Decomposing and Composing Appears 26 times in the CCSSM

Paula Beardell Krieg, a teacher, is always doing cool, creative art and math activities with her students. When she used ‘composing shapes from parts’ (in her tweet) it motivated me to search the CCSSM.

A common theme in the Common Core State Standards for Mathematics (CCSSM) is decomposing and composing numbers and geometric shapes.  I was a bit shocked to find ‘decompose’ 26 times in the CCSSM and ‘compose’ 28 times. Furthermore, of the 26 times ‘decompose’ appears, the first 24 uses are in grades kindergarten through 6th grade.

This goes hand-in-hand with the important mathematical practice (practices and processes that students need to develop to make them successful mathematics learners) of look for and make use of structure.  When students decompose a number or a geometric shape they are seeing (and using) it’s structure. This is both a way to understand and an aid in problem solving.

I won’t show all 26 times that the term ‘decompose’ appears, but I’ll lift up a 11 of the 26, to give a sense the the progression.

Kindergarten

Operations and Algebraic Thinking begins in kindergarten!  Decomposing numbers!

1st Grade

One of the 4 critical areas is composing and decomposing geometric shapes.

The CCSSM likes to plant conceptual understanding before the procedural details. Here, first graders are thinking conceptually and naturally about fractions using shapes. 😍

2nd Grade

Again, geometry is a critical area. Hands-on learning. building, drawing, and analyzing (AKA, decomposing and composing) two- and three-dimensional shapes.

3rd Grade

Wow, two of the four critical areas have to do with visualization.  (#3) understanding how arrays work and how it related to area (and ultimately multiplication) and (#4) describing and analyzing shapes (as in 2nd grade!).

4th Grade

#Fractions.  A theme of the CCSSM is thinking about a fraction as made up of (decomposed into) unit fractions.

5th Grade

Volume.  This is not just some random topic, but a critical area for 5th grade.

6th Grade

Yep, we need to be decomposing shapes in every grade.

Also in 6th grade is surface area of prisms (but not volume of prisms yet). Of course it is surface area by decomposing ‘into pieces whose area they can determine.’ 😍

8th Grade

Decomposing (analyzing) is beneficial for understanding and for problem solving. One more example: understanding the Pythagorean Theorem by decomposing.

It is clear that the Common Core authors felt that decomposing and composing numbers and shapes is key.

If students have a good foundation in K-8, they can face the challenge in HS Geometry (G.GMD.3) which involves volume of pyramids and the relationships between the various heights of the pyramid!