Task Teacher Guide

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Students select an appropriate scale based on the range of various data sets.

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The purpose of the Day 2 activities is to reinforce key concepts from Day 1. 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);
• Scale in graphs are the system of marks at fixed intervals;
• The intervals can be unitized; 
• Changing the interval selected for a scale can impact the audience’s initial notion of the data;
• The range of a set of data is the difference between the highest and lowest values in the set.

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Visual Number Talk

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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 100. Ask students to plot each of the following data points on the line using their spatial reasoning skills, presenting them one at a time and giving students enough think time before moving on to the next data point. 

Encourage students to talk to their neighbours and compare before they describe where you should plot your data point up on the board. This not only helps students solidify their own understanding of magnitude of number and spatial relationships, but also allows them to build their adaptive reasoning skills as they explain their thinking out loud.

If facilitating with the visual number talk prompt videos, you will want to ensure that you pause for each data point and encourage students to tell you where to place your finger on the line prior to revealing where the data point goes by continuing the video.

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If you are facilitating this number talk without the use of the visual prompt video, then you will prompt students to:

Draw a number line from 0 to 100.

Then, one after the other, prompt them to plot each of the following on the number line:

50
25
10
5
15
60
75
90
95

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:

Throughout this set of visual number talk prompts, students will be invited to partition the number line into halves, fourths, fifths and other fractional amounts.

As students continue to plot data points on the number line, they will have the opportunity to partition the entire number line as well as smaller segments of the number line.

Throughout this set of visual number talk prompts, students are able to leverage their spatial sense in order to strengthen their understanding of the magnitude of number as well as their fractional reasoning skills.

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If you are facilitating this number talk without the use of the visual prompt video, then you will prompt students to:

Draw another number line from 0 to 100.
Plot the following values.

Then, one after the other, prompt them to plot each of the following on the number line:

20
10
30
60
55
80
85
65
70

Again this set of visual number talk prompts will invite students to have another opportunity to partition the number line in various ways.

Observe how different students decide to locate where 20 should be plotted on the number line. For some students, they may choose to partition the entire number line into fifths; suggesting that they understand that 20 is one-fifth of 100. For other students, they might partition the line into half, then partitioning the first half into fifths to reveal units of 10.

As students continue to plot more numbers on the number line, monitor how they are choosing to partition and reason through the string.

Based on how students partition their number line, where might you go next? Should you create your own string to continue this work further on the next day or when you spiral back later? Make notes of where students are strong and where some students might be struggling.

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Purposeful Practice

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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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Resources and Downloads

Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.