# Drawing From Data

Keisha draws a circle and places the multi-link around the circle like this. What do you think she is doing?

Drawing from Data (D2) prompts learners to genuinely engage with the context of each data set. In Section A, students represent survey results on a circle — in anyway they choose. The desire for accuracy in ‘fair sharing’ the circle naturally leads to using protractors for drawing a pie chart. When students record how they spend the hours in a typical school day on a circle and on a timeline, they make connections between a pie chart and a compound (stacked) bar chart. By studying more circular contexts — clocks and cut-up cakes — students learn to see angles as a proportion of a whole. They view frequency chart data as a form of ratio table, which they can use to calculate sector angles.

In Section B, learners explore data about membership of the European Union. Again, the dot plot features as helpful way to represent the data. Students consider what it means to split a data set into quarters as a means of comparing one data set with another. The significance of the median, inter-quartile range and the associated box plot emerge. Tasked with comparing yearly weather patterns in various cities worldwide, as well as studying the maths test results of two Year 8 classes, students are repeatedly asked to make meaningful inferences and recommendations from the data at hand.

The last section of Drawing from Data (D2) focuses on helping students make sense of where the mean, median, mode and range can be seen in tabulated data. Through the context of the number of road traffic accidents and the results of a General Election, students encounter a range of data representations which they ‘’unpack’’ and ‘’re-package’’ as a way of making connections between where an average value appears in a raw data set and where it appears in the frequency chart version of the same data. To finish, students collect and analyse data showing how far you can throw a welly and consider the effect of grouping data on the measures of average.

# Overview of Drawing From Data

#### Section A: A Piece of Pie

Lessons 1: Opinions
Students draw pie charts using several informal methods. Within the context of school survey results, they share out circles in proportion to various amounts.

Lesson 2: Passing Time
Students draw connections between a stacked bar chart and a pie chart by constructing pie charts without using a protractor. In doing so, they learn to recognise that the distance around a sector is proportional to the frequency of that sector. Exploring the angles between the arms of an analogue clock, students are introduced to informal ways of thinking about the angles at the centre of a circle.

Lesson 3: School Residential
Students use proportion to justify how large each sector should be, calculating the angle at the centre of a pie chart with a ratio table. They then construct these pie charts precisely, using a protractor. Various pie charts are compared and interpreted.

#### Section B: Dot and Box Plots

Lesson 4: The European Union
Students revisit the dot plot and are introduced to measures of “spread” and box plots by drawing on data about membership in the European Union. The students use dot plots to split data into quarters and they employ this information in drawing a box plot as well. Working to synthesize this information to describe how membership of the European Union has grown, they develop a meaningful insights in to the use of concepts like median and quartile.

Lesson 5: Maths Results and Relocating
Students continue to analyse data presented in a variety of ways. These include: lists, tabulations, charts, dot plots, and box plots. They are encouraged to make statements about the data, especially the use of quartiles to make comparisons between two sets of data. Students construct box plots to compare test scores, carefully considering how this data is distributed. They critique charts and use quartiles and box plots to compare temperatures across four cities. Students then use their analysis to make recommendations.

#### Section C: Say What You See

Lesson 6: By Accident
Students study and make comments about real-life data presented in a variety of forms. Contexts include data about the number of road traffic accidents sorted by speed and location, as well as data about the 2019 general election and phone usage. Some charts show familiar representations, while others are less familiar. Students are encouraged to ask questions and interpret the diagrams in an open-ended way. This strategy supports them in embracing the meaning of the data with a critical and thoughtful eye, before focusing on the actual question.

Lesson 7: By Accident
Tasked with finding the total number of accidents from a list showing the number of accidents over 100 days, students may gravitate toward summing repeated values. This technique helps them to make sense of the data “packaging” used in frequency tables. When presented with accident data from another police force, this time in the form of a frequency table, students re-package this data – as a day-by-day list and as an ordered stem-and-leaf type tabulation. Frequency tables are notoriously difficult for students to interpret. But, in working across several representations, this lesson helps students to unpack and re-pack these tables, making links and developing meaning along the way.

Lesson 8: Frequently Does It
Students work from a disordered list of raw data, developing a frequency table and an ordered stem-and-leaf type list. They are required to focus on (i) seeing the number of pieces of data and (ii) seeing the total within various representations of the data. The inclusion of several data sets per context creates a purpose for making comparisons. Students apply a variety of strategies, including the use of ratio tables and mean average comparisons.

Examining the spelling test marks for twin brothers creates a need for finding the mean, median, mode and range of two data sets. One set of spelling test results appears as a list of marks, while the other is a tally chart. Students represent each set of marks as a dot plot, allowing them to make informal comparisons prior to using the more formal concepts listed above. Students articulate where they can see the mean, mode, median and range within (i) the list, (ii) the tally chart, and (iii) the dot plot.

Lesson 10: ‘’That’s Typical of You’’
By looking around at their class, students consider what a typical student looks like in terms of hair colour, hair length, height, number of siblings, etc. Using Activity Sheet 11 – Year Ten Data, which contains anonymised data for a sample of Year 10 pupils, students choose a category to represent graphically and find an “average” value. They repeat this process for other categories and then reflect on the relationship between the type of category (numerical or not) and the type of average chosen.

Lesson 11: Far Fetched

(CC BY-SA 4.0) Russ Hamer

Students comment on the length of welly throws for people attending a school fair by studying the data presented in a grouped frequency table. In considering how far they themselves could throw a welly boot, the students begin to question the legitimacy of the data. (A throw of nearly 70 metres?) Students could have a go at throwing a welly to provide a comparative data set, or alternatively use the teacher trainees’ genuine results. Students study a variety of grouped frequency tables, make dot plot representations and develop meaning for where the estimated mean, median, mode and range are located within a grouped frequency table.