Graphing Activities

 On the first day of school, I take a quick picture of each kiddo using my iPhone. I use these for lots of things, like the birthday displays, parent/family gifts, and portfolios and displays of student work. I never regret having those little mugs at my fingertips.

On the second day of school, we used them for our first "getting to know you" graph activity. The inspiration for this activity comes from this free download that comes with ideas for questions to pose, graphics for each one, and some headings. It's very sweet, and much cuter than the hand written stuff I usually do.

The "big ideas" I wanted to get at with doing the graphs with them were:
1) we can organize our data in different ways (this free download focuses on venn diagrams and bar graphs) and this includes tables, graphs, and tally marks.
2) when we organize our data in different ways, the data is still the same. In other words, the number of tally marks should match the number in a table, should match the bar in a bar graph.
3) we can ask and answer questions about our data.

I combined the graphing ideas in the download with a Kathy Richardson activity from this book, which I still think is one of the best resources for doing math with Littles:

 
Each student is given one unifix cube. They have to put their cube into one of the bags. This question was about whether you like to do things inside, or outside, or both. There was no "both" option in the download, as this comes up in the way it's organized as a venn diagram. In other words, you show you are both when you put your mark in the center of the overlapping circles. But I wanted to do this activity first, and so I made a "both" bag and they chose between the three options.

 Then, we make predictions...which bag do you think has the most cubes? Which do you think has the least cubes? What would no cubes mean? What can we already say for sure about our bags? (ex: "None of them are empty, so none of them have zero." etc.)

 As each cube is pulled out of each bag, students make tally marks to go with them.

Then students put each set of cubes into a tower, and we can start to ask and answer question about our data. Which had the most? The least? How much did inside and outside have together? When we put them together, do they have more or less than the "both" category? How many more is it than the "both" category? This is the most successful way I've found of dealing with the "how many more" issue with Littles. It's sometimes done in using "clue words"....like, "how many more" means subtract.

But it's so much more complex than that for little kids. First of all, if you have a lot of English Language Learners (our school is two-thirds designated as ELL), the subtlety of the language is pretty brutal.  I mean, "How many altogether" means add, and "more" means add, but "how many more" means subtract? And this is further compounded by the fact that, left to their own devices to make sense of a situation, most Littles will actually NOT subtract to solve this problem. 95 out of every 100 kids I've worked with, with no instruction on what to do with the cubes, will actually not "subtract", but rather will "count up".

In other words, if I ask how many more students like to play BOTH inside and outside, instead of JUST outside, 95% of them do not think "14 - 7 = ____"....instead, they think "7 + ____ = 14". So, to capitalize on this (which, actually, this thinking is very algebraic, so I want to encourage it, and here is this context where it comes up naturally for them, so #winning) and to help them make sense of "how many more" situations, I don't talk about it being a "subtraction" problem, but rather a "comparison" problem.

Are these the same? (no)
How do you know they are not the same? (this one has more)
So, they are different? (yes)
We can count the difference. Who has an idea, how we might count the difference? (take suggestions)
Summarize their work:  If it's more, we can actually count how many more, by counting the extras. If they are less, we can count how man fewer by counting what's missing. This is very easy for them to access and accomplish when they have the two towers to physically compare the amounts.

 They got a kick out of adding their pictures to the venn diagram. Before they added their faces I had them hash out where they thought the different options lived. We labeled an "inside" circle and an "outside" circle, and they figured out where the "both" category would go. (Some speculated it would go outside the circles, but they were convinced by others that the overlapping part would be both.)