3rd Grade - Apply Simple Problems To Harder Ones

Problem Solving
Apply Simple Problems to Harder Ones
Apply strategies and results from simpler problems to more complex problems.
Mathematical Reasoning: apply strategies, problem solving The ability to take the understanding about how to complete simple problems and apply those strategies to more difficult problems.

Sample Problems


Find a Pattern:

Roman began drawing a graphic novel. At the end of the first week, he'd drawn 8 pages. By the end of the second week, he'd drawn 13 pages. At the end of the third week, he had a total of 18 pages. If he continues drawing at this same rate, how many pages will his book have at the end of the sixth week? (33/+5)


Use a Graph:

Ten friends and family were asked their favorite food from these choices: Italian, Chinese, Mexican, Indian or American. Aunt Jo and Uncle Rob chose Indian, Rex and Herb chose Chinese, Avery picked Italian, along with Beau and Rachel. The triplets like grilled cheese, so they were placed in the American group. What type(s) of food are most popular? Use a visual to help figure out the problem. (graphing)


Choose an Operation:

Jenny is going to a garage sale. She sees an old jacket she likes for $10, a framed picture for $5 and a pair of sandals for $3. She wants to stop and get a bagel on the way home for $3.25. How much money does Jenny need to have in her pocket if she’s only bringing bills and no change? (choose an operation/ +/ $21.25, so $22)


Make an Organized List:

The smoothie store sells smoothies with either apple (A), coconut (C) or berry (B) juice with added choices of bananas (BA), strawberries (S) or frozen yogurt (Y). They all come with crushed ice added into them. What combinations could you purchase? (organized list)























Draw a Diagram:

Henry and his friends went on a weeklong hiking trip. The total distance for the trip was 70 miles. On the first day, they walked 1/10 of the total distance. On the two following days they walked 1/3 of the remaining distance. At the end of the third day, they divided the distance they still needed to travel equally amongst the last four days. (draw a diagram/picture)

How far did they walk on the first day? (7 miles)

How many miles were left? (63 miles)

How far did they walk on the second and third day? (21 miles together)

How many were left for the last four days? (42 miles)

How many did they walk on each of the last four days? (10.5 on

each of the last 4 days)

Learning Tips


The child chooses from a list of strategies:

  • Learn to omit extra information.

  • Use a graphic organizer to help clarify the problem.

  • 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.

  • 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


Encourage children to come up with their own word problem topics. If children come up with their own interests, they are more likely to pay attention to the problem because they have created ownership.

Encourage your child to write his/her own problems for you and your family to solve. It’s not even necessary for the child to know the answer to his/her own problem. Everyone can work together to find the answer.


Read the problem to determine what the question is asking.

Reread the problem and underline the information that is given.

Use a diagram or other strategy to show what is known and unknown in the problem.

Write the equation using what is known and unknown.

Solve the equation. Continue until the problem is solved.

Check to make sure the final answer makes sense and is reasonable.


Word problems don’t teach children to solve exact replications of problems, but rather the goal is to teach children to solve problems in general.


Be open to the idea that the best way to learn to solve word problems is by NOT solving them, but rather coming up with how one would solve the problem. The child then isn’t distracted by the calculating.

Extra Help Problems


Jo had $5.00. She bought a large bag of carrots for $2.50 and a $.50 orange juice. How much money does she have left? ($2.00)


Jo went back to the store with another $5.00. She bought a gift for her little brother for $2.50 and gift-wrapping for $.50. She had to pay 10% tax and handling on the items. How much money does she have left? ($1.70)


Rachel has 30 red and blue marbles in her marble collection.

She has 4 times as many red marbles as blue marbles. How many blue marbles does she have?


Joey came home at 4:15 p.m. It took him 30 minutes to ride his skateboard home from Tom’s house, where the two boys spent 1 hour and 15 minutes playing chess. At what time did Joey and Tom start playing board games?


Harry has 8 dimes, Linda has 5 quarters and Mary has 4 half dollars. How much do they have all together? ($4.05)


Sue, Jack, Barbara, and Tony are waiting in line to buy tickets.

Neither Sue nor Barbara is first in line. Tony is directly between the 2 girls. In what order are the 4 standing in line?


Jimmy and Brittany have 193 marbles together. Brittany has 47 marbles less than Jimmy. If Jimmy gives Brittany 15 marbles, how many more marbles does Jimmy have than Brittany? (17)


Brandon and Janet sold cookies. The first week they sold 1.5 dozen.

Every week they sold 1.5 dozen more than the week before. How many cookies did they sell the fifth week?


If there are four flavors of ice cream. How many double scoop variations can you make? (6)


You have five hamsters. They all are two years old and weigh 3 ounces each. How much do they weigh altogether? (15 ounces)


Andy’s dad got a new uniform and had to pay $59.95 for pants, shirt and hat. What would uniforms cost for the 20 new workers combined? (estimate the answer first=$1200; $1199)


Jack earned $164 per week for 11 weeks at his afterschool job. Robbie earned $139 per week for 13 weeks. What is the difference in the totals the two boys earned? ($3 more for Robbie)


Brenda wants to pay to go to summer camp. She has $200 saved and she got a $75 scholarship towards the camp tuition of $985. How much does she have to come up with? ($710)


The girls want to go eat pizza one night a week for $6.50. The boys want to eat burgers and fries one night a week for $5.95. How much more expensive is the pizza than the burgers over ten weeks ? ($5.50)


Five pounds of spaghetti can feed 30 people. Hal bought enough spaghetti costing $2.40 per pound to feed 45 people. He paid with $20.00. What was his change? ($2.00)


Leonard bought 3 juice boxes for $.65 each, 2 burgers for $1.25 each and a veggie sandwich for $1.75. He paid with $10. What is his change? ($4.45)


A ceiling requires a support be placed every 5 ½ feet. How many supports are needed for a ceiling that is 34 feet long? (6)


It costs $60 to feed a basketball team of 20 players. How much would it cost to feed a team of 30 players? ($90)


There are 5 kittens in Mr. Field’s house. He would like to give each of the kittens six kitty treats. Mr. Fields looked in his cupboard and found that he had 2 cod treats, 3 times as many tuna treats as cod treats, and 4 more kitty candy than tuna treats.

Does Mr. Fields have enough treats for all the kitties? (No, he only has 18 and he needs 30)

If not, how many more treats does Mr. Fields need? (He needs 12 more treats)

If Mr. Fields had 40 treats, how many would each kitty get then? (8)


The slug crawled 3 inches every 2 seconds. The snake crawled 5 inches every 3 seconds. If they both had a race to the fence post, 30 inches away, how long would it take the slug to get there? (20 seconds)

How long would it take the snake to slither there? (18 seconds)

Who would win the race and by how many seconds? (The snake would win by 2 seconds)


Cole was so hungry from boogie-boarding that he bought 3 veggie dogs, 4 bags of chips, an ice cream and a water. How much did he spend?

Ice cream costs $.20 cents

Veggie dogs cost 3 times as much as ice cream

Water costs the same as 2 veggie dogs

Chips cost half as much as a veggie dog.

Cole paid for her snacks with $5. How much change will he get back? (It costs $4.60, so Cole will get $.40 back)


Jackie baked mini-cupcakes for the school bake sale, but she got very hungry while cooking them so she ate six of the mini-cupcakes she made. There were still enough cupcakes for the sale when Jackie went to baseball practice. When she came back, she found that half the cupcakes were missing. She only had 12 left. How many did she bake in the first place? (24 were on the plate when Jackie left, but she ate 6 before she went to practice. 24 + 6 = 30 cupcakes)


Gnome Minus went for a walk in the forest with gems worth $2.10 in his pocket. Each gem is worth $.10. After he walked for 20 minutes, he noticed he had another hole in his pocket. Gnome Minus counted his gems and realized that he had lost ten gems every 4 minutes through the hole.

How much did the gnome have left after 20 minutes?

(He lost 5 dimes in 20 minutes. 16 dimes left/$1.60)


My little brother climbed the stairs at my grandmother’s house. He stopped in the middle and there are an equal number of stairs above and below him. If he goes down 4 stairs, then up 7 stairs then down 13 stairs, he’ll be on the first stair.

How many stairs does grandma’s have? (21 stairs)


A group of 68 ants crashed a picnic. Some (41) were brought there in the picnic basket and others (3 from each anthill) found their own way there. After the picnic 4 ants returned to each anthill and the rest went back in the picnic basket.

How many went back in the picnic basket? (27 came from anthills originally, 36 went back to the anthills and 32 went back in the basket)


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