Lesson 13: AI and Mathematics -- Pattern Recognition and Predictive Modeling
Student:
Date:
Teacher:
Period:
Rubric 1: Pattern Recognition Skills
Assesses the student's ability to identify, describe, and extend patterns in numerical sequences and datasets. This rubric evaluates work from the Pattern Prediction Worksheet (Section 1) and Data Detective Activity Cards.
Criteria
4 -- Exemplary
3 -- Proficient
2 -- Developing
1 -- Beginning
Identifying the Pattern Rule
Correctly identifies the rule for all 4 sequences, including the non-arithmetic sequence. Describes the rule precisely using mathematical language (e.g., "multiply by 2" or "add 7").
Correctly identifies the rule for 3 of 4 sequences. Uses mostly accurate mathematical language to describe the rules.
Correctly identifies the rule for 2 of 4 sequences. Descriptions may be vague or informal (e.g., "it goes up" without specifying how much).
Correctly identifies the rule for 0-1 sequences. Unable to articulate the pattern or provides incorrect rules.
Extending Sequences
All predicted next terms are correct. Can extend sequences confidently even when the pattern is complex (non-constant differences, real-world data).
Most predicted terms are correct (at least 10 of 12 blanks). Minor arithmetic errors may occur but the pattern logic is sound.
Some predicted terms are correct (6-9 of 12). May apply the wrong rule or make repeated calculation errors.
Few predicted terms are correct (0-5 of 12). Does not demonstrate ability to extend a sequence using a consistent rule.
Reasoning About Patterns
Provides insightful explanations about why patterns may or may not continue (e.g., "Temperature can't increase forever because seasons cycle"). Makes thoughtful connections between sequence behavior and real-world contexts.
Provides reasonable explanations about pattern limitations. Shows understanding that real-world patterns have constraints.
Provides basic explanations with limited depth. May recognize that patterns have limits but cannot explain why.
Does not provide explanations or provides explanations that show significant misunderstanding of how patterns relate to real-world data.
Assesses the student's ability to calculate and interpret mean, median, and mode, and to select the appropriate measure for a given context. This rubric evaluates work from the Pattern Prediction Worksheet (Section 2) and Data Detective Activity Cards.
Criteria
4 -- Exemplary
3 -- Proficient
2 -- Developing
1 -- Beginning
Calculating Mean
All mean calculations are correct with clear work shown (sum and division). Can calculate the mean for datasets with 10+ values accurately.
Mean calculations are mostly correct (minor arithmetic errors). Work is shown, and the process is clear.
Some mean calculations are correct, but errors in addition or division are present. Work may be incomplete or difficult to follow.
Mean calculations are mostly incorrect or not attempted. Does not demonstrate understanding of the formula: sum / count.
Finding Median and Mode
Correctly orders data and finds the median in all problems, including datasets with an even number of values (averages the two middle values). Correctly identifies the mode in all problems.
Finds the median correctly in most problems. May have minor errors with even-count datasets. Identifies the mode correctly.
Finds the median in some problems but may forget to order the data first or may not average the two middle values in even-count sets. Mode identification is inconsistent.
Unable to correctly find the median or mode. Does not order data or confuses median with mean.
Selecting the Right Measure
Consistently selects the most appropriate measure for each context and provides a compelling justification. Correctly identifies when outliers make the median more reliable than the mean.
Usually selects the appropriate measure and provides a reasonable justification. Shows some understanding of outlier effects.
Sometimes selects the appropriate measure but justifications are weak or missing. Limited understanding of when to use each measure.
Cannot articulate when to use mean vs. median vs. mode, or consistently selects the wrong measure.
Score
_____ / 4
_____ / 4
_____ / 4
_____ / 4
Mathematical Reasoning Total: / 12
Rubric 3: Data Analysis and Prediction Accuracy
Assesses the student's ability to create scatter plots, draw trend lines, make data-based predictions, and evaluate prediction accuracy using percent error. This rubric evaluates work from the Pattern Prediction Worksheet (Section 3) and group Data Detective presentations.
Criteria
4 -- Exemplary
3 -- Proficient
2 -- Developing
1 -- Beginning
Scatter Plot Construction
Axes are correctly labeled with variable names and units. Scale is appropriate and consistent. All data points are plotted accurately. Graph is neat and easy to read.
Axes are labeled. Scale is mostly appropriate. Most data points are plotted correctly (1-2 minor placement errors). Graph is readable.
Axes may be mislabeled or missing units. Scale may be inconsistent. Several data points are incorrectly plotted. Graph is difficult to read.
Axes are missing labels or have incorrect variables. Points are mostly inaccurately plotted or missing. Graph does not effectively represent the data.
Trend Line Quality
Trend line is well-positioned with roughly equal points above and below. Line follows the general direction of the data. Line is straight and extends appropriately for predictions.
Trend line generally follows the data direction with minor positioning issues. Most points are reasonably distributed around the line.
Trend line is drawn but does not balance points well (most points on one side). May be curved instead of straight, or may connect individual points rather than showing the overall trend.
Trend line is missing, wildly off, or connects all points (plotting the data rather than showing the trend).
Prediction Quality
All predictions are reasonable and consistent with the trend line. Predictions within the data range (interpolation) are within 10% of actual values. Can explain prediction reasoning clearly.
Most predictions are reasonable and within 15% of actual values. Predictions follow logically from the trend line.
Some predictions are reasonable but others are significantly off. May not read the trend line consistently for predictions.
Predictions are random or not based on the trend line. Unable to use the graph to make predictions.
Percent Error Calculation
All percent error calculations are correct. Shows clear work with the formula. Can interpret results (e.g., "My prediction was 8% off, which is fairly accurate").
Most percent error calculations are correct. Shows work. Can state whether the prediction was accurate based on the percent error.
Some percent error calculations are attempted but contain errors in the formula application (e.g., forgetting absolute value or dividing by predicted instead of actual).
Percent error calculations are missing or entirely incorrect. Does not demonstrate understanding of the formula.
Score
_____ / 4
_____ / 4
_____ / 4
_____ / 4
Data Analysis Total: / 16
Rubric 4: Collaboration and Presentation
Assesses the student's participation in group work during the Data Detective Activity and the quality of the group's presentation to the class. Each student is assessed individually for their contributions.
Criteria
4 -- Exemplary
3 -- Proficient
2 -- Developing
1 -- Beginning
Group Participation
Actively fulfills assigned role and contributes beyond it. Helps other group members. Stays on task throughout the activity. Encourages participation from all group members.
Fulfills assigned role consistently. Contributes to group discussions and stays mostly on task.
Partially fulfills assigned role. Needs reminders to stay on task or participate. Contributes occasionally.
Does not fulfill assigned role. Off task frequently. Does not contribute meaningfully to group work.
Mathematical Communication
Uses precise mathematical vocabulary (mean, median, mode, trend, percent error, scatter plot). Explains calculations and reasoning clearly to group members. Can justify predictions with evidence from the data.
Uses most mathematical vocabulary correctly. Explains reasoning with some clarity. Justifies predictions with some data evidence.
Uses some mathematical vocabulary but may use informal language instead. Explanations are unclear or incomplete.
Rarely uses mathematical vocabulary. Cannot explain reasoning or predictions to others.
Presentation Quality
Group presentation is clear, organized, and engaging. Includes visual representation of data. All claims are supported by calculations. Speaks confidently and answers audience questions.
Presentation is organized and covers main findings. Most claims are supported by data. Speaks clearly to the class.
Presentation covers some findings but is disorganized or missing key elements. Some claims are unsupported. Speaker may be hard to hear or follow.
Presentation is incomplete, inaccurate, or not delivered. Findings are not supported by data.
Score
_____ / 4
_____ / 4
_____ / 4
_____ / 4
Collaboration and Presentation Total: / 12
Overall Assessment Summary
Student:
Date:
Rubric Area
Points Earned
Points Possible
1. Pattern Recognition Skills
12
2. Mathematical Reasoning (Central Tendency)
12
3. Data Analysis and Prediction Accuracy
16
4. Collaboration and Presentation
12
TOTAL
52
Grade Conversion
Points
Percentage
Performance Level
Description
47-52
90-100%
Exemplary
Exceeds expectations. Demonstrates thorough understanding of pattern recognition, statistics, and data analysis with strong AI connections.
39-46
75-89%
Proficient
Meets expectations. Demonstrates solid understanding with minor errors. Can connect math concepts to AI applications.
26-38
50-74%
Developing
Approaching expectations. Shows partial understanding. Needs additional practice with some concepts.
0-25
0-49%
Beginning
Below expectations. Significant gaps in understanding. Requires reteaching and additional support.