We have collected data from each of the classrooms in the school about their favorite Dr. Seuss characters. We used the original 10 characters that were favorites in our classroom as a voting sheet to give to each classroom. Each teacher in the school was asked to take a poll of their student's favorites. I compiled this data so each group would know the totals from every classroom. I divided students into small groups and gave each group one of the characters. (I formed 9 groups because 1 character had no votes at all) I asked them to create an array type graph of the one character they have. I handed out large blank sheets of paper as well as 1 inch cut paper squares. I want the students to create a 1 X the number of votes array for their character. We will then put the arrays next to each other to look at most and least favorite characters for the school. I want to see if students can use the paper squares to show the number of votes for each character in an array type format that will then become a bar graph.
I want to help my students apply the parts-whole relationship to understand and solve missing addend problems. Many students, when they are given two numbers, immediately want to add them together without considering if this is the correct operation. This is because they are not thinking in terms of parts and a whole. To represent this relationship, I drew a triangle (mountain) with an open square at the top (for the whole) and one at each bottom point (for the parts). I stress with my students that the biggest number (whole) is always at the top of the mountain and that we can get this number by putting together the two parts. This triangle representation helps reinforce the notion that the parts come together to make the whole.
I showed the students several comparison problems with our data by referencing the graphs to visually see the data and then fill in the squares in the mountain to help us decide what we might need to use as a math operation to find the answer. When they look at the graph they can see if they have a larger number and a smaller number so they would want to find another smaller number to show the difference in height of the two lines on the graph. As we think about our question.. such as how many votes do the two characters have in all, we would want to put one line of the graph on top of the other and add, so we put our 2 numbers at the bottom and find the top of the mountain, but if we ask how many more does one have than the other, we are looking at how much taller one is than the other, so we already have the tall line so we fill in the top of the mountain, and we have one side of the bottom so we need to find how many more to get to the top. By modeling with graphs and the mountains (MP4), we are beginning to see the relationship between words such as how many more, or how many altogether, and the math operations we need to use.
I asked students to figure out the missing numbers for my questions. ( I am asking students to make sense of the problems I pose and persevere in solving them (MP1) and I am showing a way to model with mathematics (MP4).
A sample problem from the data would be: "there are 31 votes for the Lorax, and only 6 for the Sneech. How many more votes did the Lorax get?" I place the 31 at the top of the mountain and a 6 at the bottom. I ask students what I need to do to find the missing square? (count up or down, subtract 31 - 6) I draw the Sneech at the bottom to make it even more visual. We work together to solve the math problem.
I hand out clipboard and blank paper to students. I pose a problem and ask them to draw the mountain, fill in what they think they have and find the missing number. Student created mountainsI watch as students work to build the mountain and solve the problem. Once students have solved the problem, I call for a volunteer to show us their solution to the problem.
We work through 3 more problems together.
To end the lesson I ask students to tell what they have learned about our school data from reading and interpreting the graphs that we created.