Students learn the different sampling techniques which will help them in their statistical exploration. Choosing the right sampling method helps to move forward with the exploration.

Overview

Lesson 1: Sampling techniques

In this DP Mathematics AI set, students will use real-life data sets and Desmos’s graphing tools to enhance their understanding of SL 4.2 syllabus content and improve data handling skills for math coursework.

Content covered:

• Data presentation (discrete/continuous), frequency distributions (tables)

• Histograms

• Cumulative frequency, cumulative frequency graphs (median, quartiles, percentiles, range, IQR)

• Box and whisker diagrams

Overview

Lesson 1: Box Plot Treasure Hunt / Solution

Lesson 2: Finding Outliers Investigation / Data / Solution 

Lesson 3: A Data Investigation / Solution

Lesson 4: Box Plots for Normally Distributed Data / Solution / Resources

In this DP Mathematics common core 4.3 set, students practice their GDC skills in finding averages and measuring spread of data through quizzes and treasure hunts. In addition, students  do some explorations using real data to support their understanding of the effect of constant change on data and have an opportunity to develop their ability to show a non-GDC method in their exploration coursework.

Overview

Lesson 1: Treasure Hunt Averages / Solution

Lesson 2: Maths Ladder Quiz / Solution

Lesson 3: Salary Changes / Solution

Lesson 4: Non-Calculator Methods for IA Investigations / Solution

These materials cover the concepts of correlation as well as finding and describing the correlation from scatterplots. Students find equations of the lines of best fit. Students also find the equation of the regression line and explore the concepts of interpolation and extrapolation. In addition, causation and correlation are discussed. The final lesson includes a mini-exploration in which students create a linear model to predict information and draw conclusions.

Overview

Lesson 1: Correlation Coefficient / Solution

Lesson 2: Two Variable Statistics

This lesson will provide an opportunity for students to learn all of DP Mathematics sub-topic 4.06 in one activity. Students use a homemade trail mix to find the probability of mutually exclusive, independent, conditional, and combined events. They also use Venn diagrams, tree diagrams, sample spaces, and tables to calculate these probabilities. The activity concludes with a connection to the Chi-Square goodness of fit test.

Overview

Lesson 1: The Trail to Probability / Solution

Lesson 2: Venn Diagram Placemat

Lesson 3: Tree Diagram

This DP Mathematics common core 4.7 set begins with a guided inquiry that leads students from the familiar use of tree diagrams for probability into probability distributions. There are two Desmos activities—one for consolidation and one which introduces the concept of expectation and fair games. Three additional handouts allow students to practice these skills.

Overview

Lesson 1: Introducing Probability Distributions / Solution

Lesson 2: Venn Diagrams / Solution

Lesson 3: Applications Questions / Solution

Lesson 4: Which Game? / Solution

Students learn the characteristics of the binomial distribution along with finding the probabilities using the binomial distribution and technology. They calculate the mean and standard deviation of the distribution ending with a mini exploration on a topic which models the binomial distribution.

Overview

Lesson 1: ESP Binomial Distribution / Notes / Command

Lesson 2: Mean and Variance of the Binomial Distribution / Solution

Lesson 3: Mini-Project Binomial Distribution / Solution

This set simplifies DP Mathematics common core 4.9 content, covering Normal distribution, probability, and problem-solving. It includes seven activities and four handouts. Teachers can decide how many activities to cover per lesson. The first activity introduces the Normal distribution, followed by in-depth exploration and worksheets on probabilities, the bell curve, and problem-solving.

Overview

Teacher Notes

Lesson 1: Normal Distribution Curve

Lesson 2: Finding Probabilities 

Lesson 3: The Bell Curve Activity / Solution

Lesson 4: Problem-Solving Activity / Solution

This DP Mathematics statistics and probability set includes various activities and exercises to help students work with the Spearman’s rank correlation coefficient. Students compare it to their regular correlation and even learn how to calculate it manually in case they need it for their internal assessment.

Overview

Subtopic Notes

Lesson 1: Matching Exercise / Solution

Lesson 2: Manual Calculations / Solution

Lesson 3: Problem Solving / Solution

Lesson 4: Mini IA / Solution

In part one of DP Mathematics AI 4.11, students learn how to conduct a chi-square goodness of fit test and test of independence. They start with an intro to hypothesis testing, which includes a gallery walk. Students then complete a Desmos activity on how to conduct a goodness of fit test. The final segment is a teacher-led lesson with guided notes on how to conduct a test of independence. The content for 4.11 is divided across two sets. For the second set, visit The Amazing T-Test!

Overview

Teacher Notes

Lesson 1: Chi Square GOF / Solution

Lesson 2: Chi Square Independence / Solution

In part two of DP Mathematics AI 4.11, students learn how to conduct a two-sample t-test. Students start by comparing the average time it takes women and men to complete a maze. Next, they complete a two-sample t-test comparing the average time women and men spend on social media. Then, they compare average ratios used in art to determine if men's head heights are larger than women's. Finally, students complete a mini project using the two-sample t-test.

Overview

Teacher Notes

Lesson 1: The Amazing T-Test / Solution

Lesson 2: Two-Sample T-Test / Solution

Lesson 3: Mini Project / Solution

Lesson 4: Maze 

These DP Mathematics AI HL 4.14 subtopic materials include instructions on how to complete a linear transformation of a single random variable, the expected values, and variance of linear combinations of n random variables. It concludes with a lesson on finding unbiased estimators of population parameters.

Overview

Lesson 1: A Linear Transformation / Solution

Lesson 2: Linear Combinations / Solution

Lesson 3: Unbiased Estimators / Teacher / Student

In this DP Mathematics AI HL 4.15 set, students to explore the central limit theorem and apply it when working with linear combinations of normal random variables. Students have a chance to do some experimentation and knowledge-building (via videos) to understand the concepts.  

Subject guide content includes:

• Linear combinations of n independent normal random variables 

• Central limit theorem

Overview

Lesson 1: Investigating the Means of Samples of M&M’s Candies / Solution

Lesson 2: Linear Combinations of Normal Random Variables / Solution

Students begin with a Desmos activity to learn about the conditions for a Poisson distribution. This activity also uses their prior learning (subtopics 4.8 and 4.9) to ensure that they can distinguish between distributions. 

Subject guide content includes: 

• Poisson distribution, its mean and variance

• Sum of two independent Poisson distributions has a Poisson distribution

Overview

Lesson 1: Poisson Probabilities Practice Questions / Solution / Command

Lesson 2: Racing Cars / Solution

This DP Mathematics AI 4.18 resource offers focused notes, tables, and diagrams on hypothesis testing, along with links to video tutorials for procedures in subtopic 4.18. Students should watch, pause, and interact with the tutorials to master the techniques. The resource also includes integrated questions for pair or small group discussion.

Overview

Lesson 1: Further Hypothesis Testing / Solution

The two tasks in this DP Mathematics AI HL 4.19 set are designed to build an understanding of Markov chains and their applications. As students work through the various sections of each task, encourage them to see the links between probability, transition diagrams and matrices. The first task allows students to see how Markov chains can be used to solve problems in probability, and the second task extends their knowledge through an investigation into the classic “Gambler’s Ruin” problem.

Overview

Lesson 1: Restaurant Dining / Solution

Lesson 2: Alicia and Benjy Play Casino / Solution