Math Kangaroo: Pre-Écolier (Grades 1-2)

293 core topics + 86 prerequisite topics taught as needed · approximately 115 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

Math Kangaroo: Pre-Écolier & Écolier · 6 topics

Counting Pictures & Objects [E]	Careful counting beats fast counting.
Hops on the Number Line [E]	Equal jumps are hidden multiplication.
What Comes Next? [E]	Find the rule, then trust it.
Missing-Number Puzzles [E]	Undo the operation to find the hidden number.
Fair Sharing [E]	Division with (and without) leftovers.
Little Logic Puzzles [E]	Chain the clues in order.

Math Kangaroo: Pre-Écolier Depth (Grades 1-2) · 30 topics

Counting in Equal Groups [M]	Rows times columns beats counting one by one.
How Many Are Left? [M]	Taking away means subtracting.
Adding Within 20 [M]	Add by making a ten.
Doubles & Near Doubles [M]	Learn the doubles, then lean on them.
Hops on the Number Line [M]	Equal hops are hidden multiplication.
Skip Counting [M]	Skip counting jumps by the same amount each time.
What Comes Next? [M]	Find the step, then take one more.
Repeating Patterns [M]	Repeating patterns loop; use the loop length.
Missing-Number Puzzles [M]	Subtract to undo an addition.
Fair Sharing [M]	Deal them out one at a time.
Counting Legs [M]	Same-size groups multiply.
How Many More? [M]	Comparing means subtracting.
Counting Coins [M]	Count each kind of coin, then add.
Fewest Coins [M]	Grab the biggest coins first.
Telling Time to the Hour [M]	Hours wrap around after 12.
Days of the Week [M]	The week repeats every seven days.
Sides of Shapes [M]	Each shape has a fixed number of sides.
Squares in a Grid [M]	A grid holds rows times columns of small squares.
Cuts and Pieces [M]	Each straight cut makes one more piece.
Ordering Logic Puzzles [M]	Line the clues up in order.
Dots on Dice [M]	Opposite faces of a die add to 7.
Making Ten (and Twenty) [M]	Find the partner that fills up to the round number.
Counting Even Numbers [M]	Every other number is even.
Biggest and Smallest Numbers [M]	Put the big digit where it counts most.
Position in a Line [M]	Behind you is everyone the line hasn't counted yet.
Adding Three Numbers [M]	Add two, then add the third.
Balance Puzzles [M]	Share the balance equally.
Making Equal Teams [M]	Dividing tells how many equal groups fit.
Secret Number Clues [M]	Use each clue to pin down a digit.
Tens and Ones [M]	A tens digit counts groups of ten.

Math Kangaroo: Pre-Écolier - Deep (Grades 1-2) · 118 topics

Counting On [M]	Counting on adds a few by stepping forward.
Counting Back [M]	Counting back steps down one at a time.
The Number in the Middle [M]	One number sits right between two that are two apart.
The Number Before [M]	The number before is one less.
The Number After [M]	The number after is one more.
Counting Odd Numbers [M]	Odd numbers are every other number starting at 1.
The nth Odd Number [M]	Odd numbers jump by two.
The nth Even Number [M]	Even numbers are just double the count.
How Many Tens? [M]	A round number is built from tens.
How Many In Between? [M]	Count the gaps, not the ends.
Skip Counting Backward by 5 [M]	Each step down takes away five.
Adding Ten [M]	Adding ten bumps up the tens digit.
Adding Nine [M]	Add ten, then take one back.
Subtracting Ten [M]	Subtracting ten lowers the tens digit.
Number Bonds [M]	Two parts always rebuild the whole.
Missing Number in a Sum of Three [M]	Take the known parts away from the total.
Subtracting Within 20 [M]	Count back or use a known ten.
Fact Families [M]	The same three numbers make adds and subtracts.
Reaching the Next Ten [M]	Fill up the ones to make a round number.
Balancing Both Sides [M]	Both sides of the equals sign match.
Comparing Two Sums [M]	Add each side, then compare.
Adding Whole Tens [M]	Add the tens like single digits.
Subtracting Whole Tens [M]	Subtract the tens like single digits.
Adding Ones to a Two-Digit Number [M]	Only the ones digit changes.
Greater of Two Numbers [M]	The bigger number is further along the count.
Smallest of Three [M]	Line them up and take the least.
Largest of Three [M]	Line them up and take the greatest.
How Many Are Bigger? [M]	Check each number against the mark.
Closest Number [M]	The closest number has the smallest gap.
The Second Smallest [M]	Order them, then step in one place.
Which Number is Between? [M]	A between number is bigger than one and smaller than the other.
The Tens Digit [M]	The left digit of a two-digit number counts tens.
The Ones Digit [M]	The right digit of a number counts single ones.
Value of the Tens Digit [M]	A digit's value depends on its place.
Expanded Form to Number [M]	Tens plus ones make the number.
The Hundreds Digit [M]	The left digit of a three-digit number counts hundreds.
Building a Three-Digit Number [M]	Stack hundreds, tens and ones.
Value of the Hundreds Digit [M]	Each hundred is worth one hundred.
Adding the Digits [M]	Split into digits, then add them.
Halving Even Numbers [M]	Half means split into two equal parts.
Next Even Number [M]	Even numbers step by two.
Next Odd Number [M]	Odd numbers step by two.
Quarter of a Number [M]	A quarter is one of four equal parts.
Double, Then Double Again [M]	Doubling twice makes four times.
One Third of a Set [M]	A third is one of three equal parts.
A Quarter of a Group [M]	Split the group into four fair shares.
Ways to Make an Amount [M]	Count how many big coins you may use.
Making Change [M]	Change is what is left after paying.
How Much More Money? [M]	Find the gap between money and price.
Cost of Several Items [M]	Same price times the number of items.
How Many Coins? [M]	Share the amount into equal coins.
Total of Two Prices [M]	Add the two prices together.
Swapping Coins [M]	Trade a big coin for equal small ones.
Minutes in Hours [M]	Each hour has sixty minutes.
Hours in Days [M]	Each day has twenty-four hours.
Days in Weeks [M]	Each week has seven days.
Weeks in Days [M]	Group the days into sevens.
Month Numbers [M]	Months are numbered in order through the year.
The Next Month [M]	Months follow each other in a yearly loop.
Days Until a Date [M]	Count the days between two dates.
Date After Some Days [M]	Add the days to today's date.
One Week Later [M]	A week later is the same weekday.
Hours Between Two Times [M]	Subtract the earlier hour from the later one.
Naming Shapes by Sides [M]	The number of sides names the shape.
Corners of a Shape [M]	A flat shape has as many corners as sides.
Sides of a Named Shape [M]	Each named shape has a set number of sides.
Sides of Two Shapes [M]	Add the sides of each shape.
Which Shape Has Most Sides? [M]	Compare the side counts.
Lines of Symmetry [M]	A fold line makes two matching halves.
Next Shape in a Pattern [M]	A two-shape pattern keeps repeating.
Faces of a Solid [M]	A face is a flat surface of a solid.
Edges of a Solid [M]	An edge is where two faces meet.
Vertices of a Solid [M]	A vertex is a corner point of a solid.
Naming Solids [M]	Everyday objects match solid shapes.
Which Shape Can Roll? [M]	Round surfaces roll; flat ones do not.
To the Right Of [M]	Look one place to the right.
To the Left Of [M]	Look one place to the left.
Counting From the Back [M]	Front position and back position add up.
Steps Right and Left [M]	Left steps cancel right steps.
Quarter Turns [M]	A quarter turn on a clock moves three hours.
Numbering a Grid [M]	Full rows come before the last part row.
Forward and Back [M]	Add the forward steps, subtract the back steps.
Counting-Down Patterns [M]	Find the drop, then drop once more.
The Missing Middle [M]	Use the step to fill the gap.
Finding the Step [M]	The step is the gap between neighbours.
Doubling Patterns [M]	Each number is double the one before.
Counting in a Pattern [M]	Half the beads are each color.
Missing Skip-Count Number [M]	Keep the same jump across the gap.
Growing Patterns [M]	The jump gets one bigger each time.
Halving Patterns [M]	Each number is half the one before.
Odd One Out [M]	One number breaks the shared rule.
Which Sum is True? [M]	Check the total of each statement.
Only One Group [M]	Take away those in both groups.
How Many Are the Rest? [M]	The rest is the total take away the known part.
Making Pairs [M]	Two make a pair, so halve the count.
Older By So Many Years [M]	Older means add the extra years.
Which Comparison is True? [M]	The bigger number goes on the wide side of >.
Guess My Number [M]	Use each clue to cross numbers out.
Scaling a Balance [M]	More books need more blocks in the same ratio.
The Longer One [M]	The longer length is the bigger number.
Joining Lengths [M]	Join lengths by adding them.
How Much Longer? [M]	Subtract the shorter from the longer.
Measuring with Paperclips [M]	Compare counts of the same unit.
Height of a Tower [M]	Total height is one cube's height times the count.
Filling Jugs [M]	Cups add up jug by jug.
How Many Fit? [M]	Share the space into equal widths.
Counting Outfits [M]	Each shirt pairs with every hat.
Counting Handshakes [M]	Each pair of friends shakes once.
Ways to Line Up [M]	Try each child first, then the rest.
Choosing a Pair [M]	Count the different pairs you can pick.
Dots on a Domino [M]	Add the two halves of the domino.
Ways to Roll a Total [M]	List the pairs that add to the total.
Giving Away Twice [M]	Take away both amounts, one after the other.
More Than Someone Else [M]	'More than' means add.
On and Off the Bus [M]	Add those who get on, subtract those who get off.
Combine, Then Share [M]	Put together first, then share.
Working Back to the Start [M]	Put the given-away and the left-over back together.
How Many Cuts? [M]	One fewer cut than pieces.

Math Kangaroo (Grades 1-4) - Counting, Patterns and Picture Logic · 46 topics

Counting Every Row of a Picture [H]	Count each row of a picture and add the row counts to get the total.
How Many More in the Picture [H]	Comparing two rows of a picture means subtracting the smaller count from the larger.
Counting the Shared Ones Only Once [H]	A child who does both activities is in both lists, so the shared count is subtracted once.
Counting the Ones Left Out [H]	The children in no group are the whole class minus the children counted in some group.
Counting Hidden Animals by Their Legs [H]	Sharing the visible legs into fours counts the cows hidden behind the fence.
Counting the Dots You Cannot See [H]	Hidden rows hold as many dots as a visible row, so multiply the row length by the hidden rows.
When One Picture Stands for Several [H]	In a scaled picture graph each icon stands for several objects, so multiply the icons by the key.
How Long Is the Line? [H]	Adding a place from the front to a place from the back counts the animal itself twice.
Counting the Places Between Two Children [H]	The children between two places are found by subtracting both places and the two children themselves.
Counting Equal Groups in a Picture [H]	Counting a picture in equal groups gives the number of full groups and the leftover.
Counting Triangles in a Cut Triangle [H]	Every pair of lines from the top corner bounds one triangle, so count the pairs of lines.
Counting Rectangles in a Strip [H]	A rectangle in a strip is fixed by choosing where it starts and where it ends.
Counting All the Sides in a Picture [H]	The sides of a group of shapes are the number of each shape times its own number of sides.
Sorting the Shapes by Their Corners [H]	Selecting shapes by a corner rule means adding only the counts of the shapes that obey it.
What Color Comes Next [H]	Continuing a repeating color pattern means starting the cycle again after its last color.
Finding a Far-Away Bead [H]	A bead's color depends only on its position within one cycle of the pattern.
How Many of One Color [H]	Counting one color means counting whole cycles and then checking the part cycle left over.
How Long Is the Repeat? [H]	The period of a pattern is the shortest block of beads that is repeated over and over.
Filling a Gap in a Pattern [H]	A gap in a repeating pattern is filled by the color that its position holds in the cycle.
What Shape Comes Next [H]	A shape pattern continues either by repeating its cycle or by following its rule for corners.
Two Patterns at Once [H]	When color and shape repeat over different lengths, each one is worked out separately.
Patterns Whose Jumps Grow [H]	In a growing pattern the gaps themselves follow a rule, so the next gap is bigger than the last.
Growing Dot Pictures [H]	In a growing dot picture the figure number counts the rows, so the dots are the rows times the row length.
Staircases Built from Tiles [H]	Each step of a tile staircase adds a column one tile taller than the last, so the totals add up the counting numbers.
Patterns That Multiply [H]	A multiplying pattern is continued by applying the same rule to the last number, not by adding the last gap.
Working a Pattern Backwards [H]	Running a pattern backwards undoes its rule once for every step back to the start.
Which Place in the Pattern [H]	The place of a number in a steady pattern is found by sharing its distance from the start into steps.
Kangaroo Hops Along the Line [H]	Equal hops land only on numbers whose distance from the start is a whole number of hops.
The Shape That Does Not Belong [H]	A shape is the odd one out when it alone fails the corner rule the other four obey.
The Row That Does Not Belong [H]	A row is the odd one out when its count alone fails the sharing rule the other rows obey.
The Number That Does Not Belong [H]	A number is the odd one out when it alone is missing from the times table the others belong to.
Saying Why It Is the Odd One Out [H]	A reason for the odd one out must hold for that item and fail for every other item.
Which Sentence Fits the Picture [H]	A sentence fits a picture only when the counts read off the picture make it true.
Which List of Numbers Matches [H]	Matching a list to a picture means reading each row in the stated order and using the key.
Which Sentence Does Not Fit [H]	Finding the wrong sentence means testing every sentence against the picture until one fails.
Guessing the Shape from Its Clues [H]	Each clue rules some shapes out, and the shape that survives every clue is the answer.
Who Has the Most and Who the Fewest [H]	The most and the fewest are found by comparing every row of the picture, not only the neighbouring ones.
Second Tallest and Second Shortest [H]	Naming the second tallest or the middle bar requires putting all the bars in order first.
Putting Three Rows in Order [H]	Ordering rows of a picture means comparing their counts and listing them from the largest.
Twice as Many, Three Times as Many [H]	Finding a row that is a given multiple of another means multiplying first and then searching for that value.
The Row in the Middle [H]	The middle row of five is the third one after the rows are sorted by their counts.
Working Out Who Has What [H]	In an assignment puzzle a fruit ruled out for every other child must belong to the child left.
Guessing the Number from Its Clues [H]	Each numeric clue narrows the possible numbers, and only one number survives every clue.
Finding the Box from Two Clues [H]	A clue about a picture keeps only the rows that obey it, and two clues together may leave just one.
Who Stands Where in the Line [H]	Position clues fix a line when each clue is drawn onto the same row of places.
Finding the Animal from a Table [H]	Reading a feature table means keeping only the rows that agree with every clue at once.

Math Kangaroo (Grades 1-4) - Number Puzzles and Arithmetic · 47 topics

The Hidden Part of a Total [H]	Find a hidden part by taking the parts you can see away from the total.
How Many Went Away [H]	Compare a before count with an after count to find how many left.
The Number We Started With [H]	Undo each change in reverse order to find the starting number.
The Same Box Used Twice [H]	When one number is hidden twice, share the total equally between the boxes.
How Long Was the Hop? [H]	Find the size of a jump from the place it starts and the place it lands.
The Box in a Subtraction [H]	Solve a subtraction sentence in which either the start or the amount taken is hidden.
Signs Hidden by Ink [H]	Test each pair of signs in a number sentence to see which pair makes it true.
Which Sentence Fits the Story? [H]	Choose the number sentence that matches what a short story does.
Which One Has the Same Answer? [H]	Work out each number sentence and pick the one whose value matches.
The Smudged Digit [H]	Recover one hidden digit of a two-digit number from an addition or subtraction.
Cards That Make the Total [H]	Search a small set of number cards for the pair or trio that reaches a target.
Turning a Number Around [H]	Swap the digits of a two-digit number and work with the number that results.
Counting One Digit [H]	Count how often a digit is written, or how many numbers contain it.
The Smallest Number from Cards [H]	Build the smallest number from digit cards, remembering that a number cannot start with zero.
Sharing a Picture Fairly [H]	Share a pictured collection into equal parts, sometimes after setting a few aside.
How Many More Fill the Box [H]	Find how many more items are needed to complete a box or a set of boxes.
The Same Dots in New Rows [H]	Rearrange a fixed number of objects into different equal rows.
Making the Piles Equal [H]	Move objects from a larger pile to a smaller one so the piles match.
Counting Legs [H]	Total the legs of animals by adding equal groups, and work back from a leg total.
Adding the Same Number Again and Again [H]	Match a repeated addition to the multiplication that means the same thing.
Doubling Day After Day [H]	Follow a number that doubles at every step, forwards or backwards.
Tiles Around the Edge [H]	Count the tiles on the border of a rectangle without counting a corner twice.
Each Picture Stands for Several [H]	Use a picture key to turn a row of symbols into a total by repeated addition.
Which Coins Pay Exactly? [H]	Add up each offered set of coins and pick the set worth exactly the price.
What Can You Buy? [H]	Total a handful of coins and compare that total with the prices on offer.
Swapping Coins for Smaller Ones [H]	Exchange several coins for smaller coins of the same total value.
How Many of Each Coin [H]	Find how many coins of each kind fit both a coin count and a total value.
How Many Can You Buy? [H]	Find how many items a sum of money buys when some money may be left over.
Taking Blocks Off to Balance [H]	Remove blocks from the heavier pan until the two pans hold the same amount.
Cubes and Balls on a Scale [H]	Replace each cube by the balls it balances to weigh a group of cubes.
The Hidden Weight [H]	Find an unknown weight from a scale that balances known weights against it.
Ordering Weights from Scales [H]	Chain several two-pan weighings into one order from heaviest to lightest.
From Melons to Plums [H]	Follow a chain of two balances to swap one kind of object for another.
The Middle of the Cross [H]	Use the fact that the center card of a cross is counted in both lines.
Totals at the Edge [H]	Recover missing cells of a small grid from the row totals and column totals.
Every Line the Same Total [H]	Find the common line total from a complete line, then fill a gap in another line.
Building a Number Pyramid [H]	Fill a number pyramid upwards, where each brick is the sum of the two below it.
Working Back Down a Pyramid [H]	Recover a missing brick lower in a pyramid from the bricks above it.
Follow the Arrows [H]	Apply a list of operations to a starting number strictly in the given order.
Back Along the Arrows [H]	Undo a list of operations from the last one to the first to recover the start.
The Hidden Arrow [H]	Identify the missing operation in a chain from the starting and finishing numbers.
Does the Order Matter? [H]	Compare the results of the same two operations carried out in opposite orders.
Which Start Reaches the Target? [H]	Test candidate starting numbers through a chain of operations to see which reaches the target.
Fill the Bags, Then Share [H]	Total several equal groups first, then share that total between children.
More Than, Then Add Up [H]	Work out a compared amount first, then combine the amounts.
On and Off the Bus [H]	Track a running total through several arrivals and departures.
Half, Then a Few More [H]	Take half of an amount and then a further amount, or undo both steps.

Math Kangaroo (Grades 1-4) - Shapes, Space and Measuring · 46 topics

Naming a Flat Shape [H]	A flat shape is named by how many straight sides and corners it has.
Corners Altogether [H]	The corners of a group of shapes are counted by multiplying each shape's corners by how many there are.
Sorting Shapes by a Rule [H]	Sorting means testing every shape against the rule and keeping only the ones that pass.
Which Shape Has the Most Sides [H]	Comparing groups of shapes means multiplying each shape's sides by how many there are and comparing the totals.
Naming a Solid from Clues [H]	A solid is named from its flat faces, its corners and whether it rolls.
Solids That Roll [H]	A solid rolls when it has a curved surface, so spheres, cylinders and cones roll and flat-faced solids do not.
The Shape of a Flat Face [H]	Pressing a flat face of a solid in paint prints the flat shape of that face.
Everyday Things as Solids [H]	Everyday objects match solids: a ball is a sphere, a tin a cylinder, a dice a cube and a box a cuboid.
Faces of Two Solids Together [H]	The faces of two solids are added one solid at a time, and a prism has two end faces plus one face for each side of its end shape.
Edges of a Prism [H]	A prism whose ends have n sides has 3n edges and 2n corners.
Corners of a Pyramid [H]	A pyramid on a base with n sides has n+1 corners, n+1 faces and 2n edges.
Naming a Solid from Its Faces and Corners [H]	Two counts out of faces, edges and corners pin down which solid it is.
Which Solid the Net Makes [H]	A net folds into the solid whose faces are exactly the pieces of the net.
Finishing a Net [H]	A cube net needs 6 squares and a box with no lid needs 5, so the squares still missing are that number minus the squares already cut.
Opposite Faces After Folding [H]	In a cube net drawn as a row of four with one square above and one below, faces two apart in the row are opposite, and the square above is opposite the square below.
Matching Faces of a Box [H]	A box has three pairs of matching faces, and a face is a square only when the two edge lengths meeting at it are equal.
Cutting a Sheet of Paper [H]	Straight cuts all one way give one more piece than cuts, and cuts both ways multiply the pieces of the two directions.
Cutting Off a Corner [H]	A straight cut across a corner removes one corner and makes two new ones, so the big piece gains one corner.
How Many Cuts [H]	Cutting one strip into n pieces takes n-1 cuts, one fewer than the number of pieces.
Letters in a Mirror [H]	A letter looks unchanged in a side mirror when its left half matches its right half.
The Mirrored Square [H]	A left-to-right flip sends the square in column c of a row of n to column n+1-c, and leaves its row alone.
A Clock in the Mirror [H]	A clock face and its mirror image show times that add to 12 hours.
Arrows in the Mirror [H]	A side mirror swaps left and right but leaves up and down alone.
Turning an Arrow [H]	Each quarter turn clockwise moves a pointer one step round up, right, down, left.
Turns That Change Nothing [H]	A regular shape with n sides looks the same n times in a full turn, once every 360/n degrees.
Turning a Card Upside Down [H]	Turning a card a half turn reverses the order of the digits and swaps 6 with 9, while 0, 1 and 8 stay as they are.
Covering with Dominoes [H]	A domino covers two squares, so the number of dominoes is half the number of squares.
Triangles Making Squares [H]	Two half-square triangles make one square, so squares need twice as many triangles.
The Missing Piece [H]	A piece fills a hole only when both of its side lengths match the hole, not merely its number of squares.
The Fewest Pieces [H]	Covering a strip with the fewest pieces means using as many long pieces as possible while still filling it exactly.
Left, Right and Between [H]	A place in a row is found by counting from the stated end, and the middle of two places is halfway along the count between them.
Moving on a Grid [H]	A hop to the right adds to the across number and a hop up adds to the up number, so moves are added one direction at a time.
Touching Squares [H]	A square inside a grid has four side neighbours, an edge square three and a corner square two.
Which Way on the Map [H]	On a map north is straight up, south straight down, east to the right and west to the left.
Who Is Tallest [H]	Comparison clues link the children into one line from tallest to shortest.
Measuring with Paper Clips [H]	Measuring in units means counting how many copies of the unit fit along the object, and swapping to a bigger unit multiplies the count.
How Much Taller [H]	The difference in height is the taller measurement minus the shorter one, read straight off the chart.
Long Steps and Short Steps [H]	Measuring the same distance with a longer unit needs fewer of them, so the fewest steps means the longest step.
Reading the Clock Face [H]	The short hand gives the hour it has passed and the long hand gives the minutes, five for every number it points past.
The Clock Later On [H]	Adding a length of time to a clock time means adding the hours and the minutes separately and carrying 60 minutes as one hour.
A Clock That Is Wrong [H]	A clock that runs fast shows a time later than the real one, so the real time is found by subtracting, and a slow clock is corrected by adding.
Counting the Strikes [H]	A striking clock gives one strike for each hour number, so the strikes over several hours are the sum of those numbers.
Counting the Shaded Squares [H]	The white squares of a grid are the total squares minus the shaded ones.
Squares and Half Squares [H]	Two half squares make one whole square, so the area is the whole squares plus half the number of halves.
Which Shape Covers More [H]	The squares a rectangle covers are the across count multiplied by the up count.
Same Squares, Longer Border [H]	Shapes with the same number of squares can have different borders, and the long thin shape has the longer border.

Prerequisite material - taught automatically when the diagnostic finds gaps

Arithmetic Foundations · 3 topics

Adding & Subtracting Whole Numbers	Multi-digit addition and subtraction.
Multiplication	Multiplying whole numbers.
Division	Dividing whole numbers.

Math Kangaroo: Écolier Depth (Grades 3-4) · 18 topics

Multiplication Facts	Know your tables up to 12 × 12.
Division with Remainders	Division undoes multiplication; leftovers are the remainder.
Adding Several Numbers	Line up the ones and tens, then add column by column.
Growing Number Patterns	Add the same step each time.
Elapsed Time	Count the minutes from start to finish.
Perimeter of a Rectangle	Perimeter adds up all the way around.
Area of a Rectangle	Area counts the square tiles that fit inside.
Counting Multiples	Multiples of k are k, 2k, 3k, …
Digit Sums	Add up all the digits.
Place Value to Thousands	Each place is worth ten times the one to its right.
Magic Squares	Every line adds to the same magic number.
Trees Along a Path (Fence Posts)	One more tree than the number of gaps.
Ways to Make Change	Try each count of one coin.
Logic by Elimination	Cross out what can't be, and one answer is left.
Squares in a Grid	Multiply rows by columns.
Total Cost	Multiply the price by the number bought.
Filling the Gap	Find the step from the terms you can see.
Adding a Run of Numbers	Pair the ends to add a run quickly.

Math Kangaroo: Écolier - Deep (Grades 3-4) · 65 topics

Doubling and Halving	Doubling adds a number to itself; halving splits it in two.
Multiplying Three Numbers	Multiply two of them first, then the third.
Equal-Groups Word Problems	Equal groups mean multiply.
Rows and Columns (Division)	Divide the total by how many fit in a row.
Remainders: Rounding Up	Sometimes a leftover group still needs a whole extra.
Square Numbers	A square number is a number times itself.
Comparing Products	Work out each product, then compare.
Missing Addend	Subtract to undo an addition.
Value of a Digit	A digit's value is the digit times its place.
Comparing Four-Digit Numbers	Compare place by place, starting at the left.
Ordering Numbers	Sort from smallest to largest to find the middle.
Counting Odd Numbers	Odd numbers alternate with even ones.
Numbers In Between	Subtract, then take one away for the open ends.
Fraction Left Over	The whole is all the pieces; subtract what is gone.
Pieces That Make a Whole	It takes d pieces of size 1/d to make one whole.
Total Value of Coins	Multiply each coin by its worth, then add.
Minutes to the Next Hour	Count up to 60.
Adding Time Lengths	Add the minutes together.
Adding Lengths	Change to one unit first, then add.
Comparing Measurements	Convert to a common unit, then compare.
Area by Counting Squares	Add up the squares in every row.
Covering a Floor with Tiles	Count tiles along each side, then multiply.
Perimeter of an Irregular Shape	Perimeter is the sum of all the sides.
Naming Polygons by Sides	A polygon's name tells its number of sides.
Turns and Degrees	A quarter turn is 90 degrees.
Lines of Symmetry	A line of symmetry folds a shape onto itself.
Faces of Solids	A face is a flat surface of a solid.
Edges of Solids	An edge is where two faces meet.
Vertices of Solids	A vertex is a corner where edges meet.
Naming a Solid	Match the description to the right solid.
Diagonals of a Polygon	Each corner joins to all but its two neighbours.
Opposite Faces of a Die	Opposite faces of a die sum to 7.
Folding and Punching Holes	Each fold doubles the layers.
Turning Around a Clock	A quarter turn moves 3 numbers clockwise.
Completing a Symmetric Figure	A mirror line makes both halves match.
Shortest Path on a Grid	Add the across and up distances.
Finding the Rule	Subtract two neighbours to find the step.
Repeating Patterns	Use the remainder to find the position in the cycle.
Number Machines	Apply each step in order to the input.
Working a Machine Backwards	Undo each step in reverse order.
Add-the-Last-Two Patterns	Every term is the sum of the two before it.
True or False?	Check each statement on its own.
Odd One Out	Find the rule the others share.
Overlapping Groups	Add the groups, then subtract the overlap once.
Ordering from Clues	Chain the comparisons together.
Balancing a Scale	Share the balance equally.
Balancing an Equation	Both sides must total the same.
Missing Digit for Divisibility	A number divides by 3 when its digit sum does.
Divisibility Tests	Quick rules tell you what divides evenly.
Number Riddles	Use each clue to narrow the choices.
Making the Greatest Number	Put the biggest digit in the highest place.
Sum and Difference	Add the sum and difference, then halve.
Counting Grid Paths	Every route mixes the same east and north moves.
Ways to Roll a Sum	List the pairs that reach the target.
How Many Numbers	Pick the tens digit, then the ones digit.
Two-Step Word Problems	Do the multiplication, then the subtraction.
Times as Many	'Times as many' means multiply.
Part and Whole	The parts add up to the whole.
Working Backwards	Undo the steps from the end.
Unit Price Problems	Find the price of one, then scale up.
Reading a Table	Add the numbers in the table.
Reading a Pictograph	Each symbol stands for several items.
Reading a Bar Chart	Compare bar heights by subtracting.
Reading Tally Marks	Each bundle is five.
The Median	The median is the middle value in order.

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