Kindergarten Math

287 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

Kindergarten: Counting & Cardinality to 100 · 14 topics

Count to 100 by Ones [E]	Say the numbers in order all the way to 100.
Count to 100 by Tens [E]	Skip-count 10, 20, 30, all the way to 100.
Count Forward from a Number [E]	Begin at any number and keep counting up.
Write Numbers 0 to 20 [E]	Match number words to the numerals we write.
Count Objects (How Many) [E]	Count a group of things and say the total.
Compare Two Numbers [E]	Decide which number is greater, less, or equal.
One More [E]	Find the number that is one bigger.
One Less [E]	Find the number that is one smaller.
Order Numbers [E]	Put numbers in order and find the smallest or largest.
Ten-Frames [E]	Use a ten-frame to see numbers up to 10.
Number After / Before [E]	Tell which number comes next or just before.
Count by Twos [E]	Skip-count 2, 4, 6, 8 and keep going.
Ordinal Position (1st to 10th) [E]	Tell which one is first, second, third, and so on.
Subitizing Dot Patterns [E]	See a small group of dots and know how many at a glance.

Kindergarten: Early Operations, Shapes & Measurement · 17 topics

Add Within 5 [E]	Put groups together to add up to 5.
Add Within 10 [E]	Add two groups with a total up to 10.
Subtract Within 5 [E]	Take some away to subtract within 5.
Subtract Within 10 [E]	Take away from groups up to 10.
Make 10 [E]	Find the partner that makes a number into 10.
Break Apart Small Numbers [E]	Split a number into two smaller parts.
2D Shapes [E]	Name flat shapes and count sides and corners.
3D Shapes [E]	Name solid shapes we can hold.
Positions [E]	Describe where things are: above, below, beside.
Compare Length [E]	Tell which object is longer or shorter.
Compare Weight [E]	Tell which object is heavier or lighter.
Sort and Classify [E]	Put objects into groups and count each group.
AB Patterns [E]	Find what comes next in a repeating pattern.
More Ways to Make a Number to 10 [E]	Find the missing part that builds a number up to 10.
Compare Heights [E]	Tell which object is taller or shorter.
Compare Capacity [E]	Tell which container holds more or less.
Name Coins by Value [E]	Know how many cents each coin is worth.

Kindergarten Math - Depth · 41 topics

Count Forward to 100 [M]	Say the next number when counting up to 100.
Count by Tens [M]	Skip-count 10, 20, 30 and keep going to 100.
Count by Fives [M]	Skip-count 5, 10, 15, 20 and keep going.
Count On from a Number [M]	Start at a number and count forward a few more.
Count Back from a Number [M]	Start at a number and count backward a few steps.
Number Just Before [M]	Name the number that comes right before another.
Number Just After [M]	Name the number that comes right after another.
Number In Between [M]	Name the number that fits between two others.
One More [M]	Find the number that is one more.
One Less [M]	Find the number that is one less.
Ten More [M]	Find the number that is ten more.
Ten Less [M]	Find the number that is ten less.
Count on a Ten-Frame [M]	Read how many dots fill a ten-frame.
Teen Numbers: Ten and Ones [M]	See a teen number as one ten and some ones.
Build a Teen Number [M]	Put one ten and some ones together to make a teen number.
Add Within 5 [M]	Add two numbers with a total of 5 or less.
Add Within 10 [M]	Add two numbers with a total of 10 or less.
Subtract Within 5 [M]	Take away to find how many are left, within 5.
Subtract Within 10 [M]	Take away to find how many are left, within 10.
Make Ten [M]	Find the partner that adds up to ten.
Adding and Subtracting Zero [M]	See that zero does not change a number.
Doubles Facts [M]	Add a number to itself.
Addition Word Problems [M]	Solve a story about adding more.
Subtraction Word Problems [M]	Solve a story about taking some away.
Add Three Numbers [M]	Put three small groups together.
Which Number Is Greater [M]	Pick the larger of two numbers.
Which Number Is Less [M]	Pick the smaller of two numbers.
How Many More [M]	Find how many more one group has than another.
Smallest of Three [M]	Find the smallest number in a group of three.
Largest of Three [M]	Find the largest number in a group of three.
Name a 2-D Shape by Its Sides [M]	Match a flat shape to its number of sides.
Count the Sides of a Shape [M]	Tell how many sides a named shape has.
Count the Corners of a Shape [M]	Tell how many corners a named shape has.
Name a 3-D Solid Shape [M]	Match a solid shape to how it looks.
Position Words [M]	Describe where something is using position words.
Repeating AB Patterns [M]	Find what comes next in an AB pattern.
Growing Number Patterns [M]	Continue a pattern that grows by the same amount.
Compare Lengths [M]	Tell which object is longer or shorter.
Compare Weights [M]	Tell which object is heavier or lighter.
Find the Tallest [M]	Choose the tallest of three objects.
Sort and Count by Attribute [M]	Count how many objects share the same feature.

Kindergarten Math - Deep II · 34 topics

Read a Number Word from a Numeral [M]	Match a written numeral to its number word.
Count Backward in Order [M]	Say the numbers in reverse counting order.
Matching Halves (Symmetry) [M]	Spot a shape whose two halves match.
Match to Compare Groups [M]	Match one to one to see which group has more.
Make Five [M]	Find the partner that adds up to five.
Fill a Five-Frame [M]	Tell how many more dots fill a five-frame.
Day After [M]	Name the day that comes right after another.
Day Before [M]	Name the day that comes right before another.
Days in a Week [M]	Know that a week has seven days.
Months in a Year [M]	Know that a year has twelve months.
Name the Season [M]	Match what is happening outside to a season.
Times of Day [M]	Match an activity to the time of day.
Count Pennies [M]	Find how many cents a group of pennies is worth.
Which Coin Is Worth More [M]	Compare the values of two coins.
Name a Coin from Its Value [M]	Say which coin matches a value in cents.
AABB Patterns [M]	Continue a pattern that repeats two of each.
ABC Patterns [M]	Continue a pattern that repeats three things.
The Repeating Part of a Pattern [M]	Count how many items make up the repeating part.
Find the Missing Part of a Pattern [M]	Fill the gap in the middle of a repeating pattern.
Flat or Solid Shapes [M]	Tell a flat 2-D shape from a solid 3-D shape.
Put Shapes Together [M]	Combine small shapes to build a bigger shape.
Solids That Roll [M]	Decide which solid shapes can roll.
Flat Faces of a Solid [M]	Count the flat faces on a solid shape.
Corners of a Solid [M]	Count the corners on a solid shape.
The Shape of a Face [M]	Name the flat shape of a solid's face.
Flat Shapes Around Us [M]	Match a real object to its flat shape.
Count Shapes in a Group [M]	Find and count one kind of shape in a mixed group.
Which Shape Does Not Belong [M]	Find the shape that breaks the rule.
Left and Right [M]	Tell which thing is on the left or the right end.
Inside and Outside [M]	Tell whether something is inside or outside.
Find the Shortest [M]	Choose the shortest of three objects.
Which Is Lighter [M]	Tell which object is lighter on a balance.
Which Holds Less [M]	Tell which container holds less.
Which Sorted Group Has the Most [M]	Compare sorted groups to find the biggest one.

Kindergarten - Counting, Comparing & Number Sense (Deep) · 48 topics

Count a Row of Objects [H]	Count objects that are lined up in a row and say how many.
Count Tally Marks [H]	Read a tally chart and tell how many marks a row has.
The Last Number Tells How Many [H]	Know that the last counting word said names how many are in the set.
Counting Stays the Same [H]	Know that moving a set around does not change how many it has.
Count Dots in an Array [H]	Count every dot in a picture where the dots sit in neat rows.
How Many in Each Row of an Array [H]	Count the dots in one row of an array of equal rows.
Count the Rows of an Array [H]	Count how many rows of dots an array has.
Count Rows of Ten [H]	Count a picture of equal rows of ten by counting ten at a time.
Count Scattered Objects [H]	Count a group of objects that are scattered instead of lined up.
Which Scattered Group Has More [H]	Compare scattered groups by counting each one.
Count a Scattered Group, Then One More [H]	Count a scattered group and then find one more or one less than it.
Count On from a Hidden Number [H]	Hold a given number in mind and count on for the objects you can see.
Count On with Hops on a Number Line [H]	Count on by hopping forward one tick at a time on a number line.
Count On to Reach a Number [H]	Count on from one number to another and tell how many steps it took.
Count On from a Ten-Frame [H]	Read how many a ten-frame shows, then count on past it.
Say the Number Word for a Set [H]	Count a pictured set and choose the number word that tells how many.
Make a Set Match a Number Card [H]	Add or remove objects so a set matches a written numeral.
One More with a Picture [H]	Count a pictured set and name the number that is one more.
One Less with a Picture [H]	Count a pictured set and name the number that is one less.
One More Across a Ten [H]	Find one more than a number that ends in nine.
One Less Across a Ten [H]	Find one less than a number that ends in zero.
Which Row Has One More [H]	Find the group that holds exactly one more than a named group.
Match Rows to See Which Has More [H]	Compare two pictured groups by matching them one to one.
How Many More in the Longer Row [H]	Count the leftovers after matching to tell how many more one group has.
Do the Two Rows Match [H]	Decide whether two groups have the same number by matching them.
Which Row Has the Fewest [H]	Compare three or more pictured groups to find the smallest one.
Greater Than, Less Than, or Equal To [H]	Say whether one number is greater than, less than, or equal to another.
Compare a Number with Ten [H]	Decide whether a number is more than ten, fewer than ten, or exactly ten.
Which Number Is Closer to Ten [H]	Use a number line to tell which number sits nearer to ten.
Compare Bars on a Graph [H]	Read a bar graph to compare how many each bar shows.
Which List Is in Order [H]	Choose the list of three numbers that is in counting order.
Order Three Pictured Groups [H]	Order three pictured groups by size and find the middle one.
Which Number Fits in the Order [H]	Choose the number that keeps three cards in counting order.
Missing Number on a Number Chart [H]	Find a hidden number on a number chart by counting from its neighbours.
Fill the Missing Number in a Count [H]	Fill the gap in a run of counting numbers.
Missing Number on a Number Line [H]	Read a number line and name the number at an unlabeled tick.
How Many Numbers Do You Say [H]	Count how many numbers are said when counting from one number to another.
Which Number Was Skipped [H]	Spot the number left out of a count that jumps ahead.
Count Bags of Ten [H]	Find a total by counting groups of ten and then the loose ones.
Missing Number When Counting by Tens [H]	Fill the gap in a sequence that counts by tens.
Count Back by Tens [H]	Count backward by tens from a multiple of ten.
How Many Tens Make a Number [H]	Tell how many tens are inside a multiple of ten.
Dice Patterns at a Glance [H]	Recognize how many dots a dice face shows without counting them.
Read a Domino [H]	See both ends of a domino at a glance and give the total.
A Full Ten and Some More [H]	Read a picture of one full ten and some loose ones as a teen number.
How Many More to Make Twenty [H]	Count on from a teen number to twenty to find how many more are needed.
Compare Two Teen Numbers [H]	Compare teen numbers, which all share one ten, by their ones.
Ten and Some Ones Makes a Teen Number [H]	Match a teen number to the words one ten and some ones.

Kindergarten - Adding, Taking Apart & Shapes (Deep) · 49 topics

Join Two Groups to Add [H]	Find the total of two pictured groups by joining them.
Add Two Tally Rows [H]	Add the counts shown in the rows of a tally chart.
Add More Counters to a Ten-Frame [H]	Add counters to a ten-frame and tell how many there are now.
Add by Hopping Forward on a Number Line [H]	Add on a number line by hopping forward one at a time.
Choose the Addition Sentence for a Picture [H]	Match a picture of two joined groups to its addition sentence.
Add the Two Groups in Either Order [H]	Show that two groups give the same total added in either order.
Which Group Has the Bigger Total [H]	Add each group first, then compare the totals.
Take Away from a Picture Group [H]	Count a pictured group, take some away, and count what is left.
Take Counters Off a Ten-Frame [H]	Remove counters from a ten-frame and tell how many remain.
Subtract by Hopping Back on a Number Line [H]	Subtract on a number line by hopping back one at a time.
Choose the Subtraction Sentence for a Picture [H]	Match a picture of a group losing some members to its subtraction sentence.
How Many Were Taken Away [H]	Find how many were removed from the start amount and what is left.
How Many Were There at the Start [H]	Work backward from what is left to the starting amount.
Match an Adding Fact to a Take-Away Fact [H]	Pair an addition fact with the subtraction fact that uses the same numbers.
Add the Counts from a Table [H]	Read counts from a table and add them to answer a story.
How Many Joined the Group [H]	Find how many were added when the start and the end amounts are known.
Put Some In and Take Some Out [H]	Work through a story where a group grows and then shrinks.
Add or Take Away? [H]	Decide whether a story calls for adding, taking away, or both.
Missing Part in a Part-Part-Whole Table [H]	Find the missing part when one part and the whole are known.
Find the Whole from the Parts [H]	Join the parts in a part-part-whole table to find the whole.
Split a Group into Colors [H]	Take a pictured group apart into two colors and find the missing color.
Another Way to Make the Same Number [H]	Find a different pair of parts that makes the same whole.
Finish the List of Ways [H]	Complete an ordered list of the pairs of parts that make a number.
Which Pair Makes Ten [H]	Recognize the pairs of numbers that add to ten.
How Many More Counters Make Ten [H]	Add the parts you have, then find how many more reach ten.
Hop to Ten on a Number Line [H]	Count the hops from a number up to ten on a number line.
Ten, More Than Ten, or Less Than Ten [H]	Judge whether two or three parts make exactly ten, less, or more.
Name the Flat Shape in the Picture [H]	Name a drawn circle, square, triangle, rectangle, or hexagon.
Count the Sides of the Shape Shown [H]	Count the straight sides on a drawn shape.
Sort Shapes and Count a Group [H]	Sort shapes by a rule and count how many fit the rule.
Which Shape Fits the Group Rule [H]	Choose the shape that follows a sorting rule about sides or corners.
A Shape Turned or Resized [H]	Recognize that turning or resizing a shape does not change what it is.
Count the Flat and Solid Shapes [H]	Sort a set of shapes into flat and solid and count each kind.
The Solid Shape of a Real Thing [H]	Match a real object to the solid shape it looks like.
Stack, Slide, or Roll [H]	Tell which solids can be stacked, slid, or rolled.
Above and Below on a Shelf [H]	Use above and below to find a thing on a two-shelf picture.
Beside and Between in a Row [H]	Use beside, next to, and between to find a thing in a row.
In Front of and Behind in a Line [H]	Use in front of and behind to place people in a line.
Choose the Position Word [H]	Pick the word that describes where one thing is compared to another.
Count the Small Squares That Cover a Rectangle [H]	Count the equal small squares that fill a larger rectangle.
Cover a Hexagon with Pattern Blocks [H]	Tell how many smaller pattern blocks cover a hexagon.
Cut a Shape into Smaller Shapes [H]	Name the smaller shapes made when a shape is cut apart.
Measure a Length in Cubes [H]	Measure how long an object is by counting the cubes along it.
How Many Cubes Longer [H]	Find how many cubes longer one object is than another.
Which Object Is Longer [H]	Compare pictured lengths to tell which object is longer or shorter.
Which Is Heavier on the Balance [H]	Use the blocks that balance each object to tell which is heavier.
Compare Without Measuring [H]	Order three objects from two comparison clues.
How Many More Cups It Holds [H]	Find how many more cups one container holds than another.
Which Container Holds More [H]	Compare two containers by the number of cups each holds.

Kindergarten - Counting & Number Sense (Deep) · 42 topics

Empty Boxes on a Ten-Frame [H]	A ten-frame shows the counters and the empty boxes at the same time.
Counters in the Bottom Row [H]	A full top row is five, so the bottom row shows how many more than five.
Counters In and Counters Out [H]	Putting counters in and taking counters off changes the count step by step.
Is the Frame More or Fewer? [H]	Count the frame first, then say whether that count is more or fewer.
A Few More and a Few Fewer [H]	More means count on from the picture, fewer means count back from it.
Pairs That Make Ten in a Table [H]	Each row of the table is one way to split the same total into two parts.
The Pair That Does Not Make Ten [H]	Test each pair by counting on from the first number to ten.
Some Counters Are Hidden [H]	The hidden part is what is left of the total after the shown part.
The Other Half of the Domino [H]	A domino holds two parts, so one part and the total give the other part.
Ben Has Just as Many [H]	Two groups that match give a double: count one group, then count it twice.
Did the Count Come Out Right? [H]	Counting each object once, in order, is the way to test somebody's count.
One Cup for Each Child [H]	Giving one thing to each child pairs the two groups off one for one.
Are There Enough Cups? [H]	Matching the rows one for one tells whether a group is enough.
Which Two Rows Match? [H]	Two rows match when every counter in one has a partner in the other.
How Many Fewer [H]	The extra counters left unmatched tell how many fewer the short row has.
The Row in the Middle [H]	Putting three groups in order leaves one group in the middle.
The Number Card for the Group [H]	Counting a group gives the numeral that names how many it holds.
Counting Dots Above a Number [H]	Each dot above a number stands for one child who chose that number.
The Tallest Stack of Dots [H]	The tallest stack shows the number the most children picked.
How Many Children in All [H]	Every dot on the plot is one child, so all the dots give the whole class.
How Many More on a Bar Graph [H]	Two bars are compared by counting the steps from the short one up to the tall one.
Two Bars Put Together [H]	Adding the bars of a graph gives how many children there were in all.
The Shortest Bar [H]	The shortest bar names the group that the fewest children chose.
Comparing Tally Rows [H]	Tally marks are counted in fives, then the rows are compared.
Reading a Table of Counts [H]	A table pairs each name with its count, so the counts can be ordered.
Each Picture Stands for Ten [H]	When one picture stands for ten, count the pictures by tens.
The Number Under the Dot [H]	Count on from the nearest labeled mark to name an unlabeled one.
Counting Hops on a Number Line [H]	The number of one-step hops between two marks is the gap between them.
A Number Line That Counts by Tens [H]	Each mark on this line is one ten, so the marks are counted 10, 20, 30.
Hopping On by Tens [H]	One hop on this line is one ten, so hops are counted 10, 20, 30.
The Missing Number Counting Back [H]	A backward count steps down by one each time, or by ten on a tens count.
The Number in the Middle [H]	Order three numbers and the one that is neither biggest nor smallest sits in the middle.
Which Teen Number Comes First [H]	Teen numbers follow the counting order eleven, twelve, thirteen and on.
Closer to Twenty [H]	The number needing fewer counts to reach twenty is the closer one.
Writing the Numeral for a Number Word [H]	Every number word has a numeral that is written with digits.
When None Are Left [H]	None left is written as zero, and taking away none leaves the group unchanged.
Five on One Hand and Some More [H]	A full hand is five, so a number to ten is five and some more.
Comparing Tens up to a Hundred [H]	Tens numbers keep counting order: the one said later when counting by tens is greater.
Ten Children in Two Places [H]	Ten children split into two groups, so one group tells you the other.
How Many More Are Needed [H]	Counting on from what you have to what you want gives how many more are needed.
Show the Number on the Line [H]	Marks on a number line are in counting order, so one more is one step right.
More or Fewer Than Five [H]	Five is a landmark: a full top row of a ten-frame is exactly five.

Kindergarten - Shapes, Measurement & Sorting (Deep) · 42 topics

Count the Corners in the Picture [H]	Count the corners on a drawn flat shape.
Sides of Two Shapes Together [H]	Add up the straight sides of two or three named shapes.
Which Shape Has More Sides [H]	Compare shapes by how many straight sides they have.
Square or Rectangle? [H]	Tell a square from a rectangle by looking at its side lengths.
Flat Shape Riddles [H]	Name the flat shape that fits the clues.
Building with Triangle Blocks [H]	Two triangle blocks make one square, so squares and triangles pair up.
Big Shape, Small Shape [H]	Drawing a shape bigger does not change its sides or its corners.
More Sides Than That Shape [H]	Start from a known shape's sides, then count on or count back.
Which Sentence Fits the Shape [H]	Match a drawn shape to a sentence about its sides and corners.
Name the Solid Shown [H]	Name a drawn cube, cone, sphere or cylinder.
Corners on the Solid Shown [H]	Count the corners on a drawn solid, including the ones hidden behind.
Flat Faces on the Solid Shown [H]	Count the flat faces on a drawn solid.
Solid Shape Riddles [H]	Name the solid that fits every clue.
How Many of That Solid [H]	Sort a box of solids by kind and count one kind.
The Shape of the Flat End [H]	Name the flat shape you see on the face of a drawn solid.
How Many on the Shelf Above [H]	Use above and below to pick the right row, then count it.
The Middle Shelf [H]	Find a shelf from words like middle, above and below.
The Ribbon in the Middle [H]	Find the ribbon that is neither the longest nor the shortest.
Which Two Are the Same Length [H]	Spot the two objects whose lengths match exactly.
How Many Are Longer [H]	Compare every object with one of them, then count the matches.
Order the Towers [H]	Put three or four towers in order by height.
Which Real Thing Is Longer [H]	Compare the lengths of everyday things from what you know.
The Heaviest of Three [H]	Use the blocks each toy balances to find the heaviest or lightest.
Do They Balance? [H]	Two things balance when they hold the pans level, so they weigh the same.
How Many More Blocks [H]	Compare weights by taking one block count away from the other.
Which Real Thing Is Heavier [H]	Compare the weights of everyday things from what you know.
Big Does Not Mean Heavy [H]	How big a thing looks does not tell you how heavy it is.
What Was the Sorting Rule [H]	Name the one thing that tells the two sorted groups apart.
Which Group Does It Join [H]	Work out the rule of each group, then place a new thing.
How Many Are Not Red [H]	Count the things that do not fit a sorting rule.
How Many Groups [H]	Sorting makes one group for each different value of the attribute.
Two Groups That Match [H]	Find the two sorted groups that hold the same number.
Which Group Has the Fewest [H]	Sort a mixed pile into groups, count each one, and find the smallest.
Compare Two Tally Rows [H]	Count each tally row, then compare or add the counts.
Read One Row of a Picture Graph [H]	Find the right row of a picture graph and count its pictures.
Which Row Has the Most [H]	Compare the rows of a picture graph to find the biggest or smallest.
Look Up a Row from Its Count [H]	Count each row of a picture graph until you find the one that matches.
How Many More in This Row [H]	Match two rows of a picture graph up and count the extra pictures.
How Many Altogether on the Graph [H]	Add every row of a picture graph to find the whole group.
Which Sentence Is True [H]	Check a sentence about a picture graph against the rows themselves.
The Row with None [H]	An empty row on a picture graph means nobody chose that one.
One More on the Graph [H]	Read a row of a picture graph, then count on or count back.

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