Lesson: Displaying and Analyzing Data  Pictographs and Bar Graphs, Lesson 2
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Lesson Objective
The purpose of this lesson is to teach mathematicians how to use pictographs and bar graphs to display data.
Lesson Plan
Curriculum Standards
• Identify appropriate ways to display data. [M.44a.4]
• Construct and draw conclusions from representations of data sets in the form of tables, line plots, pictographs, tallies, circle graphs, line graphs, and bar graphs (with a scale other than 1). [M.44b.4]
The Point
When do mathematicians use pictographs and bar graphs to display data?
III. Materials Needed
• Copies of 4.1.2 Problem Solving Task
• Optional: Enlarged copy of task or transparency of task
• Math Journals/glue sticks
• Slates/ markers
IV. Lesson Outline
Time: 60 Minutes
5 min. – Understanding The Point and the ProblemSolving task
5 min. – Independent ProblemSolving
30 min. – Discussion/Practice/ Summary
5 min. – Fact power
15 min. – Math Workout
V. Learning Activities
• Understanding The Point and the ProblemSolving task (5 min.)
Distribute a Problem Solving Task slip to each student.
Students read and understand the task independently.
2. Independent ProblemSolving (5 min.)
Students work to solve the problem on their slates.
3. Discussion/Practice/Summary (30 min.)
PART I – DISCUSSION
Big Ideas:
• A pictograph is a chart that uses pictures or symbols to display data.
• Every pictograph has a title, key, labels, pictures or symbols
• Pictographs are helpful because we can see which group has the most in it by simply looking at which group’s pictures/symbols extend the farthest.
• When mathematicians read pictographs, they must pay careful attention to the key so they know how many items are represented by each picture/symbol.
*COMMON MISCONCEPTION: Pictograph scales are commonly assumed to be 1:1 and this often causes students to answer questions about pictographs incorrectly. Repeatedly stress with students that it is crucial that a mathematician read the key before interpreting a pictograph.
• Pictographs can be used to display data even when the numbers are large because a symbol or picture can be used to represent any amount.
• A bar graph is way to display data that uses bars to represent numbers.
• Bar graphs display information in a way that makes it easy to show comparisons.
• Every bar graph has a title, scale, labels on each axis and bars that show data.
• When mathematicians read bar graphs, they must pay careful attention to the scale so that they understand what numbers the bars represent.
• Sometimes a bar ends between two labeled points on an axis. When this happens, the mathematician must think of the axis like a number line and determine the value of the point on the graph where the bar ends.
• Bar graphs can be used to display data even when the numbers are large because the scale can be of any magnitude.
Possible Discussion:
• Invite a student to explain what graph they think would be the best for displaying the data in situation A.
Note* You may want to reference your chart from yesterday
• Students share their responses to Part A.
Guide students to see that Tyrique wants to compare and out of all the choices the pictograph is best for comparing because we can easily see which one has the must pictures or symbols.
• Students share their responses to Part B.
Guide students to see that Ashley is also comparing and out of all the choices the bar graph is best used for comparing.
PART II – WHOLE CLASS PRACTICE
Options:
a. Give students other situations and ask students how they might display the data chart (Only Tally charts, tables with numerals, pictographs and bar graphs… the rest will come later ):
• Give situations where the numbers are either very small or very big or when the person is walking around asking others to vote on something.
(tally charts and table with numerals)
• Give situations when the person is comparing! (bar graph or pictograph)
b. Give student a data set and tell them what you are hoping to do with it and ask them to create the graph (tally char, table with numerals, bar graph, pictograph)
• Remind students to label all axis and give the graph a title!
• If making a pictograph remind students choose an appropriate scale for their key based on the data, no keys of one because it defeats the purpose of a pictograph.
PART III SUMMARY
Stop and have students look back at the question that is The Point of today’s lesson:
When do mathematicians use pictographs and bar graphs to display data?
Students work as a class to form a statement to answer the question in their math journal as a summary of their learning from the lesson.
• Fact Power (5 min.)
Students complete worksheets/timed quizzes and work to memorize multiplication facts.
• Identify appropriate ways to display data. [M.44a.4]
• Construct and draw conclusions from representations of data sets in the form of tables, line plots, pictographs, tallies, circle graphs, line graphs, and bar graphs (with a scale other than 1). [M.44b.4]
The Point
When do mathematicians use pictographs and bar graphs to display data?
III. Materials Needed
• Copies of 4.1.2 Problem Solving Task
• Optional: Enlarged copy of task or transparency of task
• Math Journals/glue sticks
• Slates/ markers
IV. Lesson Outline
Time: 60 Minutes
5 min. – Understanding The Point and the ProblemSolving task
5 min. – Independent ProblemSolving
30 min. – Discussion/Practice/ Summary
5 min. – Fact power
15 min. – Math Workout
V. Learning Activities
• Understanding The Point and the ProblemSolving task (5 min.)
Distribute a Problem Solving Task slip to each student.
Students read and understand the task independently.
2. Independent ProblemSolving (5 min.)
Students work to solve the problem on their slates.
3. Discussion/Practice/Summary (30 min.)
PART I – DISCUSSION
Big Ideas:
• A pictograph is a chart that uses pictures or symbols to display data.
• Every pictograph has a title, key, labels, pictures or symbols
• Pictographs are helpful because we can see which group has the most in it by simply looking at which group’s pictures/symbols extend the farthest.
• When mathematicians read pictographs, they must pay careful attention to the key so they know how many items are represented by each picture/symbol.
*COMMON MISCONCEPTION: Pictograph scales are commonly assumed to be 1:1 and this often causes students to answer questions about pictographs incorrectly. Repeatedly stress with students that it is crucial that a mathematician read the key before interpreting a pictograph.
• Pictographs can be used to display data even when the numbers are large because a symbol or picture can be used to represent any amount.
• A bar graph is way to display data that uses bars to represent numbers.
• Bar graphs display information in a way that makes it easy to show comparisons.
• Every bar graph has a title, scale, labels on each axis and bars that show data.
• When mathematicians read bar graphs, they must pay careful attention to the scale so that they understand what numbers the bars represent.
• Sometimes a bar ends between two labeled points on an axis. When this happens, the mathematician must think of the axis like a number line and determine the value of the point on the graph where the bar ends.
• Bar graphs can be used to display data even when the numbers are large because the scale can be of any magnitude.
Possible Discussion:
• Invite a student to explain what graph they think would be the best for displaying the data in situation A.
Note* You may want to reference your chart from yesterday
• Students share their responses to Part A.
Guide students to see that Tyrique wants to compare and out of all the choices the pictograph is best for comparing because we can easily see which one has the must pictures or symbols.
• Students share their responses to Part B.
Guide students to see that Ashley is also comparing and out of all the choices the bar graph is best used for comparing.
PART II – WHOLE CLASS PRACTICE
Options:
a. Give students other situations and ask students how they might display the data chart (Only Tally charts, tables with numerals, pictographs and bar graphs… the rest will come later ):
• Give situations where the numbers are either very small or very big or when the person is walking around asking others to vote on something.
(tally charts and table with numerals)
• Give situations when the person is comparing! (bar graph or pictograph)
b. Give student a data set and tell them what you are hoping to do with it and ask them to create the graph (tally char, table with numerals, bar graph, pictograph)
• Remind students to label all axis and give the graph a title!
• If making a pictograph remind students choose an appropriate scale for their key based on the data, no keys of one because it defeats the purpose of a pictograph.
PART III SUMMARY
Stop and have students look back at the question that is The Point of today’s lesson:
When do mathematicians use pictographs and bar graphs to display data?
Students work as a class to form a statement to answer the question in their math journal as a summary of their learning from the lesson.
• Fact Power (5 min.)
Students complete worksheets/timed quizzes and work to memorize multiplication facts.
Lesson Resources
4.1.2 Problem Solving Task.docx 
233

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