Bobbie Bear's Buttons
Alignments to Content Standards:
K.OA.A.3
Task
Pose this question to the students:
Bobbie Bear has a box of red and blue buttons. She takes 4 buttons out of the box. How many of each color button might she have?
After students answer the question, ask them to draw pictures and write the number for each color. Students may represent their solution using drawings, equations, or both. Not all possible pairs that total 4 are required to meet this standard, but students should be encouraged to include more than one.
IM Commentary
The purpose of this task is for students to find different pairs of numbers that sum to 4. It would be appropriate to have a box of blue and red buttons on hand. Students can try to imagine a solution, and then they could reach into the box and actually see a solution (they would have to pick buttons out without looking at the colors to ensure that all the possible combinations might be found). The greater the number of students who get a chance to select out four buttons, the more likely it will be that all the possible combinations will come up. If students don't write equations, teachers should so that students can begin to see symbolic representations of these mathematical concepts.
As with several other tasks in the set, any number between 2 and 10 can be used in place of 4 to address K.OA.3. However, if students are actually picking buttons out of the box, they are less likely to pick out all possible combinations with a larger number.
The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.
This particular task helps illustrate Mathematical Practice Standard 4, Model with mathematics. Students apply the mathematics they know to solve problems arising in everyday life. For this problem, young children might arrange red and blue buttons or two-colored counters to represent the mathematical elements of the problem or write an addition sentence to describe the situation. As stated in the commentary, it might be beneficial with kindergartners to have them reach into a box of red and blue buttons and pull out four. Then, as a class compile the different pairings and decide if you have all the possible combinations of red and blue buttons. Two colored counters are useful in that students can count out four counters and turn over the counters to show all the two-color combinations. It doesn’t matter whether children use buttons or two-colored counters. The real significance lies in that students can identify the mathematical elements of the situation and use the model to represent those elements and the relationships among them.
Solution
Solutions for this task will vary, depending on which numbers students start with and how they represent their work. Students may represent their solutions in various ways, including drawings, equations, or both.
Possible equations:
0+4=4
4=1+3
1+3=4
4=2+2
2+2=4
4=3+1
3+1=4
4=0+4
4+0=4
Bobbie Bear's Buttons
Pose this question to the students:
Bobbie Bear has a box of red and blue buttons. She takes 4 buttons out of the box. How many of each color button might she have?
After students answer the question, ask them to draw pictures and write the number for each color. Students may represent their solution using drawings, equations, or both. Not all possible pairs that total 4 are required to meet this standard, but students should be encouraged to include more than one.