculation and proves it was right.
One Whole Shared Fairly [H]	Sharing one whole among d friends gives each friend 1/d of it.
More Pieces Means Smaller Pieces [H]	Cutting one whole into more parts makes every part smaller.
Writing a Fraction from Words [H]	The top number counts the parts taken and the bottom number names them.
The Part That Is Left [H]	The parts eaten and the parts left always rebuild the whole.
How Big Is One Jump? [H]	One jump between 0 and 1 is the unit fraction for that many parts.
Finding One Half on the Line [H]	One half sits at the tick with half of the jumps on each side.
Two Names for the Same Amount [H]	Equal fractions cover the same amount with pieces of a different size.
Why Is One Fraction Bigger? [H]	A comparison is only finished when the reason for it is said out loud.
Closest to 0, One Half or 1 [H]	Benchmarks sort fractions without any common bottom number.
The Parts Have to Be Equal [H]	A fraction only names a part when all the parts are the same size.
Area or Perimeter? [H]	Covering a shape needs area; going around its edge needs perimeter.
Both Around It and Inside It [H]	One rectangle carries two different measures, found in different ways.
One More Row of Squares [H]	Adding a whole row adds one row's worth of squares to the area.
From Area Back to Perimeter [H]	One side and one measure are enough to rebuild the whole rectangle.
A Later Time from a Clock [H]	Counting on past the hour needs the extra minutes carried into the hour.
Adding and Comparing Times [H]	Durations in minutes add and subtract like any other numbers.
Hours Turned into Minutes [H]	Every hour trades for 60 minutes, in either direction.
Elapsed Minutes from a Clock Face [H]	Count on from the time shown to the time given to get the minutes between.
Filling Cups from a Jug [H]	A big container holds a whole number of small equal containers.
Taking Mass Out Twice [H]	Mass problems chain: take away twice, then share or work backwards.
Comparing Three Containers [H]	Comparing a whole table means checking every row, not just two.
Comparing Kilograms with Grams [H]	Two masses can only be compared once both are in the same unit.
A Bar Graph After a Change [H]	Read the bar first, then work the change onto the number you read.
Counting Marks on a Line Plot [H]	Each mark above a tick stands for one thing measured at that length.
Reading Tally Marks [H]	Tally marks are counted in fives, with the fifth drawn across the four.
A Picture Graph with a Key [H]	With a key, every picture stands for several things, not one.

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