## This post details a scaffolded approach for multiplying multi-digit numbers by 2-digit numbers. It was originally created for a student with ADHD who understood how to do the multiplication but would rush and repeatedly made simple mistakes. It is useful for all students.

This grid and color-coding strategy was used as a means of slowing him down. He had to alternate between highlighting and writing each product for an individual multiplication of two digits. This turned out to be an effective way to teach multiplication by 2-digit factors, in general. Here is how this works.

First highlight the ones-digit in and the row for the product that results from the ones-digit. This helps unpack the place value and why the algorithm works. Note: use a lighter color of highlighter (you will see why).

Highlight the ones digit in the top factor. Multiply the ones digits. Write the product. This is where the student alternates, which can allow for thinking through the steps.

Continue highlighting and writing products using the ones digit from the bottom factor.

Now use a darker highlighter to highlight the tens digit in the bottom factor, as well as the tens row at the bottom. Because the 3 is in the tens place, we write a zero. This unpacks the place value.

As was done with the yellow highlighter, alternate between highlighting digits to multiply and write the product in the row below. The darker highlighter is used second to make it visible when drawing over the previously used lighter color.

For carrying (regrouping), the top row can be split and the color can be used for the digits that are carried.

Here is a link to the handout used for these photos. It contains the two problems shown in this post along with blank templates. Here is a link to another post that shows a scaffold I use to unpack the carrying of a digit in multiplication.

## Workshops on Math IEP Objectives and Data Collection, and Instruction for LD, ADHD, ASD

Announcing 2 workshops for educators working with students with special needs on math. These are designed to be hands on, with immediately implementation and can be delivered to schoolwide or district wide audiences.

• Identifying, writing, and monitoring progress for IEP math objectives that will support the entire year of math and that will allow all team members to track progress
• Math instructional strategies that are designed to address challenges specific to ADHD, ASD (autism), and LD (learning disabilities)

## Effective instruction is effective because it addresses the key elements of how the brain processes information. I share an analogy to help adults (parents and educators) fully appreciate this.

### Information Processing Model

Below is a model of information processing first introduced to me in a master’s course at UCONN.

Here is a summary of what is shown in the model.

1. Human senses are bombarded by external stimuli: smells, images, sounds, textures and flavors.
2. We have a filter that allows only some of these stimuli in. We focus on the ones that are most interesting or relevant to us.
3. Our working memory works to make sense of the stimuli and to package it for storage. It is like a computer, if there is too much going on, working memory will buffer.
4. The information will be stored in long term memory.
• Either it will be dropped off in some random location and our brain will forget the location (like losing our keys)
• Or it will be stored in a file cabinet in a drawer with other information just like it. This information is easier to find.

### Analogy to Classroom Learning

Here is an analogy to what happens during school instruction. You are driving down the street, like the one shown below.

There is a lot of visual stimuli. The priority is for you to pay attention to the arrows for the lanes, the red light and the cars in front of you. You have to process your intended direction and choose the lane.

Other present stimuli may be filtered out because it is not pertinent to your task: a car parked off to the right, the herbie curbies (trash bins), the little white arrows at the bottom of the photo. There is extraneous info you may allow to pass through your filter because it catches your eye: the ladder on the right or the cloud formation in the middle.

Maybe you are anxious because you are running late or had a bad experience that you are mulling over. This is using up band width in your working memory. Maybe you are a relatively new driver and simple driving tasks eat up the bandwidth as well.

### Impact on Students

For students with a disability that impacts processing or attention, the task demands described above are even more challenging. A student with ADHD has a filter that is less effective. One with autism (a rule follower type) may not understand social settings such as a driver that will run a red light that just turned red. Another with visual processing issues may struggle with picking out the turn arrows. Their brain may start to buffer, like a computer.

### Specific Disabilities

Effective instruction would address these challenges proactively. Here is a video regarding learning disabilities (LD) that summarizes the need in general for teachers to be highly responsive to student needs. This link is for a great video that helps makes sense of what autism in terms of how stimuli can be received by those with autism (look for the street scene). Another is a video of a researcher explaining how ADHD responds to sensory input (he gets to a scenario that shows how impulsiveness can be a factor).

### What to Do

• Reduce the amount of information presented in a lesson segment, i.e., chunk the lesson.
• Use color, e.g. highlighters – this helps students see the different parts of a problem
• Use hands on and visual representations in lieu of words – words are symbolic and abstract, start with forms of information easier to process.
• Connect information to prior knowledge or make it relevant.
• Scaffold the work to provide supports for unpacking the concept, following the steps, or identifying the parts.
• Relevant situations – learn by doing. Have the instructional setting mirror the real life setting as much as possible. Better yet, conduct instruction in the real life setting.

## Long Term Effects of Disabilities

Often we view disabilities in the context of the individual as a student, or a child or adolescent. The long term effects may be had to understand or extrapolate based on what we see at the younger ages.

There was teacher candidate whom I trained who had ADHD and struggled in the program in which we worked. He shared his struggles to keep up with the programming, organization, and in general, keeping up with the demands placed upon him.

I askedÂ  him to write a statement explaining his challenges that I could share with others. The statement is shared below. I hope this can help parent and educators make a more refined connection between the setting at an earlier age with the settings and outcomes the individual will face later in life. I explain to sped teacher candidates whom I train that we have an awesome responsibility and opportunity in how we can impact young lives…when they are no longer young.

## Multiplying and Carrying a Tens Digit

Carrying the TENS digit in a multiplication problem is a sticking point for many students. To address this, I use a task analysis approach to zero in on the step of identifying the product for the ONES as a prelude to carrying.

In the example below, 5 and 4 are in the ONES place and the product is 20. The task analysis steps involved:

• compute the product
• identify the digits in the product
• identify the digit in the ONES
• identify the digit in the TENS
• Understand that the TENS digit must be carried to the TENS column

By creating a place holder for the product and scaffolding it to differentiate between the TENS and the ONES, the student can visualize the product. This reduces the demand placed on working memory. Once mastery with the place holder is demonstrated, it can be faded (and used as necessary as part of corrective feedback).

NOTE: I started this mini-lesson for a student with ADHD by having him warm up with problems without carrying. Also, extra line below the 60 and 20 are used for multiplying by 2 digit numbers (next in the sequence).

Here is a post on how I use color coding to unpack the multiplication by 2-digit factors.

## Twice Exceptional and Neurodiversity

In his 1992 trip to Australia, President HW Bush gave the backwards V for victory sign. That happens to be the middle finger in Australia.

This story parallels what we encounter in special education. Several people may encounter the same idea, image, curriculum objective, lesson etc. but have a totally different perspective (see photo below).

This is certainly true for individuals with autismÂ and is true for students who are twice exceptional.

To meet the needs of such students we must work from their perspective and not ours. We must meet their needs. We must first take inventory of our bias and our subjectivity in how we perceive students, learning, doing math work etc. Here is a site, Different Brains, that I have not fully investigated but that looks interesting and important.

## Performance vs Ability

In the effort to assess student ability performance factors are likely present. It is incumbent upon the educators to mitigate the performance issues to assess true ability.

For example, I conducted an evaluation on a student in middle school who has ADHD. All of her testing records indicated that she would lose focus during the assessment and that the focus was problematic for testing. Before we met I surveyed her on her favorite snack (didn’t know Sour Skittles is a thing), brought this reinforcer along with a bottle of water. She sat through an entire 1 1/2 hour KeyMath Assessment without incident.

## List of Performance Points

Painting the letters on the ground is a performance point for the person responsible for this task. The task was discussed at some other time and location. Performance points, as explained in another post, are the situations or locations or times that a person has to perform a task. For students with special needs this is where special education gets real. It is where the supports play out. For students with more severe disabilities, e.g. ADHD, Autism or Down Syndrome, most if not all performance points require some support so identifying these points is important and often overlooked.

Below are a list of performance points students encounter in k-12 education.

• transition between classes
• using a hall pass
• arriving or leaving school
• riding a school bus
• transition to and from lunch
• transition to and from specials
• gym
• playground/recess
• entering and starting class
• packing up and leaving class
• transition between activities during class
• choice or down time during class
• following directions given in class
• retrieving, using and returning class materials
• sharpening pencil
• asking permission to use a pass
• identifying appropriate reasons to use a pass or to ask a question
• responding to questions or participating in class discussion
• paying attention to presentations
• group work
• individual work
• homework
• studying for an assessment
• long-range projects
• bringing materials to class
• organizing notebook and book bag
• using a notebook effectively, e.g. finding and following examples
• interacting with classmates in a socially appropriate manner (during classwork, free time, down time, in the hallway, at lunch, at recess) – note: socially appropriate would need to be defined withÂ observable behaviors
• empathizing with others
• reciprocating in a social conversation
• curtailing behavior when presented with negative feedback
• initiating conversation
• greeting others appropriately – initiating and responding
• identifying non-verbal cues and communication

Certainly there are more. Please comment below if you want me to add anything to the list.

## ADHD is a Self-regulation Disorder

LinkÂ to a handout presentingÂ an overview ADHD. This handout will be used as part of a webinar to be recorded and posted on this site soon.

Below is a video by Dr. Russell Barkley on ADHD as a failure to self-regulate disorder.