3rd Grade - Analyze Problems

Analyze Problems
Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Mathematical Reasoning: analyzing problems, identifying relationships, finding patterns, prioritizing information The ability to read a word problem and pick a strategy to use to solve it.

Sample Problems


Find a Pattern:

Roman began drawing a cartoon strip. At the end of the first week, he'd drawn 1 strip. By the end of the second week, he'd drawn 2 strips. At the end of the third week, he had a total of 3 strips. If he continues drawing at this same rate, how many strips will he have at the end of the sixth week? (6/+1)


Use a Graph:

Ten friends and family were asked if they like pizza. Nine people said, “yes,” and one said, “no.” Use a visual to show the results of the survey. (graphing)


Choose an Operation:

Jenny is going to go skiing for the day. Her lift ticket costs $30.00 and lunch costs $10.00. How much money does Jenny need to have in her pocket? (choose an operation/ +/ $40)


Make an Organized List:

The cookie store sells four types of cookies: chocolate-chip (CC), coconut (C), peanut butter (PB) or sugar (S). You are going to buy two cookies. What are your options? (organized list)








Draw a Diagram:

Your dad went on a walk with your baby sister pushing her wagon. They walked 6 blocks total in three days. 1 block the first day, two blocks the second day and how many on the third day? (3)

(draw a diagram/picture)

Learning Tips


A list of strategies may be helpful for some students:

  • Learn to omit extra information.

  • Use a graphic organizer to help clarify the problem. [A selection of graphic organizers is available from several online sources; a good one is listed at “Online Resources (7)]

  • First try mental math, then pencil and paper or a calculator if many steps are required.

  • Go back to the problem and make sure you have answered the required questions. Draw a table or make a list to keep track, if needed.

  • Know whether you need an exact answer or if an approximation will do.

  • Act out the problem.

  • Some problems will be easier to solve by working backwards.

  • Some problems are easier to solve if you guess at the answer and then check your work to see if you are correct.

  • Look for a pattern to help you figure out a problem.

  • Draw a picture to help understand a problem.

  • Writing a number sentence is another strategy to help solve problems.

  • Choose an operation. Is it addition, subtraction, multiplication or division?

  • Ask yourself if the answer makes sense and use your logical reasoning to determine if your answer is reasonable.


Present children with a problem for which they must find their own solution. This will help the conceptual knowledge of mathematical foundation much more than simply giving the child an algorithm to apply.


Being a good problem solver in math helps you become a good problem solver in life. Lots of problems have more than one step and require a systematic approach.

Here are some things to keep in mind:

Ask yourself what the problem is asking for.

Is all the information you need in the question?

Make a plan.

Notice the key words that might give you a clue about what is asked for or how to solve the problem.

Would a chart, list or diagram help you get organized?

Is there a formula or equation that is needed?

Is there a pattern that I see that can help me?

After you solve the problem, ask yourself if your answer makes sense.


Make sure you give your child just enough information for the child to get started.

Accept right and wrong answers without judgment.

Provide coaching and guidance by asking insightful questions while sharing in the process of problem solving.

Think carefully before intervening. Step back and let your child find his/her own way.


Let your child identify the operation needed to solve a word problem instead of always doing the operation and completing the word problem. Be careful that your child doesn’t just assume that the word problem will be identical to whatever operation you are studying at the time. Try to select word problems that prepare children for real life.

Try to use multi-step problems that advance in difficulty.

Extra Help Problems


Brenda’s little sister started to collect bugs at a steady pace. At the end of the first hour she had 2 bugs, at the end of the third hour, 6 bugs and the end of the fifth hour 10 bugs. How many bugs will she have after 8 hours? (16 bugs/x2)


Joe’s dad gives him the same amount of pennies each week. In the fourth week he had 96 pennies and in the sixth week 144. During what week will he have more than 215? (Week 9/+24)


A Native American artist drew pictures of hunting on the walls of a cave, including 43 figures of animals and people. There were 17 more figures of animals than people. How many figures of people did the artist draw? (13 people and 30 animal)


Jose and Maribel shared $410 between them. Jose received $100 more than Maribel. How much money did Maribel receive? (Maribel had $155 and Jose had $255)


What are two consecutive numbers (in a row) whose product is 42? (6 and 7)


Annie and Jane went cherry picking and they collected 24 cherries. Annie collected two times as many cherries as Jane. How many did each collect. (draw a picture—16 cherries and 8 cherries)


There are 12 kids in Jaime’s daycare. Only 4 of the kids are boys and they are all present. Are these statements true or false?

There are eight more girls than boys in Jaime’s daycare.


There are twice as many girls as boys in Jaime’s daycare.


There are four more girls than boys in daycare.


If Jaime is sitting at a table with all the girls, there are nine people at the table.


If only three of the boys are playing kickball, one of the boys is not playing kickball. (end)


Cole had 74 pistachios. He put as many pistachios as he could into eight bags. He put an equal number into each bag. He could not put ? pistachios into the bags and have it come out evenly.


There are 5,097 apples in Farmer Mike’s orchard. There are 7,000 apples in Farmer Tanja’ s orchard. How can you figure out how many more apples are in Farmer Tanja’s orchard?

(Subtract 5,097 from 7,000)


Janet baked 20 cookies. She placed half of them in a package and put the rest in a bag. She put the bag in her car and drove to her book club. She gave half of the cookies in the bag away to her friends at the book club and ate the other half herself. How many cookies did Janet eat? (5)


Three toddlers play together at the park. Sage is heavier than Gunny. London weighs less than Gunny. Which of the following is NOT true?

Sage weighs more than London.

Gunny weighs less than Sage.

London weighs more than Sage.


How many cats live in the old house. There are more than the number of days in the longest month. There are less than the product of 7 and 5. The answer is an odd number. (33)


There were 24 gifts given out at the birthday party. Each child got three gifts. How many children were at the party? (8)


Tim’s father likes to take short flights on his plane. Last night he flew more miles than the number of letters in the word “night.” He flew less miles than the number of letters in the word “airline.” How many miles did he fly? (6)


I am a unit of measurement. A dozen of me is a third of a yard. I am not metric. What am I? (inch)


I am a month on the calendar and I can be in winter or summer. All months have more days than I have. What month am I?


Helen can’t wait to watch her favorite T.V. show, So You Think You Can Dance. It’s six o’clock in the evening and the show will be starting in one and a half hours. What time will the show begin on this special viewing night? (7:30 pm)


After two hours, the movie is still going on. It’s 125 minutes long. How much longer will it last? (5 minutes)


Rachel has fourteen pets. All of her pets are mice and rats. Rachel has four more mice than rats. How many rats does she have? (5 rats/9 mice)


Cynthia has two-dozen bread rolls. She will eat three bread rolls on Sunday. On every day that follows, she will eat a number of bread rolls that is one greater than the day before. On what day will she find that the bread runs out? (Thursday)


There were twenty-one candies in a bag. Seven candies were green, seven were red and seven were blue. Noah started taking candy out of the bag. He stopped when he had two candies of the same color. How many candies did he take out of the bag?


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