## Functional Relationships

Developing the concept of functional relationships should be an ongoing process throughout the year. Understanding these relationships go hand-in-hand with problem solving. Therefore, take the opportunity of incorporating functional relationships at opportune times in other areas of the curriculum, especially when problem solving is involved. Making this connection will allow students to gain a better insight towards performing the mathematics needed outside the classroom.

Materials: eight to ten 1.69 ounce and 3.14 ounce bags of candy, napkins, and small paper of plastic bowls

Preparation: Divide the class into groups with three students in each group. Write the price of a 1.69 ounce bag and a 3.14 ounce bag on the board.

• Give each group a 1.69 ounce and 3.14 ounce bag.

• Say: Open up each bag of candy and place the contents in separate bowls. The 1.69 ounce bag should go in one bowl and the 3.14 ounce bag in another. Count the pieces of candy in each bag.

• Ask: Does everyone have the same number in their 1.69 ounce bags?
No. Make a table on the board and have representatives of each group write the number of pieces of candy in their 1.69 ounce bag.

• Ask: Does everyone have the same number in their 3.14 ounce bags?
No. Make a table on the board and have representatives of each group write the number of pieces of candy in their 3.14 ounce bag.

• This should generate a class discussion as to why there are not the exact same number of pieces of candy in each bag. The candy company only has to put at least 1.69 ounces or more in the 1.69 ounce bag. Since each piece of candy cannot exactly weigh the same, the bags may vary in the exact number in each bag.

• Ask: Which bag is a better buy, the small one or larger one? Why?
Remember to inform the children the cost that you paid for each bag. Encourage students to use mental math to find their answer. The goal is to have each group devise a strategy of their own.

• Ask: How can we determine which bag is a better buy?
There are several ways. Ask each group to explain their strategy to the class. One way is to notice that the 3.14 ounce bag is very close to twice the size of the 1.69 ounce bag. It is actually a little less than twice the size. Therefore, if you double the cost of the smaller bag, it should be a little more than the cost of the 3.14 ounce bag. If it is a lot more, then the 3.14 ounce bag is a better buy. If twice the cost of the 1.69 ounce bag is less than the cost of the 3.14 ounce bag, then the smaller bag is a better buy. Other ways would be to find the cost of 1 piece of candy in each bag and compare the unit cost.

• Ask: Which strategy is the best to use?
Engage the class in a discussion to see if the class as a whole can come up with the most effective and efficient strategy for determining the best buy.

Wrap-Up and Assessment Hints
Assessment of functional relationships should be a continual process. These concepts are used in real life. Be sure to incorporate these ideas with problem solving throughout the year. Make the assessment and lessons of functional relationships meaningful to the students. They lend themselves to the use of real life items. By using things that students encounter outside of school, such as popcorn and candy, children are more likely to gain interest and enthusiasm for doing mathematics. Of course, this will also make learning mathematics fun!

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