The graphic organizer below is used to show the student the steps for addition. It also addresses the concept of addition (which I have addressed previously) as an act of pulling “together” two parts to form a whole.

The student is prompted to move the first part (set of coins in this case) to the number chart. This can be completed with 1 to 1 correspondence or with subitizing (identifying the number of items without counting). Then, the student is prompted to move the second part while counting on, e.g. 7, 8 etc. (as opposed to starting from the left and counting from the first coin: 1, 2 etc.). The chart scaffolds the counting on and allows the student to see the total as a magnitude.

It is important to first teach the students the “rules of the game”, i.e. how to use the graphic organizer. To do this have the student simply move the first part to the number chart then the second part. The student can also be prompted to state the addition problem (written at the top). When the student is fluent with these steps the counting on can be implemented.

The next step would be to replace the coins with the symbolic representation, numbers.

The photo above shows an excerpt from the presentation of notes in an algebra class using an UDL approach. The following strategies are implemented:

Graphic organizer

Color coding (notice that the slope, which is a rate of change, is green for go – movement and notice the consistent use of the colors for prior and new knowledge)

Connections to prior knowledge

Chunking (before attempting numbers the presentation focuses on the contrast between new and prior knowledge)

This allows for Multiple Means of Representation as found in the UDL Guidelines.

List all the steps for the objective. Use this table (above) as a pretest to identify gaps.

Provide instruction on the gaps. In the photo below I used color coding to show what to multiply and scaffolding to align the digits in ONES and TENS place. NOTE: I provide the problems with some steps already completed to focus on the steps forÂ which gaps were identified.

After providing instruction on the steps with gaps data is collected on mastery of these isolated steps. NOTE: The problems are identical in nature to the gaps and the problems used in instruction. (Link to the data sheets – WORD so you can revise.)

The photo shows a graphic organizer for sorting. The process of teaching how to sort involves shaping and fading of the graphic organizer. The following files show all the graphic organizers and how they are used from simplest to almost total extinction of graphic organizer.
Organizer
organizer in use

The chart shown in the photo below was created and used by my former co-teacher and I to teach students in a high school life skills program how to count out the total value for coins (dimes, nickels and pennies). Here is how we implemented it.

The students are given a pile of coins, set next to this chart.

Students start with dimes (identifying dimes as the coin to start with is a prerequisite step that can be taught in isolation if necessary)

They line up the dimes in the dimes column as shown below.

They count out the total value of dimes (and can look at the number under the last dime)

Then the students identify the nickels as the next coin to use.

The place the first nickel in the nickels column, starting at the row below the dimes (you can use a highlighter to highlight the last dime row to scaffold where the student places the nickels)

Have the student count off 5 and place the next nickel (on the dimes column) etc.

Then follow the same steps to transition to pennies.

Have the student identify the total value by looking under the last penny.

The idea is to fade the use of the chart and have the student count out the value without the chart. This is more possible if the task demand is incremented with pennies only, then dimes only, the pennies and dimes etc. Here is a link to handouts for those.