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Math Practice U5 L10

Unit 5 Math Practice Links to L1-2, 5-7, 10
Live Lesson Recording Link
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!

Function of the Day:

What do you know? Draw the Scatter Plot.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Vocabulary Terms - Define/Illustrate

Statistical Question

Biased vs Unbiased
Probabilistic vs Deterministic Interpretation

5 Problems - SHOW ALL WORK!

The number of hours spent on math homework each week and the final exam grades for twelve students in Mr. Dylan's algebra class are plotted below.

Based on a line of best fit, which exam grade is the best prediction for a student who spends about 4 hours on math homework each week?
a) 62
b) 72
c) 82
d) 92
The scatter plot below shows the relationship between the number of members in a family and the amount of the family's weekly grocery bill.

Write a line of best fit.

_____________________________
The most appropriate prediction of the grocery bill for a family that consists of six members is
a) $100
b) $300
c) $400
d) $500
3. The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.

Write a line of best fit equation. _______________

What does the slope mean in context?

What does the y-intercept mean in context?

4. The scatter plot below shows the profit, by month, for a new company for the first year of operation. Kate drew a line of best fit, as shown in the diagram.

Using this line, what is the best interpretation of the slope?

What is the meaning of the x-intercept?

5.
Give one probabilistic interpretation of the graph.

Why would we not use a deterministic interpretation?

What is a likely statistical question asked for this unbiased study?


What do I need help with?

1 answer

Function of the Day:
The function of the day typically refers to a specific mathematical concept or formula being emphasized for the day’s lesson. For today, it may involve functions related to regression analysis or statistical interpretation, such as linear functions, correlations, or predictions based on scatter plot data.

Scatter Plot Drawing:

You can draw a scatter plot on graph paper or using graphing software. Here’s a general guide on how to approach it:

  1. Label the x-axis (independent variable) and y-axis (dependent variable).
  2. Plot the data points based on the hours spent on math homework vs. final exam grades.
  3. Ensure each point is accurately placed according to the values you have.

Vocabulary Terms - Define/Illustrate:

  1. Statistical Question:
    A statistical question anticipates variability in the data and is answered using data collection and analysis. For example, "What is the average amount of time students spend on homework?"

  2. Biased vs Unbiased:

    • Biased: A biased study favors certain outcomes over others, potentially affecting the results.
    • Unbiased: An unbiased study aims to represent the population accurately, with methods that do not favor any outcome.

  3. Probabilistic vs Deterministic Interpretation:

    • Probabilistic: This interpretation acknowledges uncertainty and variability; outcomes are described in terms of likelihood (e.g., "There’s a 70% chance").
    • Deterministic: This interpretation suggests outcomes are fixed and predictable given a particular input (e.g., if a student studies for 5 hours, they will get a score of 80).

5 Problems - SHOW ALL WORK!

  1. Prediction for 4 Hours of Homework:
    Using the line of best fit derived from the scatter plot, find the corresponding y-value for x = 4 hours. Suppose the estimated grade is 82 based on the line, the answer would be: c) 82.

  2. Line of Best Fit for Grocery Bill:
    Construct a best fit line on the scatter plot of family members vs. grocery bills and write down the linear equation derived from it (e.g., y = mx + b).

  3. Grocery Bill for 6 Members:
    Using the line of best fit, determine the corresponding y-value for x = 6. If it’s around $400 according to your line, then:
    c) $400.

  4. Line of Best Fit Equation for Farming Acres Over Years:
    Again, derive the linear equation from the plotted points: (e.g., y = mx + b).
    Equation: _______________

    • Slope Meaning: This indicates how many acres are being added or lost each year.
    • Y-intercept Meaning: This indicates the number of acres being used at the starting point (year zero).

  5. Interpretation of Profit vs. Month:

    • Slope Interpretation: Represents the monthly increase in profits. If it’s positive, the company is growing, indicating success.
    • X-intercept Meaning: The month in which the profit was zero, indicating when the company started to become profitable, if within the first year.
    • Probabilistic Interpretation: If we said there’s a likelihood of profit by the seventh month, it implies predictions based on trends.
    • Deterministic vs. Probabilistic: We choose probabilistic interpretations because future profits based on past trends can still vary due to many unpredictable factors.
    • Statistical Question: A question like "What factors affect the profit of new companies?" could be suited to this unbiased study.

What do I need help with?
Feel free to ask questions about scatter plots, lines of best fit, interpreting graphs, or any particular math problems you may find challenging!