Making Math Accessible for All Students
Many students struggle with writing equations for linear functions, even with only 2 parameters to fill in (slope and the y-intercept are parameters for the equation). This approach make a connection between the table and graph with the equation. The relevant, real life context helps students.
Link to YouTube video showing how to present the activity.
Link to Facebook Reel showing presentation.
Link to Google Slides used in video – make a copy to edit.
Link to handout used in the presentation.
Here is a link to a Jamboard for presenting the transformation (you click on the negative sign and rotate and slide it).
Here is a link to a video showing how this transformation. This video addresses the underlying concept of the transformation by showing an IOU being cancelled.
The slide show below presents all 4 pages.
Here is a link to the student handout, and a link to the teacher handout.
The introduction is presented on a Google Jamboard, to allow for movement in the pairing of inputs and outputs. It starts with analogies pairing of items using a gumball machine and a Coke machine and proceeds incrementally towards the various representations. The functions are contrasted with examples of relationships that are not functions.
Here is the link. To access the Jamboard, you need to make a copy.
The activity is presented on a Google Jamboard, which provides manipulatives. It begins with a relevant context for students, money and being paid for a job. This allows them to engage the function using money. Before using numbers, they engage the work context through images. They are presented the table and then graph representations of the function before getting into the equation. Here is a FB Reel showing the movement of the images.
There are 3 categories of slides. Here is a description of each.
Here is a link to the Jamboard. You need to make a copy to access it.
I have previously posted about a running bank balance, gift card balance, and a comprehensive set of budgeting activities. These are activities that simulate various aspects of budgeting. When I co-taught life skills math, we took the students on a field trip to the grocery store. It was then I saw the quantum leap in task demand for shopping in an authentic setting compared to the simulated activities we created at school.
To help a student unpack the concept of a spending limit and the act of overspending, I created an in person shopping experience at Barnes and Noble. I purchased a gift card with a balance of $1 (image below). The student I was helping was tasked with purchasing an item that cost over $1. He had experience with ordering and paying on his own with enough money provided. This time he was in a position to overspend. I was ready with cash and stepped in. This allowed him to experience, firsthand, the overspending and budget situation.
Clearly, we must take into account the level of anxiety a student may have with such an activity before undertaking it.
The artifact is chunked to incrementally move from multiplication of whole numbers to whole number and fraction to multiplication of fractions. The representation of multiplication as number of objects in a group times number of groups is the structure used throughout. Cookies on a plate is the context used to draw upon prior knowledge and make the idea more concrete.
This serves as an introduction. Each chunk can be followed by practice before moving on to the subsequent chunk.
The Jamboard starts with a representation of multiplication as groups of objects, first with the number of objects in a group and the number of groups. This is presented first as cookies per person to connect to prior knowledge. Then presented per plate as the plate is subsequently used to model the fractions.
f
First, whole number times a fraction is presented. This allows for a connection to prior knowledge and introduces fractions in this representation. There are still 6 cookies per group, but now there is only 1/2 a group.
The students can move the cookies onto the plate to see the group of objects. Then they can cut the group in half.
To help make sense of the fractions used in the multiplication of two fractions, the fractional parts of the cookies are presented first.
For multiplication of fractions, the process is the same. There is 1/4 of a cookie in each group, then there is 1/2 a group. As was done previously, 1/2 the group is removed. Conceptually, you can explain to the students that they have 1/4 of a cookie and they split it with a friend.
Here is a link to the Jamboard. You need to make a copy to access it.
Student prior knowledge is leveraged to provide a meaning making activity. The concept of intercepts is developed through 0 tacos or 0 burritos. Here are the steps for the activity.
Below are images of a Google Doc with the activity. You have to make a copy to edit it. Here is the link to the Demos graph with blank table and labeled axes. It is included in the Google Doc.
I provided a student with a $10 gift card to buy a hot chocolate at Barnes and Noble. This experience allowed the student to order, pay, and monitor the balance. At some point the card will not have a balance to cover another drink. Not only does this provide real life experience, it provides an anchor for other instructional activities.
The student identified the price, the tax, the total, and the balance. Then he computed the balance to see for himself how this works.
In our instructional setting, the student is provided an image of a gift card on a Google Slide and is prompted to buy 1 item at a time. This allows for immediate computation and tracking of a running balance.
In the image below, you can see a prompt for the student reflect on how the balance is computed by referring to the in person experience. I have the student compute on Google Calculator to allow me to record the work.
The running balance is recorded on the Google Calculator image ($18.75 below) and the next item is purchased with a new running balance computed.
I am in a position to conduct in person instruction at other settings. Obviously, most teachers do not have this opportunity. My recommendation is to collaborate with a parent to facilitate such activities. For example, if the family is going out to eat, the student can be provided a gift card and allow him or her to choose an item and pay independently. Another possibility is that the parent provides a student an e-gift card to spend during class with the teacher.
The Jamboard is configured in similar fashion as the Jamboard used for the Product and Quotient Rules. The exponential terms and variables are moveable parts. The background is a scaffolded to guide the decomposition. Here is a FB Reel and a YouTube video showing how it works. NOTE: I decompose the expression down to individual X values in lieu of using the Product Rule because I want them to see how many Xs there are. Also, the Product would be relatively new to them, I wanted to reduce the task demand placed on the working memory.
Here is a link to the Google Jamboard. To get access, you must make a copy.
