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# Mathematics Matters Lesson Accounts 47 - Representing Data

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Created on 29 May 2008 by ncetm_administrator
Updated on 17 June 2008 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 47 - Representing Data

 Written by Rob Simpson Organisation South Hunsley School Age/Ability Range Y7

Task – to produce graphical representations of hand span / shoe size data for the class. Introduction – 30cm rulers (or tape measures) and a pre-prepared sheet were on the students’ desks when they arrived in the classroom.
The sheet was as follows

I asked, “We are going to collect data and display it graphically, how can we collect the data?” This led to discussion on clarifying the data collection process.

Once the data was collected, the class went to an outside paved area and I said that we would represent the data on it. There followed a short discussion on labelling axes. “What should we start at?” (Student not me!)

The axes looked as shown.

I then asked them how it would be best to represent the data. I suggested standing adjacent to their shoe size on the axis.

The students did this, forming a vertical bar graph. They then suggested standing next to their hand span, thus forming a horizontal bar graph. Finally I suggested standing adjacent to both shoe size and hand span.

After forming these graphs, I then videoed the students making them. First they stood adjacent to shoe size, then hand span, then both.

In the classroom we then watched the video and the students had to recreate the graphs on squared paper.

(This video is available at www.maths-it.org.uk)

Discussion before the task. “We need all the data”.

Collection of data done by students on the whiteboard and written in on their sheets, (previously they had written only their data). Students drew scatter graph and bar charts for the data, (though not formally).

Discussion after the task “What does this show?” Eventually with some direction (Critical moment planned) “the smaller the hand span, the smaller the feet etc”
The next lesson covered formalising drawing these graphs. The pace of the lesson was sustained through a variety of fast paced activities involving all students.

Sharing ideas and looking at each others graphs. And “Should there be a set way for displaying data (a set of rules)?”

What were the critical moments?
Unplanned – during the initial data collection, “My shoes are size 6 but my trainers are 7’s.” This led to a discussion of collecting hand span data. “We should all do it the same!”

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Planned - Why it’s good to represent data graphically. The idea of correlation
Slightly off plan – How to collect data and make sure it’s reliable.

How was that mathematics learnt?
Discovery with guidance.

Other memorable outcomes
A girl in a white shirt had big hands and small feet (the rest of the class were wearing black jumpers).

Resources
Paved area with tall building.
Video camera.
Rulers.
Pre-prepared data collection sheets.

## Values & Principles

 Conceptual understanding and interpretations for representations Appreciation of the power of mathematics in society Uses rich, collaborative tasks Creates connections between topics both within and beyond mathematics and with the real world Uses resources, including technology, in creative and appropriate ways

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