246 core topics · approximately 70 hours of instruction including spaced review
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.
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |