Lesson 13: AI and Mathematics -- Pattern Recognition and Predictive Modeling
Keep this sheet on your desk throughout the lesson! Use it to look up vocabulary words, check formulas, and refer to the visual examples when working on your worksheet and activity cards.
Key Vocabulary
Pattern
A repeated or predictable arrangement of numbers, shapes, colors, or events that follows a rule.
Example: 2, 4, 6, 8, 10 -- the pattern is "add 2 each time."
AI Use: AI looks for patterns in massive datasets to find rules that help it make decisions.
Sequence
An ordered list of numbers that follows a specific rule or pattern.
Example: 3, 9, 27, 81 is a sequence where each number is multiplied by 3.
AI Use: AI analyzes sequences of stock prices, temperatures, or web clicks to predict the next value.
Arithmetic Sequence
A sequence where the same number is added (or subtracted) each time. The difference between consecutive terms is constant.
Example: 5, 12, 19, 26, 33 (adding 7 each time). The common difference is 7.
Geometric Sequence
A sequence where each term is multiplied (or divided) by the same number. The ratio between consecutive terms is constant.
Example: 4, 12, 36, 108 (multiplying by 3 each time). The common ratio is 3.
Trend
The overall direction in which data is moving over time -- increasing (upward), decreasing (downward), or flat (no change).
Example: If monthly sales go from $100 to $150 to $200, the trend is increasing.
AI Use: AI identifies trends in data to forecast future outcomes, like predicting whether a video will go viral.
Prediction
An estimate of a future value based on analysis of existing data and patterns.
Example: Based on a trend of rising temperatures, we predict July will be hotter than June.
AI Use: Weather apps, Netflix recommendations, and traffic navigation all make AI-powered predictions.
Mean (Average)
The sum of all values divided by the number of values. It represents the "balance point" of a dataset.
Example: Mean of 4, 6, 8, 10, 12 is (4+6+8+10+12) / 5 = 40 / 5 = 8
AI Use: AI uses the mean to establish baselines -- what is "normal" for a dataset.
Median
The middle value when data is arranged from least to greatest. If there is an even number of values, the median is the average of the two middle values.
Example: In 3, 5, 7, 9, 11 the median is 7. In 3, 5, 7, 9 the median is (5+7)/2 = 6.
AI Use: AI uses the median when data has outliers that would distort the mean.
Mode
The value that appears most often in a dataset. A dataset can have one mode, multiple modes, or no mode.
Example: In 2, 3, 3, 5, 7, 3, 9 the mode is 3 (appears 3 times).
AI Use: AI uses the mode to find the most common category -- like the most popular item ordered.
Outlier
A data point that is significantly different from the rest of the dataset. Outliers can distort the mean.
Example: In 80, 85, 82, 88, 15 the value 15 is an outlier.
AI Use: AI must detect and handle outliers carefully -- ignoring them can improve accuracy, but sometimes outliers represent important unusual events.
Scatter Plot
A graph that uses dots to show the relationship between two numerical variables. One variable is on the x-axis, the other on the y-axis.
Example: Plot "hours studied" vs. "test score" to see if studying more leads to higher scores.
AI Use: AI analyzes scatter plot patterns to determine if two variables are related (correlated).
Trend Line (Line of Best Fit)
A straight line drawn through a scatter plot that best represents the overall direction of the data. It is used to make predictions.
Example: A trend line through temperature vs. ice cream sales data slopes upward, showing sales increase as temperature rises.
AI Use: "Linear regression" is the mathematical method AI uses to calculate the perfect trend line. You draw one by eye; AI calculates one precisely.
Correlation
A measure of how strongly two variables are related. Positive correlation means both increase together. Negative correlation means one increases as the other decreases.
Example: Temperature and ice cream sales have a positive correlation. Temperature and hot chocolate sales have a negative correlation.
Accuracy
How close a prediction or measurement is to the actual (true) value. Higher accuracy means smaller error.
Example: If the actual temperature was 86°F and the prediction was 87°F, the prediction was very accurate.
AI Use: AI developers constantly measure accuracy to improve their models -- the goal is always to reduce percent error.
Slope
A number that describes how steep a line is. It represents the rate of change: how much y changes for every 1-unit increase in x.
Example: A slope of 1.6 on an ice cream chart means 1.6 more ice cream bars are sold for every 1°F increase in temperature.
Percent Error
A measurement of how far off a prediction is from the actual value, expressed as a percentage. Lower percent error = better prediction.
Example: Predicted 70, actual was 65. Percent error = |70-65| / 65 x 100 = 7.7%
Key Formulas
Mean (Average)
Mean = Sum of All Values ÷ Number of Values
Example: Dataset: 12, 15, 18, 21, 24
Sum = 12 + 15 + 18 + 21 + 24 = 90
Number of values = 5
Mean = 90 ÷ 5 = 18
Median
Median = Middle Value (after sorting from least to greatest)
Odd number of values: 3, 7, 9, 12, 15 → Median = 9 (the 3rd value) Even number of values: 3, 7, 9, 12 → Median = (7 + 9) ÷ 2 = 8 (average of the 2 middle values)
Slope (Rate of Change)
Slope = (y₂ - y₁) ÷ (x₂ - x₁) = Rise ÷ Run
Example: Two points on a trend line: (2, 35) and (10, 80)
Slope = (80 - 35) ÷ (10 - 2) = 45 ÷ 8 = 5.625
Interpretation: "For every 1 additional hour of practice, accuracy increases by about 5.6 percentage points."
Percent Error
Percent Error = |Predicted Value - Actual Value| ÷ Actual Value × 100
Example: You predicted 68 ice cream bars. The actual number was 65.
Percent Error = |68 - 65| ÷ 65 × 100 = 3 ÷ 65 × 100 = 4.6%
The | | symbols mean "absolute value" -- always make the number positive!
Remember: Correlation does NOT mean causation! Just because two things are related in data does not mean one causes the other. Ice cream sales and sunburn rates are correlated (both go up in summer), but eating ice cream does not cause sunburn!