## Adding ones digits in 2 digit numbers with carrying

**Tagged**2 digit numbers, add, adding 2 digit numbers, adding with carrying, addition, base ten blocks, carrying, once place, ONES, place value, TENS, tens place

.

Math is often considered an esoteric set of information that is disjointed from the reality people face, aside perhaps from money. Sadly, in school, especially in older grade levels, math is indeed presented this way.

A situation as simple as riding an elevator provides opportunities to show and engage a student with math applied in authentic and common situations. For example, the elevator buttons address counting and cardinality (4 indicates a total of 4 floors – ignoring the R), comparison (if we are on floor 2 and need to go down, which floor do we go to?) and measurement (height above ground floor measured in floors). Such situations also provides opportunities for generalization into other settings – the important settings of every day life!

Below is a photo of a typical worksheet for money. I worked with a parent of a high school student severely impacted by autism and she explained that her son worked on nothing but worksheets when he worked on math. For students with more severe disabilities the worksheet is not real or meaningful. The photos and the setting is abstract.

Below is a photo of shelves in a mock grocery store we set up at our school for students who were in a life skills program. They would have a shopping list, collect the items in a basket then compute the total cost. We had a mock register set up (eventually we procured an actual working register) and the students made the same types of calculations they would on a worksheet but in an authentic setting, which was more concrete. We would start with simple money amounts, e.g. $1.00 then make the prices increasingly more challenging, e.g. $1.73.

I have algebra students, in high school and college, who struggle with evaluating expressions like 2 – 5. This is a ubiquitous problem.

I have tried several strategies and the one that is easily the most effective is shown below. When a student is stuck on 2 – 5 the following routine plays out like this consistently.

- Me: “What is 5 – 2?”
- Student pauses for a moment, “3”
- Me: “So what is 2 – 5?”
- Student pauses, “-3?”
- Me: Yes!

I implemented this approach because it ties into their prior knowledge of 5 – 2. It also prompts them to analyze the situation – do some thinking.

I have encountered several students who struggle with 1 to 1 correspondence with the educators struggling to figure out how to teach this to these students who continue to struggle. This post reveals an approach I used with a student.

I broke down the task using a formal task analysis approach. This approach involves identifying the different individual steps and to address these steps in isolation. Here is the sequence I use and suggest.

- Conduct a pretest using a task analysis pretest data sheet I created for this topic. I do not use any scaffolding and prompt the student to count out the objects (in this case decks of cards) and to do so independently. I prompt the student after they show they cannot complete a step which allows the student to attempt the next step. (Think of teaching a student to get dressed and he cannot put his socks on. You help him with the socks then ask him to put on his shoes.)
- I then focus on the movement of the objects. I provide scaffolding for start and stop piles (see mats with track photos above). The student is asked to move the cards one at a time
**without**counting. - The student must learn the “rules of the game” which includes how to place the items in the stop pile. Students may be confused about placement, e.g. one student ran out of room while placing the decks in a straight line and I had to demonstrate that it was OK to place them on different spots on the mat. Once the student demonstrates mastery of moving the items we move on to the next step.
- We then focus on counting in isolation. The card decks are labeled with numbers (photo below) and the student does not move anything but simply reads the numbers. (More on these numbers in a later step.) More numbers can be added as necessary.
- The next step (photo below) is to have the student read the number on each card. I have a stack of decks of cars on the start pile with the numbers facing down. I show the student the number of the deck that
**I am moving**to the stop pile and the student reads off the number. I place the used deck face down to hide the number. This activity forces the students to focus on each item as he reads the number. One student kept counting ahead to the next number and I prompted him to return his focus to the current number.**This is the crucial step as it focuses on the 1 item 1 number aspect of counting.** - The next step is to have the student move the decks from the start pile to the stop pile and to read each number while doing so. I turn each deck face up as a prompt for the student to move and read.
- The student then is prompted to select the cards on his own and read (the cards can be in a pile in order by number).
- Eventually 1 then 2 then 3 decks have the number missing which adds an extra task demand for the student – identify the next number as he is moving the item.
- Finally the items do not have any numbers and the student counts, with the mats eventually be faded.

Note: this is especially effective for students with ADHD because it helps to focus and organize their task demand for the activity of counting.

%d bloggers like this: