In the second part of our Heuristics series, we will outline an 8-step method to applying Guess and Check to solve problem sums. Guess and Check is useful when you are give certain information about some items, but missing other details that you are required to find. However, by using the information you are given to help you understand the relationship between the items, you can make a Guess, followed by a Check, and repeat this process when necessary until you get the correct answer.
Note: The Guess and Check methodology and example shown are extracted from EduSCOREPlus (scroll to the bottom of this article for more information on EduSCOREPlus).
Some tips for using Guess and Check:
- Guess an answer that is TRUE FOR ANY OF THE CONDITIONS. - Use a table for easy checking.
Let us study this example:
There are 20 chickens and cows on the farm. There are 68 legs altogether.
How many cows are there on the farm?
We need to guess a possible answer and check if the condition is still correct. To find the answer, follow the steps below.
Step 1: What are the items? Step 2: Which conditions do we use? Step 3 & 4: How many columns in the table? Step 5: Guess an answer! Step 6: Are the conditions fulfilled? If yes, go to Step 7. If no, go back to step 5. Step 6: Great work! Step 7: Check your answer
Step 1: Identify the items in the question, which we know, or do not know, their values.
These are our items: - chickens - cows
Step 2: Identify the condition or conditions.
Conditions:
- 20 chickens and cows - 68 legs altogether
Step 3: Count the no of items from step 1, and the no of conditions from step 2. This will be the number of columns you need. Add one more column to check if your answer is correct.
- 2 items - 2 conditions There we need a total of 5 columns, including one for checking.
Step 4: Draw a table and fill in the title of each column. Start with the items whose values are unknown, followed by the conditions.
Step 5: Start with a guess of the possible value of Unknown Item 1.
Tip: Make use of one of the conditions to make a guess.WE should guess the number of chickens is half the total number of chickens and cows. This will help us to see if we need more chickens or more cows.
Step 6: Use the number you have guessed and one of the conditions to find the other unknown. Make use of Condition 1 to find the number of cows.
Step 7: Check if your answer is right. If your answer is wrong, guess another number. Make intelligent guesses based on the result of changing one of the unknown items.
When you change the value of one of the unknown items, are you gettin closer to fulfilling all the conditions? A cow has 2 more legs than a chicken. Each time you change a chicken for a cow, you get 2 more legs.
There are 14 cows on the farm.
Step 8: Working backwards to check your asnwer. Use the values of the unknown items you have found, to check if you get values of the conditions.
For an overview of Heuristics methods used in Mathematics, Check out these articles at www.eph.com.sg:
Heuristics methods used in Mathematics - Part 1: http://www.eph.com.sg/edutips.php?id=29
Heuristics methods used in Mathematics - Part 2: http://www.eph.com.sg/edutips.php?id=30
The Model Drawing methodology and example shown above were adapted from EduSCOREPlus Mathematics Primary 5 Companion Pack CD. Get your FREE CD when you purchase a complete EduSCORE e-Assessment Package for Pri 5 / Pri 6 (now at 30% discount for EduCommunity readers). |