Building and composing shapes
Comparing 2D and 3D shapes by their parts, building and drawing shapes, and joining shapes to make bigger ones
About three lessons of 30 to 35 minutes
Two triangles can hide inside one rectangle
Cut a rectangle straight across from one corner to the opposite corner and you get two triangles. Push those same two triangles back together along that cut and the rectangle reappears. Shapes are not always separate: a bigger shape can be built by joining smaller ones, and a bigger shape can be split back into the smaller ones it was made from.
Today you also compare 2D and 3D shapes side by side, spotting parts they share (a square and a cube both have straight sides that meet at square corners), and you build shapes yourself from materials like sticks, clay, and pencil and paper.
- Two triangles joined along one sidetogether they can make a bigger rectangle
- 3 sticks joined at their endsbuilding a triangle from straight sticks
- A square face on a cubea cube's flat face is shaped just like a square
- Clay rolled and pinched into a shapemodelling a shape by hand, not just drawing it
What students will be able to do
Students will compare 2D and 3D shapes and describe parts they share, build and draw shapes using materials such as sticks and clay, and put together simple shapes to form a larger shape.
- I can compare a 2D shape and a 3D shape and describe a part they share.
- I can build a shape from materials like sticks or clay, and I can draw a shape.
- I can join two or more simple shapes together to make a bigger shape.
Standards this unit teaches
- K.G.B.4Common Core (US)Compare 2D and 3D shapes
Analyze and compare two and three dimensional shapes, describing their parts and likenesses.
- K.G.B.5Common Core (US)Build and draw shapes
Model shapes by building them from materials such as sticks and clay and by drawing them.
- K.G.B.6Common Core (US)Compose simple shapes
Put together simple shapes to form larger shapes, such as joining two triangles to make a rectangle.
- AC9MFSP01Australian Curriculum v9 (ACARA)Sort and name familiar shapes (Foundation)
Sort, name and make familiar shapes, and spot them in objects around the classroom and home. The 'make' verb here matches this unit's building and composing focus.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Compare
- look at two shapes and describe what is the same and what is different about their parts
- Build
- make a shape using materials like sticks, straws, or clay
- Compose
- put smaller shapes together to make one larger shape
- Face
- one of the flat sides of a solid shape, such as one side of a cube
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Comparing 2D and 3D shapes
ConcretePut a square and a cube side by side. They are different, one is flat and one is solid, but they share something too: every flat face of the cube is shaped exactly like a square. Comparing shapes means noticing both what is alike and what is different about their parts.
Try another pair: a circle and a sphere (a ball). A ball has no flat faces at all, but if you traced around its widest point, the outline would be a circle. Comparing 2D and 3D shapes this way builds toward the idea, met properly in later grades, that solid shapes are built from flat faces.
- What part does a cube share with a square?
- Name one way a cone is different from a triangle.
2. Building and drawing shapes
ConcreteA shape is not just something you look at; you can make one yourself. Lay straight sticks end to end and join the corners to build a triangle or a square. Roll and pinch clay into a ball for a sphere or a flattened lump for a shape with faces. Draw a shape on paper with a pencil, tracing its straight or curved sides carefully.
Building with sticks makes the number of sides and corners concrete and countable: 3 sticks joined end to end make exactly 3 sides and 3 corners, a triangle, and no other number of sticks joined that way makes one.
You have 4 straight sticks, all the same length, and join their ends to close up a shape. What shape have you built?
- Count the sticks used: 4.
- Each stick becomes one side, so the shape has 4 equal sides.
- Joining 4 equal sides end to end, with a corner where each pair meets, builds a square.
Answer: A square, because it has 4 equal sides joined at 4 corners.
- How many sticks would you need to build a triangle?
- Could clay be used to build a solid shape like a cube? How?
3. Joining shapes to make a bigger shape
PictorialTwo triangles pushed together along one matching side can form a bigger shape, such as a rectangle or a bigger triangle, depending on how they are joined. This is called composing shapes: building a larger shape out of smaller ones.
The joined edge has to match up exactly, side to side, for the composed shape to have straight, clean edges. Try joining two identical right-angled triangles along their longest side: the result is a rectangle, with no gaps and no overlaps.
Two identical square tiles are pushed together side by side, matching edge to edge. What shape is formed?
- Each tile is a square on its own.
- Pushed together edge to edge with no gap and no overlap, the two squares form one longer shape.
- A shape with two pairs of equal sides and four right-angled corners, longer than it is wide, is a rectangle.
Answer: A rectangle, made of two squares joined side by side.
- If two triangles are joined along their longest matching side, what larger shape could they form?
- Why does the joined edge need to match up exactly for the composed shape to look right?
Common misconceptions and how to address them
MisconceptionThe child thinks 2D and 3D shapes cannot be compared at all because one is flat and one is solid.
Why it happens: The obvious difference, flat versus solid, overshadows the parts they genuinely do share, such as a cube's square faces.
How to address it: Trace around a real face of a 3D solid, such as one face of a wooden cube block, directly onto paper. The traced outline is the matching 2D shape, made visible.
MisconceptionWhen building a shape from sticks, the child uses the wrong number of sticks for the shape they are trying to make, such as using 3 sticks while attempting to build a square.
Why it happens: Without deliberately counting the sides needed first, it is easy to stop building too early or add an extra stick.
How to address it: Name the target shape first and say its number of sides out loud before starting, then count sticks used against that number as you build.
MisconceptionWhen two shapes are joined to compose a larger one, the child leaves a gap between them or overlaps them, so the joined edges do not line up cleanly.
Why it happens: Judging whether two edges truly match requires comparing both length and angle at once, which is a harder visual judgement than matching a single length.
How to address it: Physically slide the two shapes together until their edges touch fully along the whole matching side, with no visible gap or overlap, checking by running a finger along the joined seam.
MisconceptionThe child believes any two shapes can be joined to make any other shape, without regard for whether the sides being joined actually match in length.
Why it happens: Composing shapes is new and exciting, and the constraint that joined sides must be the same length is easy to overlook in the enthusiasm of building.
How to address it: Before joining two shapes, measure or directly compare the two sides that will touch. Only sides of matching length join cleanly with no gap or overhang.
Guided practice (with answers)
1. Compare a cube and a square. What part do they share?
Answer: Every flat face of the cube is shaped like a square.
2. You join the ends of 3 equal sticks to close up a shape. What shape have you built?
Answer: A triangle, because 3 sides joined at 3 corners make a triangle.
3. Two identical squares are pushed together edge to edge with no gap. What shape can this make?
Answer: A rectangle.
4. Name one way you could build a shape without drawing it.
Answer: Using sticks joined at their ends, or shaping clay by hand, are both correct answers.
5. Two triangles are joined along a matching side. Could they form a bigger triangle or a rectangle depending on how they are joined?
Answer: Yes, the shape formed depends on which sides are joined together.
6. You have 4 equal sticks. Could you build a triangle with all 4? Why or why not?
Answer: No, a triangle needs exactly 3 sides, so a fourth stick would either be left over or make a different shape, like a square, instead.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Draw the Shapes practises building shapes from a name, and the shape-sorting worksheet reinforces comparing 2D and 3D parts.
Differentiation
- Provide pre-cut paper shapes to physically join together before asking the child to draw a composed shape from imagination.
- Use only two shapes at a time when composing, before attempting three or more.
- When building with sticks, count and lay out the exact number of sticks needed before starting to join them.
- Stick with the most familiar shapes, square, triangle, rectangle, circle, for comparing and building.
- Compose a larger shape from three or more smaller shapes, not just two.
- Decompose a shape back into the smaller shapes it could be made from, the reverse of composing.
- Compare a wider range of 3D solids to their matching 2D faces, such as a cylinder's circular ends and rectangular side.
- Build the same shape two different ways, with sticks and then with clay, and compare the two methods.
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling comparing, building, and composing.
1. Compare a ball (sphere) and a circle. What part do they share?
Answer: The outline traced around a ball's widest point is a circle.
2. You join the ends of 4 equal sticks to close up a shape. What shape have you built?
Answer: A square, because it has 4 equal sides.
3. Two identical triangles are joined along their longest matching side. Name one shape this could form.
Answer: A rectangle (or a larger triangle, depending on how they are joined).
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 comparing 2D and 3D shapes by their parts (section 1), Lesson 2 building and drawing shapes (section 2), Lesson 3 composing shapes (section 3) plus the exit ticket.
- These three standards cluster naturally as the hands-on, constructive half of Kindergarten geometry, following on from the previous unit's naming and describing. Comparing shapes' parts, building shapes from materials, and composing bigger shapes from smaller ones all involve physically manipulating shapes rather than just identifying them.
- Language to keep saying: what part do they share, count the sides before you build, and no gaps and no overlaps. These phrases pre-empt the most common slips in this unit.
- Curriculum note: US Kindergarten states comparing (K.G.B.4), building (K.G.B.5) and composing (K.G.B.6) as three separate standards. ACARA Foundation folds sorting, naming and making shapes into one broader Space descriptor (AC9MFSP01), whose verb 'make' is the closest single match to this unit's building and composing focus.
- Present mode and print both work: use the Print button for a student worksheet, or bring real sticks, clay, or pre-cut paper shapes to teach the building and composing sections hands-on.