Printable guide · ages 9–10

Geometry with Piko

Name a visible property first, then test it on each shape. Each lesson has four short explanations, a counter-example and three tasks that use different touch and sort actions. Every shape sits on a fixed grid, so each answer can be checked.

Materials: The screen is enough. Optional: paper squares (2 cm) to build the shapes and fold along the dashed lines.

Open the lessons

What to notice

Notice whether the child checks every side or corner, uses the grid to count, and explains a fold or a turn in their own words.

Ask “How do you know?” or “What stayed the same after the turn?” Praise the reason, not only the answer.

Lesson 1

Sort by sides

Goal: Sorts a shape by its number of sides and by whether all its sides are equal.

Use closed polygons. The child should name the property they check, not only the shape.

Starting point: Count the sides of one triangle together.
A helpful phrase: “Are all the sides the same length? How do you know?”
A common mix-up: A rhombus and a square both have four equal sides. Only the square has right angles.
Notice the transfer: On another day, repeat the same two checks on a new shape.

Show: Touch every shape whose four corners are all right angles.

Lesson 2

Turn or mirror?

Goal: Tells a turned copy of a shape apart from its mirror image.

Turns keep the shape. Mirror images keep the lengths but reverse the handedness.

Starting point: Trace the L with a finger, then turn the paper.
A helpful phrase: “Where is the foot now? Is it still on the same side of the long arm?”
A common mix-up: Turning a J gives another J. Only a mirror turns an L into a J.
Notice the transfer: Ask the child to explain, in their own words, why a mirror image is not a turn.

Show: Touch every shape that is not a turned copy of the L.

Lesson 3

Fold lines

Goal: Identifies the fold lines (symmetry axes) that make both halves match.

Fold lines are checked by matching the halves, not by guessing where the middle is.

Starting point: Fold a paper square in half along a dashed line.
A helpful phrase: “If you fold here, do the two sides land on each other?”
A common mix-up: A line through the middle is not always a fold line. The P shape has a middle, but its halves do not match.
Notice the transfer: Ask the child which fold lines the square has, and why the P has none.

Show: Touch every shape that has no fold line at all.

Lesson 4

Perimeter: walk the edge

Goal: Measures the perimeter of a unit-square shape by counting its outside edges.

Perimeter counts outside edges only. Area counts squares inside. Keep the two ideas apart.

Starting point: Walk your finger around a 2 by 2 square and count the edges.
A helpful phrase: “Does this edge touch the outside, or another square?”
A common mix-up: Inside edges are not part of the perimeter. Counting them gives the wrong total.
Notice the transfer: Ask the child to predict the perimeter of a new shape before counting.

Show: Touch every shape with a perimeter of 12 units.

Lesson 5

Area: count the squares

Goal: Measures area by counting the unit squares that fill a shape.

Area counts squares. Use the grid so the child can check every square.

Starting point: Colour the squares of a T shape one by one.
A helpful phrase: “Did you count any square twice?”
A common mix-up: The outside line is not a square. Counting edges gives the perimeter, not the area.
Notice the transfer: Ask the child to build a new shape with the same area as the T.

Show: Touch every shape that covers 6 unit squares.

Lesson 6

Same area, different edge

Goal: Explains that equal areas can have different perimeters.

Area and perimeter are separate measures. Equal area does not fix the perimeter.

Starting point: Build a 2 by 3 rectangle and a 1 by 6 strip from six paper squares.
A helpful phrase: “Which one has more edge on the outside?”
A common mix-up: Same area does not mean same outside length.
Notice the transfer: Ask for another six-square shape, and let the child predict its perimeter first.

Show: Touch every shape that covers 4 unit squares and has a perimeter of 10 units.

Lesson 7

Cube nets

Goal: Tells which flat arrangement of six squares folds into a cube without overlap.

Test each arrangement by folding paper squares. Nets are checked by folding, not by how they look.

Starting point: Fold the cross into a cube with the child, one face at a time.
A helpful phrase: “Which square becomes the bottom? Is any face used twice?”
A common mix-up: A row of six squares looks like a net, but it cannot fold into a cube.
Notice the transfer: Ask the child to make a new net by moving one square of the cross.

Show: Which arrangement is not a cube net?

Lesson 8

Find the shape from clues

Goal: Uses several geometric clues together to identify one shape.

Clue solving is a logic habit. The child should say which clue removed which shape.

Starting point: Read a clue aloud and point to the shapes it allows.
A helpful phrase: “Which clue would remove the rhombus?”
A common mix-up: A square fits the equal-sides clue, but it is not the only shape that does.
Notice the transfer: Next time, give a three-clue puzzle with a different answer.

Show: Clue: four right angles, but neighbouring sides are not equal. Which shape is it?

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