Mean, Median, and Mode

With my 4th graders, whenever possible we begin a math investigations by doing something concrete -- hands-on. For finding median, we use interlocking cubes (but you could use stacks of non-interlocking as well) to show how many of something we have.
For example make a stack of cubes to represent:
how many people in your family
how many pencils in your desk
how many pets you have
how many blocks you live from school, etc.
Then in order to find the median we line up in order from least to greatest (left to right) and find the exact middle person. We talk about how the middle person gives us information about what is typical for whichever numerical data we are investigating. Be sure to demonstrate examples using an even number of pieces of data and an odd number of pieces of data so students can see how that works.

After doing several of these types of lining up, counting to the middle, discussing that median shows us what's typical, then you can move to a paper and pencil method for finding median, always emphasizing the importance of putting the data in order from least to greatest before finding the exact middle.

As far as connecting median to something relevant, think of some things that we make decisions about based on what we've come to believe is typical for certain situations.
For example:
vacation plans may be based on typical weather patterns, temperature or rainfall, etc.
expectations for sporting event outcomes may determine whether fans turn out (or bet on a game! I am stretching here!)
after collecting and analyzing data to determine what's typical about an athlete, coaches can make decisions on where to place a play, when to send a player in or take one out, etc.
Hopefully you are getting the idea because I'm running out of things that make sense.

One thing to remember is that median is just one kind of average -- just one way to look at what's typical. It may not give as good a picture of what usually happens as mean or mode but it is still worth considering. I hope some of this makes sense to you. Need anything more -- just post. Good luck and have fun!

Do math, and you can do anything!
Elaine

In our school (fourth grade) we do a lesson on data collection using 1/2 oz boxes of raisins. The students estimate the amount of raisins in their box and then count. Each student can then write their amount on a post it. Then have students line up for greatest to least. One from each side of the line can sit down until you reach the median. You can then use the data to make a variety of graphs to show the information. Mean and mode can be calculated from the data.
We also do a lesson about hat sizes. We pose a problem about a retailer not knowing how many hats to order in each size. Then the students in pairs measure each others head size with tape measures. Then we use post its the same way as with the raisin lesson. These lessons are from the Everday Math program.

If your school doesn't have a rule against food as manipulatives....then M&Ms are great to use for mean median and mode. You can also throw graphing and sorting in there.
Give each child (or group) a small bag of M&Ms. (didn't say it was a cheap lesson)
First have the students predict the number of m&ms in the bag and for each color (BEFORE opening bag).
Ask them to color in their predictions on a chart.
Then have them actually open the bag and count the
m&ms in the baf and for each color. I usually have my separtate them at this point too.
Compare results.
Have students record each others results.
Then have them find the mean median and mode for the number of m&ms in a bag. And the mean median and mode for each color.
You can use the information to create a class chart.

It is a lot of fun. Just make sure that your kids know that they can't eat any until the end of the lesson.

Let me know if you have any questions. The charts can easily be made in either WORD or EXCEL.
Next have them

I also use an estimation jar in my classroom to reinforce and master maximum, mimimum, range, median, and mode.

Every Friday I pass out a post-it to each student. One student walks around with the jar and allows students to glance at it without touching. Then once they have decided on an estimation they write it down (along with their name) then I have call students to go up to the dry erase board and stick their estimation post-it up. The students must put their estimation in correct number order independently (this is another mastery standard).

Once all estimations are in, the student who walked around with the jar gets to dump the jar and everyone counts the items in the jars by 5's, 2's, 3's. It is such an great way to practice counting by different numbers. Very repetative. Then as a class we see who was closest and that person gets to take home the jar to fill with items of their choice. We then take all the data and identify maximum, mimimum, range, median, and mode. After that we create a bar graph with the estimations.

The students love the activity, it helps to reinforce the skill on a weekly basis and allows the students to enjoy learning.

I just did a center using Probability. I had the kids roll a die 50 times and tally how many times each number came up. I made a chart for them to fill in and then answer some questions about their results.

I also made a two row chart and had them roll a die 11 times. They recorded their numbers in the first row as they came up, and then in numerical order in the second row.

They had to show the Median, Mode and Range for the numbers. (I gave them the definitons for them).

They seem to really like the center.

I've used this ideas in 4th grade but maybe you can adapt them.

We break the concepts into two days. The first day, we discuss median, mode, and range. There are keywords for each of these: median is like the median on the highway or the middle of the data, mode is most the one that is used the most, range is the difference between the highest and lowest numbers (think of a mountain range). We practice these with data that the students might find interesting, local basketball scores, baseball statistics, class grades (made up of course).

The next day, we discuss mean. We first do a hands-on activity with writing instruments. Each student takes out two things to write with (pens, pencils, colored pencils, crayons, etc). They work with a partner to cut a strip of paper to the length of each writing instrument. Then, they tape the strips together and fold into four equal pieces. They measure the length of these pieces and that is their average. Then, we discuss how this is the same as what we do mathematically. Finally, we apply it by finding the mean of the same data we used the day before.

Your kids could probably "get it" without the hands on activity but I think it helps reinforce what exactly they are doing.

You might also want to give some scenarios as to when you would use each- mean, median, and mode. For example, a shoe store would want to use mode to decide what shoe size to order.

Use it as a growth chart and plot children's heights four times during the year. (I'm assuming you can use all four sides). Cover it with paper first, then measure kids and mark their heights. You could attach a digital picture beside each kid's marks to show how tall they were/what they looked like at different times during the year. Kids could keep a line graph at their desks (math notebooks) charting their own individual growth during the year. At the end of the year, you can have kids find the number of inches they grew during the year. Then, turn that into a lesson on averaging. Have groups find the average # of inches they grew. Then they can find the mode, median and range in inches.

Kangroos Hopping Down Mountain drinking Chocolate Milk

A lesson I did with 7th graders that was fun was "Smile Metric Style" It isn't complicated but you can implement many other ideas with this. The students measure their own smile, using string or something else, in centimeters and cut out a paper strip the length of their smile. Each group tapes their smiles together and then the class. We added the length of each group and class and we discussed and figured mean, median, mode, outlier and graphed our results. We also figured milimeters and meters by converting our answer. We put all four classes together and our smile streched across the room!

You could have the kids graph the number of runs per inning in one of the games, then find the mean, median and mode...even outliers....for that game. Or combine the games and have them just do the ending scores. Looking up the post season game scores and things online shouldn't be to big of a deal!! And the kids might really get into it!

make posters for each one to hang on the wall ...they can have definitions and explain the steps of each oone...then students can refer to the posters when they have difficulties....i would calculate the average age for the class......throw in your own age to spice it up a little.....

Use the book Rikki Tikki Tembo and then have them use post its for their names. Make a line plot for the most letters in their names to the least letters in their name. Post the post its on the board. The largest plot is the mode, the range is the difference between the greatest amount of letters and the least amount of letters. It is a great visual and the kids really love the book!

There is a Carson & Dellossa reproducible book about using the 100's chart. We use it to find range, median, mode, etc., or solve computation with decimals...good review for "the test." (Students solve the problems and then shade in the answers on the chart, sometimes into a design and sometimes not.) You could easily make up your own to go along with what your students need to review.

I give the kids store ads and they have to spend $100. They must cut and glue the photos of what they buy and then complete the computation off to the side.

I write the numbers from 1-100 on index cards and place them in the middle of our sheet parachute. After the kids flip all of the cards off of the sheet, they collect several off of the floor. They must then find the range, median, mode, and mean of their data. They then work with a partner to correct each other's work.

they draw a picture of what they will look like in 100 years and then write about it.

Mean--The mean old math teacher made us find the average. (one way I have seen)

Mode--the most (have them run in place to see who runs the most)

Median--Number in middle when in order from least to greatest.

How about having all of your students grab one handful of manipulatives such as bear counters or cubes. Have each student count his or her counters and put the number on a post it note. Then arrange the notes in number order (like a number line). From there you can see the mode and the median. (If there is more than one child with a number I'd put the extras above the number to look almost like a graph)
I'm not sure how you get first graders to find the mean other than to tell them the steps and doing it together. Maybe your job as a first grade teacher is to just introduce the vocabulary and give them some practical experience hearing and using the terms without having them do the advanced calculations.
You could repeat this with other manips as needed.

In 2nd grade, I teach median by having the kids collect a piece of data with a number (how many buttons they have on, how many siblings, how many manipulatives are on their desk etc.) and write it on a piece of paper. THen they line up from least to greatest. TO find the median, both ends sit down when I tell them to, then the two "new" ends, etc. until there's only one left (or middle two if even number of students). It's good...very visual, and then every time they forget what it means, I remind them, "Remember when we lined up in order?" and they say "Oh yeah, the last one standing!" Might be appropriate for 1st too! Good luck on median though...not so appropriate for 1st!

Use the the term 3 Musketeer method

MODE = MOST ofter seen
MEDIAN = MIDDLE - list least to greatest, min. to max. etc. leap frog from both ends to the middle - unless list is too great
Mean = line them up - add them up - divide them up
Range = hangs around for the ride - Home on the Range seaches for lost animals in the low places and the high places - then subtract

I have had reasonalbe success - using this on 4th graders - working with 5th for the first time this year

USe the newspaper. Look at the weather section and have the kids get the mean, median, and mode for the high, low and average temperatures for your area for the week.

Marie from PA