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This problem-solving bar-graph lesson uses centimeter measurements of hat sizes
3, 4, 5
By – Cindy Frank
Primary Subject – Math
Grade Level – Grades 3-5
- Upon completion of the lesson, students will be able to:
- Measure to the nearest centimeter
- Create a bar graph and identify its use
- Determine the average from a set of data
- Apply data compiled and prior knowledge to answer a word problem
New York State Learning Standards:
- Mathematics Standards:
- Students use mathematical/multiple representation to provide a means of presenting, interpretation, communicating and connecting mathematical information and relationships. (4)
- Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. (5)
- Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics and construct generalizations that describe patterns simply and efficiently. (7)
- Tape Measure
- Charted Word Problem
- Graph Paper
- Start with a short motivator to remind students of the measurement concept that was already taught. Ask students to independently measure several lines to the nearest centimeter.
- Upon completion, discuss as a whole class the strategies that they used to measure.
- Then refer to a word problem that you posted in the front of the room.
Mrs. Woods owns a clothing store. She is trying to decide how many children’s hats to stock in each possible size. Should she stock the same number of hats in each size? Or, should she stock more hats in the more popular sizes?
Help Mrs. Woods decide. Pretend that she has asked your school to collect and organize data about students’ head sizes. She plans to combine the data for all the classes and then use the data to figure out how many hats of each size to stock.
Ask students for strategies they may use to help Mrs. Woods. Explain to them that they will be using their head sizes to help Mrs. Woods.
- Ask if they can use their rulers. They should determine that a ruler does not bend and, at this point, direct them to use a tape measure. Have the class examine the tape measure and how to use it.
- Students will now work with a partner to measure each student’s head size. Each are to record their measurement in centimeters on a Post-It.
- Inform the students that we have now collected data and ask what that term means. Students should understand that data is only worthwhile if it is looked at carefully.
- “We will now plot the data on a line plot.” Ask if any student believes that he or she has the smallest head size. If that is the lowest measurement, start the line plot from that point. Then place the post-its on the line until all students have included theirs.
- Ask students to draw conclusions based on the information displayed in the line plot.
- Distribute a handout that describes three types of graphs: a line graph, a bar graph and a circle graph. Do a shared reading of each graph’s description and ask students to determine which type of graph would show this information for Mrs. Wood’s best. (Bar Graph)
- Based on prior lessons, students should know how to create a bar graph. They should use the line plot to create a bar graph of the data and may refer to their notes for reminders and clarification. Circulate and assist students who may be struggling.
- Once graphs are complete, ask students to share why they think we graphed the data. Model one type of question that can be answered by reading the graph:
“In what hat size should Mrs. Woods carry the least amount of hats?”
- Partners are then to work together again to create one question that can be answered by looking at the graph. Each student is to record this answer under their graph.
- Questions will be shared-out.
- Now revisit the problem and determine what we will tell Mrs. Wood’s to do. Students should then record what they would tell Mrs. Wood’s.
- If time permits, revisit the concept of calculating average. Ask students to refer back to their notes and to relay the steps to finding average. Then, as a whole class, find average student head size.
- Assess each student informally and formally. Informally assess students by observing their work with partners, how they follow directions and their participation during whole class instruction. Students are expected to continually refer back to the word problem and their ultimate goal of answering it. Formal assessment should be an evaluation of their bar graphs and the questions they create.
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