Math Kangaroo: Écolier (Grades 3-4)

291 core topics + 3 prerequisite topics taught as needed · approximately 91 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 · 9 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.
Days & Calendars [E]	Weeks repeat in sevens.
Sides & Corners [E]	Shapes hide multiplication; cuts make one more piece.
Coins & Small Money [E]	Count money in groups; go greedy for fewest coins.
Little Logic Puzzles [E]	Chain the clues in order.

Math Kangaroo: Écolier Depth (Grades 3-4) · 30 topics

Multiplication Facts [M]	Know your tables up to 12 × 12.
Division with Remainders [M]	Division undoes multiplication; leftovers are the remainder.
Adding Several Numbers [M]	Line up the ones and tens, then add column by column.
Growing Number Patterns [M]	Add the same step each time.
Multiplying Patterns [M]	Multiply by the same number each step.
Missing-Factor Puzzles [M]	Divide to undo a multiplication.
Making Change [M]	Change is what you paid minus what it cost.
Elapsed Time [M]	Count the minutes from start to finish.
Clock Angles [M]	Each hour mark is 30° around the clock.
Perimeter of a Rectangle [M]	Perimeter adds up all the way around.
Area of a Rectangle [M]	Area counts the square tiles that fit inside.
Counting Multiples [M]	Multiples of k are k, 2k, 3k, …
Digit Sums [M]	Add up all the digits.
Place Value to Thousands [M]	Each place is worth ten times the one to its right.
Rounding [M]	Look at the next digit to decide up or down.
Fractions of a Group [M]	Split into equal parts, then take some of them.
Magic Squares [M]	Every line adds to the same magic number.
Trees Along a Path (Fence Posts) [M]	One more tree than the number of gaps.
Matchstick Squares [M]	Sharing sides saves matchsticks.
Counting Handshakes [M]	Every pair shakes hands once.
Averages [M]	The average shares the total out evenly.
Ways to Make Change [M]	Try each count of one coin.
Age Word Problems [M]	Everyone ages by the same amount.
Dates on a Calendar [M]	Add the days to the starting date.
Logic by Elimination [M]	Cross out what can't be, and one answer is left.
Squares in a Grid [M]	Multiply rows by columns.
Total Cost [M]	Multiply the price by the number bought.
How Many Full Days? [M]	Division tells how many full groups fit.
Filling the Gap [M]	Find the step from the terms you can see.
Adding a Run of Numbers [M]	Pair the ends to add a run quickly.

Math Kangaroo: Écolier - Deep (Grades 3-4) · 113 topics

Multiplying by 10 and 100 [M]	Each ×10 shifts every digit one place left.
Multiplying Multiples of Ten [M]	Multiply the tens, then attach the zero.
Two-Digit × One-Digit [M]	Split by place value and add the partial products.
Doubling and Halving [M]	Doubling adds a number to itself; halving splits it in two.
Multiplying Three Numbers [M]	Multiply two of them first, then the third.
Equal-Groups Word Problems [M]	Equal groups mean multiply.
Rows and Columns (Division) [M]	Divide the total by how many fit in a row.
Counting Factors [M]	Factors come in pairs that multiply to the number.
Remainders: Rounding Up [M]	Sometimes a leftover group still needs a whole extra.
Product of the Digits [M]	Multiply the digits instead of adding them.
Square Numbers [M]	A square number is a number times itself.
Comparing Products [M]	Work out each product, then compare.
Adding Large Numbers [M]	Add column by column, carrying where needed.
Subtracting Large Numbers [M]	Subtract column by column, borrowing where needed.
Missing Addend [M]	Subtract to undo an addition.
Expanded Form [M]	Add the value of each place back together.
Value of a Digit [M]	A digit's value is the digit times its place.
Comparing Four-Digit Numbers [M]	Compare place by place, starting at the left.
Ordering Numbers [M]	Sort from smallest to largest to find the middle.
Rounding to the Nearest Thousand [M]	Look at the hundreds digit to round.
Estimating Sums [M]	Round first, then add the tidy numbers.
Counting Odd Numbers [M]	Odd numbers alternate with even ones.
Numbers In Between [M]	Subtract, then take one away for the open ends.
Ten, Hundred, Thousand More or Less [M]	Change only the matching place.
Equivalent Fractions [M]	Multiply top and bottom by the same number.
Comparing Fractions [M]	Compare using a common size or benchmarks.
Fractions on a Number Line [M]	Each equal step is one over the number of parts.
Adding Fractions (Same Bottom) [M]	Same-size pieces: add the counts on top.
Fraction Left Over [M]	The whole is all the pieces; subtract what is gone.
Pieces That Make a Whole [M]	It takes d pieces of size 1/d to make one whole.
Making Wholes from Parts [M]	Group the parts into full sets.
Comparing to One Half [M]	Compare the top to half the bottom.
Total Value of Coins [M]	Multiply each coin by its worth, then add.
Adding Money [M]	Add the amounts like any numbers.
Change After Two Purchases [M]	Add the costs first, then subtract from what you paid.
Hours to Minutes [M]	One hour is 60 minutes.
Minutes to Whole Hours [M]	Divide by 60 to count full hours.
Minutes to the Next Hour [M]	Count up to 60.
Adding Time Lengths [M]	Add the minutes together.
Days of the Week [M]	The week repeats every 7 days.
Days Between Dates [M]	Subtract the earlier date from the later one.
Days in a Month [M]	Most months have 30 or 31 days.
Minutes to Seconds [M]	One minute is 60 seconds.
Meters to Centimeters [M]	One meter is 100 centimeters.
Centimeters to Millimeters [M]	One centimeter is 10 millimeters.
Kilograms to Grams [M]	One kilogram is 1000 grams.
Liters to Milliliters [M]	One liter is 1000 milliliters.
Adding Lengths [M]	Change to one unit first, then add.
Comparing Measurements [M]	Convert to a common unit, then compare.
Side of a Square from Perimeter [M]	A square's four sides are equal.
Missing Side from Area [M]	Divide the area by the known side.
Area by Counting Squares [M]	Add up the squares in every row.
Perimeter of a Triangle [M]	Add the three sides - for equal sides, multiply.
Covering a Floor with Tiles [M]	Count tiles along each side, then multiply.
Perimeter of an Irregular Shape [M]	Perimeter is the sum of all the sides.
Naming Polygons by Sides [M]	A polygon's name tells its number of sides.
Counting Right Angles [M]	A right angle is a square corner of 90°.
Turns and Degrees [M]	A quarter turn is 90 degrees.
Lines of Symmetry [M]	A line of symmetry folds a shape onto itself.
Faces of Solids [M]	A face is a flat surface of a solid.
Edges of Solids [M]	An edge is where two faces meet.
Vertices of Solids [M]	A vertex is a corner where edges meet.
Naming a Solid [M]	Match the description to the right solid.
Diagonals of a Polygon [M]	Each corner joins to all but its two neighbours.
Counting Stacked Cubes [M]	Multiply length, width, and height.
Angles in a Triangle [M]	The three angles of a triangle add to 180°.
Opposite Faces of a Die [M]	Opposite faces of a die sum to 7.
Folding and Punching Holes [M]	Each fold doubles the layers.
Turning Around a Clock [M]	A quarter turn moves 3 numbers clockwise.
Completing a Symmetric Figure [M]	A mirror line makes both halves match.
Shortest Path on a Grid [M]	Add the across and up distances.
Shrinking Patterns [M]	Subtract the same step each time.
Finding the Rule [M]	Subtract two neighbours to find the step.
Repeating Patterns [M]	Use the remainder to find the position in the cycle.
Number Machines [M]	Apply each step in order to the input.
Working a Machine Backwards [M]	Undo each step in reverse order.
Add-the-Last-Two Patterns [M]	Every term is the sum of the two before it.
Up-and-Down Patterns [M]	Two rules take turns.
True or False? [M]	Check each statement on its own.
Odd One Out [M]	Find the rule the others share.
Overlapping Groups [M]	Add the groups, then subtract the overlap once.
Ordering from Clues [M]	Chain the comparisons together.
Balancing a Scale [M]	Share the balance equally.
Balancing an Equation [M]	Both sides must total the same.
Missing Digit for Divisibility [M]	A number divides by 3 when its digit sum does.
Divisibility Tests [M]	Quick rules tell you what divides evenly.
Number Riddles [M]	Use each clue to narrow the choices.
Consecutive Number Sums [M]	The middle of three-in-a-row is the average.
Making the Greatest Number [M]	Put the biggest digit in the highest place.
Sum and Difference [M]	Add the sum and difference, then halve.
Arranging in a Row [M]	Choose each spot in turn.
Counting Combinations [M]	Multiply the choices for each part.
Counting Grid Paths [M]	Every route mixes the same east and north moves.
Ways to Roll a Sum [M]	List the pairs that reach the target.
How Many Numbers [M]	Pick the tens digit, then the ones digit.
Codes with Repeats Allowed [M]	Each position has the full set of choices.
Two-Step Word Problems [M]	Do the multiplication, then the subtraction.
Times as Many [M]	'Times as many' means multiply.
Part and Whole [M]	The parts add up to the whole.
Working Backwards [M]	Undo the steps from the end.
Unit Price Problems [M]	Find the price of one, then scale up.
Saving Over Time [M]	Add the starting amount to the weekly savings.
Distance from Speed and Time [M]	Distance is speed times time.
Reading a Table [M]	Add the numbers in the table.
Reading a Pictograph [M]	Each symbol stands for several items.
Reading a Bar Chart [M]	Compare bar heights by subtracting.
Reading Tally Marks [M]	Each bundle is five.
The Mode [M]	The mode is the value that appears most.
The Range [M]	The range is the biggest minus the smallest.
The Median [M]	The median is the middle value in order.
How Likely? [M]	Events can be certain, possible, or impossible.
Simple Probability [M]	Probability is favourable outcomes over all outcomes.
Counting Favourable Outcomes [M]	Count the sections that match the condition.

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.

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