Pattern-Block Pictures

Pattern blocks are a classic set of bright shapes — green triangles, orange squares, blue and tan rhombuses, red trapezoids, and yellow hexagons — that fit together edge-to-edge with no gaps. Your child uses them to fill outline pictures and to invent their own (a rocket, a flower, a fish), and along the way makes a powerful discovery: small shapes combine into bigger ones, and big shapes come apart. Two green triangles make a blue rhombus; three make the red trapezoid; six triangles (or two trapezoids, or three rhombuses) cover the yellow hexagon. That is the heart of composing and decomposing shapes.

  1. Free-explore first. Pour out the blocks and let your child stack, sort by colour, and push shapes together however they like — this is how they learn which edges match.
  2. Fill an outline picture. Print or draw a simple outline (a rocket, a turtle, a flower) and invite them to find blocks that fit inside the lines with no gaps or overlaps. Start with outlines that show the shapes inside, then move to blank ones.
  3. Make the big-shape discovery. Put down a yellow hexagon and ask “how many green triangles do we need to cover it exactly?” Let them lay triangles on top and count — six! Then try the blue rhombuses, then the red trapezoids.
  4. Build and name your own picture. Hand over the whole set, let them design a creature or scene, then have them name it and tell you what each part is made of (“the rocket’s nose is two triangles”).
  5. Trace around it. When they love a creation, help them trace its outside edge onto paper — both to keep it and to make a new outline puzzle for next time.

Variation: offer structured outline mats some days and a blank page for free building on others — both grow real skills. Run a “cover the hexagon as many ways as you can” challenge and count the solutions, or build one half of a design and mirror it across a “fold line” for symmetry.

Requirements

  • Space: A tabletop corner or a patch of floor — the blocks don't roll, so little room is needed.
  • Surface: A flat, hard surface so shapes sit flush without gapping; a shallow tray or baking sheet corrals the pieces and gives one child a defined work area.
  • Materials: A pattern-block set (the standard six shapes and colours, wood or plastic, ages 3+). No-cost alternative: print a free pattern-block template and cut shapes from card, cereal-box card, or craft foam, or simply cut equal-size squares and triangles. Free printable outline mats are widely available; a pencil for tracing is the only extra.
  • Participants: Lovely as 1 child + 1 adult, solo once the child is hooked, or a small group sharing one set — turn-taking and show-me-how-you-made-that talk add a language layer.
  • Supervision: Light — an adult nearby to pose a good question (I wonder how many triangles fit in there?), to resist solving it for the child, and to keep small blocks away from any under-3 sibling.

Rationale & Objective

Composing and decomposing shapes is a core early-geometry standard, not an optional extra. Common Core kindergarten standard K.G.B.6 asks children to “compose simple shapes to form larger shapes” (the classic example: joining two triangles to make a rectangle); the EYFS asks children to “combine shapes to make new ones”; and Head Start ELOF P-MATH 9 names composing explicitly. Putting small shapes together to make — and take apart — bigger ones builds part-whole reasoning and spatial structuring, and pattern blocks are unusually good for it because the pieces carry built-in equivalences (2 triangles = 1 rhombus; 6 triangles = 2 trapezoids = 3 rhombuses = 1 hexagon) that quietly seed early fractions (equal parts of one whole) and area (covering a region with repeated units). Douglas Clements and Julie Sarama mapped exactly how this grows in their research-based learning trajectory for shape composition, moving children from using one shape at a time, to making pictures, to deliberately combining and substituting shapes with anticipation (Clements, Wilson & Sarama, 2004).

Honest framing — the shape-composition trajectory is one of the better-evidenced sequences in early maths, and a randomised study found that teaching one level ahead of a child’s current level produced more learning than skipping ahead (Clements et al., 2019) — but that gain showed up mainly on closely-related tasks, the research is about guided instruction rather than casual home play, and no study shows pattern blocks alone produce lasting maths gains. The value here is a developmentally well-matched, low-pressure activity, not a guaranteed outcome.

Progress Indicators

  • Early: places blocks side by side and uses each shape for one whole job (one triangle = a tree, one hexagon = a sun); given an outline, fills it by trial and error, often leaving gaps or letting pieces overlap or stick out past the lines.
  • Developing: builds a recognisable picture and starts putting two or three shapes together to make one part, but chooses by rough “looks right” rather than exact fit — pieces don’t yet interlock economically, and they don’t predict whether a shape will fit before trying.
  • Proficient: deliberately combines shapes to fill a region, choosing pieces by their angles and sides and rotating them on purpose; knows and uses key equivalences without rebuilding from scratch (“two green triangles make the blue rhombus”) and fills a hexagon confidently.
  • Advanced: swaps one combination for an equivalent one (a hexagon for two trapezoids, a trapezoid for three triangles), predicts how many of a small shape will fill a bigger one before placing them, and finds several different ways to cover the same outline.

Safety Notes

  • Pattern blocks are small wood or plastic pieces and a choking hazard for children under 3 (most sets are labelled ages 3+) — anything that fits through a toilet-paper tube (about 4 cm across) is unsafe for a toddler, so keep the set away from little ones and pack it up before a younger sibling can reach it.
  • If you cut DIY shapes from card or foam, an adult should do the cutting for under-5s and keep scissors out of reach.
  • Clear blocks off the floor when finished — loose pieces underfoot are a slip-and-fall hazard and painful to step on.
  • Count pieces back into the container after play so strays don’t reach little hands, mouths, or pet bowls.

Hints

  • Playfulness: give the build a story, not a worksheet — “uh oh, the rocket needs a bigger window, can you make one from two triangles?” — and narrate equivalences like magic tricks: “watch, I’ll turn this one hexagon into two red pieces!”
  • Sustain interest: rotate the challenge before boredom sets in — free-build one day, an outline mat the next, a how-many-ways-can-we-cover-the-hexagon contest the day after — and photograph or trace a favourite creation for a satisfying finish.
  • Common mistake: two traps — starting with hard blank-outline mats before your child has freely explored the blocks (let free play come first), and solving the puzzle for them or saying “that piece is wrong” (instead ask “does that leave a gap? what else might fit?”).
  • Limited materials: no shop-bought set needed — print a free template and cut shapes from cereal-box card or craft foam, or just cut a stack of equal-size squares and triangles. Even a few hexagons and a pile of triangles is enough to explore “how many cover this one?”
  • Cross-domain: this is early fractions in disguise — covering one hexagon with halves (trapezoids), thirds (rhombuses), and sixths (triangles) makes equal-parts-of-a-whole concrete years before the word fraction — and it feeds art and symmetry (mirror designs, mandalas) and counting (“how many pieces did your fish take?”).
  • Progression: free play → fill a thick-outline mat that shows the shapes inside → fill a blank outline where they choose the shapes → cover one region many different ways → design and trace their own picture and challenge a grown-up to fill it.

Sources

  • Common Core State Standards for Mathematics, Kindergarten — Geometry: K.G.B.6 (compose simple shapes to form larger shapes — e.g. join two triangles to make a rectangle); Grade 1, 1.G.A.2 (compose two-dimensional shapes) as the next step.
  • Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children’s composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2), 163–184.
  • Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C., & Wolfe, C. B. (2019). Evaluating the efficacy of a learning trajectory for early shape composition. American Educational Research Journal, 56(6), 2509–2530.
  • Sarama, J., & Clements, D. H. (2009). Early Childhood Mathematics Education Research: Learning Trajectories for Young Children. Routledge (and the Building Blocks curriculum).
  • Head Start Early Learning Outcomes Framework (ELOF), Mathematics Development — Goal P-MATH 9: identifies, describes, compares, and composes shapes.
  • UK EYFS — Development Matters (DfE, 2021), Mathematics: combine shapes to make new ones; recognise that a shape can have other shapes within it, just as numbers can.
  • Montessori Sensorial materials — the Constructive Triangles (triangles that combine to build squares, rhombuses, trapezoids, and hexagons), with the Geometric Cabinet as a related shape material.
  • HighScope Preschool Curriculum — Mathematics KDI 34 (Shapes); Teaching Strategies GOLD Objective 21b (Understands shapes).