Helping with word problems

1. 

   1

   Explain the purpose of word problems. Without proper context, some students may view word problems as unnecessarily complicated. However, they’re actually intended to help students use math to solve real world problems, such as building a fence, buying enough food for a party, or adjusting a recipe. The math is still the same, but the way the problem is presented is more relevant to real life.^[2]
   

   • Ask students to work with a partner or group to identify ways that they might use math in real life. Next, have them turn that situation into a math-based story.
   • For example, they might say they use math when dividing into teams at recess. They could turn that into a story like this: “If the class has 20 students and we need 2 teams to play, how many students will be on each team?”

2. 

   2

   Help students create a word problem that fits their life.^[3]
   Have them follow the process above to create a math story-problem specific to their own life. This helps the lesson feel relevant to students, which gets them engaged. It also helps them reach higher levels of learning.^[4]
   

   • Suggest that they incorporate a hobby or favorite interest. For example, they might write a problem that has to do with a sport they play or a problem that centers around a favorite animal.
   • Have them put their name in the problem.
   • Here’s an example: “If Alex wants to score 10 soccer goals over the second half of the season and there are 5 more games left to play, how many goals should Alex score per game to stay on track?”

3. 

   3

   Take out the numbers to help students focus on the question. Students need to know what the problem is asking if they’re going to solve it, but recognizing the question is hard. It’s easy to get hung up on the numbers! Rewrite a basic word problem without the numbers, then ask students to determine what it’s asking.^[5]
   

   • You may need to do this several times for students to understand.
   • Your sample problem might look like this: “Sarah is buying pizza for her slumber party. If each pizza has a certain number of slices and she knows how many guests are coming, how can she estimate the number of pizzas she needs. What other information might she need to arrive at the answer?” Your students should point out that Sarah would need to know how many pieces of pizza her guests will eat on average. She could then multiple that number of slices by the number of guests. To get the number of pizzas, she’d then divide the total number of slices by the number of slices in a pizza.

4. 

   4

   Tell students to illustrate word problems. When students are first working with word problems, illustrating them can help better understand the context. They can draw the action of the problem, the items depicted in the problem, or whatever helps them.^[6]
   

   • For example, when determining how many pizzas Sarah will need to buy for her slumber party, the students could draw circles to represent the pizzas and stick figures to represent Sarah and her guests.
   • However, stress that this is not a requirement for arriving at your answer, as some students may find this extra step frustrating.
   • This can help visual learners better understand word problems.

5. 

   5

   Make sure the word problems match students’ language and math skills. Students must be able to understand what the problem is saying in order to know what it’s asking. Similarly, they won’t be able to arrive at the answer unless they know how to do the required math processes.

   • For example, students who can only add numbers should be given word problems that only require addition.

1. 

   1

   Summarize the CUBES process for students. CUBES provides students with an easy-to-follow process for solving word problems that includes all of the relevant steps. It’s also easy for students to remember, as it offers a fun, math-related acronym. Here is what each letter stands for:^[7]
   

   • C-Circle the numbers.
   • U-Underline the question.
   • B-Box the keywords.
   • E-Eliminate unnecessary information.
   • S-Show your work.

2. 

   2

   Tell students to circle all of the numbers, including those in word form. It’s common for word problems to include numbers in word form, even if some numbers are written numerically. Circling them can make it easier for students to come back to them once they start to work through their solution.^[8]
   

   • Although some numbers may be extraneous information, it’s important that students circle all of them during this step. They can eliminate unnecessary information later.
   • For example, your problem might look like this: “Katie asked 7 friends to sleepover on Friday, but only 4 can make it. She knows that she and each friend will eat 6 chicken nuggets, and each bag of frozen nuggets contains 15 nuggets. How many bags will she need to make sure she has enough nuggets?” Students should circle the 7, 4, 6, and 15.

3. 

   3

   Underline the question within the problem. The question is what the problem is asking the student to do. It’s what they should know once they’ve finished working the problem.^[9]
   

   • For example, they might need to know how much of something they’d need or how much of something they’d have left.
   • When students are first learning word problems, the question should be at the end of the problem. It will often have a question mark at the end.
   • In the problem above, the question is this: «How many bags will she need to make sure she has enough nuggets?”

4. 

   4

   Draw boxes around any keywords, such as “total” or “all together.” Keywords signal to the student what they’re expected to do to solve the problem, such as add, subtract, multiply, or divide.^[10]
   In some cases, synonyms of these words will be used. Students need to know how to identify these keywords, then they can box them in so that they won’t forget to use them.^[11]
   

   • For example, addition could be indicated by words like “in total” or “all together.” Similarly, subtraction should be signified by “difference” or “less.”
   • In the problem above, students would draw boxes around «only,» which will indicate subtracting. They’ll also draw boxes around «how many» and «enough,» which suggest that they’ll need to first multiply and then divide.

5. 

   5

   Show students how to eliminate unnecessary information. Many word problems have unnecessary information that complicates the process. For example, the problem might contain unnecessary numbers or extra information. Students can avoid confusion by crossing out this information before they start working on a solution.^[12]
   

   • For example, the sample problem has extra numbers: “Katie asked 7 friends to sleepover on Friday, but only 4 can make it. She knows that she and each friend will eat 6 chicken nuggets, and each bag of frozen nuggets contains 15 nuggets. How many bags will she need to make sure she has enough nuggets?” The students could cross out the 7, since it isn’t necessary for arriving at the correct answer.

6. 

   6

   Ask students to show their work. Not only will this ensure they receive full credit, it also helps students check their work. If they get the wrong answer, they can identify where they made errors and correct it moving forward.^[13]
   

   • Here’s how we would solve Katie’s slumber party question:
     • 4 friends are coming, plus Katie: 4 + 1 = 5 girls
     • Each of them will eat 6 nuggets: 5 x 6 = 30 nuggets
     • Each bag has 15 nuggets: 30 / 15 = 2 bags needed
     • Answer: Katie needs to buy 2 bags of nuggets.

1. 

   1

   Allow students to follow along as you solve word problems. Provide them with a worksheet with the problems printed on it. Then, show them what they need to do, asking them to copy down what you write onto their paper. Go slowly, taking questions as they arise.^[14]
   

   • You will need to work through several problems until your students start to grasp the concepts. Make sure the problems you choose match your students’ language and math skills.
   • You can work through the problems on the board or using a projector.
   • For example, you could solve this problem: «Diego is baking cookies for his team’s bake sale. Last year, he earned $100 to help his team. This year, he wants his sales to reach $120. If each cookie will cost $0.75, how many cookies will Diego need to bake?»

2. 

   2

   Talk through your strategy as you solve the problem. Explain each step in detail so that students can understand your thought processes as you approach the problem.^[15]
   In addition to seeing what you write, they can get an idea of how you arrived there.^[16]
   

   • Say, «I’m going to start by circling the numbers.» Circle 100, 120, and 0.75.
   • Next, say, «“Now I’m going to underline this, since I know it’s the question.” You’d underline this statement: «If each cookie will cost $0.75, how many cookies will Diego need to bake?»
   • Say, “Now I’m going to cross this out, since the problem isn’t asking me about this.» You’d cross out the sentence about Diego earning $100 last year.

3. 

   3

   Show your work. This is essential for students to understand how to do it themselves. Don’t do any of the math in your head, even if it’s something really simple. Remember, your students should be copying down everything you write so that they can refer to it in the future.^[17]
   

   • Write the steps in order to make it easier for students to copy down.
   • Here’s how to work out Diego’s problem:
     • Diego needs to make $120 by selling cookies for $0.75: 120 / .75 = 160
     • Answer: He will need to bake 160 cookies.

4. 

   4

   Point out parts of the problem that could have tripped you up. After you arrive at your answer, help students see where you could have made errors. For example, you might have included unnecessary numbers, or you may have gotten tripped up over extra information.^[18]
   

   • Not only does this show students what to watch out for, it also shows them that mistakes can happen to anyone.
   • For example, you might have accidentally used the information about Diego earning $100 last year, which isn’t relevant to the question.

5. 

   5

   Call on students to identify the next step once they catch on. This gets students to start thinking the process through on their own. At first, pause and ask students to reflect on what they need to do next. Then, call on a student. Ask a different student to supply the next step.^[19]
   

   • If a student gets the answer wrong, praise the effort, then ask another student to help. Say, “Great enthusiasm, James! We’re almost to that step, but we need to do something else first. Amy, could you help us out?”

1. 

   1

   Allow students to work in groups or pairs while they learn the process. Give the students a few practice problems to solve together. This provides built-in supports for struggling students and helps students solidify their knowledge as they explain their reasoning to their classmates. Move about the room to ensure that they are on track.^[20]
   

   • Remind them to use CUBES to solve their problems.
   • You can make sure students are on track by listening to what they are saying. Are they correctly explaining the process? Do they appear to be confused? Use your judgement to determine if you need to offer guidance.
   • Praise groups that are on track. Say, «Excellent work!» or «I’m proud of the progress you’re making!»

2. 

   2

   Ask students to write their own problems, then switch papers. This is a fun way to deepen your students’ understanding of word problems. Students can develop real word story questions that relate to their lives, then they can have fun solving their friends’ stories.^[21]
   

   • It’s a good idea to have them do this in groups, as it increases the quality of the questions. Also, it’ll allow you to check each group’s questions before they switch papers, which would be harder if each student created questions.
   • Not only is this fun for students, but it encourages higher-level learning.

3. 

   3

   Provide students with practice problems to solve individually. Students will be ready for individual practice after they’ve watched you model the process and have worked in groups or pairs. At this point, you can work with individual students who are having difficulty grasping the concept. Help them work through the CUBES process one-on-one until they start to grasp it.

   • You can make up your own worksheets, or you can download them for free online.^[22]
     Make sure that the word problems you give them match their language and math skills.
   • When making your own worksheets, it’s best to work through the problems before you give them to students to make sure all of the information is present. Also, stick to topics your students will understand, such as sports, pets, and food.
   • If a student seems to be struggling, you may want to invite them to tutoring.^[23]
     

Sample Word Problems and Illustrated CUBES Process

Ask a Question