Second Grade Picture and Bar Graphs

Transcription

1 Second Grade Picture and Bar Graphs Table of Contents Topic Suggested Number of Days Page No. Part 1: Graphs with a Scale or Key Equal to One Picture Graphs Large Picture of Bear Small Pictures of Bears Guided Practice Problem #1 Bar Graphs Warm-up Problem #1 Guided Practice Problem #2 Guided Practice Problem #3 2 days 1 day (2/27) 1 day (3/2) Part 2: Use Data to Write Problems Warm-up Problem #2 Picture Graph Bar Graph Guided Practice Problem #4 Mixed Practice Part 3: Graphs with a Scale or Key Greater Than One Picture Graphs Pictures of Small Bears Picture Graph Questions Guided Practice Problem #5 Picture Graph Partner Practice Problem Bar Graphs Bar Graph Questions Guided Practice Problem #6 Guided Practice Problem #7 Part 4: Use Data to Draw Conclusions and Make Predictions Interactive Math Notebook (Right Side) Word Bank Interactive Math Notebook (Left Side) Warm-up Problem #3 Guided Practice Problem #8 Mixed Practice 2 days 1 day (3/3) 1 day (3/4) 2 days 1 day (3/5) 1 day (3/6) 3 days 1 day (3/16) 1 day (3/17) 1 day (3/18) Additional Resources: Large Horizontal and Vertical Bar Graphs for Group Work (These should be printed on legal-size paper.) MATH_2_A_BAR GRAPHS A 2014_RES) MATH_2_A_BAR GRAPHS B 2014_RES) Enrichment Activity MATH_2_H_GRAPHS 2014_ENR Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

2 Picture Graphs and Bar Graphs TEKS 2.10A TEKS 2.10B TEKS 2.10C TEKS 2.10D TEKS 2.4A TEKS 2.1A TEKS 2.1B TEKS 2.1C TEKS 2.1D TEKS 2.1E TEKS 2.1F TEKS 2.1G explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one draw conclusions and make predictions from information in a graph Recall basic facts add and subtract within 20 with automaticity apply mathematics to problems arising in everyday life, society, and the workplace use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate create and use representations to organize, record, and communicate mathematical ideas analyze mathematical relationships to connect and communicate mathematical ideas display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Vocabulary: pictograph, picture graph, bar graph, title, heading, label, key, scale, prefer, favorite, vote, tally, tallies or tally marks, match, information, data, survey, data chart Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

3 Teacher Background In these interactive lessons, students collect data, use that data to construct picture graphs (pictographs) and bar graphs, as well as interpret those graphs to answer questions about the data presented. Students have previously learned about picture and bar graphs with a key or scale of 1 in first grade. In second grade, students are expected to deepen their understanding of those graphs by writing and solving one-step word problems they create themselves. Students understanding of graphs is also extended to include creating/interpreting picture and bar graphs with a key or scale greater than 1. Additionally, students are expected to draw conclusions and make predictions based on information given in pictographs and bar graphs. Part 1: Graphs with a Scale or Key Equal to One Materials: red, blue, yellow, and green plastic bears data chart (pg 2) large bear signs - one each color bear (pg 7) blank pictograph blank bar graph small bear pictures (pg 8) or bear die cuts in red, blue, yellow, and green paper student copies of Guided Practice Problem #1 (pg 9) student copies of Warm-up Problem #1 (pg 11) student copies of Guided Practice Problems #2 and #3 (pgs 16, 17) 1. Prior to instruction create a blank data chart on which to record information using tally marks. An example is provided below: Our Favorite Bear Colors Red Blue Yellow Green Post large pictures of the bears (one of each color---red, blue, yellow and green) in various locations within the classroom. Students will later vote with their feet by standing near the picture that is their favorite color of bear. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

4 Prepare a blank picture graph and a blank bar graph. On the picture graph, leave room for a title, headings and a key. On the bar graph, space is needed for a title, headings and the scale. Examples of the completed graphs are found on page 4 (picture) and page 12 (bar). 2. Gather and Record Information Point out the title of the data chart, Our Favorite Bear Colors. Allow students to take a plastic bear which is their favorite color bear. With bear in hand, students walk to the area where their color bear is displayed. The teacher then records the class data in the chart using tally marks. Discuss how tally marks are grouped for easy counting, i.e. four standing straight and then one crossing to hold the group together. This makes a group of five. An example of a completed data chart is given below using fictitious numbers. Our Favorite Bear Colors Red Blue Green Yellow How many tally marks should we have in our chart? We should have as many tally marks as we have students in the class. Why? Each tally mark represents one student. Have students count the tally marks to make sure the total equals the number of students in the class. Ask several students to explain their method of counting (i.e. count by 5s first and then count on the extras by 1s; use 2 of the single tallies to make two more groups of 5 and then count by 5s, etc.) and briefly discuss. 3. Picture Graphs After returning to their seats, have students color a small picture of a bear in the color they chose or give each student a die-cut bear that matches their color. Explain to students that we can display the information we collected in a picture graph or pictograph. A picture graph (pictograph) uses pictures to represent the data. Write in the title on the blank picture graph. Discuss and write the headings. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

5 Go through the data for each color as follows: Looking at the tally chart, how many students should have red bears? There should be seven students with red bears. (This should be the actual number from your class data.) Have the students with red bears come up and place their bear pictures on the graph. Explain that the pictures are aligned within the rows and in the columns so it is easier to compare the data displayed in the graph. Do this with each color separately until all the bear pictures are on the graph. A sample graph is shown below: Our Favorite Bear Colors Red Blue Green Yellow Add a key to the picture graph and discuss its importance. Each = one student Demonstrate the strategy of counting the bears in each row and recording those totals at the ends of the rows. Verify that all the data has been recorded. Our Favorite Bear Colors Red Blue Green Yellow Each = one student Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

6 Discuss and answer several questions related to the class graph. Possible questions are listed below: 1. Which color of bear was preferred by most of our class? 2. Which color of bear was chosen by the least number of students? 3. How many students picked as their favorite bear color? 4. How would the graph change if 3 more students chose yellow? Explain. 5. How many fewer students chose bears than bears? 6. How many more students preferred than? 7. What is the sum of the bears and the bears? 8. What is the difference between the bears and the bears? 9. How would the graph change if 2 fewer students chose blue? Explain. 10. Which colors were chosen by the same number of students? Use the class graph to complete Guided Practice Problem #1 with students using the 4-step problem-solving process. An example is provided below along with suggested discussion for Step 3. How many students in our class chose red or yellow bears? Main Idea: students chose red or yellow Details/Known: graph Strategy: check each color Guide students in the checking of each color with this questioning. Is red red or yellow? Yes, red is red. So we count the number of students who chose red. (Put that number in Step 3.) Is blue red or yellow? No, blue is not red or yellow. So, do we count the number of blues? No, we don t count them. Is green red or yellow? No, green is not red or yellow. So, do we count the number of greens? No, we don t use that number. Is yellow red or yellow? Yes, yellow is yellow. So, do we use that number? Yes, we need the yellow number. (Place the yellow number under the red number in Step 3.) Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

7 Discuss the action which is put together. Discuss any fact strategies that could be used when adding these numbers. For example, if the numbers were I know that is 10 and 4 is just one more than 3. So is 11. How/Why: Added 7 + 4; Found the sum of 7 and 4; etc. Have students state the answer in a sentence. Ex. Eleven students chose red or yellow. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

8 Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

9 Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

10 Guided Practice Problem #1 Use the graph created by the class to solve this question. How many students in our class chose red or yellow bears? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

11 4. Bar Graphs Warm-up: (approximately 10 minutes) Have students complete Warm-up Problem #1 (page 11) to review what they learned about picture graphs. Remind students to preview the graph by looking at the title, headings and key before they actually begin the 4-step process. This helps them get to know the graph before they start working. Discuss the solution and briefly review as needed. Have students justify their thinking. The completed problem is given below: day more than 3 but less than 7 graph between 3 and 7 more less M 3 T 8 W 7 Th 5 x x x labeled graph Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

12 Warm-up Problem #1 Name Monday Basketballs Left on the Playground Tuesday Wednesday Thursday Each is 1 basketball. On which day did the students leave more than 3, but less than 7 balls on the playground? A. Monday B. Tuesday C. Wednesday D. Thursday Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

13 Explain to students that we are now going to display the class information about favorite bear colors in a different type of graph----a bar graph. A bar graph uses bars to represent the data instead of pictures. Write the title on the blank bar graph. Discuss and write the headings. Create a bar graph using the same bear data collected previously by the class. Point out and discuss the scale of one. Review how to read a bar graph by following the line at the end of each bar to the corresponding number in the scale. Also, model how to label the values at the ends of the bars. A sample bar graph is shown below-----the class graph will match the data collected by your students. Our Favorite Bear Colors Red Blue Green Yellow Compare the bar graph to the picture graph. Discuss the similarities and differences between the two types of graphs. Display the following question. Solve with the teacher guiding the discussion and recording the 4-step process. How many students did NOT choose blue as their favorite bear color? Main Idea: students not choose blue Details/Known: graph Strategy: check each color Is red blue? No, red is not blue. So, do we count the red number? Yes, because we are looking for the students who did not choose blue. Since red is not blue, we count the red ones. (Write the number for red in Step 3.) Is black blue? No, black is not blue. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

14 So, do we count the black number? Yes, because the students who chose black did not choose blue. (Add this number to the number for red.) Go through examination of each color using this or similar questioning. The students should have an addition fact with 3 addends in Step 3. Discuss with students the fact strategies that will help with this addition. How/Why: Added all the colors not blue. Added 7 and 4 and 4. Have students state the answer in a sentence. Ex. 15 students did not choose blue as their favorite bear color. Complete Guided Practice Problem #2 with both teacher and students recording the 4-step process. Display the graph and question. Read together and insert speed bumps. Take a moment to preview the graph by looking at the title, headings and scale. Find the main idea, label the bars and record the details along with any known information that might be needed. Give students time to think about the question and a possible solution. Allow students to experience a healthy struggle. This will help them become more independent problem solvers and gain confidence in their abilities. Revisit the main idea and then ask students to share their thoughts on how to solve this question. If necessary, guide students thinking with questioning. What action is happening in this problem? put together, compare (Emphasize to students that this problem will require more than one step to solve.) What exercises are being compared? Jumping jacks are being compared to situps and pull-ups. What should we do? put the sit-ups and pull-ups together and then compare that number to the jumping jacks What operations should we use? We need to add first and then subtract the sum from the jumping jacks. Continue the 4-step process by completing the strategy and how/why sections. An example of the finished problem is shown on the next page. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

15 6 7 4 fewer jumping jacks than situps and pullups graph S 6 P 4 J Added 6 and 4. Subtracted 7 from sum. Work Guided Practice Problem #3 with students. Display the problem and give students think time to examine and ponder the graph. What do you see? What do you notice about this graph? Have students share their thoughts and observations. Discuss in particular the characteristics of this graph that make it a little different from the others we have been studying up to now. Especially focus their attention on the 2 different bars of information. Note the key in the upper right-hand corner which helps us distinguish the Sports data from the Homework data. Read the problem together and insert speed bumps. Find the main idea, label the bars of information for Sports and record the details. Have students explain why it is not necessary to label the Homework bars. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

16 Complete the 4-step process by deciding on a strategy, solving for an answer and writing the how/why. The finished problem is shown below: 4 3 hours Ben spend sports two weeks graph S w1 3 S w = 7 Added 3 and 4 to get a sum of 7. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

17 Guided Practice Problem #2 Lee took a test in PE. The graph shows the exercises he did. Lee's Exercises Number of Exercises Sit-ups Pull-ups Jumping Jacks Exercise Push-ups How many fewer jumping jacks than sit-ups and pull-ups did Lee do? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

18 Week Guided Practice Problem #3 Ben made a graph about the hours he spent on sports and homework in the past two weeks. Ben's Activities Homework Sports Week 2 Week Number of Hours How many hours did Ben spend on sports in the two weeks? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

19 Part 2: Use Data to Write Problems Materials: student copies of Warm-up Problem #2 (pg 21) question stems (pg 18) written on sentence strips copy of bar graph (pg 23) glued on anchor chart student copies of Guided Practice Problem #4 (pg 24) student copies of Graphs Mixed Practice Problems Part 2 (MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES) Warm-up: (approximately 10 minutes) Have students complete Warm-up Problem #2 (page 21) to review what they have learned about bar graphs. Remind them to get to know the graph by looking at the title, headings and scale before they actually begin the 4-step process. Discuss the solution and briefly review as needed. Have students justify their thinking. 1. Picture Graphs Display the picture graph on page 22 and discuss its features. Point out to students that this graph is missing a question for us to solve. Explain that the class will be using the data given in the graph to write our own word problem to solve. What sentence could we write to begin our word problem? Have students share their ideas. Guide them, if necessary, to choose the sentence that summarizes what the graph is about, such as Four colors of markers were sold at the store last week. Now, we are going to write a question to finish our word problem. Place sentence strips containing question stems face down (see below). Have a student choose one for the class to complete. For example, How many more red markers were sold last week than purple markers? Question Stems 1. How many more markers were sold last week than markers? 2. How many or markers were sold last week? 3. How many fewer markers were sold than markers? 4. How many markers sold were NOT or? 5. How many markers and markers were sold last week? 6. How many markers were sold last week? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

20 Let s create another question about our graph that could have also been used in our word problem. Choose another sentence strip and complete that question stem as a class. Continue in this manner until students seem comfortable with the process. 2. Bar Graphs Display the bar graph (page 23). Discuss the title, headings and scale. Explain to students that the class will now write a word problem based on the information in this bar graph. Afterwards, the class will solve the problem they wrote. Together with students write a beginning sentence such as The students in Mrs. Gray s class chose four favorite pizza toppings. Proceed to writing a single-step question. What is a question that could be answered by using the data in the bar graph? Give students time to formulate a question and then ask a student to share his/her question with the group. Record the student s question on an anchor chart which already has a copy of the Favorite Pizza Toppings graph glued at the top. Have other students share their questions. Write them on the anchor chart as well. (Before writing a student s question on the chart, quickly check that it can indeed be solved by using the data given in the graph.) Point out to students that any one of these questions could be used to finish our word problem. Choose one of the questions from the list to solve. Read the beginning sentence and the chosen question together. Discuss and complete the 4-step process with the teacher recording for the class. Next, work Guided Practice Problem #4 with both teacher and students recording the 4-step process. Read together and take a look at the title, headings and scale. Find the main idea, label the bars and record the details. Direct students attention to the addition sentence and provide a few minutes for them to re-examine the graph. Do you see any of these numbers in the bars of the graph? yes, 9 and 8 Which types of animals have those values? ducks and dogs How do you think this can help us? Let s check each answer choice to find the question that requires us to add ducks and dogs? Read each answer choice and decide if it is a question that can be solved with the addition sentence, = 17. Label with a Y for yes and an N for no. Ask students to justify their thinking for each question. Checking the answer choices is a helpful strategy for this problem. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

21 Complete Step 4 to finish the 4-step process. An example of the completed problem is shown below N Y N N graph question = 17 D 8 S 4 Sp 7 Du 9 labeled graph labeled answer choices Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

22 Warm-up Problem #2 Name Mrs. Clark s class voted on their favorite ice cream flavor. The results are shown in the graph. How many students did NOT choose strawberry? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

23 Part 2: Use Data to Write Problems Picture Graph Markers Sold Last Week Black Red Blue Purple Each = one marker Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

24 Part 2: Use Data to Write Problems Bar Graph Picture Look at the graph below. Write a question related to the graph and solve it. Favorite Pizza Toppings Cheese Pepperoni Mushrooms Sausage Number of Students Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

25 Guided Practice Problem #4 Which question about the data in the graph could you use this addition sentence to solve? = 17 Number of Animals Animals Seen in the Park Dogs Squirrels Sparrows Ducks Types of Animals A. Are there more ducks than sparrows in the park? B. How many dogs and ducks are in the park? C. What is the total number of animals in the park? D. Which animal was seen the least? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

26 Warm-up: (approximately 10 minutes) Have students complete problem #1 of Graphs Mixed Practice Problems Part 2 (MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES) to review what they have learned about writing questions using data in a graph. Briefly discuss and review as needed. 3. Independent Practice Have students work the remaining problems in Graphs Mixed Practice Problems Part 2 (MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES). These problems provide a mixed practice of all the graph material learned so far. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

27 Part 3: Graphs with a Scale or Key Greater than One Picture Graphs Materials: 16 red, 14 blue, 8 yellow and 10 green bears put into a paper bag a data chart for recording information with tally marks a blank pictograph (see pg 27) pictures of small bears (pg 30) in red, blue, yellow, green student copies of Guided Practice Problem #5 (pg 32) student copies of Picture Graph Partner Practice Problem Part 3 (pg 33) 1. Prior to instruction place 16 red, 14 blue, 8 yellow and 10 green bears into a paper bag. Also, create a data chart for recording information with tally marks (see below) and a blank pictograph (see page 27). Bears in the Bag Red Blue Yellow Green 2. Gather and Record Information Tally the colors of the bears in the bag on the class data chart. Bears in the Bag Red Blue Yellow Green Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

28 3. Construction of the Picture Graph Discuss the data contained in the data chart. Write the title and headings on the blank picture graph. (Note: Do not write a scale on the graph at this time.) Red Blue Yellow Green Bears in the Bag Red Blue Yellow Green Have students place one plastic bear on the picture graph for each tally mark in the data chart. When they run out of spaces on the graph itself, have them continue to place the bears off the edge of the graph. (This activity demonstrates the need for different graph scales.) Bears in the Bag Once all the data has been represented in the graph, ask students to share their observations. It seems that our data doesn t fit in our graph. Discuss what can be done to fix our graph. If the suggestion has not been made, suggest that two bears be placed in each square. Move the bears to show that this is a practical solution. Red Blue Yellow Etc. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

29 At this point, model making a key where each picture of a bear is equal to 2 bears. Write out the key and place it beneath the graph. Key Each = 2 bears Use one red bear picture and replace the first two plastic bears with this picture. Have students continue replacing the groups of two bears with one picture of the corresponding color. When pictures are on the entire graph, model for students how skip-counting by 2 is used to determine the value of each row. For example: Red Etc. to 16 Discuss again with students why a picture in a picture graph may need to stand for more than one item. (The graph can then hold larger amounts of information bigger numbers can be shown.) Examine several questions from Picture Graph Questions (Key > 1) on page 31 with students. Choose those that best meet the needs of your students. So they may concentrate on the new scale and how it impacts interpreting the graph, verbally guide students through the 4-step process with questioning. What are we trying to find? What information in the graph do we need to use? What do you think we should do to find our answer? How did we find our answer? Does it make sense? Why or why not? That way, students are still able to benefit from following our problem-solving plan. 4. Guided Practice Complete Guided Practice Problem #5 with both students and teacher recording the 4-step process. An example of the completed problem is given on the next page. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

30 red markers graph R 45 Counted by 5s Labeled graph 5. Partner Practice Have students work with a partner to complete the Picture Graph Partner Practice Problem Part 3 found on page 33. Encourage students to talk with each other and cooperatively determine a solution. Allow students to experience a healthy struggle. This fosters independent and confident problem solvers. If needed, support students experiencing difficulty with guiding questions to stimulate their thinking. Once they are finished, students may share their solutions and explain their thinking. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

31 Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

32 Picture Graph Questions (Key > 1) 1. How many more red bears are in the bag than yellow bears? 2. How many bears are blue or green? 3. If the blue and green bears were removed from the bag, how many bears remain in the bag? 4. How many total bears were in the bag? 5. Which color of bear is less than red but greater than green? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

33 Guided Practice Problem #5 Ms. Jones counted the class markers. She put the information in this picture graph. Class Markers Black Red Blue Purple Each = five markers How many red markers did Ms. Jones count? A. 9 B. 45 C. 40 D. 8 Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

34 Picture Graph Partner Practice Problem Part 3 Dee counted the starfish she saw on the beach each day during Spring Break. Starfish Counted on the Beach Monday Tuesday Friday Saturday Each = 2 starfish How many fewer starfish were counted on Friday and Saturday than on Monday and Tuesday? A. 6 B. 14 C. 12 D. 26 Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

35 Bar Graphs Materials: 40 red, 20 black, 35 blue, and 15 green unifix or other cubes put into a paper bag a blank bar graph (see pg 35) student copies of Guided Practice Problems #6 and #7 (pgs 40, 41) 1. Prior to instruction place 40 red, 20 black, 35 blue, 15 green unifix cubes in a paper bag. Also, create a data chart for recording information (see below) and a blank bar graph (see page 35). Unifix Cubes in the Bag Red Black Blue Green 2. Gather and Record Information Remove the unifix cubes from the bag and have students sort them into piles according to their color. Count the red unifix cubes as a class and record the number in the data chart. Following the same procedure, count the cubes in each of the other colors and record in the data chart. Unifix Cubes in the Bag Red 40 Black 20 Blue 35 Green Construction of the Bar Graph Discuss the data displayed in the data chart. Write the title and headings on the blank bar graph. (Note: Do not write a scale on the graph at this time.) An example is shown on the following page: Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

36 Unifix Cubes in the Bag Red Black Blue Green Call each color one at a time and have students place those unifix cubes onto the blank bar graph. When the cubes are placed on the graph, they will run off the edge. We seem to have a problem with our graph. What do you think we should do? Discuss with students what can be done to present all the data within the graph. Each cell can stand for more than one cube. Review what happened with the picture graph about the bears in the bag we put 2 in each space. Have students help put the unifix cubes into stacks of two. Point out the large number of stacks. Take suggestions from the class on how many unifix cubes should be put in each stack if we want to have fewer stacks. Point out they are determining the scale. The scale is the value (or number of cubes) that each space is going to represent. Eventually get to the point where the class stacks the unifix cubes into groups of 5. Place the groups of 5 within the spaces on the graph as shown below for each color. Red Etc. Remove each stack one at a time and color the corresponding space to create a bar. When all bars have been created, model how to label the x-axis with the scale. This graph has a scale of 5. Explain to students that we can count by 5s when writing the numbers in the scale. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

37 Unifix Cubes in the Bag Red Black Blue Green Read the graph by following the line at the end of each bar down to the number at the bottom and label these values at the end of the bars. Unifix Cubes in the Bag Red Black Blue Green As a class, discuss and solve several of the Bar Graph Questions (Scale > 1) on page 39. Once again, guide students through the 4-step problem-solving process verbally as done previously in the picture graph section. Complete Guided Practice Problem #6 on page 40 and Guided Practice Problem #7 on page 41 with both students and teacher recording the 4-step process. Examples of the completed problems are provided on the following pages. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

38 bar show number of llamas graph 12 llamas Labeled bars in answer choices to find 12 llamas Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

39 more 2 nd graders preferred chicken nuggets than pizza and tacos graph CN 40 P 15 T Labeled graph Added 15 and 20 Subtracted the sum from 40 Note to Teacher: This problem contains bars that fall between two numbers in the scale. Two recommended strategies are given below: Students use their knowledge of place value and making groups of 10 to help them determine the missing number (15) between 10 and 20 for pizza. It is then labeled on the scale and on the pizza bar. The nacho bar falls between numbers as well; however, that information is not needed to solve the problem so it is not labeled. This strategy is illustrated in the example above. Students rely on their knowledge of counting by 5s to label all of the missing numbers in the scale. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

40 Bar Graph Questions (Scale > 1) 1. How many fewer blue than red cubes are in the bag? 2. How many red or green cubes are in the bag? 3. Which color has between 10 and 20 cubes in the bag? 4. Which two colors have the same number as blue? 5. How many cubes are in the bag altogether? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

41 Animals Guided Practice Problem #6 Mrs. Ray s class saw the following animals during their trip to the zoo. 6 camels 12 llamas 4 tigers 18 monkeys camel llama tiger monkey Animals Seen at the Zoo Number of Animals Which bar should we use to show the number of llamas the class saw? A. llama B. llama C. llama Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

42 Guided Practice Problem #7 Favorite Lunch Pizza Food Type Tacos Nachos Chicken Nuggets Number of Students How many more 2 nd graders preferred chicken nuggets than pizza and tacos combined? Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

43 Part 4: Use Data to Draw Conclusions and Make Predictions Materials: student copies of Focus bar graph for IMN (pg 45) Word Bank written on a chart tablet (pg 46) partner copies of Word Bank student copies of Baseball Practice picture graph for IMN (pg 48) student copies of Warm-up Problem #3 (pg 51) student copies of Guided Practice Problem #8 (pg 52) student copies of Graphs Independent Practice Problems Part 4 (MATH_2_A_3 GRAPHS CONCLUSIONS PREDICTIONS IP 2014_RES) student copies of Graphs Mixed Practice Problems Part 4 (MATH_2_A_4 GRAPHS MIXED PRACTICE 2014_RES) Focus: Display the penny bar graph (pg 45) and give each student a copy. Remind them to get to know the graph by looking at the title, headings and scale. Instruct students to find the values of the bars and label these values at the ends of the bars. Provide sufficient time for them to complete the task and then briefly discuss the graph and the correct values for the bars. Emphasize that this graph shows how the total amount of pennies Kyle collected changes from day to day Explain to students that we can draw some conclusions from the data in this graph. Display the chart tablet with the Word Bank and read the words aloud together. We can often use words from the Word Bank when developing our conclusions. Let me give you an example: Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

44 When I look at the information in the graph, I see that the bars are getting higher. From that I can make the conclusion that the total amount of pennies Kyle collected is increasing from day to day. Record the conclusion on the board for all to see. Conclusions The total amount of pennies Kyle collected is increasing from day to day. What conclusion could we make if the bars were getting lower? His total amount of pennies would be decreasing from day to day. Let s form another conclusion about the data using the words more than. Allow students to study the graph for a moment and formulate a conclusion using more than. Have them share their thinking. If necessary, guide students to form a conclusion such as The total number of pennies he had on Thursday was more than he had on Tuesday. Record this conclusion in the list. Conclusions The total amount of pennies Kyle collected is increasing from day to day. The total number of pennies he had on Thursday was more than he had on Tuesday. Have students work with an elbow partner to formulate a different conclusion using a word or words from the Word Bank that has not yet been used. Have several students share their conclusions, and explain how they came to those conclusions. The teacher then adds them to the list. Some possible conclusions have been added below: Conclusions The total amount of pennies Kyle collected is increasing from day to day. The total number of pennies he had on Thursday was more than the total he had on Tuesday. Kyle had the least total pennies on Monday. Kyle had fewer total pennies on Wednesday than he did on Thursday. The total number of pennies he had on Tuesday was less than the total he had on Wednesday. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

45 2. Direct students attention back to the graph. Explain that we can also use the information presented in a graph to make a statement about what will happen in the future. A statement about the future is called a prediction. We can search the data in a graph for a pattern that will help us make a prediction that is reasonable. Let s look carefully at the data in our graph. On Monday, Kyle had a total of 20 pennies. On Tuesday, he had a total of 30 pennies. On Wednesday, he had a total of 40 pennies and on Thursday, he had a total of 50 pennies. Do you see any kind of pattern? After Monday, the total amount of pennies increased by 10 each day; On most days, Kyle collected 10 pennies. How many pennies do you think Kyle will save on Friday? 10 What prediction can we make about his total number of pennies on Friday? On Friday, Kyle will have collected a total of about 60 pennies for his class project. Is this prediction reasonable? Why? Record the prediction on another part of the board. Prediction On Friday, Kyle will have collected a total of about 60 pennies for his class project. Have students glue their copy of the penny graph on the right side of their Interactive Math Notebook (IMN). Then, have them choose 1 conclusion from the list on the board and write it below the graph. Students also record the prediction in their IMN below the chosen conclusion. See picture below. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

46 Total Pennies Collected Kyle made a graph to show the total number of pennies he collected for a class project. 70 Pennies Collected Monday Tuesday Wednesday Thursday Conclusion: Prediction: Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

47 Word Bank increases increasing increased decreases decreasing decreased more than less than least fewer most equal Word Bank increases increasing increased decreases decreasing decreased more than less than least fewer most equal Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

48 3. Display the baseball picture graph (pg 48) and give each student a copy. Give students time to take a quick look at the title, headings and key. Briefly discuss the graph and its characteristics. Have students compare this graph to the penny graph we just studied. How is this graph the same as the penny graph? How is it different from the penny graph? Guide students to see that this graph shows how many hours Jon practiced baseball each week. Instruct students to show their skip counting on the pictures and then label the total values at the ends of the rows. Remind students that we can formulate a conclusion from the information given in a graph. What conclusion can we make from the information in this graph? Have a student choose a word from the Word Bank and generate a conclusion as a class using the chosen word. Instruct students to now form a conclusion of their own that is different from the one done by the class and write it on the lines beneath the graph. A few possible conclusions are listed below: Jon practiced the least number of hours in Week 1. Jon practiced more hours in Week 3 than he did in Week 2. Jon practiced as many hours in Week 4 as he did in Weeks 1 and 2 together. Jon practiced fewer hours in Week 2 than he did in Week 4. The number of hours Jon practiced increased each week. 4. Direct students attention back to the graph, and briefly talk about making a prediction. What prediction would you make about the number of hours Jon will practice baseball in Week 5? Have them write their prediction on the lines provided on their paper. Once they have finished, they may glue their paper on the left side of their IMN. If desired, allow students to Pair-Share their conclusion and prediction with other students. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

49 Jon made a graph to show the hours he practiced baseball each week the past 4 weeks. Jon s Baseball Practice Week 1 Week 2 Week 3 Week 4 = 1 hour of practice Conclusion: Prediction: Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

50 Warm-up: (approximately 10 minutes) Have students complete Warm-up Problem #3 (page 51) in which they construct a bar graph with a scale of 2 and draw a conclusion from the information presented in the graph. Remind students they may use the Word Bank if needed. Once students have finished, briefly discuss the graph to check for accuracy. Also, have students justify and explain how they formulated their particular conclusion. 5. Guided Practice Work through Guided Practice Problem #8 with students. Read the problem together, insert speed bumps, and begin the 4-step process by finding the main idea and recording the details/known information. Examine the graph with students. Read the title, headings and scale. Look at the data from Week 1 to Week 4. What do you notice? Guide students, if necessary, to see that the last three weeks decrease by 1 minute. This is a trend in the data, and it will help us make a reasonable prediction for Week 5. Check each answer choice. Have students justify their thinking to the group and then label. Finally complete the how/why part of the process. An example of the completed problem is provided on the following page. 6. Independent Practice Students complete Graphs Independent Practice Problems Part 4 (MATH_2_A_3 GRAPHS CONCLUSIONS PREDICTIONS IP 2014_RES) independently. 7. Mixed Practice Have students complete Graphs Mixed Practice Problems Part 4 (MATH_2_A_4 GRAPHS MIXED PRACTICE 2014_RES) independently. This exercise provides a variety of graph problems for students to solve. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

51 too much too much yes too little graph reasonable prediction time one mile Week 5 Wk 1 10 Wk 2 8 Wk 3 7 Wk 4 6 labeled graph found pattern in data checked answer choices Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

52 Warm-up Problem #3 Name Create a bar graph using the data below. Label the scale by 2s. Remember to include a title and headings. 10 students like summer 6 students like spring 2 students like winter 4 students like fall Title: Season Number of Students Conclusion: Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)

53 Number of Minutes Guided Practice Problem #8 Mrs. Messer was training for a race. She made a graph to show how much time it took her to run one mile. What is a reasonable prediction for how much time it will take Mrs. Messer to run one mile in Week 5? A. In Week 5, Mrs. Messer will run one mile in 12 minutes. B. In Week 5, Mrs. Messer will run one mile in 8 minutes. C. In Week 5, Mrs. Messer will run one mile in 5 minutes. D In Week 5, Mrs. Messer will run one mile in 1 minute. Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade)