More and Fewer: Ways to Make

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SWBAT make one composite shape with more and fewer shapes.

Big Idea

Students build composite shapes and number sense in this hands on lesson.

Setting Up the Learning

5 minutes


Last week we looked at ways to make larger, composite shapes. Today we are going to apply all of the thinking we have done to think about how can make one composite shape out of more shapes and fewer shapes.


Mathematicians almost never use 1 shape by itself. Mathematicians think about how these shapes fit together to make bigger, composite shapes. Then you can use these bigger shapes to build things.


Your thinking job today is: How can I make this shape with more shapes? How can I make it with fewer shapes?

Opening Discussion

10 minutes

My goal here is for students to see how they made the hexagon and think about what they are learning about other shapes as a result-they aren't just learning how to make a hexagon, they also learned how to make a rhombus and a trapezoid. Click here for the Make a Hexagon lesson from the day before!

I'll use the online patch tool (Patch Tool Link) to show 2 of the ways students made hexagons the day before.  I'll show them one where they used 2 trapezoids, and another where they used 1 trapezoid and 3 triangles.

Guiding Questions: 

  • How are these two hexagons similar?
  • How are they different?
  • Looking at these ways to make hexagons, what does it tell me about how I could make a trapezoid? (Focus kids on the fact that the 3 triangles make the same shape)

If time, I'll do this same line of questioning with two different ways to make hexagons, but this time I'll focus on the rhombus.

Student Work Time

15 minutes

I'll present students with this challenge: You are going to get 2 copies of this star shape. Your job is to see if you can find the way to make it with the fewest number of shapes and a way with the most number of shapes. Record how many of each shape you used in the chart below.

Go to this Investigations Master Link to get the shape I used. 

Prompting Questions:

  • How could you replace one of these shapes with more shapes? 
  • I see you used a hexagon here. How did you make a hexagon before? Could you show that way in the star?
  • How many shapes did you use in total? Could you make this shape with more/fewer shapes?

If students finish both ways, I'll let them use crayons to try to represent how they made the shape. This will be very challenging for some students and will take little practice for others. It's OK if they look terrible today! As students practice representing shapes, they will get much better!

See attached pictures of student work for examples.

  • Group B Work (the "middle" of the class): Students were able to create the shape with multiple shapes but did not immediately think to use the triangles.
  • Group C Work (extension group): This child was able to use triangles to make the shape and even represent it by drawing the triangles in. This is a really advanced example of this work.

Student Share

10 minutes

We will come together and discuss how students made the shape. To make this discussion high impact, I'll hold students accountable for academic language throughout. When students explain how they made the composite shape, I'll make sure they use precise language-rhombus instead of diamond, triangle, trapezoid, etc. This is aligned to the CCSS MP6-Attend to precision.

  • First, I'll have one student share out how he/she made the shape with the fewest possible number of shapes. This is much easier for students. 
  • Then I'll have students share out if they think they made the composite shape with the most number of shapes. Whoever has the greatest number of shapes will model making it for students. 


Focus Question to end share time: To make it with the MOST number of shapes, what shapes did we use? Did we use large shapes or small shapes? Why did we need to use smaller shapes? 


5 minutes

See attached video for how I close the lesson. Here is a link to the online tool I mentioned: Patch Tool