Math problem solving strategiesSome math problem solving strategies will be considered here. Study them carefully so you know how to use them to solve other math problems. The biggest challenge when solving math problems is not understanding the problem.It is not because you cannot do math. Make a guess and test it. Example #1 The sum of 2 consecutive odd numbers is 45. What are the two integers? Before guessing, Always make sure you understand the problem. If possible, get a dictionary or look up the vocabulary words in your math textbook Sum: refer to adding numbers consecutive: In the context of this problem, it will mean that we are looking for an odd number and the next odd number that immediately follows the first one Guessing here means that you will arbitrarily pick two odd numbers, add them, and see if it is equal to 45 15 + 17 = 32. It does not work. Since 32 is smaller than 45, pick higher numbers 19 + 21 = 40. Getting closer 21 + 23 = 45. Here we go. We found the two numbers by guessing! Example #2 A kindergarten class is going to a play with some teachers. Tickets cost 5 dollars for children and 12 dollars for adults Number of tickets sold amount to 163 dollars. How many teachers and children went to the play? First, make sure you understand the problem. What the problem is really asking is the following: How many adult tickets were sold? How many children tickets were sold? Guess and check! Pretend that 3 children tickets were sold. Then, 17 adult tickets were sold Total cost = 3 × 5 + 17 × 12 = 15 + 204 = 219 The total is too high. Pretend that 14 children tickets were sold. Then, 6 adult tickets were sold Total cost = 14 × 5 + 6 × 12 = 70 + 72 = 142 The total is a little too low now. Pretend that 12 children tickets were sold. Then, 8 adult tickets were sold Total cost = 12 × 5 + 8 × 12 = 60 + 96 = 156 As you can see, it is going higher again and it is getting closer to 163. May be 11 tickets for children and 9 tickets for adults will work Total cost = 11 × 5 + 9 × 12 = 55 + 108 = 163 Here we go! 11 children and 9 teachers went to the play. Sometimes, math problem solving strategies could involve making a list. This could happen if I slightly modify example #2 Example #3 A kindergarten class is going to a play with some teachers. Tickets cost 5 dollars for children and 12 dollars for adults. A total of 20 people could go to the play. There must be at least 2 teachers to supervise the children, but no more than 10. Find all possible ways this could be done. How can the school minimize their cost? This problem involves making a list If 2 teachers go, then 18 children will go If 3 teachers go, then, 17 children will go and so forth... Total cost = 2 × 12 + 18 × 5 = 24 + 90 = 114 Total cost = 3 × 12 + 17 × 5 = 36 + 85 = 121 Total cost = 4 × 12 + 16 × 5 = 48 + 80 = 128 Total cost = 5 × 12 + 15 × 5 = 60 + 75 = 135 Total cost = 6 × 12 + 14 × 5 = 72 + 70 = 142 Total cost = 7 × 12 + 13 × 5 = 84 + 65 = 149 Total cost = 8 × 12 + 12 × 5 = 96 + 60 = 156 Total cost = 9 × 12 + 11 × 5 = 108 + 55 = 163 Total cost = 10 × 12 + 10 × 5 = 120 + 50 = 170 As you can see, the less teacher they send, the less the cost. The least expensive case is to send 2 teachers and 18 children. Other teachers will not be happy about it Math problem solving strategies could also include the use of a variable Example #4 The use of a variable means that you will let the unknown be x, write and equation, and solve the equation. Use of a variable for example 3 Let x be number of children tickets. Then, 20  x is number of adult tickets cost of children tickets + cost of adult tickets = total cost x × 5 + (20  x ) × 12 = 163 5x + 20 × 12  x × 12 = 163 5x + 240 12x = 163 5x + 240 240 12x = 163  240 5x  12x = 77 7x = 77 7x/7 = 77/7 x = 11. Math problem solving strategies involving drawing a diagram Example #5 A highway has a gas station every 2 miles, a rest area every 4 miles, and a Burger King every 3 miles. Where is the closest gas station, rest area, and burger king all at the same time? A little diagram describing the situation is all we need to tackle this problem real quick. Let red be gas station, let blue be rest area, and let green be Burger King. Draw the diagram below. The vertical arrow is point toward the location where all 3 services can be found at the same time As you can see, it is 12 miles! You may wonder. How do we get the answer without drawing a diagram? Great question! That will be important if you are dealing with big numbers To get the 12, you need to look for the Least common multiple (LCM). The smallest number that is a multiple of 2, 3, and 4 That number is indeed 12. More information on Least common multiple Among great math problem solving strategies, is working backward Example #6 One day, I woke up and feeling generous, I took all the apples in my refrigerator and I decided to give them away I went outside and I gave onehalf of my apples plus one to the first stranger I met. Then, I gave onehalf of the remaining apples plus one to the second person I met and onehalf of the remaining apples plus one to the third person. I had one apple left at the end. How many apples did I have when I left my house (This is not a true story. I made that up) Starting backward means that you are starting with the result and work your way backward until you get what you started with Third person: Received onehalf plus one. Just do the reverse of that. Give yourself one and twice 1 + 1 = 2 and 2 × 2 = 4. ( This makes sense because giving onehalf of 4 plus one means giving 2 and then 1) Second person: received onehalf plus one. Just do the reverse of that. Give yourself one and twice 4 + 1 = 5 and 5 × 2 = 10. First person: received onehalf plus one. Just do the reverse of that. Give yourself one and twice 10 + 1 = 11 and 11 × 2 = 22. So you had 22 apples in your bag The math problem solving strategies I discussed above are great examples. Make sure you understand them. Hope you had fun exploring these math problem solving strategies! 




