CRA 5 - Standard 5.G.B.3 - October 2017

5.G.B.3

LET 'EM PLAY!

Do you have a set of these incredibly useful pattern blocks in your 5th grade classroom? If not, you should ask your school, or perhaps your PTSA, to purchase a set for you (they are great tools for later Modules when students learn more about fractions, too!). In the meantime, wander down to a Kindergarten classroom and ask to borrow their set. 

The CRA Process for Learning About Attributes

Let's begin this learning activity with time to explore. Give each group a bucket full of these shapes and let them explore. Don't direct them how to explore, just let them explore for a little bit of time. 

Okay, now that they have touched the pieces and have begun to observe their physical attributes by building towers and creating flowers and robots and houses, it's time to focus these tools on the specific learning goal: Understanding how to categorize the shapes based on their attributes. 

There are a lot of ways to approach this, so modify these ideas based on the materials you have access to in your classroom. Here's one way:

Phase I: CONCRETE

Slide this template into a dry erase sleeve. Have students determine which pieces go together and to state or write the reason why. Challenge them to come up with at least four different groupings. Debrief the various ideas by having all students place the named pieces on the work mat as each group shares their discovery. Ask them to analyze the shared idea. Here are some of the groupings you might see:

• TAN, BLUE, and ORANGE all have four equal length sides
• TAN, BLUE, ORANGE, RED all have four sides
• All of them can be partitioned into equal-sized triangles
• GREEN is the only triangle
• YELLOW is the only one with 8-sides
• YELLOW, RED, ORANGE, BLUE have at least one pair of sides that are parallel
• YELLOW, ORANGE, BLUE all opposite sides are parallel
• All are polygons
• RED, BLUE, TAN, YELLOW, GREEN do not have any right angles 

Phase II: REPRESENTATIONAL

Students have experienced sorting by attributes in a concrete manner and are ready to begin looking at this topic in a Representational manner (drawings, pictures, etc.). Use your SmartBoard with images of various shapes, including the six they were exploring previously with the pattern blocks. Add in circles, rectangles, pentagons, kites, different types of trapezoids.

Have discussions and share formal definitions for the various shapes. Create a class anchor chart. This is what the Quadrilateral branch would look like. How would Quadrilaterals fit into the broader picture of a hierarchal web? 

An even broader hierarchal model of Polygons:

Phase III: Abstract

Alright, here is where the fun begins for many of your students because they now have the concrete experience on which to build some abstract ideas. 
         – you have explored shapes and their attributes using concrete materials
         – you have used images of shapes and created anchor charts depicting the hierarchy of shapes

Now it's time to make their brains hurt a little bit....
Take a look at these two definitions of trapezoid. 
The first definition is the "exclusive" definition of a trapezoid.
The second definition shown below is the "inclusive" definition of a trapezoid. 

How are the two definitions alike? Both quadrilaterals, both mention parallel sides)

How are they different? The first says "only one pair of parallel sides" while the second states "at least one pair of parallel sides" which implies that shapes with 2 sets of parallel sides, such as squares, would also be classified as trapezoids)

Do the two definitions allow for different shapes to be included in the classification of trapezoid? Yes - the second allows for squares and rectangles, but the first definition does not allow for these to be considered trapezoids)

I know... you can't stand it!
Which is correct?!

Well, that presents an interesting dilemma because this very question is a hotly debated topic throughout the mathematics and education communities. Mathematicians consider the broader definition (#2) to be correct, while many elementary educators and educational reference materials have traditionally used "only one pair" (#1) as the correct definition.

So, which do we teach? 
We should use the INCLUSIVE definition (#2) of a trapezoid.
The PARCC Informational Guide states that a trapezoid has "AT LEAST one pair of parallel sides." That means squares and rectangles will both be classified as a type of trapezoid when our students are given the PARCC and this is the definition that is used by the mathematics community.

This makes for an exciting discussion to have with students....