Square Boxes

From, Coming to Know Number, G. Wheatley, 1999

 The objective of "Square Boxes" or math squares is to enable students to make sense of adding and subtracting for the young learners.  These squares provide explicit ways for learners to construct their own way to make these operations more concise.

As in the scale activity, we have no operational or equal sign.  Students have to examine the boxes and base their actions on logic.  Instead of rote algorithms, the students must search the numbers and determine what to do with them.  There are always multiple ways of progressing.  The numbers are chosen to be compatible using ten as the standard base.

Introduce math squares as a whole class activity.  In the above example the teacher could direct the students by saying, "We have four rooms in this box.  We can see how many people are in each room.  How many people are there altogether?

Students are inspired to talk interactively.  Observe to see it they are using mental imagery of their tens frames.  Instigate students to discuss their different strategies to find the sum.

Another type of square may have a total at the bottom, but one or more rooms left empty.  The teacher may say, "Here we have four rooms.  We know how many persons there are altogether.  How many persons are in this room, and this room?"

After the small group activity, a whole class discussion should close the lesson.  Questions should be asked by the teacher:
   1.  Can you think of another way?
   2.  Which way do you prefer?  What is your favorite?
   3.  Did you hear an idea or method today you may use next time?  Did you write it in your journal?
        Do it Now.

 This square is an example of vertical, horizontal and diagonal ways of counting to get the same number.

There are numerous square activities where the student does have operational signs.  Some squares have numbers that add up vertically and horizontally with like sums.  There are decimal and fractional squares for third through fifth grades.  I hope to offer all of these on this blog!  We are witnessing internalized visual learning.  It enables deeper thinking processes that promotes memory retention.

Students are again allowed to explain and justify their successful experiences with this simple square.  This participation builds confidence because the learner is taking responsibility for his growing proficiency in number sense.

Problem Solving 



The last four posts have actually been examples of problem solving.  This term expresses many messages.  Most textbook plans have a four step approach.  Read the problem, understand it, decide on a solution and complete it.  Actually, a student is in a problem when there are no strategies or skills within to work it out.  We want our students to assess an exercise, construct patterns and their relationships, then mental images will be formed.  An open discussion with partners or groups is also necessary to listen to their own thinking. They also need others input or challenges.  That is why we start with the very young student with these kind of interactive activities.