2nd Grade Math

245 core topics · approximately 69 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 2: Place Value to 1000 & Fluency to 100 · 15 topics

3-Digit Place Value [E]	Hundreds, tens and ones inside a 3-digit number.
Expanded Form [E]	Break a number into hundreds + tens + ones and back again.
Compare 3-Digit Numbers [E]	Compare numbers by looking at hundreds, then tens, then ones.
Counting Within 1000 [E]	Find the number just before or just after any number up to 1000.
Skip-Counting by 5s, 10s & 100s [E]	Count by 5s, 10s and 100s and predict the next number.
Add Within 100 (Regrouping) [E]	Two-digit addition when the ones make a new ten.
Subtract Within 100 (Regrouping) [E]	Two-digit subtraction when you must borrow a ten.
Add & Subtract Within 1000 [M]	Three-digit addition and subtraction using place value.
Mentally Add or Subtract 10 or 100 [E]	Change just the tens or hundreds digit - no pencil needed.
Odd & Even Numbers [E]	A number is even if it splits into two equal groups.
Add Up to Four Two-Digit Numbers [M]	Add several two-digit numbers by grouping.
Fluently Add & Subtract Within 20 [E]	Recall the sums and differences within 20 from memory.
Number Names (Word Form) [E]	Read and write three-digit numbers in words.
Write Numbers to 1000 [E]	Turn a number's words back into digits.
Compare 3-Digit Numbers with <, >, = [E]	Choose the symbol that compares two three-digit numbers.

Grade 2: Money, Time & Measurement · 15 topics

Counting Coins [E]	Add up pennies, nickels, dimes and quarters.
Dollars and Cents [E]	Combine dollar bills with coins.
Making an Amount [E]	Find how many equal coins add up to an amount.
Money Word Problems [M]	Solve everyday spending and change problems in cents.
Telling Time to 5 Minutes [E]	Read a clock to the nearest five minutes.
A.M. and P.M. [E]	Tell morning times from afternoon and night times.
Choosing a Measurement Unit [E]	Pick the right length unit and estimate.
Compare & Subtract Lengths [E]	Find how much longer one length is than another.
Measuring on a Ruler [E]	Read a length between two marks on a ruler.
Elapsed Time (Hours) [E]	Find an ending time after a whole number of hours.
Coin & Dollar Word Problems [M]	Combine dollars and coins, then add or subtract.
Measure Length in Inches [E]	Read a length in inches between two ruler marks.
Estimate a Length [E]	Pick a sensible length estimate with the right unit.
Write Time to Five Minutes [E]	Match a clock to the written time, to the nearest 5 minutes.
Compare Amounts of Money [E]	Find how much more one amount of money is than another.

Grade 2: Arrays, Geometry & Data · 13 topics

Repeated Addition [E]	Equal groups add up the same amount over and over.
Arrays [E]	Rows and columns of equal objects.
Even Numbers as Two Equal Rows [E]	Any even number splits into two equal rows.
Identify 2D Shapes by Sides [E]	Name a shape from how many sides it has.
Counting Sides & Angles [E]	Count the sides and angles of common shapes.
Partition Rectangles into Squares [E]	Split a rectangle into equal rows and columns of squares.
Halves, Thirds & Fourths [E]	Name equal parts of a whole.
Picture Graphs [E]	Read a picture graph and answer questions.
Bar Graphs [E]	Read a bar graph and compare categories.
Line Plots [E]	Count data points on a line plot.
Scaled Picture Graphs [E]	Each symbol counts for more than one - multiply to read it.
Scaled Bar Graphs [E]	Read a bar graph whose scale skips numbers, then compare.
Partition Rectangles: Rows & Columns [E]	Find the missing number of rows or columns of equal squares.

2nd Grade Math - Depth · 40 topics

Add Within 100 [M]	Add two two-digit numbers, regrouping when needed.
Subtract Within 100 [M]	Subtract two-digit numbers, regrouping when needed.
Add Three Two-Digit Numbers [M]	Add three two-digit numbers together.
Add Within 1000 [M]	Add three-digit numbers, regrouping across places.
Subtract Within 1000 [M]	Subtract three-digit numbers, regrouping when needed.
Add 10 or 100 Mentally [M]	Add a ten or a hundred in your head.
Subtract 10 or 100 Mentally [M]	Take away a ten or a hundred in your head.
Missing Addend Within 100 [M]	Find the part needed to reach a total.
Value of the Hundreds Digit [M]	Tell what the hundreds digit is worth.
Value of the Tens Digit [M]	Tell what the tens digit is worth in a three-digit number.
Value of the Ones Digit [M]	Tell what the ones digit is worth.
Expanded Form [M]	Combine hundreds, tens and ones into one number.
Build a Number from Place Value [M]	Join hundreds, tens and ones to name a number.
Compare Three-Digit Numbers [M]	Decide which three-digit number is greater.
Order Three-Digit Numbers [M]	Find the largest of three three-digit numbers.
One Hundred More, One Hundred Less [M]	Jump a whole hundred up or down.
Skip Count by 2s, 5s, 10s, 100s [M]	Continue a skip-counting pattern.
Even and Odd Numbers [M]	Tell whether a number is even or odd.
Count an Array [M]	Find the total in a rectangle of rows and columns.
Repeated Addition [M]	Add equal groups to find a total.
Equal Groups [M]	Find the total when groups all hold the same amount.
Count Coins in Cents [M]	Add up quarters, dimes, nickels and pennies.
Dollars and Cents [M]	Change dollars and cents into total cents.
Making Change [M]	Find the change from a one-dollar payment.
Time to the Nearest Five Minutes [M]	Read the minutes when the hand is on a clock number.
A.M. and P.M. [M]	Choose the event that fits a.m. or p.m.
Elapsed Minutes [M]	Find the time a few minutes later within the hour.
Add Lengths in Centimeters [M]	Add two measured lengths.
Difference in Length [M]	Find how much longer one object is than another.
Choose the Right Length Unit [M]	Pick centimeters or meters for a measurement.
Read a Bar Graph [M]	Find one value from a bar graph.
Compare Bars on a Graph [M]	Find how many more one bar shows than another.
Read a Picture Graph [M]	Use a key to count symbols on a picture graph.
Read a Line Plot [M]	Count the marks above a value on a line plot.
Two-Step Word Problems [M]	Solve a story with two operations.
Numbers on a Number Line [M]	Find a missing number on an evenly-spaced number line.
Round to the Nearest Ten [M]	Round a two-digit number to the closest ten.
Compare with >, <, = [M]	Choose the symbol that compares two three-digit numbers.
Compare Amounts of Money [M]	Decide which amount of money is more.
Name Polygons by Sides [M]	Match a polygon to its number of sides.

2nd Grade Math - Deep II · 67 topics

Doubles Facts [M]	Add a number to itself.
Near Doubles [M]	Add two numbers that are one apart.
Make a Ten to Add [M]	Find the partner that completes ten.
Add Across a Ten [M]	Add two one-digit numbers whose sum passes ten.
Subtract Across a Ten [M]	Subtract a one-digit number by going down through ten.
Fact Families Within 20 [M]	Use related addition and subtraction facts.
Add a One-Digit to a Two-Digit [M]	Add a small number to a two-digit number.
Subtract a One-Digit from a Two-Digit [M]	Take a small number from a two-digit number.
Add Multiples of Ten [M]	Add two numbers that are whole tens.
Subtract Multiples of Ten [M]	Subtract one whole ten amount from another.
Add a Multiple of Ten to a Two-Digit Number [M]	Add whole tens to any two-digit number.
Add Tens to a Three-Digit Number [M]	Add whole tens to a three-digit number.
Missing Number You Take Away [M]	Find how much was subtracted.
Missing Starting Number [M]	Find the number you started with.
Estimate a Sum by Rounding [M]	Round each number to a ten, then add.
Estimate a Difference by Rounding [M]	Round each number to a ten, then subtract.
Name the Digit in a Place [M]	Say which digit sits in a named place.
One Hundred as Ten Tens [M]	See a hundred as a bundle of ten tens.
How Many Tens in All [M]	Count all the tens inside a number.
One More and One Less [M]	Step up or down by one within 1000.
Ten More and Ten Less [M]	Jump a whole ten up or down.
Number Just Before or After [M]	Name the neighbor of a number.
Count On by Hundreds [M]	Continue a counting pattern of hundreds.
Count Back by Tens [M]	Continue a pattern that goes down by ten.
Word Problem: Result Unknown [M]	Find the total after more is added.
Word Problem: Change Unknown [M]	Find how much was added to reach a total.
Word Problem: Start Unknown [M]	Find the starting amount before more was added.
Word Problem: Take From [M]	Find how many are left after some are removed.
Word Problem: How Many More [M]	Compare two amounts to find the extra.
Word Problem: How Many Fewer [M]	Compare two amounts to find how many fewer.
Word Problem: Put Together [M]	Combine two parts into a whole.
Even Number as Equal Groups [M]	Split an even number into two equal parts.
Pair Up to Test Odd or Even [M]	Pair items to see if any are left over.
Balance an Equation [M]	Make both sides of an equation equal.
Which Equation Is True [M]	Pick the equation that is correct.
Values of Coins [M]	Know how many cents each coin is worth.
Fewest Coins to Make an Amount [M]	Use the largest coins first to use fewer.
Add Two Money Amounts [M]	Add amounts of money in cents.
Change from Any Amount [M]	Find change when paying more than the cost.
Count Dollar Bills [M]	Add up one-dollar and five-dollar bills.
Two-Step Money Problem [M]	Add two costs, then find the change.
Half Past the Hour [M]	Know that half past means thirty minutes.
Quarter Past the Hour [M]	Know that quarter past means fifteen minutes.
Quarter To the Hour [M]	Know that quarter to means forty-five minutes past.
Write Time in Digital Form [M]	Show a time as hour and minutes with a colon.
Minutes Until the Next Hour [M]	Find how many minutes are left in the hour.
Time Facts [M]	Recall how time units fit together.
Measure and Compare in Feet [M]	Compare lengths given in feet.
Centimeters and Meters [M]	Change meters into centimeters.
Inches and Feet [M]	Change feet into inches.
Estimate a Length in Meters [M]	Pick a sensible length in meters.
Estimate a Length in Inches [M]	Pick a sensible length in inches.
Length Word Problem [M]	Solve a story about cutting a length.
Sum on a Number Line [M]	Add by jumping forward on a number line.
Difference on a Number Line [M]	Subtract by jumping back on a number line.
Name a 3D Shape [M]	Match a solid shape to its description.
Count Faces of a Solid [M]	Count the flat surfaces of a solid.
Edges and Vertices of a Solid [M]	Count the edges and corners of a solid.
Identify Quadrilaterals [M]	Find the shape with four sides.
Equal Shares in a Whole [M]	Count how many equal shares fill a whole.
Name the Equal Shares [M]	Name the parts when a shape is split evenly.
Read Tally Marks [M]	Count tallies grouped in fives.
Total from a Bar Graph [M]	Add every bar to find the whole total.
Combine Two Bars [M]	Add two chosen bars from a graph.
Compare on a Picture Graph [M]	Use the key to compare two rows.
Total Marks on a Line Plot [M]	Count all the marks on a line plot.
Most Common Length on a Line Plot [M]	Find the value with the most marks.

2nd Grade - Place Value & Multi-Digit Computation (Deep) · 48 topics

Read Base-Ten Blocks [H]	Read a three-digit number from a picture of hundred, ten and one blocks.
Trade Ten Tens for a Hundred [H]	Find the value of a block set that has ten or more of one kind.
Same Digit, Different Value [H]	Give the value of a repeated digit from the place it sits in.
Zero as a Place Holder [H]	Write a three-digit number when one of its places is empty.
Missing Part of an Expanded Form [H]	Find the hundreds or tens part that is missing from an expanded form.
Expanded Form with an Empty Place [H]	Write or match the expanded form of a number that has an empty place.
Number Names with an Empty Place [H]	Match a number to its name in words when a place is empty or a teen.
Skip Count from Any Number [H]	Continue a count by fives or tens that starts at a number in between.
How Many Fives or Tens Make a Number [H]	Count how many equal jumps of five or ten reach a number.
Skip Count Across a Hundred [H]	Keep a five or ten count going as it passes a new hundred.
Count Back by Hundreds [H]	Continue a pattern that goes down by one hundred each time.
Name the Skip-Count Rule [H]	Decide what a number pattern is counting by and in which direction.
Compare Using Expanded Form [H]	Compare two numbers when one or both are written in expanded form.
Find a Number in Between [H]	Pick a number that is greater than one number and less than another.
Put Three Numbers in Order [H]	Arrange three three-digit numbers from least to greatest or the reverse.
Which Number Is Closer [H]	Choose the number whose distance to a target number is smallest.
Build the Greatest or Least Number [H]	Arrange three digit cards to make the greatest or the least number.
Add Tens and Ones Separately [H]	Add two two-digit numbers by adding the tens and the ones separately.
Subtract by Counting Up [H]	Find a difference by counting up from the smaller number to the larger.
Check a Subtraction by Adding [H]	Use the matching addition fact to check whether a subtraction is right.
Add a Friendly Ten, Then Take Back [H]	Add a number near a ten by adding the ten and then adjusting.
Subtract a Friendly Ten, Then Add Back [H]	Subtract a number near a ten by subtracting the ten and then adjusting.
Follow a Chain of Steps [H]	Work through several add and subtract steps in order within 100.
Add Four Numbers by Making Tens [H]	Add four two-digit numbers by pairing ones digits that make ten.
Add Four Amounts from a Table [H]	Read four numbers from a table and add them to find a total.
Find the Missing Addend of Four [H]	Find one missing number when the other addends and the total are known.
Add Hundreds, Tens and Ones [H]	Add two three-digit numbers by adding each place and combining the parts.
Subtract from a Number with a Zero [H]	Subtract when the number you start from has a zero in the tens place.
Word Problems Within 1000 [H]	Solve a story that adds or subtracts three-digit numbers.
Missing Part Within 1000 [H]	Find a missing addend or a missing starting number within 1000.
Jump by Hundreds and Tens [H]	Add or subtract whole hundreds and whole tens by jumping on a number line.
Ten More Across a Hundred [H]	Add or subtract ten mentally when the number crosses a hundred.
Name the Jump That Was Made [H]	Decide whether one, ten or one hundred was added or taken away.
Move on a Number Chart [H]	Use one more and ten more to find a missing number on a number chart.
Combine a Hundred and a Ten [H]	Move by a hundred and a ten in the same problem.
Two Steps: Total, Then Compare [H]	Add each person's parts first, then find the difference between totals.
Two Steps with Equal Groups [H]	Find the total of equal groups, then add or subtract one more amount.
Two Steps: Change, Then Share Equally [H]	Adjust an amount first, then split the result into two equal groups.
Which Step Comes First [H]	Choose the first calculation to make in a two-step story.
Use Only the Numbers You Need [H]	Solve a story that also contains a number the question does not need.
Match a Story to a Number Sentence [H]	Choose the number sentence that matches what a story describes.
Odd or Even Sums [H]	Decide whether a sum is even or odd from the parts being added.
Pair Up a Picture [H]	Decide odd or even by pairing the objects shown in a picture.
The Next Even Number [H]	Name the even number just after or just before a given number.
Write the Addition for an Array [H]	Choose the repeated addition sentence that matches an array.
Add an Array by Columns [H]	Find an array total by adding the same number once for each column.
Add a New Row to an Array [H]	Find the new total when one or two equal rows are added to an array.
Compare Two Arrays [H]	Find each array total by repeated addition, then compare the totals.

2nd Grade - Measurement, Money, Time & Shapes (Deep) · 47 topics

Same Object, Two Different Units [H]	Relate the size of a length unit to how many of them an object measures.
Feet with Inches Left Over [H]	Split a length in inches into whole feet and the inches left over.
Order Three Lengths [H]	Order three measured lengths and name the longest, shortest, or middle one.
Estimate a Length in Centimeters [H]	Choose a sensible length in centimeters for a familiar object.
Estimate a Length in Feet [H]	Choose a sensible length in feet for a familiar object.
How Close Was the Estimate [H]	Find how far an estimated length is from the real measured length.
Longest and Shortest in a Picture [H]	Measure drawn objects in units and compare the longest with the shortest.
Compare Lengths in Two Units [H]	Change one length into the other unit, then compare the two lengths.
Find a Length from a Comparison [H]	Find an unknown length when it is described as longer or shorter than a known one.
Add Three or More Lengths [H]	Add three or more measured lengths laid end to end.
Find the Missing Piece of a Length [H]	Find one missing piece when the whole length and the other pieces are known.
How Much More Length Is Needed [H]	Find how much more length is needed to reach a required amount.
Read a Point on a Number Line [H]	Name the number a marked point sits on by counting the equal steps.
A Length Drawn on a Number Line [H]	Read a length off a number line diagram and add another length to it.
Count Equal Jumps on a Number Line [H]	Count how many equal jumps reach a number, or find how long each jump is.
Which Hour the Clock Shows [H]	Use the hour hand to name the hour a clock time belongs to.
Say a Time as Minutes To the Hour [H]	Say a time past the half hour as so many minutes to the next hour.
Later Time Past the Next Hour [H]	Find a later time when the added minutes carry past the next hour.
An Earlier Time on the Clock [H]	Find the time a given number of minutes before the time shown.
Order Times Across a.m. and p.m. [H]	Put clock times in order using both the hour and the a.m. or p.m. label.
Read a Schedule [H]	Find how long an activity lasts by using the start times in a schedule.
How Long an Activity Lasted [H]	Find how many minutes passed between a start time and the time on a clock.
Count Coins Shown in Rows [H]	Count a set of coins drawn in rows to find the total value in cents.
How Much More Money Is Needed [H]	Find how many more cents are needed to afford an item from a price list.
Total Cost from a Price List [H]	Add prices read from a price list to find the total cost of several items.
Which Item Costs the Most [H]	Compare prices in a list to find the most or least expensive item.
What You Can Buy with Your Money [H]	Decide which items a given amount of money is enough to pay for.
Dollar Bills and Coins Together [H]	Find the total value in cents of dollar bills and coins together.
Change from Dollar Bills [H]	Find the change in whole dollars after paying with dollar bills.
Fewest Bills to Make an Amount [H]	Make a dollar amount with as few bills as possible by using the largest bills first.
From a Tally Chart to a Bar Graph [H]	Turn tally counts into the heights of the bars on a bar graph.
Find the Missing Bar [H]	Use the total and the drawn bars to find the height of a missing bar.
Most and Fewest on a Bar Graph [H]	Name the category with the most, the fewest, or the second most on a bar graph.
Sort a List into Categories [H]	Count how many entries in a list belong to each category.
Draw the Right Number of Symbols [H]	Use the key of a picture graph to decide how many symbols to draw for a value.
Find What Each Symbol Stands For [H]	Work out the key of a picture graph from one row, then read the other rows.
Tallest and Shortest on a Line Plot [H]	Read the largest and smallest measurements shown on a line plot.
Count Measurements Above a Length [H]	Count how many measurements on a line plot fall above or below a given length.
Make a Line Plot from a List [H]	Turn a list of measurements into the stacks of dots of a line plot.
Count the Angles in a Picture [H]	Count the angles of a drawn shape and compare that count with another shape.
The Shape of a Solid's Faces [H]	Name the flat shape that forms the faces of a solid.
Flat Faces on Round Solids [H]	Count the flat faces on solids that also have curved surfaces.
Name a Solid from Its Faces [H]	Identify a solid shape from a description of its faces.
Count the Squares in a Rectangle [H]	Count the same-size squares covering a rectangle drawn in rows and columns.
Read Rows and Columns from a Picture [H]	Read the number of rows and the number of squares per row from a tiled rectangle.
Cover a Rectangle with One-Inch Squares [H]	Use the side lengths of a rectangle to count the one-inch squares that cover it.
Two-Step Question on a Bar Graph [H]	Combine bars and then compare the groups to answer a two-step graph question.

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