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Problem Solving With Equations For 4 th Grade Math Club Cherry Crest Elementary School Bellevue, WA Dejun Zhou Nov. 04, 2014 Slide 2 Slide 3 Solving Equations with One Variable: Slide 4 Slide 5 Step 1: Step 2: Step 3: Slide 6 Step 1: Step 2: Step 3: Slide 7 Practical Question Solving #1 (2008 AMC8 question #3) Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than 100 pounds or more than 150 pounds. So the boxes are weighed in pairs in every possible way. The results are 122, 125 and127pounds. What is the combined weight in pounds of the three boxes? Assuming the 3 boxes weigh x, y, z pound respectively There is a simpler way too! Slide 8 Practical Question Solving #2 (2009 AMC8 question #23) On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class? Assuming there are x boys and y girls 1. Assuming the answer is (C), then x = 16, y = 14. However, 16*16 + 14*14+6 = 458 > 400, the answer has to be (A) or (B). 2. Assuming the answer is (A), then x = 14, y = 12. 14*14 + 12*12 +6 = 346 < 400, so the answer cant be (A). 3. Verify (B) is the answer. x = 15, y = 13, 15*15 + 13*13+6 = 400. Bingo!!! Slide 9 Practical Question Solving #3 (2012 AMC8 question #9) The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds? Assuming the number of birds is x, and number of mammals is y To solve this, we need to reduce the variable to only x Slide 10 Tests 15 minutes Problem 1: Amy tried to put a pile of apples into a few buckets. Each bucket need to have same number of apples. If she put 10 apples in each bucket, there are 8 apples left. 2 apples remaining if she put 11 apples into each bucket. How many buckets does Amy have? Problem 2: In a group of dogs and their owners, there are exactly 20 heads and 64 legs. How many dogs are in the group? Problem 3: If you triple Jens age and subtract 16, the result will be the same as when you double her age and add 8. How old is Jen? Slide 11 Summary Math is Fun! 1.Assign variable to unknown values 2.Build same number of unique equations as the number of variables 3.Solve variables by building new equations which contains only one variable.