Logic-Based and Strategic Problem Solving -- Week 2 Prep

I was amazed by the diligence of the children this week. Almost every student completed the full-length practice test. Many of them came to class with questions that they could not understand even after reading the explanation. This is the most important step in the improvement process. Each week they will improve on their strategic approach to problem solving. 

The most important strategy I could give them was to organize their thinking using 2-3 column graphs. For example, question 9 in the 3rd grade test asked how many hours a cafe was open in a week with different opening hours for Monday-Thursday, Friday-Saturday and Sunday. The knowledge requirement is that a.m. goes through 12 noon. We developed a process of recording each of the three work days: 

• M-Th 6am-2pm 8 hours x  4 days = 32 hours
• F-Sat 6am-11pm 17hours x 4 days = 34 hours
• Sun  9am-5pm 8 hours x   1 day  = 8 hours
• Then vertically adding 32 + 34 + 8 = 74 hours total

Our secondary focus this week was algebra based problem solving. For example, if Mary is 3 years older than Sally and together their ages add up to 17 years, we can say:

• M = S + 3
• M + S = 17

If we substitute S + 3 for M in the second equation we get (S + 3) + S = 17; then 2S + 3 = 17; then by subtracting 3 from both sides of the equation we get 2S = 14; then by dividing both sides of the equation by 2 we get S = 7 and by adding 3 we get M = 10; to check our answer, adding 7 + 10 = 17.

Of course, most children use guess and check which is fine now but with algebra they can solve questions of any difficulty. They will get more comfortable with every new algebra question.

The third focus of this week was the concept of ambiguity in questions. When a question is clear we say it is unambiguous; when open to interpretation it is ambiguous. I intentionally chose some ambiguous questions to see how they would react. For example, if a wagon can carry 37 pounds and each pumpkin weighs 6 pounds, how many pumpkins can the wagon hold? Most children said six by either adding 6 + 6 + 6 ... until reaching 36 and some divided 36 by 6 and got 6. However, some children were able to see that the remainder of 1 pound allowed the wagon to carry another 1/6 of a pumpkin. This question is ambiguous since it did not say "whole pumpkins." This conversation will continue and is intended to inspire them to challenge their teachers (in a nice way) to clarify ambiguous instructions of any type.

I gave them a second 20-questions practice test at their grade level or one above. Please have them:

• take the test in pencil
• parent help in pen and 
• self-grade in pen