1st Grade Math

293 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 1: Addition & Subtraction to 20 · 13 topics

Counting On to Add [E]	Start at a number and count forward.
Addition Within 20 [E]	Sums up to 20.
Subtraction Within 20 [E]	Take away to find how many are left.
Making Ten to Add [E]	Break a number apart to reach a friendly 10 first.
Adding Three Numbers [E]	Add three whole numbers in any order.
Fact Families [E]	The same three numbers make addition and subtraction facts.
Missing Addend [M]	Find the number that completes the sum.
Relating Addition & Subtraction [M]	Subtraction is an unknown-addend problem.
Word Problems to 20 [M]	Add or subtract to solve a short story.
True or False Equations [E]	Decide whether a number sentence is true.
The Meaning of the Equal Sign [M]	Equals means the two sides are the same amount.
Fluency Within 10 [E]	Add and subtract within 10 quickly, from memory.
Add a Two-Digit and a One-Digit Number [E]	Add ones to ones and keep the tens.

Grade 1: Place Value, Time & Measurement · 14 topics

Tens and Ones [E]	A two-digit number is some tens and some ones.
Building Two-Digit Numbers [E]	Put tens and ones together to make a number.
10 More and 10 Less [E]	Change the tens digit by one.
Counting by Tens [E]	Skip-count 10, 20, 30, and so on.
Adding Tens [E]	Add a multiple of ten to a two-digit number.
Comparing Two-Digit Numbers [M]	Use <, >, or = to compare.
Telling Time to the Hour [E]	Read a clock on the hour.
Telling Time to the Half-Hour [E]	Read a clock on the half-hour.
Comparing Lengths [M]	Order objects by length using clues.
Measuring Length in Units [E]	Count how many whole units long an object is.
Putting Events in Order [E]	Decide what comes first, next, and last.
Count to 120 [E]	Count on past 100, all the way to 120.
Subtracting Tens [E]	Take away 10, 20, 30 from a multiple of ten.
Measuring with Non-Standard Units [E]	Lay same-size objects end to end and count them.

Grade 1: Geometry, Fractions & Data · 13 topics

Sides of 2D Shapes [E]	Count the straight sides of a flat shape.
Vertices of 2D Shapes [E]	Count the corners where sides meet.
Composing 2D Shapes [E]	Put shapes together to build new shapes.
Naming 3D Shapes [E]	Match solid shapes to real objects.
Halves and Fourths [E]	Split a whole into equal fair shares.
Naming a Half and a Fourth [E]	Say the name of one equal part.
Counting Data in Categories [E]	Add up counts across up to three groups.
Reading a Picture Graph [E]	Read one category from a chart.
More and Fewer from Data [E]	Compare two groups to find how many more.
Fair Shares [E]	Split a total into equal groups.
Reading Tally Marks [E]	Count tally marks, five to a bundle.
Which Category Has the Most [E]	Read three groups and find the biggest.
Interpreting Data: How Many More [E]	Compare two of three categories to find the difference.

1st Grade Math - Depth · 40 topics

Add Within 20 [M]	Add two numbers with a total of 20 or less.
Subtract Within 20 [M]	Take away to find how many are left, within 20.
Doubles to 20 [M]	Add a number to itself, up to 10 + 10.
Near Doubles [M]	Add two numbers that are one apart using a double.
Adding by Making a Ten [M]	Break a number apart to make a friendly ten first.
Missing Addends [M]	Find the number that completes an addition.
Add Three Numbers [M]	Add three numbers by looking for a friendly pair.
Fact Families [M]	Use a known addition to find a subtraction.
Add Ten to a Number [M]	Add one whole ten to a two-digit number.
Add Multiples of Ten [M]	Add tens like you add ones.
Count to 120 [M]	Keep counting past 100 all the way to 120.
Count by Tens to 120 [M]	Skip-count by tens up toward 120.
How Many Tens [M]	Read the tens digit of a two-digit number.
How Many Ones [M]	Read the ones digit of a two-digit number.
Value of the Tens Digit [M]	Tell the value the tens digit stands for.
Build a Number from Tens and Ones [M]	Join tens and ones to make a two-digit number.
Ten More, Ten Less [M]	Jump a whole ten up or down from a number.
Compare Two-Digit Numbers [M]	Decide which two-digit number is greater.
Greater Than, Less Than, Equal [M]	Choose the >, <, or = symbol that compares two numbers.
Order Three Numbers [M]	Find the smallest of three two-digit numbers.
Tell Time to the Hour [M]	Read a clock when the minute hand is on 12.
Tell Time to the Half-Hour [M]	Understand what half past means on a clock.
Hours Later [M]	Find the time a few whole hours later.
Count Nickels [M]	Find the value of a handful of nickels.
Count Dimes [M]	Find the value of a handful of dimes.
Count Mixed Coins [M]	Add up the value of nickels and pennies together.
Measure Length with Units [M]	Measure how long something is using same-size units.
Compare Two Lengths [M]	Decide which of two objects is longer.
Order Objects by Length [M]	Find the shortest of three objects.
Combine Lengths [M]	Add two lengths placed end to end.
Defining Shape Attributes [M]	Tell which features truly define a shape.
Compose Shapes [M]	Combine smaller shapes to build a bigger one.
Halves [M]	Understand cutting a whole into two equal parts.
Fourths (Quarters) [M]	Understand cutting a whole into four equal parts.
Half of a Number [M]	Split an even number into two equal parts.
Count Equal Shares [M]	Match the name of a share to how many parts.
Skip Count by Twos [M]	Count 2, 4, 6, 8 and keep the pattern going.
Skip Count by Fives [M]	Count 5, 10, 15, 20 and keep the pattern going.
Compare Word Problems [M]	Find how many more one person has than another.
Two-Step Word Problems [M]	Solve a story with two changes in a row.

1st Grade Math - Deep II · 31 topics

Counting Back to Subtract [M]	Subtract a small number by counting back from the bigger one.
Doubles Minus One [M]	Add two numbers one apart using the higher double.
Making a Ten to Subtract [M]	Subtract across ten by stopping at ten on the way.
Order Does Not Change the Sum [M]	Use the fact that addends can be added in any order.
Ten-Plus Facts [M]	Add a one-digit number to ten to make a teen.
Expanded Form [M]	Break a two-digit number into its tens and ones values.
Two-Digit Number Words [M]	Match a two-digit number word to its numeral.
One More, One Less to 120 [M]	Add or take away one anywhere up to 120.
Numbers In Between [M]	Name the two-digit number between two others.
Digital Clock Times [M]	Match an o'clock or half-past time to a digital clock.
Count Quarters [M]	Find the value of a few quarters.
Count Dimes and Pennies [M]	Add the value of dimes and pennies together.
Count by Twenty-Fives [M]	Skip-count 25, 50, 75, 100 like counting quarters.
How Many More Cents [M]	Find how many more cents are needed to reach a price.
Build with Solid Shapes [M]	Combine solid shapes to make a new solid.
Equal and Unequal Shares [M]	Know that fair shares must be equal in size.
Thirds [M]	Understand splitting a whole into three equal parts.
Bigger: a Half or a Fourth [M]	Compare the size of a half to a fourth.
A Fourth of a Number [M]	Split a number into four equal groups.
Name the Shaded Fraction [M]	Say the fraction name for one shaded equal part.
Parts That Make a Whole [M]	Count how many equal parts rebuild the whole.
How Many Fewer [M]	Find how many fewer one group has than another.
Read a Bar Graph [M]	Read the value of one bar on a bar graph.
Which Category Has the Fewest [M]	Read three groups and find the smallest.
Add-To: Change Unknown [M]	Find how many were added when the total is known.
Take-From: Start Unknown [M]	Find the starting amount when some were taken away.
Put-Together: Missing Part [M]	Find one part when the whole and the other part are known.
Greatest of Three Numbers [M]	Find the biggest of three two-digit numbers.
How Much Longer [M]	Find how much longer one object is than another.
Two-Digit Minus One-Digit [M]	Subtract a one-digit number from the ones place.
True or False Subtraction [M]	Decide which subtraction sentence is correct.

1st Grade - Addition & Subtraction Strategies (Deep) · 46 topics

Count On from the Bigger Number [H]	Add by starting at the larger addend and counting on the smaller one.
Count On with Hops on a Number Line [H]	Add on a number line by hopping forward one space for each one added.
Count Back with Hops on a Number Line [H]	Subtract on a number line by hopping back one space for each one taken.
Count Up to Find a Difference [H]	Find a difference by counting up from the smaller number to the larger.
Plus One, Plus Two, Plus Three [H]	Add one, two or three to a number by naming the next counting numbers.
Partners That Make Ten [H]	Name the number that pairs with a given number to make ten.
Break Apart to Make a Ten [H]	Split the second addend so the first one grows into a ten.
Add Nine by Adding Ten [H]	Add nine by adding ten and then taking one away.
Take Ten from a Teen [H]	Subtract ten from a teen number to leave the ones.
Doubles Plus Two [H]	Add two numbers that are two apart by using the smaller double.
Choose the Helping Double [H]	Pick the doubles fact that helps with a near-doubles sum.
Doubles in an Array [H]	Read a double from two equal rows of dots and total them.
Which Number Was Doubled [H]	Find the number that was added to itself to give a total.
Use a Known Fact: One More [H]	Find a new sum from a known sum when one addend grows by one.
Use a Known Fact: One Less [H]	Find a new sum from a known sum when one addend shrinks by one.
The Matching Subtraction Fact [H]	Write the true subtraction sentence that uses the numbers of a known sum.
Pairs with the Same Total [H]	Recognize two addition pairs that have equal totals.
Give and Take to Add [H]	Move ones from one addend to the other so the sum becomes ten plus ones.
Subtract by Thinking Addition [H]	Solve a subtraction by finding the addend that completes the whole.
Check a Subtraction by Adding [H]	Test a subtraction answer by adding it back to the number taken away.
Check an Addition by Subtracting [H]	Test an addition answer by subtracting one addend from the total.
Take-From: How Many Were Taken [H]	Find how many were taken away when the start and the rest are known.
Add Three: Make a Ten First [H]	Add three numbers by pairing the two that make ten first.
Add Three: Use a Double First [H]	Add three numbers by pairing the two equal ones first.
Three Numbers with One Missing [H]	Find the third addend when three numbers and their total are given.
Choose the Easiest Pair First [H]	Decide which two of three addends to add first to make the work easy.
Unknown in the First Place [H]	Find the first addend when the second addend and the total are known.
Unknown at the Start of a Subtraction [H]	Find the starting number when the amount taken and the rest are known.
Unknown Amount Taken Away [H]	Find how much was subtracted when the start and the result are known.
Match the Story to the Equation [H]	Choose the number sentence whose unknown sits where the story needs it.
Balance Both Sides [H]	Make an equation true when both sides are additions.
Balance with a Subtraction [H]	Make an equation true when one side is a subtraction.
True or False on Both Sides [H]	Judge whether two additions on either side of the equal sign match.
The Total Written First [H]	Solve an equation whose total is written before the equal sign.
True or False with Three Numbers [H]	Judge whether a three-addend sentence gives the correct total.
Find the Number That Makes It True [H]	Fill an unknown on the left so the two sides of an equation match.
Which Sign Makes It True [H]	Choose the plus or minus sign that makes a number sentence true.
Compare: How Many More [H]	Find the difference between two amounts shown side by side.
Compare: Find the Bigger Amount [H]	Find the larger amount when one group has a stated number more.
Compare: Find the Smaller Amount [H]	Find the smaller amount when the larger group has a stated number more.
Fewer Than: Find the Bigger Amount [H]	Find the larger amount when the smaller group is a stated number fewer.
Two-Step: Put Together Twice [H]	Combine two groups and then join a third to find a total.
Two-Step: Some Join, Some Leave [H]	Work through a story where a group first grows and then shrinks.
Two-Step: Take Away Twice [H]	Work through a story where two amounts are taken away one after another.
Two-Step: Compare Then Total [H]	Find one amount from a comparison, then add both amounts together.
Two-Step: Find the Hidden Change [H]	Find an unknown change that comes after a known first step.

1st Grade - Place Value, Measurement & Shapes (Deep) · 52 topics

Count Forward to 120 [H]	Keep counting forward by ones from any number up to 120.
Missing Number on a Number Chart [H]	Fill a blank square in a number chart using one more and ten more.
Count a Big Group by Tens [H]	Count equal bags of ten and any loose ones to find a total.
Number Words Past One Hundred [H]	Match a number word between 101 and 120 to its numeral.
Count Backward from 120 [H]	Count backward by ones from numbers up to 120.
Read Base-Ten Blocks [H]	Read a two-digit number from a picture of ten-rods and single cubes.
Extra Ones Make Another Ten [H]	Rebuild a number when the ones are ten or more.
Trade a Ten for Ten Ones [H]	Show the same number with fewer tens and more ones.
Ten Tens Make One Hundred [H]	Count tens past one hundred, where ten tens make a hundred.
Jumps of Ten on a Number Line [H]	Land on the right number after jumps of ten on a number line.
Ten More Past One Hundred [H]	Find ten more or ten less for numbers near and past one hundred.
How Big Was the Jump [H]	Decide whether a number changed by one or by ten, and by how many tens.
Ten More in a Story [H]	Solve a story problem where an amount grows or shrinks by ten.
Compare Numbers Shown with Blocks [H]	Compare two two-digit numbers shown as tens and ones.
Same Tens, Compare the Ones [H]	Compare two-digit numbers that have the same tens digit.
Compare a Number to a Sum [H]	Work out a sum of tens and ones, then compare it with another number.
Which Comparison Is True [H]	Check comparison sentences and pick the true one.
Add Ones and Make a New Ten [H]	Add a one-digit number when the ones make a new ten.
How Many More to the Next Ten [H]	Find how many ones are needed to reach the next ten.
Missing One-Digit Addend [H]	Find the missing one-digit addend in a two-digit addition.
Two-Digit Plus One-Digit Story [H]	Solve a story problem that adds ones to a two-digit number.
The Tens Digit After Adding [H]	Decide how many tens the answer has after adding ones.
How Many Tens in All [H]	Add groups of tens and say the answer as a number of tens.
Add Tens to a Two-Digit Number [H]	Add a multiple of ten to a two-digit number without changing the ones.
How Many Tens Were Added [H]	Find the multiple of ten that was added to reach a total.
Adding Tens from a Graph [H]	Read two multiples of ten from a bar graph and add them.
Subtract Tens from a Two-Digit Number [H]	Take a multiple of ten away from a two-digit number.
How Many Tens Were Taken [H]	Find the multiple of ten that was subtracted.
Taking Away Tens in a Story [H]	Solve a story problem where whole tens are given away.
Fact Families with Tens [H]	Match addition and subtraction facts made from the same three multiples of ten.
Compare Lengths Without Measuring [H]	Compare two objects using a third object they were both compared to.
Rules for Fair Measuring [H]	Apply the rules that make a length measurement fair.
Smaller Units, Bigger Number [H]	Relate the size of the measuring unit to the size of the count.
Order Ribbons by Length in a Picture [H]	Order three drawn objects by how many length units each one covers.
Measure from a Cube Picture [H]	Count same-size units in a drawing to measure and compare lengths.
Where the Hour Hand Points [H]	Read the hour hand at an o'clock time and at a half past time.
What the Minute Hand Tells [H]	Use the minute hand to tell an o'clock time from a half past time.
Half an Hour Later [H]	Find the time a half hour or an hour and a half after a given time.
Before or After a Given Time [H]	Decide whether a clock time comes before or after another time.
How Many Half Hours [H]	Count how many half hours fit inside a number of hours.
How Many in All Three Groups [H]	Add every category in a graph to find the total.
Put Two Categories Together [H]	Add two chosen categories from a three-category graph.
Find the Missing Bar [H]	Use the total and the bars shown to find a missing category.
Most and Fewest: the Difference [H]	Find the difference between the largest and smallest categories in a graph.
Sort a List into Categories [H]	Organize a list of choices into categories and count them.
What Does Not Change a Shape [H]	Separate the attributes that define a shape from those that do not.
Name the Shape from Its Clues [H]	Name a flat shape from the number of sides and corners described.
Faces and Corners of Solid Shapes [H]	Count the flat faces or corners of a common solid shape.
Which Solids Roll and Stack [H]	Tell which solids roll and which stack, using their flat and curved parts.
How Many Triangles Fill the Shape [H]	Count the smaller shapes needed to fill several copies of a bigger shape.
Cutting a Shape Makes New Shapes [H]	Name the shapes made when a flat shape is cut with a straight line.
Equal Parts in More Than One Whole [H]	Count halves or fourths across several wholes.

1st Grade - Addition, Subtraction & Place Value (Deep) · 42 topics

How Big Was the Hop [H]	Counting from the start to the landing place gives the size of the hop.
Where the Hop Began [H]	To find where a hop began, undo it: hop the same size the other way.
The Missing Number on the Line [H]	Find the counting rule from the labels, then use it on the gap.
Equal Hops on the Line [H]	Equal hops skip count, so the landing place and the hop count match up.
Empty Boxes in a Ten-Frame [H]	Counters and empty boxes in a ten-frame always add up to ten.
Putting More Counters in the Frame [H]	Count on from the counters shown; past ten the total becomes a teen.
Taking Counters Out of the Frame [H]	Taking counters out leaves fewer counters and more empty boxes.
A Full Frame and Some More [H]	A full frame is one ten, so a teen number is ten and the extra ones.
Ten and Some More [H]	Filling the frame rewrites a hard sum as an easy ten-plus fact.
Landing on Ten First [H]	Subtract from a teen in two easy hops: back to ten, then the rest.
Nothing Added, Everything Taken [H]	Adding zero changes nothing, and taking a number from itself leaves zero.
Which Card Is Bigger [H]	Work out each total first, then compare the totals.
Two More, Two Less [H]	Change one addend by two and the total changes by two the same way.
One More Here, One Less There [H]	Moving one from an addend to the other keeps the total the same.
The Same Fact, Ten Bigger [H]	Adding ten to an addend adds ten to the total, and the ones stay put.
Which Fact Helps Most [H]	Pick a helper fact that is close to the sum and easy to say.
Keeping Both Sides Equal [H]	The equal sign says the two sides are worth the same amount.
Take-Away on Both Sides [H]	Work out the side you can, then make the other side match it.
True or False with Tens [H]	Adding tens to tens counts tens, so only the tens digit changes.
Another Name for a Number [H]	One number has many names: sums and take-aways can all mean the same.
How Many More to Fill the Order [H]	A missing addend is the gap between what you have and what you want.
How Many More to Twenty [H]	Count on from where you are to twenty to find what is still missing.
Filling In a Part-Whole Table [H]	The parts add up to the whole, so any one of them can be found.
Two Parts That Fit the Clue [H]	Check every pair against both the total and the clue before choosing.
Three Groups in a Picture [H]	Read each row of the picture, then join only the rows the question asks for.
Adding Four or Five Numbers [H]	Add a long line of numbers two at a time, keeping a running total.
Which Numbers Make the Total [H]	Test each list by adding it, and keep the one that lands on the total.
Fewer Than: Find the Smaller Amount [H]	"Fewer than" names the smaller amount, so take the gap away.
Add-To: How Many Were There at First [H]	When things were added, work backwards from the end to the start.
Making Two Amounts Match [H]	The gap tells how many to add on; sharing the gap fairly halves it.
The Number You Do Not Need [H]	Use only the numbers that answer the question asked.
Comparing Two Rows of a Table [H]	Find the two rows the question names, then compare only those.
Is That Enough? [H]	Compare what you have with what you need, then say the gap.
Finishing a Base-Ten Picture [H]	Match the blocks to the digits: tens blocks to the tens, ones to the ones.
Swapping the Two Digits [H]	Swapping the digits swaps their jobs, so the number changes a lot.
Number Riddles with Tens and Ones [H]	Work out each digit from its clue, then write the tens digit first.
How Many Ten-Frames Does It Take [H]	The tens digit counts full frames; the ones digit is what is left over.
Jumping Ten More Than Once [H]	Each jump of ten changes only the tens digit, so count the jumps.
Ten More or Ten Less [H]	Ten more moves the tens digit; one more moves the ones digit.
Adding Tens to a Block Picture [H]	One more tens block is ten more, so only the tens digit moves.
Which Digit Changes [H]	Adding a multiple of ten moves the tens digit and leaves the ones alone.
Tens First, Then Ones [H]	Add the tens to the tens first, then deal with the ones.

1st Grade - Measurement, Time, Geometry & Data (Deep) · 42 topics

Which One Is the Longest [H]	The longest object is the one with the most cubes in its row.
Which One Is the Shortest [H]	The shortest object is the one with the fewest cubes in its row.
The One in the Middle [H]	Ordering three lengths leaves one object between the other two.
Longer and Shorter from Clues [H]	If A beats B and B beats C, then A beats C without any measuring.
Measuring with Cubes in a Row [H]	Lay same-size cubes end to end and count them to measure a length.
The Gap Between Two Cube Rows [H]	Line up two rows of cubes and count the extra cubes on the longer one.
Joining Lengths End to End [H]	Two lengths joined end to end add; a missing piece is found by taking away.
Longer and Shorter Stories [H]	Shorter means take the gap away; longer means add it on.
Does It Fit Inside [H]	One thing fits inside another only when it is the shorter one.
O'Clock on a Clock Face [H]	On the hour the long hand points at 12 and the short hand names the hour.
Half Past on a Clock Face [H]	At half past the long hand points at 6 and the short hand has just passed the hour.
Whole Hours Later [H]	One hour later moves the short hand on by one and leaves the long hand alone.
Half an Hour On from Now [H]	Half an hour later turns o'clock into half past, and half past into the next o'clock.
Saying a Time Two Ways [H]	The same time can be said in words or written with two dots.
Putting Times in Order [H]	Earlier times have smaller hour numbers, and o'clock comes before half past.
Counting Whole Hours [H]	Count the hours from one o'clock time up to another.
What Each Coin Is Worth [H]	A penny is 1 cent, a nickel is 5 cents and a dime is 10 cents.
Adding Up a Purse of Coins [H]	Count the dimes by tens, the nickels by fives, then add the pennies.
How Many Coins Make the Amount [H]	Skip count by the coin's value until you reach the amount.
Who Has More Money [H]	More coins is not always more money, so work out each total first.
Is That Enough Money [H]	Add the coins up, then compare that total with the price.
Cents Left After Spending [H]	Total the coins first, then take away what was spent.
Naming the Shape You See [H]	A flat shape is named by how many straight sides it has.
Counting the Sides [H]	A side is one straight edge, counted once all the way round the shape.
Counting the Corners [H]	A corner is where two sides meet, and a flat shape has as many corners as sides.
Which Shape Has That Many Sides [H]	Going from a side count back to a shape name is the same list read backwards.
What Really Makes the Shape [H]	Sides and corners decide a shape's name; color, size and turning do not.
Making a New Shape from Shapes [H]	Shapes pushed together with no gaps make one new, bigger shape.
Naming a Solid Shape [H]	Solid shapes are named by their flat faces and their curved parts.
Solids All Around Us [H]	Everyday objects match the solid shapes: balls, cans, hats and boxes.
The Flat Face of a Solid [H]	The flat face of a solid is itself a flat shape you can name.
Sorting Shapes by Their Sides [H]	Sorting a list of shapes means checking each name against the rule.
Naming One Equal Part [H]	Two equal parts are halves and four equal parts are fourths.
How Many Pieces [H]	The name of the part tells how many pieces the whole was cut into.
Fourths and Quarters [H]	Fourth and quarter are two words for the same part of a whole.
Reading One Row of a Tally Chart [H]	Tally marks come in gates of five, so count by fives and then by ones.
Which Group Has the Most [H]	The biggest group is the row with the most tally marks.
Which Group Has the Fewest [H]	The smallest group is the row with the fewest pictures.
How Many More Chose It [H]	Match the two rows picture for picture; the extras are the difference.
How Many Altogether [H]	Adding every row of a chart gives how many children were counted.
The Group That Is Not Shown [H]	Take the shown groups away from the total to find the hidden group.
Sorting a Class List into Groups [H]	Sorting a list means counting the rows that belong to each group.

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