Once your student understands counting with manipulatives and identifies where whole numbers fall on a number line, you can add using both of this visuals. Start with adding 1+1, put out two beans and push the one and one together. The student should come up with 2. Have the child count the one and one and then count it again as 2. Show the numbers with dots on a paper. One dot plus one dot equals two dots. Now add 2+1 and move through the same process.

1+1, 2+1. 3+1, 4+1, 5+1, 6+1…

Then add 1+2 and look at 2+1 again to show student that 1+2 and 2+1 gives you the same number of beans or dots. This is COMMUTATIVE PROPERTY. Shows that you can add in either direction and get the same thing.

Move to the number line now. Put your finger or a pencil on the number 1. Adding one means moving right by one number. This will also show that 1+1=2. Show it with beans, dots and number line for several examples.

Go back and ask if 4+5 = 5+4 to revisit commutative property.

Continue to practice single digit addition until student feels confident.

Start with Natural Numbers in another post. What you will do now is share that Whole Numbers are Natural Numbers plus the number zero. We don’t learn to count using zero. Explain the zero means nothing. Show a number line at this point. Have the students use counters (beans, pennies, cubes, etc… under each of the above numbers. Explain that there are no counters under the zero. Ask questions to see if student understands the concept of zero.

Parents and teachers, remember the importance of providing the concrete foundation for numbers. Here is an easy guide to give children a great foundation to:

IDENTIFYING NATURAL NUMBERS

Teach children how to count aloud. (1,2,3,4,5,6,7,8,9,10…

Show them what the number look like as they say them.

Show them with number of dots that each number represents. (1. 2: 3:. 4:: 5::

Show them one-to-one correspondence with a manipulative (Something they can touch and hold in their hands- beans, pennies, cubes…)

Work on natural numbers (how we naturally learn to count) for as long as needed in order to gain full understanding. Ask the child to give you a number to build.

This process gives children something to recall, a picture of in their mind. This is called CONCRETE. If students do not have the objects, they can work on the problem by drawing it if necessary. This is called REPRESENTATION. Finally using the numbers and symbols, this is the ABSTRACT. Learning should occur amongst the three forms when learning a new skill. Going straight to abstract without the concrete foundation leaves children to memorize and not truly understand WHAT they are learning.

Beginning with one-to-one correspondence teaches them that each item is counted as one. This will allow students to learn much more advanced levels when they have the opportunity to build problems with Hands-On materials.