Line Plots and Bar Graphs Solving Problems Involving Fraction Operations

Kenisha: Welcome, math masters! new scroll has arrived at the dojo gates. Inside is challenge designed to strengthen your mind and elevate your math skills. Today, you'll begin training to earn the Line Plots and Bar Graphs badge. group of students measured how far they could jump. Their jump distances in feet are shown. Create line plot and bar graph to display the jump distances. Use your graphs to solve: How many students jumped less than 2 and 3/4 feet? What's the combined distance of all the jumps that measure 2 and 1/2 feet? Study well. The path to mastery begins now. Jenna: Welcome back, math masters! have feeling we'll need our knowledge of displaying data and working with fractions to conquer today's challenge. Have your guided notes ready! Training starts now. Before today's challenge, let's complete similar problem to review the skills we'll need. This dataset shows the number of hours different soccer players practiced last week. That's lot of numbers! Can we make this data easier to work with? Here's Power-Up Technique! Organizing data into frequency chart makes it easier to interpret. For example, 2/3 appears 4 times, so its frequency is 4. 1 player practiced for 1 hour, 2 players practiced for 1 and 1/3 of an hour, and 4 players practiced for 1 and 1/2 hours. Now that our data is organized, let's continue training and create bar graph. The x-axis, or the horizontal axis that goes from left to right, labels the categories. That's the hours practiced. The y-axis, or the vertical axis that goes up and down, shows the number of data points in that category, which is the number of players that practiced for each time length. Since the most is 4, the scale counts by ones. Let's make the bar graph! 4 players practiced for 2/3 of an hour, so the bar goes to 4. Pause the video to finish creating the bar graph. Check your bar graph! Each bar shows how many players practiced for the given length. Nice work! Making bar graph is just one way to organize data. The next part of our training is displaying the same data on line plot. line plot is graph that shows the frequency of values in dataset by representing each value as an on number line. In our example, the number line shows the hours practiced. Let's start with the first row of data. 4 players practiced for 2/3 of an hour. We need to add four x's above the 2/3 point, but only whole numbers are labeled. Where's 2/3 on this number line? It's between 0 and 1. The number line is split into 6 parts, meaning each tick mark represents 1/6. So, to find 2/3, we'll find an equivalent fraction with denominator of 6. In the denominator, we go from 3 to 6 by multiplying by 2. We'll also multiply the numerator by 2, so 2/3 equals 4/6. The fractions are equivalent, so we'll label 2/3 on the number line to match the value in our dataset. Now place 4 x's above it to show the frequency. Pause to complete the rest of the line plot. Check your work! 1 player practiced for 1 hour, so add an above 1. 2 players practiced for 1 and 1/3 hours. 1 and 1/3 equals 1 and 2/6, so count 2 marks past 1 and add 2 x's. Finally, 4 players practiced for 1 and 1/2 hours. 1 and 1/2 equals 1 and 3/6. Count 3 tick marks past 1 and add 4 x's. This bar graph shows how many players practiced for each amount of time. Here's the same information shown on line plot, which helps us notice how the times are spread out along number line. Examining both together gives us clearer picture of the data. Now, let's answer question about the dataset. What is the difference between the longest and shortest practice time? what does it mean if we need to find "the difference"? It means figuring out how much longer the kids who practiced the most did compared to those who practiced the least. And how do we find difference? By subtracting, yeah! Let's examine the line plot. Since it shows the practice times on number line, it's easier to identify the shortest and longest times. What's the longest practice time? The longest has to be the greatest value, which is the farthest right. It also must have x's above it, showing people practiced that length. So, it's 1 and 1/2 hours. What's the shortest practice time? It's the lowest value with x's plotted, which is 2/3 of an hour. You've got this! Pause the video to subtract 1 and 1/2 minus 2/3. To subtract, the fractions need common denominators. 6 is multiple of 2 and 3, so 6 is our common denominator. Now we have 1 and 3/6 minus 4/6. Let's change 1 and 3/6 to an improper fraction by multiplying 1 by 6 to get 6 and then adding 3, giving us 9/6. 9/6 minus 4/6 is 5/6. So, the difference between the longest and shortest practice time is 5/6 of an hour. Great work breaking down the data! Your challenge awaits. Complete it, and the Line Plots and Bar Graphs badge is yours. group of students measured how far they could jump. Their jump distances in feet are shown. Create line plot and bar graph to display the jump distances. Use your graphs to solve: How many students jumped less than 2 and 3/4 feet? What's the combined distance of all the jumps that measured 2 and 1/2 feet? Pause to complete the challenge. There's frequency chart in the guided notes you can use to organize the data. How'd you do? Here's the data organized in frequency chart. Now, check your bar graph and line plot with mine. Feel free to pause the video if you need more time to check your work. Now that our data is displayed on the bar graph and line plot, let's answer the questions. How many students jumped less than 2 and 3/4 feet? Here's 2 and 3/4. The values to the left are less than. 3 students jumped 2 and 1/4 feet and 3 students jumped 2 and 1/2 feet. So, 6 students jumped less than 2 and 3/4 feet. The next part of our challenge is to find the combined distance of all the jumps that measured 2 and 1/2 feet. 3 students jumped 2 and 1/2 feet. Which operation helps us combine amounts? Addition! Let's add the three distances of 2 and 1/2 together. Adding the whole numbers first, 2 plus 2 plus 2 is 6. Then, adding the fractions equals 3/2. That's improper, so regroup 2/2 as one whole, making the answer 7 and 1/2, meaning the combined distance is 7 and 1/2 feet. Nice! You've solved our challenge. So, what have we learned today? We learned bar graphs and line plots show the frequency of data. Line plots show how spread out the data is by representing each value as an on number line. When interpreting data, we can apply skills we already know. You've earned the Line Plots and Bar Graphs badge, but your training isn't over just yet. Be sure to complete the practice questions and extension activities that go with this lesson to practice working with data and graphs. Once you've completed all the lessons for this unit and earned all the badges, you'll earn your purple belt, so keep training hard. And remember, math masters, in math, as in training, progress comes with patience and practice. I'll see you next time!