Today I am linking up with Focused on Fifth to bring you a fabulous event - Unwrapping Holiday Classroom Ideas: Celebrate the 12 Days of Christmas with Focused on Fifth. For twelve days lots of great bloggers will be joining together to bring you classroom ideas for this holiday season. Today we are blogging about holiday math ideas.

I am just finishing up a class for my math endorsement about using algebra in the elementary classroom. We have been working with variables, functions, and graphs and how they can be introduced into the classroom. I have been amazed at how well my students have taken to thinking algebraically within mathematical tasks. I haven't asked them to graph any functions yet and I wanted to see how they would do with it in an inquiry based lesson. So with no prior teaching of graphing functions, I gave my fifth grade class this problem:

The tasks are to:

#### 1. Create a function table for all houses one through ten.

Here are a few examples of the charts my students made to show how many cookies Santa had eaten after each house. We have created tables in the past, so this was pretty quick and easy for them. If you haven't done them in the past, then you might want to spend your time helping them create a table up to 10 or 12 and then really focus on how many cookies would Santa eat after 45 houses, 100 houses, 124 houses?

#### 2. Find an expression that will tell how many cookies Santa has eaten for any given house. It should work for all numbers.

Some of my student wrote h x 2 = c and others wrote 2 x h = c. In both cases, h stood for the number of houses Santa had visited and c stood for the number of cookies Santa had eaten. This provided for a great discussion about what 4 x 2 means compared to 2 x 4. Then we applied our thinking to h x 2 = c compared to 2 x h = c, which is why some of the students in the pictures above crossed out one of the equations.

#### 3. Create a graph that shows how many cookies Santa has eaten. Include up to house number 12.

This is our first attempt at creating graphs for our expressions, so I knew it would be interesting. Here are two attempts that were started when most kids were still scratching their heads.

I asked this student how this chart was different from his function table and he didn't have an answer. I never did figure out why he has a column of zeros in there. |

This student was giving it a try but she was unsure what to do with the number of cookies Santa ate after every house. |

After some of these failed attempts (and there were more), I helped students see that we just wanted to mark the number of cookies Santa had eaten after the first house. Right about then, one young mathematical yelled out, "This graph is only going to go up." That provided for a great conversation as we talked about why he said that. Most of my students agreed that when we multiply with 2 each time, our slope would only go up. Here is an example of what most student graphs looked like by this time.

Most kids did not connect the line until I mentioned that if they wanted to connect the dots, it might help them see the slope. |

We went a little further and discussed these questions: What do you notice about this graph? If you kept on graphing the number of cookies Santa had eaten up to house number 100, what would your graph look like? When does the graph stop? We also talked about some of the features of a graph. We talked about the x-axis and y-axis and the differences between them. One student made my day when I mentioned a dependent variable and she said, "That must be the number of cookies Santa ate." I asked her to go a little further with her thinking and she said that for whichever number of houses he has been to, that gives a specific number of cookies. So the number of cookies is dependent on the number of houses. Not too bad for a first introduction to graphing functions and a such a fun lesson to teach.

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In the third table it's the column of zeros which are a puzzle. The row of zeros at the start describes Santa's situation at the beginning of his trip.

ReplyDeleteThis is a lovely start towards functions. Like it!

You are right. I meant to say the column of zeros. I never did figure them out. Fixing my typo now. Thanks.

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ReplyDeleteThis is a great idea! I bet your students learned a lot from trying to create the graphs themselves!

DeleteLove this post. Thanks for sharing. I liked reading about your problem solving ideas...got my synapses firing.

ReplyDeleteWhat a clever way to introduce function tables. The students are so much more invested when you can put a holiday spin on it. Thanks so much for sharing.

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