She was also the first student to solve the problem. Janice is one of the strongest students in this Level 1 class. Both of her methods were very typical of the students in both classes. When the first didn’t work, she thought of an alternate approach and was successful with that one. I chose to talk about Ioka’s paper because she worked with two different methods, maybe even three. In the end, she added columns of 2’s and 4’s (not shown) and solved the problem. At one point she wanted to use her calculator but decided not to. With each attempt, she was becoming increasingly frustrated. She initially tried to draw the two sets of animals and count their legs but wasn’t successful.
How might you use these two equations to find a solution?. Could you write an equation to represent the number of animal feet? What wold it look like?. Can you write an equation to represent the number of animals? What would it look like?. How would the next two cells/rows of the table look?. What total, in the table, must change/has changed? What must remain/has remained the same?. Can you tell me the pattern you see in this column?. Is there a pattern you see developing in this table/chart?. What do you know about chickens? About goats?. How could you maintain your total of 22 animals but reduce the number of feet you got?. What does the sum of 22 and 56 represent?. To support students’ efforts and nudge them toward a solution, I might ask any or all of the following, as well as any others that would facilitate a student’s progress. be upset because I won’t automatically give them the answer, but instead require them to think their way through by asking them questions. work out a solution that satisfies one condition but not the other. in some cases, give up before really trying anything because the answer won’t be obvious or workable using a “standard” pathway, or they are paralyzed by the fear of being wrong. probably divide the number of animals by 2, then not know what to do with the answer they get. try to add the animals and the feet together, not understanding that their sum will represent neither. Multiply to calculate the total number of feet (guess and check) until you arrive at the correct totals. Select an arbitrary number of animals of each kind. Work backwards from 56 and 22, by adding and subtracting as needed. Mark off 4 marks for each goat and 2 for each chicken. Create a system using columns of 4’s and 2’s. Start with a guess and check, then add or subtract animals and corresponding feet until you arrive at numbers that satisfy both conditions of the problem. Draw pictures representing 4-footed goats and 2-footed chickens. There are lots of other ways that students could solve this problem. I complete my table, systematically decreasing the number of feet by decreasing goats and adding chickens, while maintaining the necessary number of animals. If I’m using this method to show a possible solution pathway, this would be the point at which I ask the students if they see a pattern developing. I begin by deducting one goat, adding one chicken, and reconciling the number of feet row by row. I can then work backwards to my solution. 
Once my columns are in place I can see that I have 10 feet too many. Using this info, I could create a six-column table. I might divide 22 by 2 and use 11 + 11 as a jumping-off point. Start with a guesstimated number for the two animals. Finally, I checked my values by substituting both into the second equation. I found that there must be 6 goats and 16 chickens. Once I had the value for g, I used it to solve for c in the first equation. Then I substituted my new value for c into the second equation. To solve this problem, I used an algebraic system of two equations, letting c represent the number of chickens and g represent the number of goats.įirst, I solved for one variable in terms of the other in the first equation. It is non-discriminatory in that I can, have, and did give this and a similar problem to students learning at the most basic level and those taking the HSE exam in the same week. This problem pushes students to think outside the box.
seeing the light come on in students’ eyes when they arrive at the solution.being surprised at who solves the problem and how.seeing the different ways students draw the chickens and goats.the potential fun for students and their joy in working it out.the variety of possible solution methods: arithmetic, algebraic, pictorial, mathematical, and representational.I chose to write about this problem because I love it! I love:
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