Students will continue to investigate how removing or adding a value in a data set impacts the mean and the shape of the data. Students will consolidate their understanding that the range of the data will influence the level of impact.

The purpose of the Day 4 activities is to reinforce key concepts from Day 3. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas. 

• There are different types of data;
• Data is often characterized as continuous or discrete;
• Discrete data is often countable and can only take on certain values;
• Continuous data is measurable and can take any value (within a range);
• The range of a set of data is the difference between the highest and lowest values in the set;
• A measure of central tendency for a data set summarizes all of its values with a single number;
• Mean can be revealed through division;
• Removing data from a data set has an impact on a measure of central tendency;
• Removing data from a data set can alter the shape and distribution of the data.
•  An outlier is a data point that differs significantly from the rest of the data set. 

This number talk can be facilitated using a chalk/whiteboard or using the visual number talk prompts provided below.

If facilitating without the visuals, use a metre stick to draw a line on the board. Label the line 0 to 10. Ask students to plot each of the following data points on the line using their spatial reasoning skills.

5
2.5
1
0.5
4
6
7.5
9
9.5

Determine the range, mean, median and mode of this data set.

If you are intending to use the set of visual number talk prompts, then begin playing this video and be prepared to pause where prompted throughout:

The first prompt will ask students to:

Draw a number line from 0 to 10.

Then, students are asked to:

Plot 5 on your number line.

The goal of this portion of the visual number talk is to leverage and build on student spatial reasoning skills and also a better sense of the magnitude of number (i.e.: how numbers relate to one another).

Students will be asked to partition the number line in various ways including partitioning into halves, fourths, fifths and more.

Throughout this exercise, students will also be tasked with plotting decimal numbers as well which increases the complexity of the task.

Finally, once all values have been plotted on the number line, students will be asked to find the range, mean, median and mode of the dataset.

Since the values have been placed on the number line, it becomes easier to visualize these different measures that help to describe the characteristics of the data set.

For the mean of the dataset, rather than simply following the procedure of:

“Summing the values and dividing by the number of values”

We can help students conceptualize the mean of the dataset as “the great equalizer.“ In other words, we are highlighting that the mean redistributes values so that all “groups” receive the same amount.

For the median of the dataset, students can work their way from the outside data points towards the centre to find the median of the data set or the data value in the middle.

This dataset is not ideal for diving deeply into the mode of the dataset, but it is worthwhile to mention to students that since we have no data value occurring more than the other data values, the mode is not helpful here.

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Question #1:

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Question #2:

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Question #3:

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Question #4:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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