Elementary Data Analysis MASSI
MASSI: Math Activities with Scripted Systematic Instruction
Activity: Analyzing How Students Get to School
Grade Band: Grades 3-5 Concept: Data Analysis |
Common Core State Standard | Core Content Connectors | MASSI OBJECTIVES |
3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. | 3rd 3.DPS.1g1 Collect data, organize into picture or bar graph | Reading a table and filling in a bar graph |
3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. | 4th 4.DPS.1g3 Collect data, organize in graph (e.g., picture graph, line plot, bar graph) | Collecting data and organizing it in a bar graph |
5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | 5th 6.GM.1c6 Find coordinate values of points in the context of a situation | Creating a line graph |
Be sure to provide specific practice to students on the skills that correspond to their grade level.
Teaching Materials: Cutouts of Ms. Smith's class, blank sorting page, blank table for recording Ms. Smith's class data, blank coordinate grids and graphs (cut apart to use as response cards), cut apart symbols to use on tables/graphs, blank graphs (for picture and bar graph – can laminate to reuse), data set for Ms. Carter's class (not cut up), blank line graph (can be laminated for reuse), data tables for car riders
Other Materials: Blank sorting page, blank table for recording Mr. Whatley's class data, Mr. Whatley's class cut out cards, cut apart symbols to use on tables/graphs (laminated if needed), blank graphs (for picture and bar graph – can laminate to reuse), data set for Mrs. Bishop's class (not cut up), blank line graph (can be laminated for reuse), data tables for bus riders, writing utensil (pen, pencil, marker, etc.)
Worksheets: There are student worksheets to review each component of the lesson.
Assessments: Progress Monitoring for taking data during the lesson; Skills Test
TEACHING OVERVIEW: The first section of the MASSI provides remedial practice on identifying and counting data sets, identifying the x and y axes, and making a picture graph. 3rd graders will learn to read a table and fill in a bar graph. This is a good review for your 4th and 5th graders. The 4th graders will be collecting data and organizing it in a bar graph. This is useful for your 3rd and 5th graders to gain fluency with these concepts and practicing numeracy skills. The 5th graders have to create a line graph. While the 5th graders work on line graphs, you can let the 3rd and 4th graders practice creating picture and bar graphs.
\[\[File:Insert Picture here.jpg\]\] This may be a good stopping point. Have the student take a poll of how the student's in their class get to school. Students can raise hands when asked "Who comes to school on a bus?" and so on. Students can also use the symbols to identify how they get to school and put them on a class wide picture graph. There is a generalization worksheet with this level. You can use this for additional guided practice or to send home as homework.
Give each student the Data Analysis Skills Test: Concepts and Symbols. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. \[\[File:Insert Picture here.jpg\]\]
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3rd BUILD A GRADE ALIGNED COMPONENT: Reading a Table and Filling in a Bar Graph
4th and 5th GRADE BUILD ESSENTIAL UNDERSTANDING: SYMBOLS: Reading a Table and Filling in a Bar Graph INTRODUCE THE ACTVITY/PROBLEM: Present students with the tables from the previous sections showing how students in both Ms. Smith's class and Mr. Whatley's class get to school. Remember before when we looked at how students in Ms. Smith and Mr. Whatley's class get to school? Now we are going to learn a different way to graph the same information. A bar graph is like a picture graph, except that it uses bars to show the data instead of pictures. MODEL THE PROCESS: Watch me as I make a bar graph to show the data for how the students in Ms. Smith's class get to school. Here's the table showing the data for Ms. Smith's class. Show students the completed table for Ms. Smith's class (3 car riders, 4 bus riders, 2 walkers). First, I look at my table and see that there are three car riders in Ms. Smith's class. So I find the car rider column on the graph and draw a line across from the 3. After I draw a line at the number 3, I draw two lines straight down finishing the bar and color it in. Now I do the same for bus riders. I see there are four bus riders. I find the bus rider column on the graph and draw a line across from the 4. After I draw a line at the number 4, I draw two lines straight down finishing the bar and color it in. Last, I need to graph the walkers. There are two walkers. I find the walker column on the graph and draw a line across from the 2. After I draw a line at the number 2, I draw two lines straight down finishing the bar and color it in. \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Give each student a completed table for Mr. Whatley's class (3 car riders, 5 bus riders, and 1 walker) and a blank graph. Now it's your turn. Look at the table and use it to create a bar graph that shows the data for how students in Mr. Whatley's class get to school. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. \*\*Note: Students who are unable to draw a line to create the bar graph can point to the correct placement on the graph and have the teacher fill it in or the teacher can ask "Do I draw the line here?" and students can respond yes/no using assistive technology. Also, drawing the vertical lines and coloring in the bar are not scored. CHECK AND SCORE STEP Teacher Says/Does Student Response "Create a bar graph showing how the students in Mr. Whatley's class get to school." or "How many car riders are in Mr. Whatley's class?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for car riders on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of car riders." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph. Wait for students to independently initiate this step or say "How many bus riders are in Mr. Whatley's class?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for bus riders on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of bus riders." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph. Wait for students to independently initiate this step or say "How many walkers are in Mr. Whatley's class?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for walkers on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of walkers." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph.
INDEPENDENT PRACTICE: Data Analysis Skills Test Teacher Says/Does
Give each student the Data Analysis Skills Test: 3rd Grade Aligned Component. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. \[\[File:Insert Picture here.jpg\]\]
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4th BUILD A GRADE ALIGNED COMPONENT: Collecting Data and Organizing it in a Bar Graph 5th GRADE BUILD ESSENTIAL UNDERSTANDING: SYMBOLS: Collecting Data and Organizing it in a Bar Graph INTRODUCE THE ACTVITY/PROBLEM: Now students are going to graph information they collect from a new set of data (Mrs. Bishop's class). Remember before when we looked at how students in Ms. Smith and Mr. Whatley's class get to school? We have two new sets of data for two other teachers' classes, Mrs. Bishop and Ms. Carter. We are going to collect the data by counting the number of students that get to school by car, bus, or walking and put that on a bar graph. MODEL THE PROCESS: Watch me as I make a bar graph to show the data for how the students in Ms. Carter's class get to school. Show students the data set for Ms. Carter's class (do not cut out the individual student pictures, instead you will count them on the sheet as provided). First, I count how many car riders are in Ms. Carter's class: one, two, three, four. So I find the car rider column on the graph and draw a line across from the 4. The teacher can demonstrate either by counting up the number of lines or finding the four on the y axis and following that line across to the correct place, whichever is more appropriate for their students. I draw two lines straight down finishing the bar and color it in. Now I do the same for bus riders. I count the bus riders, one, two, three, four. I find the bus rider column on the graph and draw a line across from the 4. After I draw a line at the number 4, I draw two lines straight down finishing the bar and color it in. Last, I need to graph the walkers. There are zero walkers, so I leave the column blank. \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Give each student the picture data set for Mrs. Bishop's class and a blank graph. Now it's your turn. Look at the data and create a bar graph that shows the data for how students in Mrs. Bishop's class get to school. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. CHECK AND SCORE STEP Teacher Says/Does Student Response "Make a bar graph showing how the students in Mrs. Bishop's class get to school." or "How many car riders are in Mrs. Bishop's class?" Student counts the number of car riders (stopping at the appropriate number). Wait for students to independently initiate this step or say "Find the column for car riders on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of car riders." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph. \*\*Students can either count up the correct number of lines or find the appropriate number on the y axis and following it over to the correct column. Wait for students to independently initiate this step or say "How many bus riders are in Mrs. Bishop's class?" Student counts the number of bus riders (stopping at the appropriate number). Wait for students to independently initiate this step or say "Find the column for bus riders on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of bus riders." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph. Wait for students to independently initiate this step or say "How many walkers are in Mr. Whatley's class?" Student counts the number of walkers (stopping at the appropriate number). Wait for students to independently initiate this step or say "Find the column for walkers on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a line showing the number of walkers." After students draw the line, they can draw the two vertical lines and color the bar in (not scored). Student draws a line at the correct number in the correct location on the graph.
INDEPENDENT PRACTICE: Data Analysis Skills Test Teacher Says/Does
Give each student the Data Analysis Skills Test: 4th Grade Aligned Component. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. \[\[File:Insert Picture here.jpg\]\]
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5th BUILD A GRADE ALIGNED COMPONENT: Creating a Line Graph INTRODUCE ACTIVITY/PROBLEM: Remember when we made picture and bar graphs to show how students in different classrooms came to school? Now we are going to use a line graph to see how data can change over time. A line graph is a graph that shows a series of data points that are connected by a data path. A data path is a line that connects all the data points. We are going to see how the data for car riders in Mrs. Green's class changes over time. MODEL THE PROCESS: Show students the blank line graph and the table with data for car riders. Watch me as I graph the data for car riders. First I will graph the data for Monday. There were four car riders Monday, so I find Monday and draw a point/dot at four where the lines cross. The teacher can demonstrate either by counting up the number of lines or finding the four on the y axis and following that line across to the correct place, whichever is more appropriate for their students. On Tuesday there were three car riders, so I find Tuesday and draw a point/dot at three where the lines cross. On Wednesday there were five car riders, so I find Wednesday and draw a point/dot at five where the lines cross. On Thursday there were six car riders, so I find Thursday and draw a point/dot at six where the lines cross. On Friday there were six car riders, so I find Friday and draw a point/dot at six where the lines cross. The last thing I do is draw a line connecting all the data points. \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Give each student the table data set for bus riders and a blank line graph. Now it's your turn. Look at the data and create a line graph that shows the data for how bus riders change throughout the week. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. CHECK AND SCORE Step Teacher Says/Does Student Response "How many bus riders were there Monday?" Student states, points to, or otherwise identifies the correct number. \*\*Students can either count up the correct number of lines or find the appropriate number on the y axis and following it over to the correct column. Wait for students to independently initiate this step or say "Find the column for Monday on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a point/dot showing the number of bus riders on Monday." Student draws a point/dot at the correct number in the correct location on the graph. "How many bus riders where there Tuesday?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for Tuesday on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a point/dot showing the number of bus riders on Tuesday." Student draws a point/dot at the correct number in the correct location on the graph. "How many bus riders where there Wednesday?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for Wednesday on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a point/dot showing the number of bus riders on Wednesday." Student draws a point/dot at the correct number in the correct location on the graph. "How many bus riders where there Thursday?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for Thursday on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a point/dot showing the number of bus riders on Thursday." Student draws a point/dot at the correct number in the correct location on the graph. "How many bus riders where there Friday?" Student states, points to, or otherwise identifies the correct number. Wait for students to independently initiate this step or say "Find the column for Friday on the graph." Student identifies the corresponding column on the graph. Wait for students to independently initiate this step or say "Draw a point/dot showing the number of bus riders on Friday." Student draws a point/dot at the correct number in the correct location on the graph. Wait for students to independently initiate this step or say "Draw a line to connect the data points." Student draws a line from Monday's data point to Tuesday's data point. Wait for students to independently initiate this step or say "Keep going." Student draws a line from Tuesday's data point to Wednesday's data point. Wait for students to independently initiate this step or say "Keep going." Student draws a line from Wednesday's data point to Thursday's data point. Wait for students to independently initiate this step or say "Keep going." Student draws a line from Thursday's data point to Friday's data point.
Give student the Data Analysis Skills Test: Conversion of Units of measure and area. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing.
Troubleshooting and Data-Based Decision Making for Data Analysis Skills Test: If student is unable to complete any items on the measurement/geometry test independently and correctly, go back and teach one problem step-by-step. MASSI CULMINATING ACTIVITY: Have the student take a poll of tracking how different types of data change across the week or how students came to school on different days. Students can raise hands when asked "Who comes to school on a bus?" and so on. Students can also use the symbols to identify how they get to school and put them on a class wide picture, bar, or line graph. Teachers can even compare the different types of graphs to see how they show the data similarly or differently. Students may also go ask another class and graph their results. |
BUILD TOWARDS FULL GRADE LEVEL COMPETENCE
Here are ideas to build competence towards the full grade level competence using this same activity. See the unit plan and talk with the general education teacher for more ideas.
Component | Activity | What Student Does | Generalization/ Fluency |
Using a picture or bar graph to answer one and two step problems. | Show students a bar graph representing data with several categories; ask students "which has more" and "which has less…" questions. | Analyzes the bar graph and responds by answering the question (e.g., naming the appropriate category). | Vary the types of graphs, numbers of categories, and types of questions. |
Using a picture or bar graph to answer one and two step problems. | Show students a bar graph representing data with several categories, ask "how many more…" and "how many less…" questions. | Analyzes the bar graph and responds by answering the question (e.g., stating the correct numerical answer, such as 4). | Vary the types of graphs, numbers of categories, and types of questions. |
Identifying the first quadrant of a coordinate plane | Introduce the coordinate plane and teach quadrants. | Identifies different quadrants and the differences between those quadrants. | Present a range of different coordinate planes. |
Graphing points in the first quadrant of a coordinate plane and interpret values of the points in context | Teach students to plot points in the first quadrant of a coordinate plane, then have students identify trends, patterns, and outliers. | Plotting points in the first quadrant of the coordinate plane. Analyzing the data for trends, patterns, and outliers | Students plot points on a range of different coordinate planes, show a range of patterns (increasing, decreasing, no trend, etc.) and outliers. |
Worksheet 1 Generalization: Concepts and Symbols
Circle all the dogs.
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How many buses are there? _______________________ \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\]\[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] |
Worksheet 2 Generalization: 3rd Grade Aligned Component
Worksheet 3 Generalization: 4th Grade Aligned Component
Worksheet 4 Generalization: 5th Grade Aligned Component
Materials: Ms. Smith's Class (cut out cards)
Sorting Page
Tables for recording data
Mr. Whatley's Class (cut out cards)
Blank Coordinate Grids and Graphs \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\]
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Symbols to use on picture graph (cut out, can laminate if needed)
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Data Set for Ms. Carter's Class (do not cut up) \[\[File:Insert Picture here.jpg\]\]
Data Set for Mrs. Bishop's Class (do not cut up) \[\[File:Insert Picture here.jpg\]\]
Graph to use for Creating a Line Graph
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'Tables for data on Car (teacher) & Bus Riders (student) across a week'
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Car Riders |
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Bus Riders | |||
Monday | 4 | Monday | 6 | |
Tuesday | 3 | Tuesday | 4 | |
Wednesday | 5 | Wednesday | 5 | |
Thursday | 6 | Thursday | 2 | |
Friday | 6 | Friday | 1 |