Introducing Histograms

In grade 8 in Ontario histograms are one of the new data management topics. Below is a series of activities that range from paper & pencil to virtual manipulatives. They start by a simple comparison of bar graphs and histograms to identify characteristics, then moves to some consolidation of ideas using a Desmos Sort. Then some data collection of student heights to formally introduce creating a histogram followed by some practice making histograms by hand and then with Google Sheets. If you did everything here it should take about 2-3 classes.

Grade 8

• collect and organize categorical, discrete, or continuous primary data and secondary data (e.g., electronic data from websites such as E-Stat or Census At Schools), and display the data in charts, tables, and graphs (including histograms and scatter plots) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, spreadsheets, dynamic statistical software); 
• select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph (i.e., from types of graphs already studied, including histograms and scatter plots);
  
• read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., election data or temperature data from the newspaper, data from the Internet about lifestyles), presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);
• demonstrate an understanding of the appropriate uses of bar graphs and histograms by comparing their characteristics
• Could also be used as a review in MBF3C or MDM4U

• If you are doing the physical card sort then print graphs to card stock (we suggest each set is a different colour so that if students mix them up they are easy to separate). We also suggest lamination. There are two pages for a total of 16 cards. 
• If you are doing any of the online activities then chromebooks/laptops/computers/iPads will be needed. You will also need to make copies of the Desmos version of the card sort and/or the Desmos card sort consolidation.
• Copies of the handout. 

1. The purpose of the card sort is to start to distinguish both histograms and bar graphs and continuous vs categorical data. But first have them do an open sort. Hand out cards to students (or give students the code for the Desmos Sort). Ask them to sort them in any way they wish. The only stipulations are that there should be at least two groups and each group must have at least two cards. Students will sort them in all kids of ways (by the numbers, by the topics, by the looks). Circulate and encourage them to explain how they were sorted.
2. Once sorted it is likely that most will not have them sorted how you wish. Have them describe their sorts then ask them to sort them in a way so that there are only two groups. 
3. By this time some may have them sorted into bar graphs and histograms. If not show one bar graph and then one histogram stating that you want those cards to represent characteristics of each group (you can use the slideshow to show the graphs). Use these graphs to develop the difference between continuous and discrete data.
   
4. Time to change the pace and have students collect some data. Have students measure their heights and put them on a dot plot on the board. Use this to create a histogram (without creating a tally). You might want to collect their heights in a spreadsheet so that you can create a histogram with it later. 
5. Walk through the front of the handout to show how to create a histogram from data. 
6. Likely you will be at least done one class at this point (if not more). At the beginning of the second class, start with the consolidation Desmos card sort (with some stuff on average) to remind students of continuous and discrete data. Another possible way to start is to have students use this Google form to enter some examples of continuous and discrete data. You can take up the results. 
7. Once done taking up the worksheet you can then introduce students to creating histograms using Google Sheets. Share this sheet with continuous data. This video will tell you how. 

• Card Sort Google Docs, PDF, Desmos Slide show of each graph
• Desmos Consolidation
• Handout Google Docs, PDF 
• Handout Answers Google Docs, PDF
• Discrete/Continuous Form
• Spreadsheet Graphs, Answers

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks 

Data Management Scavenger Hunt

This is an activity that we adapted from a TIPS activity (Grade 8 Unit 11, Day1, Pg 3). In this activity student are given a set of data (with no labels) and asked to find their matching graph and title (which are randomly placed around the room). Once finding their cards they are given a question card to use with their graph and data. It's actually a surprisingly difficult activity but it helps bring out conversations about types of data and what they should look like.

• Gr7DM - select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph; read, interpret, and draw conclusions from primary data and from secondary data presented in charts, tables, and graphs (including relative frequency tables and circle graphs);
• Gr8DM - select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph; read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);
• MBF3C - D1.5 identify different types of one-variable data, and represent the data, with and without technology, in appropriate graphical forms (e.g.,histograms, bar graphs, circle graphs, pictographs)
• MAP4C - D1.4 create a graphical summary of two-variable data using a scatter plot , with and without technology
• MDM4U - D1.5 interpret statistical summaries to describe the characteristics of a one-variable data set (note that this certainly can be used as review of all types of data)

Data Management Cards Prep work: Print, laminate (optional) and cut the cards out. Separated out the sets of data from the graphs and Titles. Each page contains one set of data, graph and title (note that one set has two possible matching graphs). Also included in the set are a page with extra questions and a page with the answer key on it.

1. Prep the classroom by randomly sticking the graphs and the titles around the room for students to find. Note that this activity was originally made for grade 8 but if you wanted to do it for grade 7 you should probably consider taking out any graphs with scatter plots.
2. Put students into groups of 2 or three (there are 17 different sets of cards)
3. Each group gets a set of data and are told to wander the room looking for their matching graph and title. Some of these are not easy so students should work together to decipher the information. You should probably circulated to give hints (with your answer key).
4. Once a group finds their matching cards, they are given a question card to answer regarding their graph.
5. If they finish early give them another set of data to try.

Data Management Scavenger Hunt (Doc) (PDF)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Sort Graphs into Types of Data

This is a simple and quick sorting activity for graphs to help introduce the idea of types of data. And although that is the intended purpose it is done as an open sort so that students can (hopefully) start to see that there are different types of data without being formally introduced to them. This is not intended to be a long activity but just a short Minds On type to begin a class. Keep in mind that if students don't sort them by data type then you may have to ask some leading questions to help move them that way. Though this was originally developed for the MDM4U class, by removing some of the graphs, it could be used for grades as low as 7 (for example, grade 7 students will likely not have seen histograms).
[Updtae - Now a Desmos Card Sort version exists]

• Gr7DM, Gr8DM - collect and organize categorical, discrete, or continuous primary data and secondary data
• MBF3C - identify different types of one-variable data (i.e., categorical, discrete, continuous)
• MDM4U - distinguish different types of statistical data (i.e., discrete from continuous, qualitative from quantitative, categorical from numerical, nominal from ordinal, primary from secondary, experimental from observational, microdata from aggregate data)

• One set of graph cards per group

1. put students in groups
2. distribute cards with graphs 
3. ask them to sort in any way they see fit. Use the results to steer towards types of data. Students should focus on both the look of the graph and the characteristics of the data being shown.
4. possible leading questions: "Can you arrange these so that there are only two groups? If so can you arrange each of those two groups into sub groups?" 
5. As an extension or alternate activity, students could sort by types of graph.

Note that the graph of the number of friends is a histogram which might lead some to think it is continuous data. This could be a good talking point as the number of friends a person can have can only be a discrete amount. 

Types of Data cards (doc) (pdf)
Desmos Card Sort (with self checking feature for numerical and categorical)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks