This post provides details for a discovery activity for intercepts. Students shop for tacos and burritos at Taco Bell. They are to find combinations of number of tacos and number of burritos. This will include no tacos or no burritos. The activity is provided on a Google Doc.
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.
The students are tasked with spending the entire balance of the $30 in gift cards on tacos and burritos.
They are to find all the combinations that are possible.
Students enter the combinations into a table found on a linked graph on Desmos. The image below shows the final product, upon completion.
Then they are tasked to identify the two combinations that standout in the table.
Finally, they unpack why these two combinations are unique in the graph.
At that point, the teacher can present the “mathy” term, intercepts.
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.
Budgeting is a challenging topic for many students with special needs. The process has many components, multiple steps, and involves application of money and shopping math topics. This post describes an activity to develop competence in budgeting by shopping for a food for a week with a money limit.
The activity is presented on a Google Doc and can be completed with online shopping at a grocery store of choice or at Stop and Shop. A gift card image is used to lead into a discussion or lessons on balance. This is a preview of a full budget activity shared on another post.
Identifying Food Items
The first step is to identify the foods to eat. To keep it simple, only the meals for a single day are identified and will be extrapolated to cover the whole week. This will not take into account snacks to reduce the task demand. This also leads into lessons on nutrition, e.g., identifying macronutrients and what they provide our bodies.
The student identifies the food item for each meal and enters the item, cost, and of servings. A discussion or minilesson on number of servings may be conducted first.
After shopping, the student determines if there are enough servings to cover all 7 days. If not, the number packages (bottles, etc.) are determined. This can be done by multiplying by 2, 3, 4 until more than 7 is computed. Then the total cost for the food item is computed.
Then the grand total is computed at the bottom. This leads to a discussion about the budget as the student compares the total with the amount or balance on the gift card(s).
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.
The Jamboard incorporates scaffolded handouts. The compare problems has two separate scaffolded sections. The first is to unpack the concepts of difference and compare, followed by writing a math sentence.
Here is an introductory Jamboard to help students visualize and conceptualize change situations. Here is a video you can show to help students see movement and to get an idea of how to implement.
Here is an introduction to solving equations using a Jamboard (see photo at very bottom for how to make a copy). A seesaw is used to unpack the concept of an equation as two sides that are equivalent. The box is used to unpack the concept of a variable representing an unknown number (or oranges in this context). The form of a solution for an equation is established, with students revising to create other solutions. Here is a YouTube video and a FB Reel showing how it works.
Students are then provided a couple slides to match seesaw representations with actual equations. The matching provides a scaffold to support the connection between representations.
Then the seesaw and box representation is used to unpack the steps. Students are provided the steps as written directions on how to model the given solving steps with the seesaw.
The students are then provided the equation and seesaw representation, along with the solving steps provided as moveable pieces. Students slide pieces and move seesaw objects to make the connection between the two. Here is a link to a post with an updated version of this handout.
Finally, students are given the equation and tasked with completing all of the steps including the initial set up. This slide can be copied with new equations entered for additional practice (including having the variable on the right or writing the number before the variable (e.g., 5+m=8).
Here is a Google Slides file as a follow up to the Multiplication Word Problems Matching and Creating Groups post.
Each slide has a multi-step word problem (multiplication and either addition or subtraction) that continues the use of the grouping approach. The boxes (for groups) and dots (for items) and dynamic and can be copied as needed. I suggest having an example that can be a We Do to guide the students through the use of this application. For subtraction, groups of items can be created and the dots taken away and maybe changed to red.
Here is a matching activity on a Google Slides file for various multiplication word problems and matching groups of items. The students use gallery view of the slides and sort them to match. Then they can change the background color with a different color for each word problem and groups. This allows them a visual to represent the problem and an opportunity to analyze the components of the word problems. Slide 2 shows a template of an editable group of objects to allow you to create additional slides.
Here is a matching activity on a Google Slides file for various representations of a set of linear functions: verbal, symbolic (equation), graphical, and tabular (or data). The students use gallery view of the slides and sort them by function. Then they can change the background color with a different color for each function. This invokes their analytical skills to decipher key elements of the function and of each representation, for example they may identify the value of the y-intercept in the equation and find a graph with the same value.
Below are images of artifacts I created for work on factors and Multiples. The first is a Jamboard (you make a copy and then edit). The second is a handout to introduce factors and multiples. Here is a Superteachersworksheets has these Venn Diagrams problems on handouts.