Documenting Learning

Learning How to Add in Grade One

The process of learning how to add is an important concept we teach in grade one.  Before we can begin to introduce the concept, students must have some prior knowledge of number, they must have mastered one to one correspondence, and they must be able to grasp the idea that a symbol like (+) can mean you must combine two numbers.

The Instruction

When I begin to introduce the concept of addition, we begin by using ourselves and our classmates to tell "stories".  Children at this age have grasped the concept of a story, they know that characters are introduced, something happens and then it ends.  When I start with addition stories, I let them know that we are going to learn all about addition.  All about adding two numbers and finding out what they equal (this is the first introduction to this concept). I begin by telling a story using them, for example: One day Jenna and her friend Martina were walking, (Jenna and Martina would come to the front of the room), suddenly Scott and Stephen jumped out and scared them, (the two boys would act this out).  The four of them decided to go and get some ice cream together.  After telling a few stories like this I divide the class into small groups of at least 5 children and have them decide who will be the story teller and who will be the actors, they then take turns telling stories.  

      Children's Responses           

After one of these sessions I overheard students talking about what they understood about the addition process:  "Adding isn't hard, it's just putting things together, it's just like counting", "yeah, this is easy"  When I hear these casual comments I know that a) the students understand they are combining things and b) they have experienced success and are ready to move to the next level.

The Instruction

The next time we meet I'll remind the students of the previous stories and ask them to tell me what they remember.  I'll then have them find a partner and using manipulatives and a story board, tell stories to each other trying to use the math language; ___ and ___ makes ___, or __ plus __ equals __ in all.  As I walk around the room listening to their mathematical stories I can hear:

      Children's Responses           

"One kitten was in the hay, the other kitten came in, then the horse and the snake came in, they were playing then the frog jumped over them, the horse screamed..." - With this conversation I can tell that this child is involved in the story but may not understand the task of combining, I might suggest that one partner is one number and the other partner who comes onto the scene is another, I would then have the partners model a story for me. 

I also hear "there were two cars on the beach, two people came in, now there is four, the one car drove away, this car stayed..." - This tells me that this child understands the concept and is ready to learn about separating as well.

The Instruction

I give children lots of opportunity to practice this story telling.  When we are ready I have them use a simple manipulative like bingo chips or buttons and have them act out my story.  Two bingo chips plus two more equal (they would show me two chips, put two more on and count how many are there now).  In partners children copy this format to experiment with addition to 10.  As I circulate I listen to the conversations for the language that tells me they understand; plus, now I have, equals.

When I find a small group who have mastered the manipulative forms of this process I have them meet me in small groups of 5 where I can show them how to use numbers and symbols to record the addition process.  We write on chalkboards initially and practice making + and =.  At this stage it is easy to recognize and document how children are grasping the concept, by looking at what they are writing we can easily see if they understand.

Moving from the concrete into the abstract understanding...

After we practice with manipulative and children have mastered the language and the concept of combining numbers.  I move onto solving questions that first have pictures illustrating what we have practiced into ones that only involve numbers.  When we get to this stage we begin to discuss different strategies for addition, we have learned the first strategy; using manipulatives.  I then ask them what else they could use to solve the problem.  Quickly they suggest using their fingers.  We practice with this strategy for some time, as we come to larger numbers, we find that we just do not have enough fingers.  This is when I suggest "counting up" as a strategy.  We put the highest number in the problem in our heads, then use our fingers for the other number and count up to find the solution.  I make sure that children have many opportunities to practice these strategies, as a way to document their learning, I have them divide into partner groups and record one strategy they can use to solve addition problems.  They record this strategy using pictures and words.  Here are some examples:

      Children's Responses           

	Here the instructions are written with arrows to follow along.  These children know how to use your fingers to add - an effective strategy for them!
These children also use their fingers to add, they have drawn talk bubbles to further explain  the process.
	These children have written  step by step instructions for the adding strategy of 'counting up'.
It is interesting here, how the children made many boxes to write the steps into but only used half of them.  I asked the group about this and they told me "we thought we'd need more" - perhaps addition still feels quite complicated to these children!
	This very colorful list of instructions is short and sweet!

The Instruction

As an added opportunity to practice our adding skills and to challenge the children's understanding of adding.  I incorporated "number of the day".  After our calendar routine, a child draws a number from 1-100 and we glue it onto a blank hundreds chart.  Then we decided how we could add to get that number, all the ways we can think of.  I record them on a chart as they think of the ways.  Children learn quickly the patterns you can follow to equal a number.

           Children's Responses        

For example:

Teaching the process of addition is very exciting.  It is wonderful to listen to what children have to say and how they rationalize the process.  By listening, one can understand how they have or have not grasped a concept.

Page submitted by Kathy