More Ways Than One

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Objective

SWBAT create the same shape using different combinations of pattern blocks.

Big Idea

Students explore ways they can make a given shape using a different number of pattern blocks. Students push their number sense with the challenge: Can you do it with more shapes?

Setting Up the Learning

5 minutes

CCSS Context:

In this lesson, students use concrete manipulatives to practice building composite shapes (1.G.A2). This lesson offers students open-ended opportunities to problem solve and use structure. This is specifically aligned to MP7, Make use of structure. Students start with open ended exploration of the shapes, but then practice making specific shapes that might help them fill pattern block puzzles more efficiently. If students know that they can put two triangles together to make a rhombus, they can use that understanding to build shapes in different ways. 

Review:

We have been learning about shape names all week. To practice we will review shape names and the anchor charts we have around the room about flat shapes.

Connect to the real world:

In the real world, we have to put shapes together to make new, composite shapes. When you grow up, you may be a designer. Designers have to think about how to put shapes together to make art, furniture, even bridges!

Objective:

Your thinking job is: How do all of these shapes fit together? How can I make one shape in other ways?

Opening Discussion

15 minutes

Brainstorm:

This will be my students' first time really interacting with the pattern blocks, so I budgeted some time for exploration of the tool before we discuss strategies for combining the shapes. 

First, I'll have students brainstorm what they could create using their shapes. I'll post a list of objects students could attempt to build with their shapes. Examples might be a rocket, flower, house, a cat, etc. I'll make sure to clarify to students that we are making flat shapes, not stacking the shapes right now.

 

Student Exploration:

I'll then give students some time to experiment with how the pattern blocks fit together. As I circulate, I am going to be paying attention to how students are thinking about putting them together.

  • Are they using trial and error to see I they fit together? 
  • Or are they putting sides against sides right away? 

 

At this point, this is purely formative data. By the end of the lesson, I want students to put sides and sides to create composite shapes efficiently. However, we will practice that more in the student share.

Guided Exploration

10 minutes

Partner Talk: What are some of the things you created?  What shapes did you use to create your design? 

"Now that you have had some time to explore with the pattern blocks, we are going to think about how the shapes fit together. This will help you use the shapes even more efficiently when you get to build composite shapes." 

I’ll give students shapes to work with at their desks. I’ll also have them work with a partner to give each other ideas on how to make the shapes.

 

Guiding Questions: These questions move from the most basic to the most complex. Students at first create a fairly basic shape, the square. But then students have to analyze whether or not shapes are possible to create. 

  • Can you create a square using shapes other than squares?
  • Can you create a rectangle using shapes other than rectangles?
  • Can you create a trapezoid?  A triangle?  A circle?
  • What shapes were you able to create?  How did you do it?
  • What shapes were impossible to create?  Why?

 

Independent Practice

15 minutes

Students work on creating a shape in multiple ways. Students also attempt to represent what shapes they used to fill the puzzle. 

Group A: Intervention

Students get a pattern shape and show at least 1 way to fit the pattern blocks inside the larger shape. Students record how many pattern blocks they used.

Group B: Right on Track

Students get a pattern shape and show at least 2 ways to fit the pattern blocks inside the larger shape. Students record how many pattern blocks they used.

Group C: Extension

Show one way you can make it with MORE shapes. Show another way you can make it with FEWER shapes.

See this link for the document I used. These documents are from the Investigations curriculum, but are available in pdf form. For Group A/B, I am just now focusing on the more/fewer aspect. 


Closing

5 minutes

Students share one way they created the shapes with a partner. Students compare how they did it. 

Sentence stem I'll give them to aid in conversation:

Partner 1: To fill the puzzle, I ______.

Partner 2: I did the same thing/I did something different.