Understanding Bar Graphs Unit of Study: Data Global Concept Guide: 3 of 3

Content Development Classroom discussion should continue to foster connections between line plots, tally charts, picture graphs, and bar graphs. Interpreting a bar graph requires students to comprehend the graph is a model of data. Go Math! identifies several skills students must apply to interpret a bar graph.  The title and topic of the data  Labels for categories and the scale  The individual categories of data  The amounts the bars represent Teachers should be cautious to not focus on the techniques of graph construction to the exclusion of data comprehension. Students should be able to write statements which include numerical data about a bar graph and be involved in discussions about why data was collected and how it is was organized for the “reader”.

Day 1  Essential Question: How do you use a bar graph to show data?  Show students a picture graph and bar graph that display the same data (see below).  Facilitate a whole-group discussion based on the students’ observations. Some discussions you may want to highlight are:  What is the graph about? How do you know  How are the graphs similar? How are they different?  What does each smiley face represent? How do you know?  Who had the most? Who had the fewest? How do you know?  How would the graph change if Rosie had two more?  Which two students had the same amount?

Day 1 continued  The focus of day 1 is on interpreting the data represented by a bar graph. Students should understand a bar graph is another way to model mathematics. Models presented to students should include horizontal and vertical bar graphs.  Presenting students with a bar graph lacking a title, category labels, and scale is a suggestion for emphasizing the value of these components for students. Generalizations can be made about the graph, yet students will struggle to find true meaning in the graph. As the components are added, students will be able to construct meaning to the bar graph and generalize the value of these components for the reader.  Sample Engage:  Have them turn and talk to a neighbor and state 3 things that they notice about the picture graph.  Facilitate a whole group discussion based on the students observations. Some discussions you may want to highlight are:  What is the graph about? How do you know  What does each bar represent? How do you know?  Who had the most? Who had the fewest? How do you know?  How would the graph change if red had two more?

Day 1 continued  Elements of GO Math Lesson 10.4 can be used on Day 1 to help students understand how data can be displayed in a bar graph.  Focus on questioning students about elements of the graph including analysis of the data presented in the graph.  Possible Journal Question: Bar GraphsBar Graphs  By the end of Day 1, students will be able to accurately read and interpret data presented in a bar graph.

Day 2  Essential Question: How do you create and display data on a bar graph?  Day 2 engages students in construction of a bar graph. A title, category labels and a unit scale are expectations. Students may use prepared data and complete graphs as per lesson Student products should be monitored for accuracy of data representation as per the unit scale.  Sample Engage:  Survey students on their favorite candy: Skittles, Starbursts, Sweet tarts, Jelly beans.  Record the data in a Tally Chart.  Have students work in small groups to determine how to display the data from the Tally Chart in a bar graph.  Students should include, a title, labels, and a unit scale. Remember, per the standard, students are using one-to-one correspondence in their graphs.  Classroom discussion should include comparing information shown on a bar graph and solving problems related to the data. The “On Your Own” and “Problem Solving” components from are suggestions for comprehension combined with accuracy in completing a bar graph.

Day 2  Some students may be ready to pose their own survey question, gather the data, and represent the data on a bar graph.  Possible Journal Question: Bar GraphsBar Graphs  By the end of Day 2, students will be able to create a bar graph from a set of data.

Day 3  Essential Question: How do you solve problems using data from a bar graph?  Day 3 combines the accuracy of bar graph construction with analyzing data. The goal is for students to understand graphs convey factual information and provide opportunities to make inferences based upon data.  Teach & Talk from 10.6 is an example. Teachers may prefer to use data collected from class survey questions or science investigations.  Students should be encouraged to write statements about graphs using numerical data and be able to make generalizations about data trends and implications. Join together, separate, and compare problem solving structures using the data within the bar graph is appropriate.

Day 3  Students can utilize elements of Go Math Lesson 10.6 on Day 3.  Although it is important that students understand how to construct a bar graph, it is equally important that students be able to read and interpret data represented in bar graphs.  Possible Journal Question: Bar GraphsBar Graphs  By the end of Day 3, students will be able to solve problems based on information presented in a a bar graph.

Sample Survey Questions for Collecting Data  How many letters in your last name ?  Which of these is your favorite color?  Which coins in our scoop? (scoop a handful of coins and sort)  Which of these fruits is preferred at lunch?  Which Dr. Seuss book is your favorite?  Which type of seed should we plant?

Enrich/Reteach/Intervention Reteach:  Reteach p. R97  Reteach p. R98  Animated Go Math Model: Make and Interpret Bar Graphs Animated Go Math Model: Enrich:  Enrich p. E96  Enrich p. E97 Students who need support may benefit from connecting snap cubes together to represent data quantities for each category. Students would record the titles and labels on index cards or sentence strips and use the snap cubes as a concrete example of the bar graph. See TE page 477A. Proceed by having students construct a representation of the model on prepared grid paper.

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