Using the State Curriculum: Mathematics, Grade 4

four sets of data

• Provide students with the following data and a description of the data.
  
  Data Set A: 1, 4, 5, 5, 7, 9, 10
  Median: 5
  Mode: 5
  Range: 9
• Have students make individual conjectures about the meaning of median, mode and range. Discuss with a partner. Discuss as a class.
• Break students into three groups and provide them with three additional data sets. Give them more time to make independent conjectures. Then discuss as a group. Allow each group to work with each data set to revise their definitions.
  
  Data Set B: 10, 12, 17, 23, 25, 32, 34, 34
  Median: 24
  Mode: 34
  Range: 24
  
  Data Set C: 8, 9, 11, 14, 32
  Median: 11
  Mode: none
  Range: 24
  
  Data Set D: 128, 128, 130, 140, 150, 160, 170, 180
  Median: 145
  Mode: 128
  Range: 52
• After all groups have seen each data set, have a final class discussion to develop a definition for median, mode and range. Discuss the need for these terms. When would you want to use the median in making decisions? When would the mode be a more appropriate reflection of the data? Why is the range important when analyzing data?

Follow up:

Kelly and Joe ran a concession stand at their swim meet on Saturday. The following chart shows the amount of candy sold each hour:

What was the median amount of candy sold for that day?

Answer: 28 is the correct answer because if you put the numbers in order from least to greatest: 22, 22, 28, 32, 35

28 is the number in the middle of the data points which is the median.

paper bag and Unifix cubes

• Have each student take a handful of Unifix cubes
• Ask each student to link the cubes together.
• Ask students to line up side by side in order from least to greatest according to the number of cubes each has. (If the same number occurs, have those students line up in front of each other.)
• Make sure that the students are in numerical order.
• Have the students at the two ends step forward and announce their number. Ask the students what the difference is between these two numbers. Explain that this difference between the lowest and highest data points is called the range of the data. Have students discuss why this is a good name for this difference.
• Now have students with the next lowest and next highest values step forward to join the first pair. If there is more than one student for any value, have all students with that value step forward together.
• Repeat this with each next lowest and highest values until only one or two values are left in the line. Ask the students how they would describe the position of this student or pair of students left in line. [These are the students that were in the middle of the data. They are like the median strip in the middle of the road dividing the road in half.]
• Explain that this data value is called the median because it is the 'middle' point of the data group. Half of the data is above it and half below it. If there is one student left, this value will be the median of the data. If there are two students left, find the average of their two numbers. This will be the median of the data.
• Ask which data value appear most often in our graph. Once identified, explain that this data value with the most people is the mode.
• If you have a digital camera available, take a picture of the line to display the data.

Ask students to explain how the range, median, and mode were found. Discuss when you might use the range, median, and mode to analyze data.

Ask students to create a set of data where:

• The range is 5, the mode is 10, and the median is 12
• The range is 2, the mode is 6, and the median is 6

an index card for every student in the classroom and an index card for the teacher

• Have every student write a number from 0 to 15 (or any number less than the number of students in your class) on their index card. Circulate around the room to ensure that at least one number is written more than once. If a number is not written more than once, use your card to duplicate another student's number. This ensures that you will have at least one mode
• Have the students place the index cards in a box.
• Have a student pull a card at random and place it on a number line.
• Have a second student pull another index card. Ask, "Is this number greater than, less than, or equal to the first number?" The index card is placed on the number line to the right, to the left or above the first card depending on whether the number on it is greater than, less than or equal to the number on the first card.
• The students continue to pull cards, asking the same questions over and over until all cards are arranged on the number line in order from least to greatest.
• Students look at all the cards and are asked "What number appears the most number of times? Ask student what name we have given the number that appears most often. [Mode]
• Using the same index cards, have the students subtract the lowest number chosen from the highest number chosen. Ask student what name we have given this difference. [Range]
• Using the same index cards, have the students remove the cards for the lowest and highest values on the number line. Have them continue this process until there is/are only one or two values remaining. If one value is remaining, ask students what name we have given this value based on its position on the number line. [median] Ask students how we find the median if two cards remain. [Find the average of those two numbers. We add them together and then divide by 2.]

Followup:

Ask:

• Suppose two more students chose numbers between 0 and 15. Would that change the range? Why? Why not? Give an example to support your answer. [As long as you already have a card at 0 and 15, the range would not change. But if 0 or 15 have not been chosen before and one of these students chose one of the, then the range would change.]
• Would it change the median? Why? Why not? Give an example to support your answer. [It could change the median depending on which numbers the new students chose. Their choices could throw of the balance depending on where their choice falls within the data set.
  Example: Original Data set:   2 3 5 5 6 7 8   Its median is 5.
  Updated Data set:   2 3 5 5 6 7 8 9 10   With the two new data pieces added, the median is now 6, not 5 as before.]

paper, meter sticks

• Read a book about airplanes or begin a discussion about airplanes and their design.
• Have each student create a paper airplane.
• Each student will fly three trial flights and measure the distance flown using a meter stick. Have students measure the distance to the nearest centimeter.
• Students would then use their data to create a class line plot of the data. This can be done on the board. Ask students how they would begin to construct the line plot. [They should find the smallest and largest values and then add values between at 1 unit intervals.]
• Ask students if they know what a "median strip" is. They should answer that it divides the highway into two equal parts. In mathematics the word median is used to tell us something about a set of numbers. Ask, "What do you think it tells us?" [It is the point that separates a set of numbers into two equivalent sets.] Have students work with a partner to find the median of the set of numbers on the line plot. One way is to begin removing numbers from either end of the set at one time. This process is continued until only a single number remains. Have partners share their method with the class. Identify the number on the middle card as the median.
• Students would then decide which was the greatest and least distance traveled and find the range or difference between those two distances.
• Students would then look for a distance that occurred most often. This data point would be the mode.

Adapted from www.illuminations.nctm.org/LessonDetail.aspx?id=L297

Ask:

• Do you think the line plots would look different for boys and girls?
• Do you think the range would be different for the two groups?
• Do you think the median would be different for the two groups?

Create two separate line plots for the two groups to answer the questions.