Mathematical Highlights Introducing Algebra
In Variables and Patterns, you will study some basic ideas of algebra and
learn some ways to use those ideas.
Some things never seem to change
In mathematics, science, and
The sun always rises in the east and business, quantities that change are
sets in the west. The United States called variables. Many problems
holds a presidential election every require predicting how changes in
four years. Labor Day always falls the values of one variable are related
on the first Monday of September to changes in the values of another
But many other things are always
To help you solve such problems,
changing. Temperatures rise and fall
you can represent the relationships
between variables using word
within a day and from season to
season. Store sales change in response equations. The mathematical ideas
descriptions, tables, graphs and
to rising and falling prices and shopper and skills used to solve such
demand. Audiences for television
problems come from the branch of
shows and movies change as viewers
mathematics called algebra. This
interests change. The speeds of cars
unit introduces some of the basic
on streets and highways change in
tools of algebra.
response to variations in traffic
density and road conditions
You will learn how to
• Identify variables in situations
• Recognize situations in which changes in variables are related in useful
patterns
• Describe patterns of change shown in words, tables, and graphs
• Construct tables and graphs to display relationships between variables
. Observe how a change in the relationship between two variables affects
the table, graph, and equation
• Use algebraic symbols to write equations relating variables
• Use tables, graphs, and equations to solve problems
• Use graphing calculators to construct tables and graphs of relationships
between variables and to answer questions about these relationships
As you work on problems in this unit, ask yourself questions about problem
situations that involve related quantitative variables:
What are the variables in the problem?
Which variables depend on, or change in relation to others?
How can I use a table, graph, or equation to display and analyze a
relationship between quantitative variables?
What does it mean when I see regular and predictable changes in a table
of data or a graph?
How can I use these regular or predictable changes to make estimates or
predictions about other data vales?
What is the The variable in this problem

This task builds on important concepts you've learned in this unit and allows you to apply those concepts to a variety of situations. the task has several parts, each in its own section. mr. hill's seventh grade math class has been learning about random sampling and how it tends to produce samples that are representative of an entire population. they've also learned that if a sample is representative of the entire population, then estimates or predictions made based on the sample usually apply to the population as well. today, in class, they are also learning about variation in random sampling. that, although predictions and estimates about the population can be made from a random sample, different random samples will often produce slightly different predictions or estimates. to demonstrate this concept to his students, mr. hill is going to use simulation. he begins the lesson by explaining to the class that a certain university in the united states has a student enrollment of 19,100. mr. hill knows the percentage of students that are male and the percentage of students that are female. using simulation and random sampling, he wants his seventh grade students to estimate both the percentage of male students and the number of male students that are enrolled in this university. to conduct the simulation, mr. hill has placed one hundred colored chips in a bag, using the appropriate percentages of enrolled male and female university students. red chips represent males, and yellow chips represent females. each seventh grade student will randomly select twenty chips, record the colors they selected, and put the chips back in the bag. at this point, each seventh grade student will only know the results of their own random sample. before you begin, it's a good idea to look over each part to get oriented to the whole task. additionally, it's best to complete the sections in order, since they build on each other. finally, the work you complete will be a combination of computer-graded problems and written work that your teacher will grade. in some cases, you will need to complete work outside of the problem (in a word processing document or on paper, for example) and upload it for grading. to get started click work on questions. questions: 1. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the percentage of enrolled university students that are male? 2. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the number of enrolled university students that are male? 3. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. how many yellow chips were in their sample? 4. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. based on this sample, what is a good estimate for the number of enrolled university students that are female? 5. based on your dot plot, make a new estimate of both the percentage and number of males that attend this university. use complete sentences in your answer and explain your reasoning. 6. compare your estimates for the percentage of male university students from part a and part b. which estimate do you think is more representative of the population? use complete sentences in your answer and explain your reasoning. 7. once you have created both sets of numbers, complete the following tasks. in each task, make sure to clearly label which set you are identifying or describing. identify the elements of each set that you created. calculate the mean of each set. show your work in your answer. calculate the mean absolute deviation of each set. show your work in your answer. describe the process you used to create your sets of numbers under the given conditions.