Category Archives: K

Making Sense of Problems by Seeing How They are Structured.

  By drawlins • June 1, 2017 , ,

 Kindergartners Use Dramatic Play to Model the Structure of Addition and Subtraction Problems.

Kindergartners related math stories to birds, their current social studies and science topic, by using dramatic play to act out addition and subtraction problems. Through these stories, students explored the action in different structures of problems (see chart below). Some examples of addition structure bird stories that students acted out were result unknown, change unknown, and both addends unknown. “Students who are taught to approach problems by looking at their structures through the use of a visual model are more likely to perform better than students who do not” (NCTM, 2014, pg. 50). This approach helps students make better sense of the action that is happening in problems and rely less on using keywords that can often be interpreted in many different ways (Karp, 2014, pg. 21).

An Example of Student Work Showing Change Unknown Structure Along With a Structure Diagram:

“Six pigeons were pecking on the sidewalk on Bleecker Street. Some more pigeons came to see what they were pecking at. Then there were ten pigeons.” (CHANGE UNKNOWN/ADD TO). 

Addition/Subtraction Problem Structures:

2014 Karp, Karen S., Teaching Children Mathematics. National Council of Teachers of Mathematics

2014 NCTM. Putting Essential Understanding of Addition and Subtraction into Practice

How Many Ways Can We See Six Tiles?

  By drawlins • June 1, 2017 , ,

Laying the Foundation for Addition by Exploring Parts of Six. 

Kindergarten students decomposed the number six by placing square inch tiles into different arrangements and then recorded how they saw the arrangements using numbers. One of the goals of this problem was to help students understand that numbers can be decomposed (broken apart) in many ways. Developing an understanding of part-part-whole relationships is the first critical step to grasping the concepts of addition and subtraction, properties, and algorithms (NCTM, 2014, pg. 11). For example, in later years, decomposition (part-part-total understanding) of multi-digit numbers are used in place value concepts and the operations of addition/subtraction, multiplication/division by applying the various properties of commutative, associative, and distributive.

Differentiating Through an Open Problem:

How Many Ways Can Six Tiles Be Arranged?

Each child arranged tiles in as many ways as they could. This open problem was accessible to every student in the class, and at the same time provided differentiation because of the challenging open-ended nature of the problem (see below, the same problem given at the college level). The class came together and examined all of the possible ways of arranging six tiles “side-to-side, and corner-to-corner”. Through this exploration, the geometric concepts of congruence and transformations (flips, slides, turns), were introduced. The students found 20 ways to arrange six tiles.

Six Tiles Problem by Professor David Meredith:

Below is the same six tiles problem given to mathematics students at San Francisco State University by Professor Meredith, of the mathematics department. Prior to San Francisco State Univ., David was a professor at MIT, and a Woodrow Wilson Fellow. Meredith’s students found 35 distinct non-congruent ways to arrange six tiles.

2014 National Council of Teachers of Mathematics, Putting Essential Understanding of Addition and Subtraction into Practice.