Have you ever noticed that the prices of everyday items can be different depending on where you are? This article looks at how the prices of common grocery items, like toilet paper and toothpaste, differ between Duluth, Minnesota, and New York City.
In Duluth, a package of toilet paper costs $3.99. However, in New York City, it costs $8.95. Similarly, toothpaste is $1.95 per tube in Duluth. While in New York City, it is $5.25 per tube.
To make these price differences easier to understand, we can use a grocery matrix. This matrix shows the prices clearly for each city:
This matrix helps us easily compare and analyze the prices.
The article also discusses how we can set up the matrix differently while still showing the same data. It’s important to keep the rows and columns consistent to make sure the prices are represented accurately.
Here’s another way to organize the matrix:
In this setup, the data still shows the same information:
As long as the rows and columns are clearly defined, the matrix will be accurate.
It’s crucial to keep the data organized correctly in the matrix. If the rows and columns are mixed up, the matrix won’t show the right information. For example, if you think the first row is for Duluth but it actually has New York City data, it can lead to mistakes.
When looking at specific parts of the matrix, like G(2,1), which means the second row and first column, you need to make sure the values are correct. If G(2,1) doesn’t equal $5.25, it means the matrix might not be set up right.
In conclusion, while prices for groceries can be very different in various cities, using a matrix can help us analyze these differences. However, it’s important to keep the data organized properly to avoid drawing the wrong conclusions. Careful structuring of the matrix is key to understanding pricing accurately.
Using the information from the article, create your own price matrix for another set of grocery items. Choose two different cities and two different products. Make sure to organize the data clearly and accurately. Share your matrix with the class and explain your setup.
Divide into two groups. One group will argue why prices are higher in New York City, while the other will argue why prices are lower in Duluth. Use evidence from the article and additional research to support your points. Present your arguments to the class.
Work in pairs to create a matrix with a different setup from the article. Exchange your matrix with another pair and check if they can interpret the data correctly. Discuss any challenges faced in understanding the matrix.
Visit a local supermarket or use online resources to find the prices of the same items mentioned in the article. Compare these prices with those in Duluth and New York City. Present your findings and discuss any surprising differences.
Practice setting up matrices with different data sets. Ensure that the rows and columns are consistent and accurate. Exchange your matrix with a classmate and check each other’s work for accuracy. Discuss any errors and how to avoid them.
Matrix – A rectangular array of numbers or expressions arranged in rows and columns. – In algebra class, we learned how to add two matrices together by adding their corresponding elements.
Prices – Numerical values representing the cost of items, often used in algebraic problems to calculate total expenses or savings. – The math problem asked us to calculate the total cost by multiplying the prices of the items by the quantities purchased.
Compare – To examine the similarities and differences between two or more numbers, expressions, or equations. – We were asked to compare the solutions of two quadratic equations to determine which one had a greater value.
Analyze – To examine mathematical data or expressions in detail to understand their structure or meaning. – The teacher asked us to analyze the graph of the function to find its intercepts and vertex.
Rows – Horizontal lines of elements in a matrix or table. – In the matrix, each row represents a different set of data points.
Columns – Vertical lines of elements in a matrix or table. – To solve the problem, we needed to add the numbers in each column of the matrix.
Data – Information, often numerical, collected for analysis or used to reason or make decisions. – The data from the experiment was plotted on a graph to observe the trend.
Setup – The arrangement or organization of elements or conditions in a mathematical problem or experiment. – The setup of the equation was crucial to solving the algebraic problem correctly.
Elements – Individual numbers or expressions that make up a matrix or set. – Each element in the matrix was multiplied by 2 to form a new matrix.
Consistency – The property of a system of equations where all equations are compatible and have at least one solution. – The system of equations was checked for consistency to ensure that there was a solution that satisfied all equations.
