Matching Stats With Line Plots
Students complete a card sort that requires them to match sets of statistics with the corresponding line plots.
Students match cards with simple line plots to the corresponding card with measures of center. Some cards include mode, mean, median, and range, and some have one or two measures missing. Students discuss how they determined which cards would match.
To complete the card sort in this lesson efficiently, students must be able to relate statistical measures with line plots. If they start with the measures that are easy to see, they can narrow down the possible matches.
- The mode is the easiest measure to see immediately. It is simply the number with the tallest column of dots.
- The range can be found easily by subtracting the least value in the plot from the greatest.
- The median can be found fairly quickly by counting to the middle dot or by pairing dots on the ends until reaching the middle.
- The mean must be calculated by adding data values and dividing.
Goals and Learning Objectives
- Apply knowledge of measures of center and range to solve problems.
- Discuss and review strategy choices when problem solving.
Discuss the Math Mission. Students will use their statistical knowledge and skills to match line plots with measures of data.
Use your statistical knowledge and skills to match line plots with measures of data.
Match Line Plots to Measures of Data
Have students work independently for this activity.
SWD: Making connections between the different solution methods for the same problem will bring out the mathematics of the problem. Allow students time to process why there were different solution methods and let students discuss with a partner to further their understanding.
Mathematical Practice 1: Make sense of problems and persevere in solving them.
- There are many different ways to approach the card sort. Encourage students to think of several strategies, then determine which is the best (e.g., easiest, most efficient) for them before beginning to match cards.
Students have trouble getting started.
- Decide whether you want to start with a plot and find the matching statistics or start with a set of statistics and find the matching plot.
- Pick just one card to start.
- Think about the statistics that are easy to see right away in a line plot. Start with those and see if you can eliminate any of the possible matches.
Students start with a line plot card and have difficulty matching a statistics card.
- What statistics are obvious just from looking at the plot?
- Does the data have a mode? Can you use it to narrow down the statistics cards that might match?
- What's the range of the data in the plot? Can you use this to eliminate more statistics cards?
- Next use the plot to find the median. Can you eliminate more cards?
Students start with a statistics card and have difficulty matching a line plot card.
- If you start by looking at just the mode, can you eliminate any line plot cards?
- Now look at the range. Does that help you eliminate any possibilities?
- What statistic should you look at next?
SWD: Struggling students may still need explicit instruction and guided scaffolding to recognize the relationships between the line plot and measures of data. Provide small group instruction to help them use specific strategies to match the line plot with the given measures of data.
ELL: If students are struggling to get started, ask these questions to ELLs, ensure your pace is adequate, and you are providing ample wait-time to allow for a thoughtful response. Present the questions from the Interventions in writing, and allow students to use dictionaries before responding, if there are words in your question(s) that they don't understand.
Match Line Plots to Measures of Data
You will see 12 statistics cards (mode, median, mean, and range) and 12 line plot cards.
- Match a card from one set with the correct card from the other set. Some of the statistics cards have missing data that you will have to calculate.
- After you have paired all the cards, make sure you have filled in all of the missing data for each stats card.
HANDOUT: Match Line Plots to Measures of Data
- Which measures on the stats card are easy to see on a line plot just by looking?
- Use those measures to narrow down your choices of line plot cards.
Prepare a Presentation
Students will prepare a presentation to share with classmates about their strategies they used to match up the statistics cards and line plot cards in the interactive.
Preparing for Ways of Thinking
Look for students who used reasoning skills to narrow down their options for knowing which line plots went with which mean, median, mode and range. Also, look for different strategies students used to fill in the missing statistics for some of the cards.
Make note of students were struggling with how to fill in the missing statistics or had trouble matching up cards, so you can clear things up during Ways of Thinking presentations.
- Answers will vary.
Prepare a Presentation
Prepare a presentation that explains the strategies you used to match the line plots with the statistics cards.
Choose one of the statistics cards.
- Create a data set with 11 or 12 values that has the statistics listed on the card but is different from the matching line plot card.
Have students share their strategies for matching the cards. Encourage students to explain their reasoning as precisely as possible.
Students may have noticed the following:
- Line plots A and F are symmetrical and will have the same mode, median, and mean.
- Line plot D and I are the only ones with a range of 5.
- Line plot A is the only one with a range of 2.
- Only line plots J and K have 12 data points; L has 13 and the rest have 11.
Consider these questions:
- Did you need to calculate the mean each time?
- Did you start with a line plot and then look for the correct statistics card or vice versa?
- How does this activity help you connect the visual display of data (the line plot) with the measures of the data (mean, median, mode, and range)?
SWD: Thinking aloud is one strategy for making learning visible. When teachers think aloud, they are externalizing their internal thought processes. Doing so may provide students with insights into mathematical thinking and ways of tackling problems. It also helps to model accurate mathematical language.
Ways of Thinking: Make Connections
Take notes as your classmates share their strategies for matching the cards.
As your classmates present, ask questions such as:
- What strategies did you use to find matching cards?
- Which pairs were easy to match? Why?
- Which pairs were difficult to match? Why?
- How did you figure out the correct values for the statistics cards with missing information?
What I Learned About Data
Students will write a summary of what strategies they used in the card sort.
A Possible Summary
To match statistics with line plots, start with the statistics that are easiest to see in the plot, like the mode and the range. This will eliminate some possibilities. Matching the median takes a little more time, but is also pretty easy and quick. If you still haven't found a match, you can calculate the means of the plots you have left.
Summary of the Math: What I Learned About Data
Write a summary of the strategies you used to complete the card sort.
Check your summary.
- Did you discuss which of mean, median, mode, and range, you can identify on the line plot without doing any calculations?
Reflect on Your Work
Have each student write a brief reflection before the end of class. Review the reflections to find out what strategies students found helpful while working on the card sort.
ELL: Asking students to reflect on their learning provides opportunities for ELLs to develop literacy in English and proficiency in mathematics. Make sure students use both academic and specialized mathematical language when reflecting on their learning at the end of each session.
Write a reflection about the ideas discussed in class today. Use this sentence starter below if you find it to be helpful.
A strategy I found useful in working on the card sort is …