Circles, triangles, squares, rectangles, pentagons and hexagons, named by counting sides and corners, never by color or size. Flat shapes and solid ones, and why a square is a rectangle. Putting small shapes together to make bigger ones, and counting squares in rows and columns. Then equal shares: halves, thirds and fourths of a circle and a rectangle, and why the parts must be the same size but not the same shape. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
Four sides, all the same length. Four square corners. That makes it a square.
Rule, not look. Count the sides and the corners — that is what names a shape, no matter how it is turned. And equal shares means equal SIZE, not the same shape.
Two things people get wrong
⚠️People often think…
A square tipped on its corner is a diamond, not a square.
Turning a shape never changes its name. Four equal sides and four square corners is a square whichever way it is sitting. The same goes for a long skinny triangle — three sides, three corners, still a triangle.
Count the sides and corners. Ignore the angle you're looking from.
⚠️People often think…
A fourth is bigger than a half, because 4 is bigger than 2.
More pieces means SMALLER pieces. Cut a pizza into 4 and each slice is smaller than if you cut it into 2. And two pieces only count as halves if they are the same size.
The bigger the bottom number, the smaller the piece.
Count the parts, not the cuts
1Watch one
Is a square still a square when it is tipped on its corner?
Count the sides: four, all equal.
Count the corners: four square ones.
That is the rule for a square.
Yes. Turning it changed nothing.
2Do one with me
Cut a circle with two straight lines, both through the middle.
How many cuts did you make?
How many pieces is it in now?
So each piece is called a
💬One sentence, then you move on
Why doesn't turning a shape change what it is called?
3Try one
Half of a pizza, or a fourth of the same pizza — which piece is bigger? Write “half” or “fourth.”
I want a hint first
Sharing one pizza between two people, or between four. Who gets more?
Where this goes
Where this lives
Splitting a snack so nobody complains, reading a road sign by its shape, cutting something down the middle.
What this feeds
Next unit is what multiplication and division actually mean.
Name something you would cut into equal parts, and how many.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🔺 Naming a shape — the three steps
Count the straight SIDES by tracing each edge with your finger → count the CORNERS by touching each point (it should match) → check the corners: are they square corners, like a sheet of paper? and the sides: are they all the same length? 3 sides → triangle. 4 sides → quadrilateral; with 4 square corners → rectangle; with 4 square corners AND 4 equal sides → square. 5 → pentagon. 6 → hexagon. No straight sides → circle.
Count sides, count corners, check the rule.
⚖️ The whole topic in one idea
A shape gets its name from a RULE about its sides and corners — never from its color, its size or which way it is turned. And a share gets its name from how many EQUAL parts fill the whole: 2 equal parts are halves, 3 are thirds, 4 are fourths. Equal means the same size; the parts do not have to be the same shape.
Rule, not look. Same size, not same shape.
⚠️ Traps the test loves
Saying a tilted square is a “diamond” and not a square. Turning a shape never changes its name.
Saying a long, skinny triangle is not a triangle. Count the sides: 3 sides, 3 corners — it is one.
Saying a square is not a rectangle. It has 4 sides and 4 square corners, so it is one.
Calling any 2 pieces “halves.” Halves must be 2 EQUAL pieces.
Saying a fourth is bigger than a half because 4 is bigger than 2. More pieces means smaller pieces.
Counting the cuts instead of the parts. Two cuts through the middle of a circle make 4 parts — fourths, not halves.
🟦 Shapes and shares — the chart
Name
The rule
Looks like
Circle
round, no straight sides, no corners
a coin, a plate
Triangle
3 sides, 3 corners
a slice of pizza
Rectangle
4 sides, 4 square corners
a door, a book
Square
4 square corners AND 4 equal sides
a cracker, a window pane
Pentagon
5 sides, 5 corners
a house shape
Hexagon
6 sides, 6 corners
a honeycomb cell
Halves
2 equal parts
a sandwich cut once through the middle
Thirds
3 equal parts
a candy bar snapped into 3 same-size pieces
Fourths
4 equal parts
a pizza cut with a plus sign
🎯 How the test will ask
A drawing of a shape — “what is it called?” Count sides and corners. Ignore color, size and tilt.
“Which shape has 4 sides and 4 square corners?” More than one can — a square AND a rectangle.
“Draw a shape with 5 sides.” Any 5-sided shape counts.
A solid — “how many faces?” Count the flat parts: a cube has 6.
A rectangle cut into rows and columns — “how many squares?” Count one row, then add for each row.
A shape cut into parts — “halves, thirds or fourths?” Count the PARTS, and check that they are equal.
Two pieces — “are these halves?” Only if they are the same size.
✅ Before the test, can you…
Name a circle, triangle, square, rectangle, pentagon and hexagon by counting sides?
Tell a flat shape from a solid one, and name a cube, sphere, cone and cylinder?
Explain why a square is a rectangle?
Put two triangles together to make a square, or count the squares in rows and columns?
Cut a circle and a rectangle into halves, thirds and fourths?
Say why two unequal pieces are not halves?
Explain that halves can be different shapes but must be the same size?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: sort shapes by counting their sides, name the equal parts of a circle and three rectangles, line shapes up from fewest sides to most, then settle an argument about whether two triangles can be halves. Every activity checks itself, and hints are free.
Meet the shape
Tap a figure. Count the sides before you say the name.
Same rule as the microscope: look first. Color and size do not count. Only the sides do.
A figure
Tap the three-sided one, the four-sided one, the six-sided one, or the one with no straight sides.
Names stay off until you ask. Count first.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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Supported
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Hints used
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Cards studied
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Lab
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Traps met
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Explained in own words
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The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.