Guess & Check Problem Solving

Guess & Check Is very effective by giving you a place to start. Helps you understand the problem and set up algebraic equations By organizing your guesses in a systematic way, you are able to make more refined guesses. Anybody can guess. Anybody can check. Used together, they are a problem-solving tool.

Guess & Check It is simply a tool for organizing information in such a way that the information becomes more useful to you and more powerful in your hands.

Steps to Use 1. Make a guess. 2. Follow the guess through to a reasonable conclusion. 3. Evaluate the guess. 4. Modify and guess again. 5. Repeat steps 3 and 4 as necessary. 6. At end, check to see what the question was and answer in a sentence.

Steps to Use Wrong guesses are merely a step in solving the problem. The guesses can help you bracket the correct answer. BE CAREFUL that your arithmetic is correct because of two difficulties: you might not be able to tell if your answer is too high or too low and even worse, if you make a mistake on a guess that would be the right answer, you will be really confused because you won’t make that guess again.

Example: Dan has twice as much money in nickels as he does in quarters. He has 33 coins in all (all nickels and quarters). How much money does he have? Note that the problems talks about money, not that Dan has twice as many nickels as quarters.

Example Set up some type of chart to organize the information and evaluate your guesses. The chart that I chose shows the money value of the number of coins since that is what the question is. The too high, means too many quarters to maintain the money ratio.

Problem Solving – Guess & Check Quarters Nickels Total Coin $$ Quarters $$ Nickels Total Money Check 10 23 33 $2.50 $1.15 $3.65 High 5 28 $1.25 $1.40 $2.65 2 31 $0.50 $1.55 $2.05 3 30 $0.75 $1.50 $2.25 RIGHT 3 quarters and 30 nickels yields a total of $2.25 with twice as much money in nickels as in quarters.

More comments Sometimes it is very difficult to figure out whether a particular guess is too high or too low. When this happens, use your next guess to help you. Use some type of organized list and perhaps even a drawing to help you. Do not be afraid to start guessing with one variable, and then switch to another.

Another Example – Distance*Rate*Time A train leaves Roseville heading east at 6:00 a.m. at 40 miles per hour. Another eastbound train leaves on a parallel track at 7:00 a.m. at 50 miles per hour. What time will it be when the two trains are the same distance away from Roseville?

Roseville Trains 6:00 Train Time 7:00 Train Speed 7:00 Train Speed Distance Rating 10 hr 9 hr 40 mph 50 mph 400 mi 450 mi ??? 14 hr 13 hr 560 mi 650 mi Worse 3 hr 2 hr 120 mi 100 mi Low 5 hr 4 hr 200 mi Right So, it will be 11:00 am when both trains are at the same distance away from Roseville. Note you could also answer the question of “How far away from Roseville are the trains when the later train catches up?”

Key Points Start guessing. Keep work organized. Be ready to start over if your first approach is not productive. Reorganize your listing. Start with small numbers and build up to larger numbers. Let your guesses skip around so you can bracket the answer. Sometimes you might mis-rate a guess such as rating a high guess to low. Pay close attention to guesses made previously.

Key Points – con’t Be very careful with your arithmetic: a. If you make a mistake in rating, you will then make subsequent guesses in the wrong direction. b. If you make a mistake with the right answer, you may never guess that number again.

Key Points – con’t Put a lot of information into your column titles so that you know what each column represents. You may have to use several lines to accommodate the long titles. Generally the columns will be numbers, so they don’t have to be wide, but they must be descriptive.