Academics · Elementary · Kindergarten to grade 5

Stretch a band.
Meet the shape you made.

Tap pegs to build any shape and the board names it and measures it exactly. Then try the challenges for your grade: a square on its point, two rectangles with the same area, a shape with one line of symmetry.

Open the geoboardWhat you get
24challenges in three grade bands
49pegs on the board
8measurements for every shape

The geoboard

Tap pegs to set corners and tap the first corner again to close the band. Drag a corner to change the shape. Load the example to see a house measured.

Loading the geoboard. If nothing appears, turn on JavaScript.

One square, four names

Each step adds a rule and keeps the ones before it. The Measure panel shows the same family for any shape you build.

4 sides

Quadrilateral

Any closed shape with four straight sides.

+ two pairs of parallel sides

Parallelogram

Opposite sides run side by side and never meet.

+ four square corners

Rectangle

A parallelogram whose corners are all right angles.

+ four equal sides

Rhombus

A parallelogram whose sides are all the same length.

square corners and equal sides

Square

Follows every rule above, so it carries all four names.

Two more relatives sit beside the parallelograms. A trapezoid has one pair of parallel sides; some books say exactly one pair and some say at least one, which would make every parallelogram a trapezoid too, so ask which meaning your class uses. A kite has two pairs of equal sides that touch. Turning or flipping a shape never changes its name.

What you get

Academics · ElementaryFree

What you finish with
Shapes built by hand and measured exactly, up to twenty-four solved challenges matched to the grade, a saved book of up to twelve shapes with their measurements, and a printed book or dot paper for work away from the screen.
Who it is for
Children from kindergarten to grade 5 learning shapes, area, perimeter, angles and symmetry; younger children building beside an adult; parents, homeschool families and teachers who want a geoboard station without the rubber bands.
Format
Browser geoboard with challenges. Works by touch, mouse or keyboard on a phone, tablet or computer. Prints a shape book and blank dot paper; saves the shape list as a .csv.
Access
Free. No account and no sign-in. Shapes and solved challenges are saved only in this browser; no names are asked for and nothing is sent to Caveat.
Where it lives
The Elementary space in Caveat Academics.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Pick a grade band, then tap pegs to set the corners of a shape. Tap the first corner again to close the band.
  2. Read the Measure panel. In grades 2 and up, tick Show the squares to see how the area is counted.
  3. Open Challenges, pick one, build a shape for it and press Check my shape. A miss tells you what to change.
  4. Save the shapes you like to My shapes and print the book, or print dot paper and draw the next one by hand.

Open the geoboard

How the measuring works

Exact arithmetic on the peg positions, and how to use the board at each age.

How each measurement is found

  • Area comes from the corner positions with the shoelace formula, so it is exact even for slanted shapes. Show the squares draws the same answer as whole squares, half squares and cut pieces.
  • Perimeter adds the side lengths. One unit is the gap between two pegs. A slanted side is longer than the gaps it crosses, so it is shown as “about” unless it comes out whole, as the long side of a 3-4-5 triangle does.
  • Square corners, parallel sides and angle kinds are tested with whole-number arithmetic on the sides, never by eye, so a corner that is almost square is not counted.
  • Lines of symmetry are found by flipping every corner across each possible fold line and checking that the shape lands on itself. In grades 4–5 the lines are drawn on the board.
  • Pick’s shortcut (pegs inside + pegs on the band ÷ 2 − 1) is checked against the area for every shape the page’s tests build.

For the adult nearby

With a four- or five-year-old, skip the challenges: take turns making a shape and naming it, and count the corners together by touching each one. The K–1 band shows only names, sides and corners.

In grades 2 and 3, turn on Show the squares before talking about area, and try the two area-12 challenges back to back: same area, different perimeter. In grades 4 and 5, ask for a prediction before each check, then let the dashed symmetry lines and the family names settle it.

A real geoboard and rubber bands, or the printable dot paper, make the same activities work away from a screen.

The three grade bands

BandWhat the panel showsChallengesOne of them
Grades K–1Make shapes, name them, count sides and corners.8Make a square that sits on a point, like a diamond.
Grades 2–3Area in square units, perimeter and square corners.8Make a rectangle with an area of 12 and a perimeter of 14.
Grades 4–5Parallel sides, symmetry, angle kinds and shape families.8Make a quadrilateral with exactly one line of symmetry.

Sources

  1. Common Core State Standards for Mathematics (2010), Geometry and Measurement: naming shapes whatever their size or turn (K.G.A.2), defining attributes (1.G.A.1), shapes with given numbers of angles or sides (2.G.A.1), area by counting unit squares and by multiplying side lengths (3.MD.C.5–7), perimeter, and rectangles with the same area and different perimeters (3.MD.D.8), categories of quadrilaterals (3.G.A.1), angle kinds, parallel and perpendicular lines and lines of symmetry (4.G.A.1–3), and classifying figures in a hierarchy (5.G.B.3–4).
  2. Common Core Standards Writing Team, Progressions for the Common Core State Standards in Mathematics: Geometry, K–6 (2013), on the two definitions of a trapezoid (exactly one pair of parallel sides, or at least one pair).
  3. Georg Pick, “Geometrisches zur Zahlenlehre” (1899): for a shape with corners on grid points, area = interior points + boundary points ÷ 2 − 1.
  4. The measurements are checked against an exact reference written for this page (guide/suite/geo_ref.py, whole numbers and fractions only) on random shapes and on every challenge.

The geoboard measures shapes on a 7 by 7 grid of pegs; one unit is the gap between two neighbouring pegs. An equilateral triangle and a regular pentagon or hexagon cannot be built on square pegs, so they do not appear. Practice with the ideas, not a full geometry course. Support: team@caveatacademic.com.