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SBAC and PARC problems used to test CCSS are challenging and often draw upon context unfamiliar to students. This means students must navigate the content, problem solving and deciphering context. Below is an SBAC problem dealing with photo albums…PHOTO ALBUMS. Do kids today understand this? In the subsequent pictures you will see the work of one of my students on handouts I created that develop an understanding of the SBAC problem – note the “x-2″ at the end. The idea is to shape their ability to do such problems.
Dragon Box (link to website here) presents solving equations, proportions (and fractions and expressions) using an alternative representation and in a highly engaging game format (different platforms!).
In the photo above, the goal is to get the treasure chest by itself. To do this, the fly looking thing and the snake have to be eliminated. First eliminate the snake with the black background (a night card) by placing the other snake card on top of it (a day card). The day card snake must be placed on the right side as well. The day and night card (representing positive and negative numbers) become a circulating hurricane looking card (which represents a zero).
I used it with my 5 year old son (video here) and he could solve 2 step equations (on the game) independently within a couple hours. This is a game changer in teaching kids algebra.
This chart is what we use to teach students to count total value for given coins. Students start by placing coins in order from most value to least. We start with pennies only, then nickels, dimes then combinations. Students learn value of coins with initial matching then through working with the coins as they count total value.
At my school we are looking to develop a track for math for students with disability for whom the traditional math courses are inappropriate. Many of the topics and concepts from the traditional courses are addressed but in a practical approach with the principles of UDL incorporated. This is not a typical dumping ground situation that many of us have encountered. These are courses for students who need support in being independent and who will not benefit from being exposed to simplifying (5x + 2y – 3xy) – (7x – 8y + 9xy). Contact me if you would like more info!
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.
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.
The following shows steps to introducing the concept of the value of money and of adding coins.
The concept of a dime is presented as 10 pennies (see below). The dime is compared to a penny, nickel and quarter using these representations. Repeated use of these representations leads into an intuitive understanding of the coins.
Next is determining the value of multiple coins. The place to start is with pennies, which is relatively easy as the number of pennies represents the value. The next step is to count dimes because counting by 10s is relatively easier than counting by 5s or 25s.
Dr. Russell Gersten is a guru in special ed. At a presentation at the 2013 national Council for Exceptional Children he explained that number sense is best developed using the number line. With this in mind I created a CRA approach using the number line.
Upon demonstrating mastery of counting dimes, the student moves from using coins (concrete) to a representation – see photo below.
This approach is used for nickels and then a combination of nickels and dimes (corresponding blog post forthcoming).
Slope is one of the most important topics covered in high school algebra yet it is one of the least understood concepts. I have two observations about this. First, slope is often introduced with the formula and not as a rate of change. Second, students intuitively understand slope as rate of change conceptually when presented in a relevant, real life context. The challenge is compounded when slope is presented with the y-intercept.
In the photo I present slope and y-intercept in a context students can understand (money is their most intuitive prior knowledge). The highlighting makes it easier for them to see the context, specifically the variables. I have the students work on this handout and I circulate and ask questions.
Here’s a typical exchange – working through problems 11, 12:
I point out that you can find this rate or slope in the equation, the table and in the graph.
Because you should teach according to your student's needs!
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