Counting Shapes

Noticing and using mathematical structure
Grade level
Use an App
pattern shapes
Pattern Shapes

What can you count? What can you compare?

A large triangle made out of pattern shapes

There is a lot to see and count in this image. 

  • What do you notice? 
  • What shapes do you see? 
  • What can you count? 
  • What can you compare?
How could you get started?
  • How many triangles can you count? What shapes can you see that are composed of more than one pattern block piece? 
  • Are there more trapezoids or more rhombuses? How do you know?
  • What shape do you see the greatest number of? What shape do you see the least number of?
Ready to explore more?
  • What could you change to make this image have more than one line of symmetry? 
  • Can you create a large shape using smaller shapes from the Pattern Shapes app? Invite your friends to share what they notice and what they can count.
For Teachers: More about this activity

This task asks students to notice and count shapes and colors. Using these counts, they can compare the number of shapes sorted by defining and nondefining attributes. Students may engage in a range of geometry skills as they engage in this task, including recognizing and naming shapes, classifying shapes by their attributes, and using small shapes to compose larger shapes.  

While many students may count the total number of pieces or count and compare the number of the same shape or same color pieces, they may also notice shapes composed of more than one pattern block. Students who consider composed shapes might count the total number of triangles they see, counting both single green triangles or triangles composed of two or more shapes, including the entire shape. In addition to triangles, students might consider the number of composed rhombuses, trapezoids, or hexagons they can see within the entire shape. They might also notice more than one type of quadrilateral and consider the combined total of rhombuses and trapezoids. 

Using the Pattern Shapes app, students can use the drawing tools to make notes or reference marks on the shapes or to circle or outline groups of shapes. They might choose to drag shapes to sort them into groups based on attributes. They might also use the app to overlay pattern shapes or change the colors of existing shapes as they count or compare.   

Students may count and compare individual shapes. If they do this, you can ask: Where do you see triangles/quadrilaterals/hexagons composed of more than one shape? To push their thinking further, ask: Can you make the same size shape using the same total number of shapes but fewer trapezoids? Students might reason about ways they can create trapezoids using three triangles or a triangle and rhombus. Or, they might combine two trapezoids to make a hexagon and explore trades they could make to ensure the same number of total shapes in the large composite triangle. Invite them to find multiple ways to solve the problem or compare their solution with a classmate’s solution.