Adding ones digits in 2 digit numbers with carrying

A major obstacle in math for many students with special needs is carrying in addition problems. Below is a task analysis approach.

First, I target the step of identifying the ONES and TENS place in the 2 digit sum in the ONES column (below it is 12). In a scaffolded handout I create a box to for the sum with the ONES and TENS separated. At first I give the sum and simply have the student carry the one.

sum of ones given.jpg

Then I have the student find the sum and write it in the box (14 below). Once mastered I have the student write the sum and carry the 1.

sum of ones given

They would have mastered adding single digit numbers before this lesson. I revert back to single digit numbers to allow them to get comfortable with writing the sum off to the side without the scaffolding. (In the example below I modeled this by writing 13.)

sum of ones with color no scaffolding

The last step is to add the TENS digits with the carried 1. I use Base 10 manipulatives to work through all the steps (larger space on the right is for the manipulatives) and have the student write out each step as it is completed with the manipulatives.

sum of ones with carrying with base 10 blocks first

Finally, the student attempts to add without the scaffolding. I continue with color but then fade it.

adding 2 digit numbers with carrying with color no scaffold

Place Value Representation

Here is an easy way to create and implement strategy to unpack place value for students (created by one of my former graduate students). I suggest using this after manipulatives and visual representations (drawing on paper) in a CRA sequence. It is hands on but it includes the symbolic representation (numbers). Hence is another step before jumping into the mathy stuff.

pace value representation just numbers.jpg

The focus can shift to money as well.

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The I in Instruction can be the same I in IEP and IDEA.

I am consistently surprised by the reliance on canned items for students who struggle. There are different reasons students struggle but we know that there are secondary characteristics and factors that inhibit effective information processing that can be addressed with some Individualization.

In a math intervention graduate course I teach at the University of Saint Joseph, my graduate students are matched up with a K-12 student with special needs. The graduate student implements instructional strategies learned from our course work. Below is the work of one of my grad students. From class work and our collaboration we developed the idea of using the fish and a pond as base 10 blocks for the student my grad student was helping. He likes fish and fish will get his attention. The grad student explained that if he has 10 fish the 10 fish go into a pond. In the photo below the student modeled 16 with a TEN (pond) and 6 ONES (fish).

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Similarly, another student likes Starbursts and that student’s respective grad student created Starburst packs to represent TENS and ONES (there are actually 12 pieces in a pack so we fudged a little).  The point is that it was intuitive and relevant for the student. The student understood opening a pack to get a Starburst piece.

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