Measurement. When Smaller Is Better. Activity:

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1 Measurement Activity: TEKS: When Smaller Is Better (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: (A) estimate measurements (including circumference) and evaluate reasonableness of results; (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; (6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; Overview: Materials: Grouping: Students will investigate measurement tools, accuracy, and precision. Students will generalize the effects on estimating area as the units of the measurement tool become more precise. Students will apply this knowledge to problem-solving situations. Class Chart paper Markers Class Data Collection Sheet Per Group 1 plain sheet of paper 1 cm 2 grid paper (Various types of grid paper can be found at cm 2 grid paper 0.25 cm 2 grid paper 1 inch 2 grid paper 0.5 inch 2 grid paper 0.25 inch 2 grid paper Calculator Per Student Pipe cleaners Student Data Collection Sheet 3 students per group When Smaller is Better Page 1

2 Time: One 55-minute class period Lesson: 1. Lesson Setup Students will work in groups to investigate the effect on area as the size of the grid decreases. Each student will conduct the experiment at least twice using at least two different sizes of grid paper. As an example: Student 1: 1 cm 2 grid paper and 0.25 inch 2 grid paper Student 2: 0.5 cm 2 grid paper and 1-inch 2 grid paper Student 3: 0.25 cm 2 grid paper and 0.5 inch 2 grid paper Each group will also have one blank sheet of paper. You want students to make several generalizations during this lesson: Using a more precise measurement tool gives more accurate measures. As the intervals of the measurement tool increases, precision increases and measurement error decreases. In a class of 28 students, there should be about 8 10 sets of data using each type of grid paper. The class will find the mean of the area of each regular polygon, using each type of grid paper. The introductory portion of this lesson could actually be assigned as homework if students do not complete estimating the areas within the given class period. Each student will have a pipe cleaner. All pipe cleaners should measure approximately the same length. Students will bend their pipe cleaners into the shape of an equilateral triangle and then approximate the area of the triangle. If time permits, students can investigate other regular polygons. 2. Pre-Assessment Activity 1 List several different objects on the board: one that would be measured using linear measurement Think-Pair-Share Give students one minute to think about the question individually. When Smaller is Better Page 2

3 one that is 2-dimensional one that is a 3-dimensional object Examples would be: the edge of a textbook the surface of their desk a shoe box Students will share their thoughts with their group. Have the class share out. This pre-assessment activity will give you an idea of what students understand about measurement properties, measurement tools, and units. Have students list the measurable properties of each object, the tools they would use to measure, and the units they might use to measure. Optional: Pre-Assessment Activity 2 Write the following categories in a list on the board. Student groups will have two minutes to generate a list of items that belong in each measurement category. The goal is to get more information on what students know about measurement. Measure by Length Measure by Area Measure by Volume 3. Setting the stage: Mr. Hernandez is building a bookshelf for his daughter, Veronica. He needs to decide on a measurement tool. He has a meter stick with no other units marked on the stick, a meter stick with only centimeters marked on the stick, and a meter stick with millimeters marked on the stick. Which measurement tool do you think Mr. Hernandez should use? Today we will investigate measurement tools and precision in measurement. Pose this question to students. Give students one minute to record their prediction on a sheet of paper. Students are to put that paper away until after they have conducted their experiments. Accurate means "capable of providing a correct reading or measurement." A measurement is accurate if it correctly reflects the size of the thing being measured. When Smaller is Better Page 3

4 4. To begin the lesson, each student will take a pipe cleaner and bend it into the shape of an equilateral triangle. Place the triangle on the paper and trace the triangle. Ask students to determine the area of the triangle. Precise means "exact, as in performance, execution, or amount." In mathematics it means "repeatable, reliable, getting the same measurement each time." The goal is to have students realize the need for appropriate measurement tools and units to determine the area. 5. Students will begin their measurement activity using the first piece of grid paper that has been given to them. Each student will trace the triangle on the grid paper. They will determine the area of the triangle by counting the number of square units in the inner area of the triangle and then counting the square units in the outer area of the triangle. Using this data, find the mean of the square units for the inner and outer areas. Inner area: count all of the square units that are completely within the area of the polygon Estimating area using the mean of the inner and outer area may be a new process for some students, so do an example with the entire class before students begin to work independently. This is also a very nice technique to determine the area of irregular shaped objects. The inner area of this triangle is 8 square units. Outer area: Count all of the squares that are completely covered or partially covered by the polygon. Count partially covered squares as one whole unit. When Smaller is Better Page 4

5 The outer area of the triangle is 18-square units. Calculate the mean of the two counts = 13units 2 Students will use this number as the area of the equilateral triangle. Explain to students that the class will combine the data at the end of the data collection and determine the mean for each equilateral triangle for a specific grid paper. This is a good time to have a discussion about the differences in measurements among and between the groups for the same grids. Facilitate the students work and ask questions about their observations. 6. Have each group transfer their data, to the Class Data Collection Sheet. Assign each group a different grid paper dimension. The group will calculate the mean for each triangle and transfer that information to the Class Data Collection Sheet. 7. As a class, compare the area measurements of the.25 cm 2 grid paper to the 1-cm 2 grid paper. Ask if the areas are the same. If not, why? Which area do you think is closer to the actual area of the equilateral triangle? On chart paper, draw six different class recording sheets, one for each grid paper dimension. The recorder for each group will record the group s data on the specified charts posted. Ask if the areas are the same. If not, why? Areas should not be the same. Which area do you think is closer to the actual area of the equilateral triangle? The area When Smaller is Better Page 5

6 8. Lesson Summary Ask students for responses to the questions 1 and 2 on the Student Data Collection Sheet. determined by the.25 cm 2 grid should be closer to the actual area of the triangle (more accurate) because the grid is smaller (more precise). When asking for student responses, call on more than one student to share their reasoning. 1. Which of your two sheets of grid paper gave you a more accurate area? Why do you think this happened? 2. Predict which grid paper will have the most accurate measurement of the area. Explain your reasoning. 9. Closure: Back to Mr. Hernandez Mr. Hernandez is building a bookshelf for his daughter, Veronica. He needs to decide on a measurement tool. He has a meter stick with no other units marked on the stick, a meter stick with only centimeters marked on the stick, and a meter stick with millimeters marked on the stick. Which measurement tool do you think Mr. Hernandez should use? 10. Journaling Based on your observations about measurement tools and units of measurement, why is it important in science and medicine to have precise measurement tools and devices? Ask students to refer back to their response to the opening question about Mr. Hernandez. Ask if anyone wishes to change his or her response. Give students time to change their responses if needed. Students must explain why they changed their responses. Each student will complete the journaling question. References: The Annenberg/CPB at Learning Math: Measurement For a discussion of precision versus accuracy see When Smaller is Better Page 6

7 When Smaller is Better Student Data Collection Sheet of Grid Paper #1 of Grid Paper #2 of Grid Paper #3 of Grid Paper #4 Triangle Area 2. Which of your sheets of grid paper gave you a more accurate area? Why do you think this happened? 3. Predict which grid paper will have the most accurate measurement of the area. Explain your reasoning. When Smaller is Better Page 7

8 Grid 1 cm by 1 cm.5 cm by.5 cm When Smaller is Better Class Data Collection Sheet Equilateral Triangle.25 cm by.25 cm 1 by 1.5 by.5.25 by.25 Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Group 9 Mean of the Area When Smaller is Better Page 8

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The following shows how place value and money are related. ones tenths hundredths thousandths

2-1 The following shows how place value and money are related. ones tenths hundredths thousandths (dollars) (dimes) (pennies) (tenths of a penny) Write each fraction as a decimal and then say it. 1. 349