Lesson 11 — Activity 1: Guess, Check, and Revise
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Lesson 11 — Activity 1:
Guess, Check, and Revise
There
are other strategies
that can be used as you think through a plan for solving problems. One strategy is called guess, check, and revise.
As you practise these strategies, you will also carry out the plan and solve the problem using the steps you learned for the 4-Step Method.
Guess, Check, and Revise
Beginning with a Guess
If you aren't sure where to begin, take a guess that is reasonable. What does reasonable mean? It simply means: does your guess make sense within the context of your word problem?
For example, if you were asked to take a guess that is reasonable for the following question:
34 + 55 =
You might guess 80 (because you know that 30 + 50 = 80) or you might guess 90 (because you know there are also more ones to add so the answer might be closer to 90).
This is called a reasonable guess because it makes sense within the context of the problem.
Now, let's take a look at the question again.
34 + 55 =
If you were to guess that the answer was one million, would that be reasonable? Not really, because when you add two 2-digit numbers, you can only get a maximum of a 3-digit number; whereas one million is a 7-digit number.
The guess of one million is not reasonable, because that is a really large number that doesn't make sense!
When you start your problem by coming up with a reasonable guess, you put your guess into the problem and work back to check if it is correct. Then you decide whether you need to go up or down before making another guess.Look for
clues in the problem that will help you make an educated guess. For
example, if the problem asks for three consecutive numbers (numbers that
follow each other in order) that have a sum of 33, you wouldn't start
with 28 (because 28 + 29 + 30 = 87, which is WAY more than 33). |
Revising Your Guess
This is a very important step to solving the problem. You will need to recognize whether the guess is too small or too large before revising your number. Revising simply means to change your guess.
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For example, consider the problem below.
Jared and Chris were playing Monopoly. At the end, Chris had $40 more than Jared. Together they had $480. How much did each person have?
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Start with a reasonable guess.
Chris
had $250 and Jared had $210. That totals $460, which is too low because the problem says they had $480 together. To
revise your answer, go back and start with bigger numbers.
Chris had $260 and Jared had $220. That totals $480. That is the correct amount, but you need to check to see if Chris had $40 more than Jared: $260 – $220 = $40, so you are correct with this guess!
Chris had $260 and Jared had $220. That totals $480. That is the correct amount, but you need to check to see if Chris had $40 more than Jared: $260 – $220 = $40, so you are correct with this guess!
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Let's try another one!
Busra went to her grandfather's farm. Her grandfather has chickens and goats on his farm. She asked him how many chickens and how many goats. Because her grandfather likes mathematical puzzles, he told her that his animals had 26 heads and 68 legs and from that information she could calculate the number of chickens and the number of goats. If you were Busra, how would you solve the problem?
To use the guess, check, and revise strategy, you think about the problem and start by making a guess. You expect your first guess to be wrong, but it will give you some information to help you make a better guess next time. You could start by guessing 13 chickens and 13 goats. It's a good idea to keep a record of your guesses, like this:
You see that the number of legs you guessed is too high, because Busra's grandfather said that there are 68 legs. So you guess again — you have to add more chickens and subtract some goats.
Now you have 64 legs and you need four more. But you can't add any more heads, since 26 is the correct number of heads. So you take away two chickens (two heads and four legs) and add two goats (two heads and eight legs).
Now you have the correct answer: 18 chickens and 8 goats!
Self-check!
Try This!
Use the strategy of guess, check, and revise to answer the following word problem.
When you are finished, click on the tab below to check your answer!
