A hidden treasure is the Common Core of State Standards Math Coherence Map. It is an interactive flow chart that shows connections between the various standards.
If you are teaching math, you can see the connections between what you are teaching, what was taught previously, and how you are preparing students for their future math education.
If you are a special education teacher, you can see the progression of prerequisite skills. If you write IEP objectives for grade level standards, you can address the prerequisite standards and progress made through these prerequisites can show progress towards mastery of the IEP objectives.
In this post, I show the progression from 1st grade standard on the = sign and 2nd grade standard of repeated addition all the way to interpreting slope in high school math.
After clicking “Get Started” you will narrow your focus to the grade, the cluster, and then the math domain.
The flow chart shows connections between a selected standard and others, including prerequisites. In this case 8.F.B.4 – 8th grade content that is a prerequisite for the high school math work. Click on the 8.F.B.4 standard and it pops up (below right).
In turn, the 8th grade standard is connected to a 7th grade prerequisite regarding ratios and proportions.
Notice that the 7th grade standard, 7.RP.A.2, appears to be a dead end (bottom left). I picked up the path by clicking on Grade seen at the top left of the screenshot and made my back to that standard and the connections to prerequisites appeared. (Same happened in 3rd grade shown further down in this post.)
The path continues from ratio and proportions in 7th grade to unit rate in 6th grade, multiplication word problems and multiplication in elementary school.
I want to emphasize that students are working on unit rate and slope problems in ELEMENTARY SCHOOL! 3.OA.A.1 below addresses groups of objects model for multiplication and 4.OA.A.2 addresses word problems involving multiplication.
I was recently working with a student entering middle school on multiplication word problems. To unpack the word problems and the concept of multiplication in context, I had her draw (photo below) groups and groups of objects to help her identify the unit rate (although we don’t use that term yet). This work will impact her math education through the high school math and even into college (slope has been a common gap for the college students in the math courses I taught at various colleges and universities).
This approach I used with the student could be used for high school students, especially those with special needs.
Most testing for IEPs involves standardized testing. As I wrote in a previous post, this is important testing but is not sufficient. A major focus of special education is to make the general education accessible as possible. Hence, curriculum based testing is an important complement to the standardized based testing. For example, the KeyMath3 assessment will speak to problem solving or geometry but those are broad categories. If I am working with a 3rd or 4th grade student, I would be interested in the student’s level of mastery in computing the perimeter of a rectangle.
Also, math is very different than reading because math has a variety of categories of math, aka domains. A student testing at a 4th grade level in math does not reveal much information, as I explain in this previous post.
When I conduct evaluations or assessments, I go to the Common Core Standards and assess each with curriculum based problems, see below. The photo shows my planning document and then I transfer the problems to a student handout for the student to complete.
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.
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).
In math, many students with special needs fall behind. What results is a Catch-22 in programming and services. If the student is provided extra time to work on the gaps, he or she likely falls behind with current content. If the student is provided extra time to receive support for current topics, the gaps are not addressed
In both cases the extra support time can actually be counterproductive.
The focus on gaps likely results in the student working on different math topics which in effect means the student has TWO math classes – just what a student with math anxiety doesn’t need.
The focus on current topics means the student is trying to learn math topics for which he or she doesn’t have the prerequisite skills needed.
I recommend identifying the prerequisite skills for a current math topic and address ing these skills concurrently in math support or during the summer. For example, I used a Common Core coherence map (top photo below) to identify Common Core prerequisite standards for the standards a student faces in her upcoming school year. Then I listed these with each grade level standard (bottom photo below). The prerequisite skills can be identified using a task analysis approach as well.
This approach allows for a systematic approach to fill in gaps and to prioritize when they are to be addressed. When implemented effectively, the student can see the immediate benefit of the support time – it helps them in math class. Even better, the support teacher can match instruction and work with what is covered in math class.