Ant Math

052014_4409You might have noticed some oddly shaped “art projects” coming home this week.  They seem to be shrunken  boxing mitts or maybe another attempt at creating our own lungs.  However, you are missing the main ingredient.  Black beans.

Yes, I did say black beans, but the children wouldn’t think of them as such.  In their minds, they are ants.  The two larger ovoid shapes are ant chambers connected by a tunnel.  These abstract pieces of ant inspired architecture are the basis for our latest math mat.

In Pre-K, we practice early addition and subtraction concepts through the use of stories, frequently using a math mat as the backdrop.   By playing with manipulatives as they combine and separate groups, the children gain a strong understanding of the relationships between numbers.  They are also learning to identify the vocabulary used when making and breaking sets.

Now that it is at  home, you can join in on the fun.  Ask your child to tell you a story using any small manipulative.  It could be tiny toys or small, dried beans of your own. Now make one up for them.  You can play this as a game where you move the manipulatives and find an answer when your child tells the story and vice versa.

 

Here are some examples to start you off:

Once upon a time, three worker ants went to check on the queen.  Later, two more ants came. How many ants were there all together?

One day eight ants were walking through the tunnels.  Four ants stopped in the sleeping chamber for a nap. How many ants were left?

 

Ways to Make 10

Often, parents and grandparents wonder when we’ll start teaching Math in Pre-K.  What they are really wondering is when we’ll begin using traditional equations to represent abstract mathematical data.  To be honest, you won’t find many traditional equations in Pre-K.  Instead, we focus on the underlying concepts needed to understand adding more to, or taking some away from, a set.

For the past week, we’ve been exploring making sets of numbers in more than one way.  With our first experiment, we used two colors of links and asked the children to make a chain of 8.  As the children had not yet been exposed to this type of activity, they naturally fell back on what they knew.  Without any further prompting, every child made a pattern with the two colors of links.  This vividly showed us that, although they had a strong understanding of patterning, they really weren’t sure what we were aiming for with our seemingly vague directions.

So, after a few Morning Meeting discussions and rearrangements of link/chain distribution over two days, the children began to see what we were practicing.  Once they were able to design chains with two colors to make sets of 9 with confidence, we moved on to more complicated directions.

Our most recent attempt opened up the number of colors available.  Each child was free to choose any two colors and create a set of 10.  Their goal was to try to come up with a set that didn’t match any other student’s.  As you can see, at this point, most of them are still focusing on the color differences rather than the quantity differences within the sets.  They are just beginning to realize that some of the number sets look the same even though the color sets differ.  As we continue to practice this way of thinking, the properties of sets will become more solid for them.

Mystery Project 101

Last week we began our first “Mystery Project”.  You might have noticed it penciled into the weekly specials schedule.  The basic premise of Mystery Project was inspired by TLC Lessons I used many years ago in Kindergarten.  This type of lesson is called a “directed art lesson”, but I would never call it an art project.  I would call it a “following directions math lesson”.  In my mind, an art project should be a creative expression of a person’s mood, thoughts, and ideas.  Instead, Mystery Projects have specific directions for completion and practice targeted skills.  I no longer use the designs and lessons created by the TLC group, but have integrated some of their ideas for introducing scissor and folding techniques in my plan.

The Mystery Project you see on the right was created using basic shapes.  Each child had a brown rectangle, a white rectangle, a large blue rectangle, and a black square.  The children had to listen carefully to see which piece to use and whether to hold it “like a window” (horizontally) or “like a door” (vertically).  We did talk about the correct mathematical terms, so if they start laying on the floor and talking about horizontal, don’t be too surprised.

The children also had to practice patience when learning how to cut the shapes.  When doing Mystery Projects, we often want our rectangles and squares to become ovals and circles.  For children who have had lots of experience cutting, their first plan is to begin trimming around and around and around the outside edge until they have a teeny, tiny ovoid.  I teach them a different method.  The first step is to use your scissors to cut off all of the corners.  Next, you take itty bitty bites with your scissors to cut off all of the pointy parts.  This gently rounds your shapes while remaining close to the original size of the rectangle/circle.  It is also important to address the fact that sometimes we accidentally cut off too much.  No Biggie! Just snip off the newly formed pointy parts.

A few days after our pictures were completed, we moved on to the manipulative portion of the mathematics activity.  This part of Mystery Project was inspired by my experiences with Problem Solving with Story Boxes.  In this instance, we are using our “math mat” to tell the story of some bears and their interactions with a cave and a child.  I begin the lesson by telling the children a story that they can “act out” on their mat.

Once upon a time there were three bears in the cave.  Then, four bears came and stood on top of the cave.  How many bears were there all together?

For this story, we used rocks to represent bears.  Mrs. Pless and I were looking at a few different skills as we watched how the children approached this problem.  We observed an understanding of positional words, comfort with one to one correspondence when counting, and an understanding of combining sets.  Most of these skills we do not expect to see fully developed at this time, but this gives us a chance to both differentiate for those who are ready and to support those who are at the beginning of their mathematical journey.

As a final practice, the children then join with a partner and play “My Turn, Your Turn”.  Each student invents a new math story for their friend to act out using their mat.  This gives us an even better concept of how well the children understood the activity.