Did you know that the white dots on dominos are called pips? Miss Amico's crazy Italian grandparents have a set of dominos with 0 - 9 pips on them. The dominos we have in our classroom have 0 - 6 pips on them and 28 come in a set. How many dominos come in a set with 0 - 9 pips on them?
We taught students in this multiage grade fourth - fifth classroom several domino games, as well as read aloud the book The Math Curse by Jon Scieszka and Lane Smith, which speaks about how life can be seen as a math problem. Recently, I had been playing dominos with a relative and we were not sure if we were playing with a complete set of dominos. We had to figure out this dilemma in order to be sure our game was fair. I explained this to students and how real life is filled with problem-solving situations. This task is accessible to students in a variety of ways since many strategies can be used to solve the task. The task affords many students the opportunity to use an efficient or sophisticated approach if patterns and relationships are discovered and are used as strategies. Most students will begin by randomly listing possible domino configurations and then will start over generating the same data in a more organized manner. Most students begin to see a pattern and use that pattern to solve the task. Mathematical representations are created to represent the task visually and assist students in drawing a conclusion. 2 hours This task fits in well with a unit on games. As mentioned earlier, students were taught different domino games, constructed domino chains and explored other problem solving tasks involving dominos. It is important for students to have the opportunity to have some time to play with dominos and become familiar with their appearance before starting this task. We played domino games as a class, creating dominos which could be played on the overhead projector for all to see. Many domino games reinforce math facts and number sense, as well as allow students to practice reasoning and logic skills.
- Dominos
- Calculators
- Graph paper
There are 55 dominos in a set with 0 - 9 pips.
This student misunderstands the task, reaching an incorrect mathematical conclusion. It is unclear what the student is attempting to do to solve the task and the task shows no mathematical reasoning. The student seems to attempt to deal with dominos having pips 0 - 6, but does not address dominos with pips 0 - 9.
This student has a correct answer, but does not clearly explain his/her reasoning and some of his/her reasoning is incorrect (ex: I found that you start with zero and instead of ending with nine you end with 10 because it has a zero in it.). It is unclear whether or not the student truly understands the task. The student does include a sum of 45 on his/her representation page and 55 as well. The student does not communicate this discrepancy and come to a resolution about it.
This student uses a systematic approach to solving the task by finding a pattern of how the dominos increase each time you add a pip to the game. The student gives evidence of his/her thought process and creates a representation to express his/her solution. This student could be encouraged to look more closely at his/her results to see if s/he can notice any patterns, relationships or generalizations and probably could do so given the organization s/he used in his/her approach.
Besides demonstrating a true sense of voice in his/her writing, this student solves the task in a very novel way. The student uses a visual observation to create a strategy for solving the task. When concretely organizing the dominos with 0 - 6 pips, s/he notices the shape of the data and uses that shape to try a series of trial and error approaches to discover a formula for solving the task. Although the student does not communicate this approach as clearly as we may have liked, his/her approach was truly sophisticated for a fifth grader. Once the student made oral comments about the shape of the data, we prompted him/her to use that information to reach a solution. Although the student comments, "Mrs. Amico hinted that since it was half of a square I should divide by two," in reality, after asking the student how s/he would find the area for the right triangle, s/he made the determination that s/he needed to divide by two. The student uses sophisticated math language to communicate his/her solution and verifies his/her formula by substituting other numbers.
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