3rd Grade - Break A Problem Into Smaller Parts

Break a Problem into Smaller Parts
Determine when and how to break a problem into simpler parts.
Mathematical Reasoning: breaking problem into simpler parts, problem solving The ability to break larger problems into smaller problems. More complex problems are often easier to manage when broken down into little steps.

Sample Problems


A runner is training for the marathon. She decides to run one lap around the track on the first day and double the number every day for seven days. How far will she run on Day 6? (the child needs to make a chart to find the number 32)


A nursery school has 14 play tables that fit one child on each side. If all 14 tables are put together to make one long table, how many children can sit and play? (The child needs to draw a picture/42)


How many outfits can you make from six pieces of clothing: 1 black pants, 1 brown pants, 1 red skirt, 1 white tank top, 1 beige long sleeved shirt, and 1 black short sleeved top. (the child must make a list to figure out the combinations)


There are ten elves that help Santa Claus in shifts, but Santa only likes to work with two elves at a time. Name each elf and figure out the combinations that Santa will work with.


A woman has to be at work at 8am. It takes her 20 minutes to walk to work, 15 minutes to eat and 35 minutes to get dressed. What time should she get up? (6:50am)

Learning Tips


Children need to be able to form mental images of word problems in their minds to complete them successfully. To practice mental imagery, you might give the child a variety of shapes, some of which can be folded to make a box. Students will need to “see” the box in their minds in order to choose the correct shapes. Origami and other paper folding activities are also good to practice visualization.


Good problem solvers are methodical and systematic. They use successful techniques to solve problems, such as breaking a problem down into simple steps, making a plan to solve the problem, choosing the right strategies to solve the problem and pulling out key ideas that they need. Look at the problem in different ways before choosing how to solve it and think ahead to predict the outcome of that choice.


First, look over the entire problem. When a problem seems complex or has many parts to it, break it down to smaller problems. It is easier to do these kinds of problems in little steps rather than trying to solve it all at once. Ask yourself if you have seen that type of problem before. Think about what strategies you used. Monitor yourself after each step and ask yourself if you’re using the right strategy or rule.

As you break a problem up into a series of logical steps rather than trying to solve it all at once, think about the order of the steps. Keep reevaluating to make sure you’re on the right course. Say the steps out loud as you think through the problem. Decide what needs to be done first and then what action should follow.

Decide which parts need an algorithm then choose an algorithm to use. A checklist or a mnemonic can be used to keep the child organized and remembering what to do next.


Use a set of questions to help the child down the right path. For example, “What am I asked to do? What are the important details? What does this question remind me of? What numbers do I need to pay attention to?”


Post these or similar reminders on the wall: Understand the problem, break the problem into steps and plan how to solve it, select a strategy or strategies to use to solve it, carry out the plan and reevaluate the results (does my answer make sense?). Some steps can be done in the child’s head, but encourage him/her to verbalize those steps in the beginning. Sometimes this overall plan needs to be altered because the strategy isn’t working. Encourage the child to be flexible enough to change the plan mid-stream.

Extra Help Problems


10 + 5 (Come up with a word problem to go with this number sentence.)


If I place 3 red marbles in a bag and one purple marble in the bag, which color marble am I most likely to pull out? (practice visualization)


Visualize a pizza and imagine ½ of it being taken by hungry children. Now, see the other half sitting on the tray waiting to be taken.


Farmer Tom buys a cow for $60, sells the cow for $70, buys the cow again for $80 and then sells it again for $90. Did Farmer Tom make any money? Did he break even or lose money? If so, how much?


Jenny likes to paint and mix three colors together. She has red, blue, yellow, orange, green and purple. How many different ways can she mix three colors together?


What day of the week is tomorrow if 5 days before the day before yesterday was Tuesday?


It’s Christmas time and Jack and Jill want to deliver cookies to all the families in the Kingdom of the Golden Crown. Jack delivers 4 cookie packages in the time that Jill delivers 5. They have 54 packages to deliver. How many will Jack deliver?


There are six girls swimming in the pool. Each girl has one doll that is swimming with her and each doll has a set of doll twins that are swimming, as well. How many legs are in the pool?


Larry has six fewer coins than Horatio. Together they have 89 coins, how many coins does Horatio have?


Harry the dog has a head that measures 6 inches long. His body is as long as his head and tail together. His tail is as long as his head. (His body is 12 inches)


Libby can paint the picture in 6 days, while Griffin takes 10 days and Sally takes 15 days. All of them have already worked four days. How much longer will it be before Griffin and Sally finish? (Griffin 7 days; Sally 11 days)


How many markers does Jan have if all of them are red except two, all of them are blue except two, ad all of them are yellow except two?


Two numbers added together equal 19. If one number is subtracted from the other the answer is 3. What are the numbers?


Ten kids sit around and divide jelly beans to eat. They each get 10. Suddenly, Janie’s little sister comes in and steals one jelly bean from each of the kids. How many jelly beans are left?


How do you know whether to use multiplication or division in a word problem? (e.g., ask yourself if you could use addition to solve the problem? Or is the problem asking for an answer or another unknown number in the problem?)


There are 9 kids at the birthday party. How many piñata candies can each of them get if there are 113 candies?


Hilary had 8 raffle tickets. She bought 12 more, then gave half of the tickets to her brother. How many did she give to her brother?


Laura had 3 packs of gum. There were four sticks in each pack. She lost 3 sticks of gum. How many did she have left?


Dane had 28 stickers. Cole gave him three more. He lost 6. How many did he have left?


Thirty-two children went to camp. 17 of them walked to the camp and 5 came by bike. The rest came by car. How many kids came to camp by car?


Six kids made cookies. They made 12 vanilla cookies and 12 chocolate-chip cookies. They shared them equally. How many cookies did each have?


Sarah’s mom said she could invite 20 children to her birthday party. She invited 7 boys and 9 girls. How many more children can she invite?


Lisa and Frank are going to go swimming. It costs $.80 and Lisa pays for both of them with a $5.00 bill. How much change does she get.


Minnie wants to buy a CD that costs $10.00. She is saving $2.00 a week for the purchase and so far she has $4.00. How many more weeks does she need to save?


A water slide park has 4 levels. 50 kids can wait in line on each level. At 12:30 there are 180 kids waiting in line. How many spaces in line are there left?



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