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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

Georgia Wood, Teacher says:

about 6 years

Students might benefit from using two sided counters at first. For the first problem when there are 4 buttons the student could be given 4 two sided counters. That way the student is scaffolded and they can't create an equation which is four red buttons and four blue buttons (adding up to eight buttons total).

Stacie Kaichi-Imamura says:

over 6 years

Great lesson for this standard K.OA.3. If teachers don't have red and blue buttons, teachers could always use two-color counters, cubes, unifix or multi-link cubes, etc. Should teachers want students to produce some kind of student work, one could fold a blank sheet of copy paper into fourths (one fold horizontally and one vertically so there are four quadrants) and have the students draw the possible solutions after they find solutions with the manipulatives. Depending on the time of year, teacher may have students write the number of red buttons (using a red crayon) and the number of blue buttons (with a blue crayon) under their button pictures. Using a very similar activity during the middle of the school year, I had students try and write equations and it was still too abstract for them. The students were at the point where the symbols meant nothing to them and it just made it more confusing. The lesson is correct in saying the even if the students are unable to do it, the teacher should write it to begin giving the students some exposure to what equations look like. I found that by the end of the school year, the students found much more success with writing equations.

Kristin says:

over 6 years

Thanks for your comments on this task!