1st Grade Math

209 core topics · approximately 58 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]	Recognise 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.

🖨 Print / save as PDF ← All courses