Research One Hundred

Since our number system is based on ten and the powers of ten, counting to one hundred is an awesome feat for the primary learner.  They soon hear the words, thousands, and ten thousands.  Realizing one hundred is complex and needs to be addressed in a constructual way.  By first grade, the students are learning ones, tens and a single unit of one hundred.  Fives and tens can become a mental milepost.

Young learners must learn to know numbers from one to one hundred by intellectually sensing the milestones of 10, 20, 30, 40, 50, 60, 70, 80, 90.  A second grader may have little connection to the number 54.  It could be just a number in counting.  It may be a collection of 54 objects.  He may understand that it comprises five tens and four ones.  The real question is how is it related to 44 and 64?  Unless these students can relate that 44 is ten less than 54 and 64 is ten more than 54, they have not constructed the number in a deeper sense.

The hundreds board is a great tool with so many possibilities.  It help students coordinate tens and ones, two-digit numbers begin to take on meaning in relation to other numbers.  Students can visually examine that 15 is above 25 and is 10 more.  It takes practice.  We of course start at the far right at 10.  This is so familiar because the students are accustomed to counting by tens to one hundred.   After explanation and practice, the young learners will see that every step down is ten more.  Every step up is ten less, wherever you land on the hundreds board.

This illustration is from Coming to Know Know Number, Grayson Wheatley

One game I keep for first graders is hundreds board puzzles.  The small hundreds board is cut up into puzzle pieces.  The students work with a partner to put the pieces together to properly reconstruct the board.  I always have a hundreds board on display in the classroom.  Using a blank hundreds board will help the students move from counting on to constructing an abstract number model with patterns and their relationships.

As a class warm-up, you can place a nickel or penny somewhere on a blank hundreds board transparency.  Ask students what number belongs in this spot?  Have the students share their strategies in their decision.
Repeat this activity several times a week.

Coming to Know Number, G.Wheatley, 1999

Take a blank hundreds board and cut it up into irregular pieces as seen above.  Put a random number in one of the boxes.  (Make sure that it logically fits on the hundreds board)   For convenience sake, laminate these pieces to use with white board markers for re-use.  This another abstract collection created by the student that empowers deeper learning.  It forces the imagery of patterns and their relationships.

The hundreds board is an excellent tool to reinforce collections of grouping or adding.  It can also be a tool for deconstructing or subtracting.  Teachers use Doubles (5 + 5 or 6+ 6), Turnarounds, (4 + 5 or 5 + 4).  Also, there is Doubles Plus One, (5+ 5 = 10 so 5 + 6 = one more, 11.  The pattern relationships continue with counting by twos, fives, tens (count by tens irregularly with numbers like 6 or 9 instead of 2, 5 or 10 that we automatically go to.  This makes the hundreds board a whole unit made up of single parts of one.

Teachers are able to stretch these lessons to " less than" and "more than".  What comes before, what comes after?  At the top of this post the hundred board if highlighted to show odd and even numbers.

One way I taught odd/even is the following.  If the number is even, say, 6, pretend this is six friends.  Do all the friends have a partner ( or buddy)?  The students would start out drawing six circles and draw lines to see.  Yes, everyone was connected to a partner.  Then we have an even number.  No one is left out!  Somehow this really resonated with the young students and they wanted to repeat it to the classroom teacher and classmates.

  Over time and practice, I explained that we only had to concern ourselves with the numerals 0,1,2,3,4,5,6,7,8,9 in seeking out odd and even numbers.  Very quickly, the early learners understood how to master this activity.  I later extended this lesson to explore that even in two digit and three digit numbers, it is still simple to find the odd and even number.  I directed them to underline the number in the ones place (repeatedly).  This number in the ones place determines whether the whole number is odd or even.