HS Algebra

Where Do We Meet? REI

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WHERE DO WE MEET?

Where do we meet is an interactive activity that uses technology and mathematical concepts to create and solve real life scenarios. One of the Vernier products to compliment this lesson is the Motion Detector. This device allows for data to be collected through a calculator (or a computer software) where students can then analyze their findings. For this activity students will be able to see a real life scenario of the usage of the mathematical concept of Solving Systems of Liner Equations using a motion detector, calculator and themselves. In this activity, students will be able to part of the creation of data that will be used to create equations. Students will then take part in solving the system of equations using technology and on writing (mathematically). Students will be able to use this activity that ties to the following Common Core State Standards:

INQB.2 Collect, analyze and display data using calculators, computers, or other technical devices when available

APPD.2 Use computers, probes, and software when available to collect, display, and analyze data.

M3.2.H Formulate a question that can be answered by analyzing data, identify relevant data sources, create an appropriate data display, select appropriate statistical techniques to answer the question, report results, and draw and defend conclusions.

H.A.REI.1– Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

H.A.REI.2– Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

H.A.REI.5– Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

H.A.REI.6– Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

vernieractivity-wheredowemeet

Planning a Party HSA.CED.A.2

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cupcakes

 

You have a big birthday party coming up soon. You invited 16 people for the occasion.  The problem is, you haven’t gotten cupcakes yet. While considering the number of cupcakes to buy, your rule is each person attending (including yourself) must have 2 cupcakes each. Assuming that each person you invite will come and have their 2 cupcakes, how many cupcakes should you buy to hold true to your rule (2 cupcakes for everyone)?

This problem can be manipulated in many ways. For instance, what if you wanted each person to have 3 cupcakes? 5? We can let the number of cupcakes you are buying to be y and the number of cupcakes per  person be x and create an equation for the number of cupcakes you should buy for your party (n) and the number of cupcakes per person (x).

Now you are having second thoughts. Instead of yourself having the same number of cupcakes as everyone else, you want to have one more (so you would have x+1 cupcakes and everyone else would have x). How would this change your equation above? Create a new equation demonstrating this new rule with the same variables.

Now that you have established how to manipulate the equation based on changing information, you want to create an equation for future parties that you host showing the amount of cupcakes (or other food items) you need to have based on: the number of food item you want for each person, the number of people that will be there, and the amount (if any) more you want to have for yourself. Let these variables be x, y, and z respectively and the number of food items you need be the variable n. Create a brand new equation given these variables for the number of food items you need.

At times, it can be very difficult to engage math students in a classroom. Story problems are somewhat recommended because they can bring relevance from the students’ lives into a math problem. What preceded is an extended story problem involving something that all students will love: food. Along with the problem, the picture should make students’ mouths water. This problem should be relevant to almost all students and possibly give them some party planning advice.

The Common Core State Standard this problem is aligned with is HSA.CED.A.2:
Create equations in two or more variables to represent relationships between quantities.