Data : Data involving one and two variables

Connections With Other Strands

By integrating the concepts of statistics and data into other mathematical strands, students can better understand how the different strands are interconnected and how they can be used together to solve complex problems in various contexts. This also reinforces students’ overall understanding of mathematics and their ability to apply their knowledge naturally in the real world.

When examining each question, reflect on the knowledge and skills from the overall and specific expectations in the Data strand that students will use, as well as the connections to the key concepts.

Number: Percentages and Proportions

Specific Expectations: B3.3, B3.5, D1.2, D2.3, D2.4
Mathematical Processes: Reflecting, Communicating, Selecting Tools and Strategies

Students collect data on the duration of the commute to and from school according to the mode of transport used.

Calculate Ratio and Percentage: Determine the ratio and percentage of students in the school who use each mode of transportation relative to the total number of students.
Understand the Negative Sign: Determine the difference in average time between the commute to and from school for each mode of transportation. What does a negative result mean? What does a positive result mean?
Create a Box Plot: Choose the most used mode of transportation and create two box plots for travel times, one for the trip to school and one for the return trip home. What can you say about the similarities and differences between the outbound and return trips?

Algebra: Linear Relations

Specific Expectations: C3.1, C3.3, D1.3
Mathematical Processes: Problem Solving, Connecting, Selecting Tools and Strategies

Students conduct an experiment to measure the length of different ropes (varied lengths and thicknesses) based on the number of knots tied in the rope.

Determine a Linear Regression Model: Using technology, create a scatter plot for each rope, then determine the equation of the linear regression model based on the collected data.
Make Predictions: Use the equation to make predictions about the maximum number of knots possible for each rope.
Determine the Point of Intersection: Choose two ropes and determine how many knots are needed to make the two ropes almost the same length.

Geometry and Measurement: Interior Angles

Specific Expectations: D1.2, D1.3, E1.2
Mathematical Processes: Selecting Tools and Strategies, Reasoning and Proving

Students will generalize the sum of the interior angles of an n-sided regular polygon.

Create a Table of Values: Starting from the principle that the sum of the interior angles of a triangle is 180°, use technology to create a table of values indicating the number of sides, the number of internal triangles, and the sum of the interior angles for all regular polygons from 3 to 20 sides.
Determine a Linear Regression Model: Create a scatter plot representing the relationship between the sum of the interior angles and the number of sides of the regular polygon, and then display the equation of the most appropriate linear regression model for the scatter plot.
Make Connections: Explain the connections between the equation and the data in the table of values.

Financial Literacy: Budget

Specific Expectations: D2.3, D2.4, F1.4
Mathematical Processes: Problem Solving, Connecting, Reflecting

The school’s store must establish a budget to determine the products that will be purchased for sale next year. The profits from the store are used to organize activities and/or help students in need.

Collect Secondary Data: Take an inventory of the products that have been sold over the past six months and those that remain in the store.
Collect Primary Data: Survey students to determine the products they would like the school store to sell.
Complete and Plan a Budget: Create an actual budget for the current year and a budget forecast for next year based on the data collected.
Adjust a Budget: Adjust the budget knowing that the school has received a $1,000 donation for the store.

Multi-Strand Task

Specific Expectations: B3.5, C1.5, C3.1, C4.4, D1.3, D2.3, D2.4
Mathematical Processes: Problem Solving, Reasoning and Proving, Connecting, Selecting Tools and Strategies

Students conduct a survey of energy consumption in homes in their community to raise awareness of energy conservation.

Collecting and Analyzing Data: Students collect data on the energy consumption of various homes over a one-month period. They use technology to organize and represent the data using graphical representations (circle graphs, histograms).
Calculating the Surface Area: Students calculate the surface area of different houses in square metres (m²) using provided plans or dimensions.
Establishing a Linear Regression Model: Students analyze the relationship between the size of the house, in square metres (m²), and the monthly energy consumption, in kilowatt-hours (kWh), by creating a scatter plot and determining the equation of the linear regression model based on the collected data.
Predicting and Optimizing: Using the equation, students predict the energy consumption for houses of different sizes and propose ways to optimize this consumption.

Reflection

What are the most effective ways to integrate algebra, data, and measurement concepts into an activity to create an authentic and engaging learning experience for students?
How can I encourage students to discover and understand the connections between different mathematical strands and see how these concepts interact and apply in real-world contexts?
What are the best approaches to structuring a task that prompt students to apply their data analysis skills to solve measurement or algebra problems, and understand the relevance of connections between different mathematical strands?