3rd Grade - Check If An Answer Is Reasonable

Check if an Answer is Reasonable
Evaluate the reasonableness of the solution in the context of the original situation.
Mathematical Reasoning: evaluation, problem solving Evaluate the reasonableness of the solution in the context of the original problem. Does the answer make sense in that particular situation?

Sample Problems


My dad mowed the lawn for 40 minutes, weeded for 25 minutes and then planted new tomatoes for 20 minutes. Is it reasonable to say that he came inside an hour later? (No, he came in 1.5 hours later)


Martha read four books spread out evenly over the summer. They had a total of 48 chapters and she read for 12 weeks. Is it reasonable to think that Martha read four chapters a week over the summer? (Yes, we don’t know for sure, but 12 x 4 = 48, so that would spread the reading out evenly)


Jenny the cake maker made a four-tiered cake for the upcoming wedding. The bottom tier fed 45 people, while the second and third tier fed 30 people each. The top tier fed 20 less than the bottom. Could the cake feed all 150 guests at the wedding? (Nope, the cake will feed 130)


The piano teacher told Rachel that she needed to practice 5 minutes the first week each day, 10 minutes the second week each day and 15 minutes the third week. Rachel practiced 70 minutes the second week and more than 2 hours the third week total. (No, Rachel practiced 105 minutes, not 120 minutes)


Is it reasonable:

If the dog barked the last three Tuesdays and Thursdays, is it reasonable to think that the dog will bark next Tuesday and Thursday? (Yes. There could be many reasons why, such as a mail delivery, an owner leaving or coming home, a loud truck that drives by those days)

Learning Tips


This study of “reasonable answers” to mathematical problems is just an extension of a principle that you are teaching your child already: “Think before you speak.” (or write!) Even if your child’s computation is incorrect, and therefore incorrect, he/she can at least take pride in knowing that the answer was a close approximation as opposed to a “silly” answer.


Help your child form the habit of checking for reasonableness by requiring him/her to tell you if the answer is reasonable enough times that it will become a habit. Typical “rules of reasonableness” include:

A problem involving subtraction cannot end up with an answer larger than the minuend (the “top number” in a subtraction problem written in traditional style).

A problem involving addition will end up with an answer larger than either of the numbers added together, unless one of the numbers is added to 0.


When a child’s answer to a math problem is incorrect, ask your child to show you how he/she obtained it. From the explanation it will often be easy to tell if an incorrect computation was made or if the child did not know how to set up the problem correctly; i.e., did not use the correct math operation (+,—, X, /) or did not perform the steps in the correct order.


If your child’s method of solving a word problem is incorrect, talk through the problem again with your child to see if your child can see where his/her first reasoning went astray. Your child will learn more from this approach than from your offering to “show” him/her the correct way before the child has a chance to try again.


Another way to help your child understand how/why his/her approach to the solution of a word problem is not reasonable is to ask your child to devise a problem for which this approach would work very well. For example, if your child is asked to calculate how many pieces of paper each child in the class will need if each child needs 4 pieces and there are 20 children, and your child answers 24, ask your child to imagine the 20 children in the room and with only 4 more pieces of paper than there are children, what could be wrong with this answer? Then ask if your child can think of an occasion when 24 would be the correct answer to a problem that involved a 20 and a 4. He/She might then suggest this problem: that if there are 20 children and 4 more joined the class, then the class now has 24 children. Your child can easily see that what he/she did was to add but while you can add children together, you can’t add paper and children, so another approach must be needed. Reasoning practice like this example will help your child to understand mathematical principles much better than will being told the answer.

Extra Help Problems

  • My mom made a dozen cookies. She gave 1/2 of them to my aunt. Then she gave 7 to our neighbor. How many cookies are left?

(She cannot give away cookies because she only has 6 cookies left.)


Is this answer reasonable?

The problem asked me how many animals were in the circus all together? I saw 15 snakes and 4 elephants. I answered 11 because 15 - 4 = 11. (No, that doesn’t make sense. You should have added the numbers together to get 19)


Is this answer reasonable?

My dad took 7 boys in his car to the zoo, but two parents met him at the zoo and took their boys home with them. How many did my dad take home in his car? I think he took 5 home. Am I right? (Yes, it makes sense that he would have two less children in his car)


Is this answer reasonable?

The lady at the picture shop said she wanted three paintings and they each cost $75 dollars. I think she paid $150. Am I right? (No, you forgot one of the paintings. She paid $225)


Is this answer reasonable?

The same lady came back and bought 2 more paintings for $50 each. She paid $100 more. (Yes, that’s right. Two 50’s are 100)


Is this answer reasonable?

My mother says that I should put in about a half a cup of chocolate chips. I reached in and pulled out a handful. Is that about right? (Yes, that should be about ½ cup and it probably doesn’t need to be exact with chocolate chips)


Is this answer reasonable?

I completed the race in 1 minute 15 seconds. My next time was 1 minute 30 seconds. I completed the second race 15 seconds faster than the first, right? (No, your first time was 15 seconds faster)


Is this answer reasonable?

My uncle brought our family a huge cake for the holidays. My mother wanted to divide it for all of us to share. There are 5 people in our family and she divided it into 6 pieces. Is that right? (Yes, if your uncle stays for cake, you’ll need 6 pieces)


Is this answer reasonable?

I had three friends over for the afternoon and I wanted to share my bag of M&M’s. I counted 36 left in the bag. I gave each of us 11. Is that right? (No, you cold have given each 12)


Is this answer reasonable?

My sister and her ten friends went to Target to buy hair ribbons. They each spent $1.50. I think they spent $150. Is that right? (No, they spent $15)


Is this answer reasonable?

The ten friends then went horseback riding and paid $30 each. I think they spent $300 all together. (Yes, that’s right)


Henry bought 10 strawberries. He ate 4. Then he gave 2 to each of his 4 sisters. How many strawberries does he have left?

(He cannot give 2 strawberries to each sister because he has only 6

strawberries left.)


If I left by car for the train station at 9:30 and live 90 miles away, can I make my 10:30 train? (It’s not reasonable to think you can travel 90 miles in less than one hour)


If I leave for the same train at 7:30, will I make it? (Yes, that’s a much better estimate of time it takes to travel)


Cody is making a bookcase. He wants to make three shelves that are 1.5 yards long each. He has a piece of wood that is 4 yards long. How much will be left over. (None, he doesn’t have enough wood. He needs 4 ½ yards)


Dane’s class planted corn. At the end of the first week it was 10 cm tall. In the second week it grew another 12 cm and in the third week 20 cm. The corn is almost 60 cm tall! Is that correct? (No, the corn is only 42 cm tall)


Janet is baking cakes. She needs 4 cups of flour for every cake and she wants to make 6 cakes. Her flour bags have 8 cups of flour in each bag. I think she needs 3 bags of flour. Is that right? (Yes, because each bag will make 2 cakes)


My apple weighs 5 ounces and I want to buy a pound of apples. I think I need about 6 apples to make a pound, right? (No, three apples would be almost a pound at 15 ounces)


My mother made burritos for our relatives and their friends (about 75 people) and she made two crock-pots of beans. Each crock-pot makes about 40 burritos. I think the two crock-pots will be enough to feed everyone.


We went across the country on a car trip. In the first day we wanted to travel 200 miles and make some stops along the way. In the first hour we traveled 50 miles and in the second 65. I think we have about 125 more to go. (No, you have 85 to go)


I poured out 3 ounces of my 8-ounce soda. I think I have less than half left. (No, you have more than half left)


A carton of juice will provide 20 cups of juice and I’m having 50 people at my party. I think I’ll buy three cartons of juice. Is that right? (Yes, three cartons will provide 60 drinks)


My dog needed medicine and my mom had to give him 1 dropper full for every 20 pounds. My dog weighs about 30 pounds and my mom gave him a dropper and a half. Is tha right? (Yes.)


Jenna’s dad went roller-skating at the rink for 3 hours with Jenna. They left at 2:00pm and didn’t come home until 6 pm. Is that about right? (Yes, if driving time is in the total)


Lenny watched television for two hours starting at 3:30. He watched 30 minutes of cartoons and 45 minutes of a nature show. I think he watched 45 more minutes before turning it off. Right? (Yes.)


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