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Geometry

One ladder. Adding is a length, multiplying is an area, cubing is a volume — and Pythagoras is where length and area meet.

1-DA length. Dots in a line, touching — a ruler.
seven as seven dots

Measure It

Touching dots are a ruler. Compare, lay end to end, read a ruler, find how much longer.
1-D and 2-DThe fence is a length round the outside. The field is an area inside.
nine as a three by three square

Fence and Field

Rows and columns make the area; walk the fence and it straightens into one line — the perimeter.
Where they meetLengths don't add up to the long side. The areas on them do.
twenty-five as a five by five square

Pythagoras

Pour the squares on the two short sides into the square on the long side: 9 + 16 = 25. Then back: 25 − 9 = 16.

 sixteen as a four by four square

Add Up the Lengths

Columns are lengths; added up they fill an area. Two staircases make a rectangle, the odd numbers make a square.
3-DA volume. The square, stacked that many times.
twenty-seven as two ten-triangles and seven

Build the Cube

Stack the layers and skip-count your way to the cubes.
Shapes and placesCorners, halves and where a dot sits.
three as a triangle of dots

Shapes

Touch the corners, name the shape, build one yourself — triangles, rectangles, angles, symmetry.

 twenty-four as two ten-triangles and four

Equal Parts

Cut a block of dots into equal parts and check by counting: two halves of 24 are 12 each.

 eight as eight dots

Dot Map

(3, 5) is three dots along and five dots up. Read a dot's numbers, put a dot there, draw shapes.