Data Investigations and Assessment in the Math Classroom For 1 st grade

Transcription

1 Data Investigations and Assessment in the Math Classroom For 1 st grade By: Darlene Riewer- driewer@bemiji.k12.mn.us and Angie Rogers-Elstad- arogers@bemidji.k12.mn.us Data Investigations and Assessment in the Math Classroom Bemidji State University July 2-20,

2 Introduction This Data unit was designed to be used in a 1 st grade classroom. It is intended to build upon itself and to be used for 8 days. A pre-test is given to asses their prior knowledge before the unit begins. This unit is to introduce tally marks and graphs to the 1 st grade classroom. After the unit has been taught a post-test is given to measure the growth the students made. 2

3 First Grade Pre-Test (Teacher will read the test to the students) Name: Write the tally marks for the number of apples below. 3

4 Write the tally marks for each problem. 3. # # # # # # # # # # 4

5 Complete the chart below. Number of Votes Tally Mark

6 Lucy was taking a survey. She wanted to find out what types of pets her classmates had. Here are the results of her survey. type of pet cat dog turtle hamster rabbit gerbil 1. How many students had cats? a. 10 b. 17 c. 2 d. 4 number of students who own this pet 2. How many students had turtles? a. 7 b. 2 c. 10 d What two pets had the same number of tally marks? a. cat and dog b. rabbit and gerbil c. hamster and gerbil d. dog and turtle 6

7 Take a survey of your classmates. Write tally marks for each student s answer. Use the survey form below. What is your favorite subject in school? Subject Math Tally Reading Science Social Studies Spelling Computers Writing Handwriting Gym Art Music (Note: Teacher may want to put a checklist of student s names at the bottom of the page so students know who they have surveyed.) 7

8 Teddy Bears Susan Mike Lynn Rob Cole = 1 teddy bears 1. How many teddy bears does Mike have? Which child has 6 teddy bears? Rob Lynn Cole 3. Which child has the same number of teddy bears as Mike? Susan Cole Rob 8

9 Introduction to Tally Marks Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- The student will be introduced to tally marks for data representation. Materials- student slate boards, chalk, pet tally chart Activity- Explain to the children that they will be learning a new way to record, count, and write numbers using tally marks. Write tally marks and /////// on the board and ask children to count the tally marks with you. Count aloud, 1, 2, 3, 4, 5, 6, 7, as you write //// // Ask the following questions: How are these tally marks different from the tally marks we made before? The fifth tally mark crosses the first four. What is the advantage of having the fifth mark cross the first four? It is easier to count the tally marks. When we record numbers in this way we can count the groups by 5 s. Practice writing other single digit numbers greater than 5 on the board. Model the counting process starting with 5 and counting on by 1 s. Call out single-digit numbers and have children practice drawing tally marks on their slate boards. Next ask the kids if they could draw 10 on their slate boards using tally marks. //// //// The number 11? //// //// / Display the Pets chart on the board. Explain to the children that they are going to use a chart and tally marks to find how many pets are owned by everyone in the class. Have children come up to the Class Data Chart, a few at a time, to fill in the chart. They should make one tally mark for each pet they own. Check that every fifth tally mark is made correctly. When all children have had a turn, have them count the tally marks together and record the total number for each row. 9

10 Extension: Make a listening tally. To apply the children s understanding of making and counting tally chart have the children make a tally mark on their slates each time they hear a penny drop. Drop a selected number of pennies into a container, one at a time. (Do this out of the children s view). Have them count the tally marks and write the total number of pennies on their slates. Continue to play the game as time permits. 10

11 Pet Tallies Total Cat Dog Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Other Objective- Materials- No Pet 11

12 Dice Roll Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- The student will have experience with equal chance events. Materials- Dice worksheet, dice Activity- Show the kids a die. Show them that the dots on the surface represent a number. Ask the children which number they think will come up most often when they roll a die. Explain to the children that they are going to practice rolling the die to find out. Tell them that they will be using tallies to record their results. Divide the class into partners. Partners take turns rolling a die. Both children make tally marks next to the appropriate die on the worksheet. After 2 minutes, ask children to pause. Have the kids predict which number or numbers will come up most often. Have the children continue to roll a die and record the results. Go for another 3-4 minutes. Have the kids record the total number of rolls for each number. Discuss the results with the students. Theoretically, each number has the same number of chances to be rolled since there is a different number on each side. Ask the children what would happen if 2 sides of the die were the same number, or 3 sides. Have a discussion about the probability of a number happening when it appears more often. 12

13 Dice-Roll and Tally Roll a die. Use tally marks to record the results on this chart. Tallies Total Tasty Treats 13

14 Tasty Treats ( Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- Students will interpret data by reading bar graphs and pictographs using whole unit data. Materials- A two column graph on the board, sticky notes (one per student), one box of Goldfish Crackers, one box of Teddy Graham Crackers, one pencil per student, provided worksheet Activity- The teacher will draw a two column bar graph on the board. The teacher may label one column Goldfish and the other Teddy Grahams. Explain to the students they are going to taste two different kinds of snacks and they are to decide which snack they like the best. Give each student one Teddy Graham cracker and one Goldfish cracker. Ask the students to eat the crackers one at a time and to decide which one they like best. Give each student a sticky note and ask them to draw a picture of the snack cracker they liked the best. Explain to the students that they are going to place the picture they drew on the two column bar graph. Explain to the students that they will sort the drawings by "Goldfish" crackers and "Teddy Graham" crackers. Ask the students to place their drawing on the two column bar graph with all of the "Teddy Graham" crackers on one side and the "Goldfish" crackers on the other side. After the students have completed the graph, ask the students which group has the most: "Goldfish" or "Teddy Grahams"? Which group has the least? How many more of one cracker is there than the other? How many less of one cracker than the other? How many people liked "Goldfish"? How many people liked "Teddy Grahams"? How many people participated in our graph? Ask the students what kind of information we can gather from graphs. As the students are answering the questions the teacher will make observations of who is using the graph to interpret the data needed to answer the questions correctly. As a final activity, distribute the below listed worksheet and instruct the students to create a graph based upon the amount of Teddy Grahams and Goldfish represented in the box. After the students have completed their papers, collect them and use as a means of formal assessment. 14

15 Tasty Treats Name Directions: Count the number of Teddy Grahams and Goldfish on the graph and answer the questions listed below Goldfish Teddy Grahams 1. How many Teddy Grahams are on the graph? 2. How many Goldfish are on the graph? 3. Which snack is represented the most? 4. Which snack is represented the least? 5. How many more crackers are there than the other? 6. How many less crackers are there than the other? 15

16 On Our Way to School ( Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- Students will interpret data by reading bar graphs and pictographs using whole unit data. Materials- A four-bar graph drawn on the board, sticky notes for each student, one pencil per student, crayons for each student, provided attachment, pencils Activity- Ask the students to think about how each one them gets to school in the mornings. Tell the students that today we are going to interpret data on how everyone gets to school each morning by creating a class graph. Explain to the students that through graphing we will compare and sort how we come to school. Tell the students that they will each receive a small piece of paper with a sticky backing. Explain to the students that they need to draw and color how they get to school on the paper. Explain to the students they are going to place the notes on the four column bar graph with each column labeled car, van, bus, and other. Allow four volunteers at a time to place the sticky notes on the board. After eight students have placed the sticky notes on the graph, ask the students to predict which group they think will have the most and the least. The teacher will write the students predictions on the board. Continue to let the rest of the class place the way they come to school on the board. Ask the students to look at the bar graph. Ask the students if the modes of transportation are sorted in any way. Ask the students what we can tell about how we come to school by looking at the graph. Explain to the students this is the first step in interpreting data. Data is the information we gather from the chart. The following questions may be asked to help the students further assess the data: Which column has the most? Which column has the least? Are there more or? How many more than? How many people participated in the graph? The teacher will write the questions and answers on chart paper to review with the students how the data was gathered. Finally, ask the students if the predictions of which column had the most or least was correct. Close the lesson by distributing the below listed worksheet. Read the directions to the students and have them look at the graph. Then, direct the students to answer the questions. After the students have completed the worksheet, collect the papers and use as a means of formal assessment. 16

17 On Our Way to School Name Directions: Count the number of means of transportation on the graph and answer the questions listed below. Bus Car Van Bicycle Walk 7. How many people ride in a car to school? 8. How many people walk to school? 9. Which way do people travel the most? 10. Which way do people travel the least? 11. How many more people ride in a van than walk? 12. How many less people ride in a bus than ride in a car? 17

18 Construction Time with Graphs Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- The students will construct simple graphs using concrete objects such as blocks and squares. Materials- overhead projector, overhead pattern blocks, graph transparency ( Make a copy of the graph attachment), pattern blocks, graphing grid for each student, pattern block graph recording sheet for each student, pencils, crayons Activity-The teacher will introduce the lesson by telling the students that they will work today on constructing graphs. Teacher will use the overhead, overhead pattern blocks, and a transparency of the graphing attachment to demonstrate graphing to the students. The teacher will place a small amount of pattern blocks on the overhead and explain to the students that she is going to put the pattern blocks on the graph. The teacher will ask the students how the pattern blocks should be graphed. The teacher should take the students lead in placing the pattern blocks on the graph by shape. The teacher will place the pattern blocks on the overhead graph. Ask the students the following questions about the graph: What does this graph tell us? Are any rows the same? Which row has more? Which row has the fewest? How many are there? Are there more or? Are there fewer or? How many are there altogether? What else could we say about this graph? Now tell the students that they are going to make their own graph. Give each student a variety of pattern blocks and a graph recording sheet. Instruct the students to answer the questions on the recording sheet that represents the number of each shape. Then, direct students' attention to the graph page. Tell the students to draw each of the shapes at the bottom of the graph and color in a box for each shape represented. As the students are completing their graphs, check each student's graph individually for accuracy. At this time, the teacher can discuss the graphs with the students and check for students' understanding. After checking the papers, collect them and use the graphing sheets as a means of formal assessment. 18

19 Graphing Sheet Name 19

20 Pattern Blocks How many? How many? How many? How many? How many? How many? 20

21 Yummy Graphing Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- - Students will interpret data by reading bar graphs and pictographs using whole unit data. Materials- one graphing sheet per student- see attachment, enough trail mix for the class (M&Ms,marshmallows, pretzels, raisins),graph recording sheet for the trail mix -see attachment, glue, pencils Activity- Explain to the students that graphing is important to us because graphs help us organize materials or information. Tell the students that we are going to make a real graph. A real graph uses real objects on a grid for comparison. Direct the students' attention to the overhead projector and display the below listed transparency sheet. Have the students assist you in completing the graph. Now tell the students they are going to get to make their own graph. Give each student a graphing sheet and a portion cup with a small amount of trail mix. Explain to the students that they need to sort the trail mix and then glue it onto the graphing grid. There should only be one piece of trail mix in each grid. Tell the students that at the end of the lesson everyone will get to enjoy the rest of the trail mix. Ask the students to carefully look the completed graph. Explain to the students that they will use the graph recording sheet to help them interpret data from the graph. Give each student a trail mix recording sheet to complete. Ask for volunteers to share the interpretation of their graph and recording sheets. Did everyone's graph turn out the same? Why do think everyone's graphs turned out the way it did? 21

22 Fish and Bears Name Directions: Count the number of bears and fish that are in the box and create a graph to represent your findings Fish Bears 22

23 Graphing Sheet Name 23

24 Yummy Graphing Recording Sheet Name How many M&Ms? How many marshmallows? How many pretzels? How many raisins? Do you have more M&Ms or raisins? How many more? Do you have less pretzels or marshmellows? How many less? What else can you tell about your graph? 24

25 Graph It Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- - Students will interpret data by reading bar graphs and pictographs using whole unit data. Materials- two sheets of chart paper, red and blue markers, provided attachments, red and blue manipulative cubes for each student Activity-Before beginning the lesson, prepare two charts similar to the ones listed in the provided attachment. Tape the charts to the board so that the students will be able to reach them. Teacher will also need to gather a class set of colored cubes for the students to use during the graphing activity. Introduce the lesson by telling the students that they are going to help you create a couple of graphs in today's lesson. Tell the students that in order to graph something, you have to have data, or information, that will be presented on the graph. State that for the first graph, the data will be how many people in the class are right-handed and how many people are left-handed. Direct the students' attention to the chart paper with the right- handed/ left-handed grid on it and call on the students one at a time to go up and shade in the box that represents their handedness. Tell the students who are right-handed to use a blue marker and the students who are left-handed to use a red marker. This will make the data stand out more. Once each student has had an opportunity to go to the board, have the students help you count the number of right and left-handed students in the class orally. Explain to the students how to look at the numbers on the left and follow it across to determine the data amount. Repeat the same process in step one using the "boy" and "girl" chart, but this time tell the students that they are going to create a chart of their own at their desk which will represent the same data as the graph on the chart paper. Distribute the below listed grid and the blue and red colored cubes. Again, call the students up individually and have them shade in the box on the chart paper that reflects their gender-- red for girls and blue for boys. As each person goes to the chart, have the students at their seat place a cube on the graph that represents the student's gender. Continue until each of the students have shaded in a box and completed their graphs at their seats. When finished, count the results on the graph and have the students check to see if they have the same amount of cubes on their graphs. Check each student s graph and record on the provided checklist. Finally, have the students continue to create graphs using their cubes. Call out various data orally to the students and have them use their red and blue cubes to represent the data. For example, tell the students to graph ten red cars and three blue cards with the corresponding colored cubes. Continue with examples similar to this by using red/ blue data such as candy, toys, gum, etc. Each time the students create their graph, walk around 25

26 the room and use the checklist to mark their understanding. When the students have completed the graphs, collect the cubes and papers and review if necessary. 26

27 Boy Girl Right-Handed Left-Handed

28 Graph It Checklist Student s Name Correctly graphed the boy/ girl graph Correctly graphed the red/ blue car graph Correctly graphed the red/ blue candy graph 28

29 M&M graphing Minnesota Standard: Number and Operation Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones Use counting and comparison skills to create and analyze bar graphs and tally charts. Objective- - Students will interpret data by reading bar graphs and pictographs using whole unit data. Materials- A small graph with the different colors of M and M's, snack size bags of M&M's, a large piece of paper to make another graph to display everyone's favorite color of M & M Activity- Pass out a handful of M & M's to every child in the class. Have them put the colored M & M's on the correct spot on their graph. Have them count how many green ones they have. Then how many brown ones and so on... Let the children then eat the M & M's and then ask them what their favorite color of M & M is. Then make a chart showing the children's favorite M & M colors. Have them answer questions such as what is the most favorite color of the class? What is the least favorite color? List the favorites in order from greatest to smallest. 29

30 Name: M&M s Candy Color Chart r red b blue y yellow g green b brown o orange 30

31 First Grade Post-Test (Teacher will read the test to the students) Name: Write the tally marks for the number of apples below. 31

32 Write the tally marks for each problem. 3. # # # # # # # # # # 32

33 Complete the chart below. Number of Votes Tally Mark

34 Lucy was taking a survey. She wanted to find out what types of pets her classmates had. Here are the results of her survey. type of pet cat dog turtle hamster rabbit gerbil number of students who own this pet 1. How many students had cats? a. 10 b. 17 c. 2 d How many students had turtles? a. 7 b. 2 c. 10 d What two pets had the same number of tally marks? a. cat and dog b. rabbit and gerbil c. hamster and gerbil d. dog and turtle 34

35 Take a survey of your classmates. Write tally marks for each student s answer. Use the survey form below. What is your favorite subject in school? Subject Math Tally Reading Science Social Studies Spelling Computers Writing Handwriting Gym Art Music (Note: Teacher may want to put a checklist of student s names at the bottom of the page so students know who they have surveyed.) 35

36 Teddy Bears Susan Mike Lynn Rob Cole = 1 teddy bears 1. How many teddy bears does Mike have? Which child has 6 teddy bears? Rob Lynn Cole 3. Which child has the same number of teddy bears as Mike? Susan Cole Rob 36

37 Outline to assess instructional changes. 1). Lesson Plans- see attachment 2). What actual changes are you making? We are teaching the students about tally marks and graphing. We are using more hands on activities to help the students better understand the concepts. 3). What effect should these changes have? The students should be able to understand showing, writing, and reading tally marks through different ways. They will be able to read graphs and use tally marks to make their own graphs. They also should be able to meet or exceed the Minnesota standards that are required. 4). Formulate hypotheses-null and alternative Null Hypothesis = There was no change in the students ability to record and interpret data using tally marks and in their ability to interpret graphs. Alternative Hypothesis = There was an increase in the students ability to record and interpret data using tally marks and in their ability to interpret graphs. 5). Experimental design for collecting data A pre-test will be given before any instruction. A unit lesson will be taught for eight days. A post-test will then be given to see if there have been any gains. After collecting the data from the pre-test and the post-test we will measure the changes (if any) by using a two-sample t-test. It is nice to look at data in many different ways so we will also use a line graph and box and whiskers plot to assess the data. 6). Data is collected, reviewed for problems and documented Data will be collected after the pre-test and after the post-test. 7). Data analysis-statistical tools you will use to analyze your data. i) Graphical tools: Bar graph, Histogram, Box plot, time plot,. ii) Statistical tools: mean, median, paired-data t-test, two sample t-test,.. A two-sample t-test will be used to assess the data. 37

38 8). Statistical results and statements of conclusions 9). Interpretation in the appropriate context 10). Action and dissemination i) Local-students, administrators, parents, community ii) State-conferences iii) National-conferences and journals (Note: Do 6-10 in the classroom when the school year starts) 38