Making Math Accessible for All Students
The handout starts with a review of prerequisite skills of identify slope and intercept in the equation.
Below are slides from a Google Slides version.
Link to handout here. Link to Google Slides version here (make a copy to use it).
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.
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.
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.
Below is an excerpt from a handout used to introduce such word problems. It starts with the unit rate and unit quantity provided. This is more accessible for students and allows for a visual representation. This allows students to “see” the multiplication and make a connection to the word problem.
This is followed by situations in which the unit quantity is unknown. Students still draw a visual, but use the 3 dot symbol for etc. to indicate the unknown quantity.
The same problems are used but students now write the symbolic representation. First they write the expression with both factors provided, then with the unknown. The “?” emphasizes there is an unknown quantity before writing the variable.
Here is a link to the handout. It is in WORD format to allow you to enter your own problems.
The images show sections of a handout. Slope is a measurement of a graphed line. It measures steepness and also indicates direction. The handout starts by drawing on prior knowledge of measurements for newborns.
Prior knowledge of steepness and up and downhill are invoked.
How to measure steepness is introduced through a focus on stairwells.
The measurement of the length and height of steps leads into the rise and run of a hill. I use “right” and “up” or “down” which focus on direction. The terms “rise” and “run” can be addressed subsequent to the introduction. This part of the handout is scaffolded to reduce task demand and focus on the concept.
Finally, the students are provided a line and apply the ratio procedure. Note: the slopes are not the same as in the prior section.
An accompanying Jamboard will eventually be shared in this space.
This post outlines an activity to introduce linear functions (or scatter plots). The students are tasked with shopping for a used car – a specific make and model. They go to Carmax.com to find mileage and price for 10 cars for sale. They have to find a make and model that has at least 10 cars and can change the search radius to include all locations of Carmax as necessary.
They enter the data for each car into a table on a Google Doc. They are not to include the “k” or the “$” or “,” for price. This allows easier transfer of data. I do not use 0s for the mileage as the slope is more meaningful per thousand miles. For example, -$104 per thousand miles vs $.104 per mile.
Before they graph, you can provide them a common set of data to guide them through a trial run. This way you can show them your graph of the data to allow them to verify that they did it correctly. The data sets shown below are linked at the bottom of this post. (This can be useful for introducing systems of equations as Mustangs typically have a higher intercept and a steeper slope, which allows for a cluster of dots from both in an intersection.)
They copy and paste the mileage and price into a Google Sheet and attempt to graph. You can provide a link to a YouTube video on graphing a scatter plot to free you up to help individuals. The title of graphs should have the variable(s) and the individuals under study. A subtitle can be included to show when data was collected or a data set was accessed. The variables should include units.
A next step would piggy back off of this activity with a Jamboard addressing mileage and price to help students interpret scatter plots.
Here are links to items used for this activity.
There is a difference between proportional relationships and linear functions, which is addressed in another post. Proportional relationships are a subset of linear functions. They can be used as an entry point by citing it as prior knowledge and then showing how they have a constant rate of change.
The students complete the table with the images then the table with the variables. This leverages the context to help them make sense of the table and graph. You can follow up by asking them the total for 0. This allows you to highlight the intercept.
Linear functions are introduced in similar fashion, including with 0 toppings for the intercept.
Here is a link to the handout.
Here is a link to the document, with images showing the notes. This is a mini-lesson with the following components.
