Intro to Writing Equations for Linear Functions – Pizza and Toppings
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.
“All I Really Need to Know” in math is From Elementary and Middle School
A spin off to Fulghum’s book (below) is that by high school, students have been presented with almost all of the math they need if they are not pursuing college.
High school math, aside from some exceptions, is largely designed to prepare students for college and subsequent careers.
If your student is entering high school and does not have a postsecondary goal of college (2 or 4 year) then you can turn the main focus of the math education to topics covered before high school.
Some of the topics in geometry and statistics are applicable to real life and most of those would have been covered in the Statistics or Geometry and Measurement domains from previous grades. There are topics unique to high school math that are prerequisites for some vocations, e.g., trigonometry for surveying. Some applications of the high school math address real life, but the focus is on the math and not the applications.
The image below shows a breakdown of a sample of topics for life skills math and for two vocations. Here is a link to a PDF of the document shown above. You can see the math topics. Here are the links to the pages for the plumbing topics and the welding topics.
Related to this value of college education for certain job sectors. The director of the Office of Higher Education in Connecticut, Tim Larson, stated that many companies have proprietary software, programs, or procedures that they will teach new hires. The take away from this is that much of the actionable knowledge needed would not be covered in college. Many of the skills they are looking for are not academic in nature. The Wall Street Journal published two articles that speak to the change in requirements for some jobs, in which a college degree is no longer a requirement (“Rethinking the Need for College Degrees“, “Is this the end of college as we know it?”)
A college education (or at least the degree) provides incredible opportunities, but it is not needed for many students.
Helping students understand and implement a monthly budget is challenging, especially for students with disabilities that make it harder for students to conceptualize abstract ideas. I previously posted about a full budget activity. This post shows a means of scaffolding the concept of partitioning money in a budget context. The idea is to keep it simple for now and build from there.
A parent of a student I support came up with the following idea. We start with a couple major budget items (rent, groceries, utilities) and the temporary idea that the remaining money is discretionary (not the word we use with the student). Money is printed (legal if the printed bills are small enough and only 1 sided) in lieu of fake money that does not look like the bills they would see.
The activity is guided by slides on a Google Slides presentation (link at bottom of this post). Note: the activity can be rerun as needed and the Google Slides slides can be copied, pasted, and information removed. This allows you to keep a record of each trial with this activity.
Job and Pay
The student can either search for a job on a site like Indeed.com or an ad for a job can be provided. The hourly rate is established and the student is prompted to compute the total pay on Google Calculator to allow a screenshot to be produced.
The student then uses the chart to provide a visual and scaffolding to compute the total pay for a month. I go with 4 weeks of 5 work days each, with no taxes to keep it simple.
The student counts out the money, first by grouping hundreds together to get a $1,000. Then the total is moved next to the envelopes.
The pay is entered into a bank balance table to provide practice with the format of a check register. This helps provide structure and having the money counted out on the table allows the student to see a concrete representation of the bank balance table. (Note: I slide the money to the left to allow space to move the money to the envelopes as the student pays bills.)
The first bill is rent. The student is prompted to search for an apartment on a website like Apartment.com, take a screenshot, and paste into a slide.
The student then pays the bill by counting out the money and sliding the money towards the envelope.
The student then enters the rent into the bank balance. I then point to the money pile on the right in image above and refer to it as rent. I then point to the rent entry into the bank balance. Similarly, I point to the pile on the left, refer to it as the balance and count it out, then point to the new balance in the table. This provides a concrete representation for the bank balance.
I found a website that provides average bill amounts for our state. The student clicks on the link, takes a screen shot of the average costs, and pastes it into the slide.
We focused only on heat and electricity. The student identifies both amounts (I round to the nearest 5 to keep it simple) and then pays both by moving the money over.
Both bills are entered into the bank balance. I then point to the two piles of money used to pay the bills, point to the entries into the table below, point to the pile of remaining money, and point to the entry into the balance in the table below.
Finally, the student makes a shopping list of food items for all 3 meals for the week. To make it easy, we can assume the the same meal each day. The student is provided a lot of leeway in what he or she chooses and what amounts. The amounts they choose may not be enough for a week. That can be addressed in grocery shopping activities conducted in isolation.
The student shops online for the items and takes a screenshot of the cart.
The student completes the table to determine the total cost for a month.
The student moves the money over and then this total cost is entered into the bank balance. The same comparisons between money piles and cost and balance are presented. Then the remaining money is free to use for whatever the student wants. At this point, you can have the student go shopping for clothes or whatever.
The Google Slides File
Here is the Link to the Google Slides file. You can make a copy to access it.
This post provides details about a handout for simplifying rational monomial expressions. It incorporates a couple strategies to make the simplification of rational monomial expressions more accessible. The strategies include address prerequisites skills ahead of time, chunking, and scaffolding. This incrementally walks the students through the steps.
The Pages of the Handout
The handout has 3 pages.
Page 1 is an initiation with two parts. There is a review of prerequisite skills aligned with the new topic. There is also a preview of the new topic with scaffolding to separate the factors into individual fractions.
Page 2 provides a Before and Now to draw upon student prior knowledge of simplifying using exponents rules. This is followed by scaffolded steps to separate the expression into individual fractions for each type of term (e.g., Xs). This provides a load reduction for what the student has to focus on.
Page 3 involves negative and 0 exponents with an additional step to address each.