A school's recycling program collected the following number of pounds of recyclables each week:
12, 19, 26, 33, 40, , ,
a) What is the rule? The sequence by each time.
b) Predict the next three terms: , ,
c) Using this pattern, how many pounds would the school collect in Week 12? Show your work.
A viral video's views doubled every day after it was posted:
150, 300, 600, 1,200, 2,400, , ,
a) What is the rule? Each term is by .
b) Predict the next three terms: , ,
c) On what day will the video first surpass 100,000 views? Show your work.
A city's average monthly temperature readings (in °F) from January through June:
28, 32, 42, 56, 68, 79
a) Is this an arithmetic sequence (constant difference), geometric sequence (constant ratio), or neither? Explain your reasoning.
b) Predict the temperature for July: °F
c) Predict the temperature for August: °F
d) Would this pattern continue forever? Why or why not?
An AI model is being trained to recognize images. The table shows how its accuracy improves as it processes more training images:
| Training Images | 100 | 200 | 300 | 400 | 500 | 600 | 700 |
|---|---|---|---|---|---|---|---|
| Accuracy (%) | 52 | 61 | 68 | 74 | 79 | 83 | ? |
a) Calculate the change in accuracy between each pair of consecutive values:
100→200: 200→300: 300→400: 400→500: 500→600:
b) Do you notice anything about how the differences change? Describe the trend.
c) Predict the accuracy at 700 training images: %
d) Do you think the accuracy will ever reach 100%? Explain your reasoning.
The school cafeteria tracked how many pizza slices were sold each day for two weeks (10 school days):
| Day | Mon | Tue | Wed | Thu | Fri | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|---|---|---|---|---|
| Slices Sold | 132 | 98 | 145 | 110 | 178 | 140 | 105 | 145 | 115 | 182 |
a) Calculate the mean (average) number of slices sold per day:
b) Find the median. First, order the values from least to greatest:
c) Find the mode:
d) The cafeteria manager wants to predict how many pizza slices to prepare for next Monday. Which measure of center would you recommend and why?
e) Notice the pattern: Fridays have the highest sales (178 and 182). Why might this be? How could an AI use this day-of-week pattern?
A fitness tracker recorded a student's daily step counts for 9 days:
4,200 6,800 5,500 3,100 7,200 5,500 8,400 5,500 15,300
a) Calculate the mean: steps
b) Calculate the median: steps
c) Find the mode: steps
d) The value 15,300 is much larger than the others (perhaps a hiking day). This is called an outlier. How does this outlier affect the mean compared to the median?
e) If an AI fitness app wanted to predict this student's "typical" daily step count, should it use the mean or the median? Explain.
A school tracked the outdoor temperature and the number of ice cream bars sold from the cafeteria each day:
| Temperature (°F) | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 |
|---|---|---|---|---|---|---|---|---|
| Ice Cream Bars Sold | 8 | 14 | 18 | 25 | 34 | 40 | 52 | 58 |
a) Plot these 8 data points on the coordinate grid below. Label the x-axis "Temperature (°F)" and the y-axis "Ice Cream Bars Sold."
b) Draw a trend line (line of best fit) through the data. Try to have roughly the same number of points above and below the line.
c) Using your trend line, predict how many ice cream bars will sell when the temperature is:
d) The actual values were: 95 °F = 65 bars, 50 °F = 4 bars, 100 °F = 70 bars. Calculate your percent error for each prediction:
| Temperature | Your Prediction | Actual Value | |Difference| | Percent Error |
|---|---|---|---|---|
| 95 °F | 65 | |||
| 50 °F | 4 | |||
| 100 °F | 70 |
e) An AI model predicted: 95 °F = 64 bars, 50 °F = 3 bars, 100 °F = 72 bars. Whose predictions were closer -- yours or the AI's? Why do you think that is?
A teacher surveyed 10 students about how many hours they studied for a math test and recorded their scores:
| Student | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Hours Studied | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |
| Test Score (%) | 52 | 58 | 65 | 68 | 74 | 79 | 83 | 88 | 90 | 95 |
a) Plot the data on graph paper or the grid below. (x-axis = Hours Studied, y-axis = Test Score)
b) Draw a trend line through the data.
c) Use your trend line to predict: If a student studies for 6 hours, what test score would you predict? %
d) Estimate the slope of your trend line. Pick two points on the line (not data points) and calculate:
e) What does the slope mean in this context? Complete the sentence:
"For every additional hour of studying, a student's test score increases by approximately points."
f) Could this trend continue forever? Would studying for 20 hours guarantee a score above 100%? Explain why predictions have limits.
1. Describe in your own words how AI uses patterns to make predictions. Use at least two math vocabulary words from today's lesson.
2. Which was harder: finding the pattern in the sequence problems (Section 1) or making predictions from the scatter plot (Section 3)? Why?
3. Give one real-world example of an AI system that uses pattern recognition and predictions. Explain what data it analyzes and what predictions it makes.
4. Rate your confidence in making predictions using math (circle one):
1 - Not confident 2 - A little confident 3 - Somewhat confident 4 - Very confident 5 - Expert level
Explain your rating: