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A detailed explanation of averages, specifically focusing on mean, median, mode and range. It includes instructions on how to teach children about averages using manipulatives and real-life examples. The document also explains how to handle remainders when averaging.
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There are technically at least three different types of averages – mean, median, and mode. They will all be covered in a later lesson. Here, only the mean is covered. In general conversations, when people refer to “the average” they are usually referring to the “mean”.
To average is to even things out so that you find out how much there would be if everyone got the same amount.
To explain average, you can say that “averages make things fair .” You can teach the concept of average even before you teach division, and you can even bring younger siblings into the demonstration. Children who haven’t been taught division can still understand average and figure averages using manipulatives. (They do this all the time – they just don’t know the terms.) Take a handful of something small that can be easily divided. Ideas include small edible items, such as nuts, crackers, pretzels, small cookies or candies; small toys, such as Legos ®^ or jacks; or pennies. Make sure that you start with an amount of items that can be evenly divided by the number of participants. At the end, each person should be able to have the same amount.
NOTE: Be sure to use items that are safe for the ages of the children involved.
Give each person a different amount and let each person count them (if edible, don’t eat yet) and compare — have the items been distributed fairly? Does everybody have the same amount? We can average to make it fair. Here is how.
a. Put everything in the middle and add them together.
b. Now divide the items up evenly, putting one piece at time in front of each person.
That is really all that averaging means — add the items all together, then divide them evenly. The divisor is determined by counting how many participants there are in the demonstration.
Here are the steps to use when practicing averaging.
1. Practice averaging using manipulatives. 2. Average with manipulatives, but also write down what you are doing.
Example: 3 people, one gets 10 items, one 6 items, and one 14 items.
Write down on the board:
Operations
NOTE: If your averaging lessons include beginning math students, you may want to keep them working with manipulatives.
3. After you have done this several times, then average numbers without using manipulatives. 4. The last step is to teach your child what to do with remainders. (This is also a good tie-in to fractions.)
Handling Remainders
Average a group of numbers, such as 2 , 6 , and 5. (You can do this with manipulative also — brownies or cookies work well, dividing them among three people.)
There is a remainder of one. In order to divide that remaining one evenly among three, it must be divided into three pieces, and each person gets one piece, or 1/3. If you were to repeat the averaging process with 3 , 6 , and 5 , there would be a remainder of two. If those two were cut into three pieces each, there would be two pieces for each person. To handle remainders when averaging, put the remainder as the numerator and the divisor as the denominator.
2 + 6 + 5 = 13
one divided into three pieces
4 3 13 12 1
4 3 14 12 2