## The effort to provide intervention to fill in gaps is challenging for different reasons. One reason is the effort to balance support for current content while filling in gaps. This post shows an example of how to fill in gaps while working through the current topic.

### Overview

Various rubrics used to assess teacher instruction includes an effort to build on or connect to prior knowledge. If the student has gaps with prior knowledge, the lesson becomes less accessible for students with the gaps. Previously, I addressed how to support both current content and fill in gaps. The idea is to systematically fill in gaps by addressing prerequisite skills as they arise in new lessons.

### Example

The handout out below shows an example of how this can play out. The first page is used as a do now for the content presented on page 2. If you are teaching a student how to solve 1 step equations and are moving into integers, page 1 is a a means of supporting the new content while filling in possible gaps. The first image shows the student will need to evaluate -13 – 3 as part of the solving in the lesson. This can be addressed in the do now, as shown in the 2nd image, page on the right. (Notice all the problems on page 1 are steps to solve on page 2 problems.) This is useful for students with special needs and for differentiation.

Here is what we are doing at home during school closure time. I created a Google Classroom (anyone with Google account can create a class on the Google Classroom app) and posted links to IXL topics (photo at bottom). (NOTE: this is one method I use to differentiate at school.) If the school is providing online work, you can enter this into the classroom as well.

## Worksheet Websites I Use and Recommend

The following are screen shots of online math worksheet websites I use. The variety and the options in the criteria you select for your worksheets for some of these sites allows for differentiation in the classroom.

I will start with my favorite site, Math-Aids.com. This site allows for dynamic selection of criteria for each handout (see 2nd photo below) such as choosing the types of coins in problems for counting out the total value. The coin images are outstanding! It also offers content up to Calculus.

Super Teacher Worksheets is often used elementary schools. It offers content in science and language arts as well. It requires a \$25 annual subscription which I easily find to be worthwhile.

Common Core Sheets is very useful site if you want to find handouts for specific standards by grade level (see 2nd photo below). It offers multiple versions of each handout.

Dads Worksheets provides a large bank of worksheets – multiple versions of each worksheet.

Math Worksheets 4 Kids offers multiple versions of each worksheet and content in science and language arts. There are many worksheets that provide unique support in how the work is presented, e.g. the Ratio Slope worksheet shown in the 2nd photo below.

Visual Fractions – title speaks for itself.

Worksheet Works is my 2nd favorite. It offers options in the criteria you choose, e.g. difficulty level (2nd photo below). They also offer unique types of handouts such as a maze with math problems to solve to find the path (2nd photo).

## Counting Money as a Game

The Allowance Game is retail game tailored to students who are learning to count money.

I revised it to make it more authentic and more functional.

• I changed some money amounts to necessitate the use of pennies (see below)
• I use real dollars and cents to provide more opportunities to handle real money
• I differentiate by creating different task demands. For example
• I was using the modified version with 2 clients
• One was learning to count out dimes and pennies only, but could manage ONES simultaneously
• This student would also be provided a coin chart I use to teach students how to count with coins
• The other was practicing with ONES, and all coins up to a quarter
• I collected data on a data sheet – 1 per student

The students loved playing the game, it was engaging so they practiced the counting out money, I was able to collect data, and I was able to differentiate. When I co-taught a Consumer Math course, I would assign a para (instructional assistant) to facilitate the game with a couple students and to collect data.

## 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.

## Basic Skills Older Students

A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5Ã·2. Often the challenges arise from learned helplessness developed over time.

How do we address this in the time allotted to teach a full secondary level math course? We cannot devote class instruction time to teach division and decimals. If we simply allow calculator use we continue to reinforce the learned helplessness.

I offer a 2 part suggestion.

1. Periodically use chunks of class time allocated for differentiation. I provide a manilla folder to each student (below left) with an individualized agenda (below right, which shows 3 s agendas with names redacted at the top). Students identified through assessment as having deficits in basic skills can be provided related instruction, as scheduled in their agenda. Other students can work on identified gaps in the current course or work on SAT problems or other enrichment type of activities.

• Provide instruction on basic skills that is meaningful and is also provided in a timely fashion. For example, I had an algebra 2 student who had to compute 5Ã·2 in a problem and immediately reached for his calculator. I stopped him and presented the following on the board (below). In a 30 second conversation he quickly computed 4 Ã· 2 and then 1 Ã· 2. He appeared to understand the answer and this was largely because it was in a context he intuitively understood. This also provided him immediate feedback on how to address his deficit (likely partially a learned behavior). The initial instruction in a differentiation setting would be similar.
• ## Making Formative Assessment Formative

The photo at the top shows a portion of a cumulative formative assessment for a student in algebra 1 part 1. At the bottom is a handout with problems aligned with the formative assessment. A copyÂ isÂ made for each student and the student is assigned (usingÂ highlighting) problems on this follow up handout that are aligned with problems missed on the assessment. This allows for differentiation and formative assessment for the whole class – not an easy task. Â (Note: in this post the samples are not for the same student.)

## Streamlining Differentiation

Photo below shows a grid I use to identify the daily activities for my 12 high school Consumer Math students (all with IEPs) in an 86 minute block.

Our daily agenda is comprised of a warm up puzzle (to get them settled and to allow me to coordinate with the other adults – between 2 and 4) and two rounds of activities. Each column is used for a student. The “C” indicates computer use (we use IXL Math mostly and have 4 computers in the room) and the colors indicate the adult supervising.

Each student has a manilla folder which contains all handouts needed, including the daily puzzle, and the IXL modules to complete taped to the inside front cover.

Â

In a given day we may have different students counting nickels and pennies, identifying coins, identifying bills needed to pay a given price, computing sales tax and total price and creating a monthly budget on Power Point, with photos. The system allows me to track the many details.