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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
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  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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March 11, 2021

7 Fun Activities For Teaching Word Problems That Actually Work!

Word problems are an important part of math instruction because they show students how they can use the math they are learning in the classroom in real life. A skill they will be using constantly throughout their life!

For this reason, I try to make learning this skill as fun as possible so that students will be engaged enough to really learn and understand the concept!

Here are some of my favorite tips for teaching word problems!

word problems

  • Use picture books – Model real-world problems using actual books. This is so easy to do with pretty much any picture book. All you need are pictures! While you’re reading, look for any changes with adding and subtracting in the pictures. For example: in Eric Carle’s The Very Hungry Caterpillar, you can point out the adding one concept using the food. This is a good start for helping students understand that word problems have a beginning, change, and an end. For modeling subtraction, I found this book One Big Pair of Underwear. It’s hilarious! The kids really liked the funny pictures and obviously, anything with underwear captures their attention.

word problems

  • What do you know? 
  • What do you need to solve? 
  • How might you solve that?

 This supports your little learners by helping “read” the world problem and it integrates with your listening and speaking standards. 

word problems

  • Use rewards – Motivate your students to complete word problems. You can use this FREE Word Problem pack to do that. When students complete a word problem, they simply color, stamp, or place a counter over a space. When they’ve completed a certain amount, they earn a reward of their choice. For example, if a student completes five word problems, then the student can take their shoes off. 

word problems

  • Making Movies – is another way I like to teach my students how to solve word problems. Have them close their eyes and visualize what is happening in the story. Is the information missing in the beginning, middle, or end of the story?

word problems

  • DIY Word Problems – Create your own math word problems. Have students roll dice to create their own math word problems. This helps engage them in learning and gets them to work independently. You can grab these by clicking here ! 

solve the following word problem learning task 3

  • Get Hands-on -Use math manipulatives to model word problems. My favorite math manipulative is using an abacus. I model with one row the first part of the story. Then, I model the second part on the second row. Finally, I model the third part on the third row. Wherever the missing information is (beginning, middle, or end), we don’t model it, and this is where we show our answer. You can also use a tens frame with counters. This hands on manipulative organizes the information for kids to see and it’s an essential tool that will appear over and over again in K – 2. 

solve the following word problem learning task 3

  • Play Games – There are so many benefits to doing this. You can read about those here. You can get extra practice with word problems using these games. I’ve made sure to create a balance with word problems that have a missing beginning, missing middle, and a missing end. There are some with a change and some that compare.

These activities have always been a hit in my classroom. Making learning fun is such a simple and great way to increase student engagement and learning outcomes!

What are your favorite ways to teach word problems? Let me know in the comments!

solve the following word problem learning task 3

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Strategies for Solving Word Problems – Math

solve the following word problem learning task 3

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

solve the following word problem learning task 3

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

  • Circle any numbers you’ll use.
  • Lightly cross out any information you don’t need.
  • Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

3rd Grade Math Task Cards Mega Bundle | 3rd Grade Math Centers Bundle

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

th Grade 960 Math Task Cards Mega Bundle | 4th Grade Math Centers

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

5th Grade Math Task Cards Mega Bundle - 5th Grade Math Centers

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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Teaching with Jennifer Findley

Upper Elementary Teaching Blog

December 5, 2018 | 1 Comment | Filed Under: Decimals , Fractions , Geometry & Measurement , Math , Math Centers , Multiplication & Division , Word Problems

Word Problem Strategies : Analyzing Word Problems with Free Organizers/Mats

Word problems used to be the bane of my existence as a new teacher. Thankfully, I learned new strategies and resources to help me implement and teach word problem strategies all year. To be honest, teaching word problems all year was the ONE thing that I did that had the greatest impact (if you are interested in more information about word problems and how I teach them, see the links at the bottom of this article). On this post, I will share one of those word problem strategies that involves helping students think through and analyze word problems using graphic organizers or word problem mats.

One of my go-to word problem strategies to help my students comprehend and solve word problems involves using graphic organizers or mats. Read more and grab free versions of different organizers on this post.

Teaching Word Problem Strategies with Word Problem Organizers

These word problem graphic organizers/mats help walk students through the thinking and analyzing process that is automatic for us. Through this analysis, the students have a better chance of comprehending the word problem, choosing the correct operation to solve it, and determining if their answers make sense.

In the same manner that we teach students to comprehend texts, we should also teach them how to breakdown and analyze a word problem. Using graphic organizers/mats helps break the process down into manageable steps for the students.

The free download (available a few sections down) has several different versions to allow you to choose which works best for your students and their needs. Having the different versions will also allow you to differentiate the organizers.

Practice solving word problems with these free word problem organizers.

My go to version to begin with has the students following these steps:

  • What operation are you planning to use? Write or underline the evidence from the problem that supports that operation.
  • Solve the problem and show your math work.
  • Write the answer in a complete sentence.

And here is an example from one of the more advanced organizers with more steps:

  • Retell the problem in your own words.
  • What operation are you thinking will solve this problem? Why?
  • Write the answer to the problem in a complete sentence.
  • Prove your answer is correct.

Using the Word Problem Organizers

You have a ton of variety in how you choose to use these organizers, however I definitely recommend following this sequence:

  • Introduce the organizer/mat by going over the steps and how they help the student comprehend the word problem and/or organize their work. Understanding the purpose behind the organizer is huge with students because you don’t want them to view it as busy work.
  • Model how to complete the organizer/mat whole group with at least one word problem (and more if the students need it and depending on the complexity of the organizer you choose).
  • Allow the students to work in pairs or triads to complete the organizer as a form of guided practice before they are required to do so independently.

The graphic organizers/mats can also be used as a guide for students when discussing the word problem with partners. They don’t always have to fill in each part of it, but instead they can discuss some of the parts. This will give the same benefits in less time.

Also, placing the word problem organizers/mats in page protectors and letting the students use expo markers instantly makes it more engaging.

Here are some ways you can use these word problem mats to help your students practice analyzing word problems:

  • Math centers
  • Small group teaching
  • Independent work
  • Homework – send home a page protector and expo marker and let the students use the mats at home or they can use the mats as a guide as they work through word problems. These organizers will also help parents support students if they struggle with a word problem.

Analyze word problems with these free word problem mats.

About the Digital Word Problem Organizers

There are digital versions of each of the word problem organizers included in the download below. The digital access link can be found on page 6. Each slide has text boxes for students to type into and interactive ways to complete some of the tasks.

The digital organizers are available in two versions, one with a designated spot to write a word problem and one without the space.

Download these digital word problem organizers for your upper elementary math students!

Should the students use the mat with every word problem they solve?

They certainly can (especially if you use dry erase markers and/or have them discuss some of the parts instead of recording it all) but they don’t have to. Using the organizers will help them work through complex problems but will take more time. When I use these in math centers, I only require one word problem to be worked on fully on the more advanced organizers. However this depends on the mat you choose. Some of them are more simple and don’t require any extra work- the mat simply organizes the work they would already do.

Download the Word Problem Strategies Mats

Click here or on the image to download the Word Problem Mats. Remember there are several versions so you can choose the ones that work best for your grade level and your students’ needs.

One of my go-to word problem strategies to help my students comprehend and solve word problems involves using graphic organizers or mats. Read more and grab free versions of different organizers on this post.

Need More Word Problem Strategies and Resources?

Check out these helpful resources, blog posts, and freebies for even more help teaching word problems.

Teaching Word Problems without Key Words (And What to Teach Instead)

Word Problem of the Day: FREE Starter Packs

8 Ways to Help Students Be Successful with Word Problems

Show the LOVE with Word Problems: Helping Students Answer Word Problems Effectively

Teaching Students How To Justify Answers in Math

Close Reading in Math Strategies and Freebies

10 Ways to Get Students Writing in Math

Solving Multi-Part Word Problems

4th Grade Word Problem of the Day TpT Resource

5th Grade Word Problem of the Day TpT Resource

The task card word problems shown in the images are part of my task card collections for 3rd-5th grade math. Click on the links below if you wish to see these resources in your grade level.

3rd Grade Common Core Math Task Card Collection

4th Grade Common Core Math Task Card Collection

5th Grade Common Core Math Task Card Collection

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Analyzing word problems involving multiplication.

Many problems can be solved in different ways. Decide if the following word problems can be solved using multiplication. Explain your thinking. Then solve each problem.

  • Liam is cooking potatoes. The recipe says you need 5 minutes for every pound of potatoes you are cooking. How many minutes will it take for Liam to cook 12 pounds of potatoes?
  • Mel is designing cards. She has 4 different colors of paper and 7 different pictures she can glue on the paper. How many different card designs can she make using one color of paper and one picture?
  • Nina can practice a song 6 times in an hour. If she wants to practice the song 30 times before the recital, how many hours does she need to practice?
  • Owen is building a rectangular tile patio that is 4 tiles wide and 6 tiles long. How many tiles does he need?

IM Commentary

The purpose of this task is for students to analyze different contexts in which multiplication is appropriate. Research indicates that students often do not make sense of word problems. Instead, to come up with an answer, they just apply the most recent algorithm taught, chose operations based on the types of numbers involved, or apply other approaches that do not require sense making. In this task, the students are asked to analyze the problems and explain their thinking before they find an answer. In the process, they are thinking more carefully about different contexts that can be represented by multiplication.

Note that none of the contexts involve multiplicative comparison, which is intentionally left until 4th grade (see 4.OA.A.1).

Solution: Analysis

  • While you can solve this by repeated addition (5+5+5+….), this problem can also be solved by multiplication since adding 5 together 12 times is the same as $12\times5$.
  • This can be solved by multiplication, because for each of the four colors, there are seven different pictures from which to choose, so 7 pictures on the first color + seven pictures on the second color + 7 pictures on the third color + 7 pictures on the fourth color gives four groups of seven or $4\times 7$.
  • This is a division problem since the number of hours needed can be determined by counting the number of groups of six needed to make 30, or $$30 \div 6 = ?$$ On the other hand, we can think about this in terms of multiplication by asking what times six equals 30, which we can write symbolically as $$? \times 6 = 30$$

It is a good idea to draw a picture:

We can count the number of tiles one by one, or we can see that there are four rows, each with six tiles, so we can think of it as a multiplication problem $4 \times 6$.

Solution: Solving explicitly

$12\times5$ is 12 groups of 5, which we can see in the picture below:

12 groups of 5 is the same as 6 groups of 10:

which is 60. So Liam needs 60 minutes to cook the potatoes.

An array makes it easier to see:

There are 28 different possible cards.

  • If we multiply the number of hours she practices by 6, we know the answer must be 30: $$?\times 6 = 30$$ Since 5 times 6 is 30, she has to play for 5 hours if she wants to practice the song 30 times.
  • Looking at the picture above, we can see that Owen needs 24 tiles.

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Praxis Core Math

Course: praxis core math   >   unit 1.

  • Algebraic properties | Lesson
  • Algebraic properties | Worked example
  • Solution procedures | Lesson
  • Solution procedures | Worked example
  • Equivalent expressions | Lesson
  • Equivalent expressions | Worked example
  • Creating expressions and equations | Lesson
  • Creating expressions and equations | Worked example

Algebraic word problems | Lesson

  • Algebraic word problems | Worked example
  • Linear equations | Lesson
  • Linear equations | Worked example
  • Quadratic equations | Lesson
  • Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

  • Translating sentences to equations
  • Solving linear equations with one variable
  • Evaluating algebraic expressions
  • Solving problems using Venn diagrams

How do we solve algebraic word problems?

  • Define a variable.
  • Write an equation using the variable.
  • Solve the equation.
  • If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • (Choice A)   $ 4 ‍   A $ 4 ‍  
  • (Choice B)   $ 5 ‍   B $ 5 ‍  
  • (Choice C)   $ 9 ‍   C $ 9 ‍  
  • (Choice D)   $ 14 ‍   D $ 14 ‍  
  • (Choice E)   $ 20 ‍   E $ 20 ‍  
  • (Choice A)   10 ‍   A 10 ‍  
  • (Choice B)   12 ‍   B 12 ‍  
  • (Choice C)   24 ‍   C 24 ‍  
  • (Choice D)   30 ‍   D 30 ‍  
  • (Choice E)   32 ‍   E 32 ‍  
  • (Choice A)   4 ‍   A 4 ‍  
  • (Choice B)   10 ‍   B 10 ‍  
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Solving Word Problems (Grades 3-6)

Our Solving Word Problems lesson plan for grades 3-6 provides students with more advanced strategies for solving word problems. Students learn how to use pictures or diagrams to solve word problems and how to solve word problems involving more advanced operations.

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Our Solving Word Problems (Grades 3-6) lesson plan strengthens strategies for solving word problems. This interactive lesson plan equips students to identify and define keywords and use pictures or diagrams for math problem solving (all operations). Students are asked to create word problems and use their presentation skills to share their problem-solving steps with the class. Students are also asked to individually complete practice problems in order to demonstrate their understanding of the lesson.

At the end of the lesson, students will be able to identify and define keywords and use pictures or diagrams for math problem solving (all operations).

State Educational Standards: LB.Math.Content.3.OA.D.8, LB.Math.Content.4.OA.A.3

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Word problems with variables

Equations with variables.

These worksheets formulate problems involving variables.  These are relatively simple word problems requiring addition,  subtraction, multiplication or division to solve; however, the problems are expressed in terms of a stated variable , and the student is asked to write an equation using that variable , before solving the problem. The intent is to familiarize students with the use of variables to represent unknowns.

solve the following word problem learning task 3

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solve the following word problem learning task 3

Learning Task 3: Solve the following word problems involving Pythagorean theorem. 4. A ladder 13m long is placed on the ground in such a way that it touches the top of a vertical wall 12m high. Find the distance of the foot of the ladder from the bottom of a wall.

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Jennifer Van Blair

The 3 Step Method to Teaching Word Problems

by Jennifer Van Blair | Sep 30, 2022 | Math

Teaching Word Problems

Word problems are difficult. Most adults surveyed can recall struggling with word problems in school, some even saying that they STILL struggle with word problems. That’s why I developed this 3 step method for teaching word problems.

As a student, I was good in upper elementary school working through procedures to solve math problems. However, I remember my distinct hatred of word problems. No matter how successful I was at solving a problem in isolation, I would almost always solve that same problem incorrectly when in word problem form.

Word Problems are Stories:

They have a setting, characters, and a plot that has a conflict requiring a solution. Yet, as teachers we teach math and reading separately, coming up with magic formulas to make word problems easier for our students. 

However, teaching reading skills during math and focusing on making sense of the text (word problem) is precisely what our students need in order to make sense of word problems.

My research and 10+ years of classroom teaching experience focused on word problem instruction has led me to develop my three part approach to teaching word problems. 

If you want to help your students understand word problems better, then you have to make word problem instruction a regular part of your day.

Using a daily word problem a day strategy, I support my students in understanding word problems that not only grows their accuracy, but their confidence when approaching word problem situations.

3 STEPS METHOD to Teaching Word Problems Successfully:

Numberless Word Problems for Upper Elementary

  • Numberless Word Problems

Increasing student awareness of word problem type and structure happens when the numbers are taken out of word problems. We have created a culture of answer getting. Students are trained to find the answers as quickly as possible without thinking about the problem as a whole.

As soon as students see numbers in problems, they have blinders on, grabbing any and all numbers and TRYING the first operation they think will successfully work.

What we need to do is take the blinders off. We need our students to slow down, look at the context of the word problem, and make sense of its meaning. The solution of the problem is not the correct answer when we use numberless word problems.

Instead, asking our students what a problem is about, the story, is what we want our students to focus in on first.

We expect students to identity story elements in the texts they read. We should also expect and model to students how to make sense of a word problem before deciding how to solve.

We do this through numberless word problems.

Try this: Start your morning math time by displaying a numberless word problem of the day. Discuss the story of the problem using the following questions:

  • Who are the characters in this problem?
  • What is the setting?
  • What is happening (the plot, conflict, verbs being used)?
  • Have you ever done _____ before (make connections to students’ experiences)?
  • What did you do in this situation?
  • What can you infer we can do here to solve this problem?
  • Can you make a picture (either illustration or model) to represent your thinking?

Numberless word problems are a necessary first step to helping students feel confident with word problems. The more we can help them understand the types of situations found in word problems, the more we increase their experience with problem types.

Research shows that broadening their experience with problem types increases their accuracy to select similar solutions to problems in the future. Therefore, a daily practice of numberless word problems will improve their experience, knowledge, and success with word problems overall.

STEP #2: Substitute Values

After students have made sense of the word problem, you can invite them to substitute numbers into the problem and solve using the ideas generated during the numberless discussion.

Student generated numbers are useful for a variety of reasons:

  • Increases ownership of classroom learning
  • Engagement increases as students are working with numbers they are comfortable with.
  • Differentiation is easy when students are working with numbers that are at their level – you can also vary these numbers in small group situations to ensure ALL students have access to word problems at their level.
  • Builds student understanding of word problem structure in selecting numbers that are appropriate for the task being solved.

Have students solve the problem using their solutions, then discuss the results that they found. It is okay that students have different numbers. Having a variety of results to discuss if the problem works encourages what we know is good for science: the more evidence and results the better.

solve the following word problem learning task 3

STEP #3: Writing their own problems

When do we learn the most? When we create and make our own learning. That’s why it is essential that you have students write their own word problems using the daily word problem as a model.

When students write their own word problems using the daily example, they increase their understanding of the problem type. Just as we do in regular writing, we support students during the process. 

Asking students to write a multiplication problem can be challenging, especially when we think about all the situations when multiplication is required: arrays, equal groups, or area problems.

The problem of the day model focuses student attention on one specific problem type. Let’s say our problem of the day was for national crayon day on March 31. This day would be the perfect day to discuss equal groups problems as stores sell boxes of crayons in set amounts or for a set price.

Instead of telling students to write a multiplication problem, focusing their attention on an equal groups problem requiring multiplication means that they know the TWO FACTORS, but do not know the total amount. 

Support students in the writing process by displaying the equal groups anchor charts and sentence frames, either in print or digital form.

Students could then write their own word problem for the day, using a notebook page, or for special occasions like Halloween, you could use the word problem chains template to write their own problem and decorate the classroom . 

Having students exchange their word problems with classmates or solve their own are also great ways to take the stigma out of word problems. 

The benefit of keeping a word problem journal is that you could use student created word problems in your classroom learning, thus furthering student ownership and community.

Building word problem confidence doesn’t mean you have to use tricks and strategies that take the rigor out of learning. This three step daily routine not only builds student knowledge, confidence and accuracy with word problems, but it develops a classroom culture of community and math identity.

I created this daily routine to help my students find the joy of math, something that was lacking in my own classroom as a student. By

  • Focusing on problem context with numberless word problems
  • Building confidence by substituting numbers based on student abilities
  • Authoring their own word problems

Your students will come to find that word problems aren’t scary and in need of magic formulas to solve them.

Are you ready to stop using word problem strategies that don’t work and put this three part plan into practice tomorrow?

I created a workshop on PopPD that helps you build confident word problem solvers. Learn more by clicking HERE .

Either way, I can’t wait to hear more about your students journey with word problems. Be sure to share connect with me on Instagram and share more of what your students are learning, or struggling with when it comes to word problems.

solve the following word problem learning task 3

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Module 9: Multi-Step Linear Equations

Apply a problem-solving strategy to basic word problems, learning outcomes.

  • Practice mindfulness with your attitude about word problems
  • Apply a general problem-solving strategy to solve word problems

 Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

A cartoon image of a girl with a sad expression writing on a piece of paper is shown. There are 5 thought bubbles. They read,

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in the cartoon below. Read the positive thoughts and say them out loud.

A cartoon image of a girl with a confident expression holding some books is shown. There are 4 thought bubbles. They read,

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

  • In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

  • In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

  • Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 6. Check the answer in the problem and make sure it makes sense.

  • We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

  • The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

The top reads,

We list the steps we took to solve the previous example.

Problem-Solving Strategy

  • Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
  • Identify what you are looking for.
  • Name what you are looking for. Choose a variable to represent that quantity.
  • Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
  • Solve the equation using good algebra techniques.
  • Check the answer in the problem. Make sure it makes sense.
  • Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

  • Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
  • Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
  • Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Understanding Word Problems in Mathematics

On this page:, introduction, strategies to help students, online resources, in the classroom, online teacher resources.

For many students who struggle with mathematics, word problems are just a jumble of words and numbers. However, you can help students make sense of these problems by teaching them problem-solving processes. Indeed, as students move forward in their mathematical learning, they will need to apply problem-solving processes to more and more complex situations so they become college and career ready. The first Common Core State Standard (CCSS) for mathematical practice focuses specifically on problem solving:

  • CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

Proficient students are able to explain the meaning of a problem and look for entry points to its solution. They are able to analyze givens, constraints, relationships, and goals. They make conjectures about the form and the meaning of the solution, and they plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and they try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress, and they change course if necessary. In contrast, students who struggle with mathematics may find it difficult to successfully carry out parts (or, indeed, all) of this complex process.

To solve a word problem, students need to understand its context and develop a strategy to solve it. There are many ways to help your students build these skills and understand how to use them in specific situations (see UDL Checkpoint 6.2: Support planning and strategy development ).

One strategy is to use a process chart, which can guide students as they tackle a new problem. It helps to focus on how each step of the process supports students as they work to access the problem. An example problem-solving process is provided below:

  • Read the problem, then reread it and highlight key words and numbers. Reading the problem a second time with annotations helps students sort out the core information from the background noise.
  • Draw a picture of the situation that the problem presents. It may be helpful to first visualize a story or imagine a movie scene. Visualizing a story can be a powerful strategy that helps students create a picture or diagram of the problem.
  • Determine the goal of the problem.
  • Establish a strategy or write an equation to represent the picture. Estimate an answer, if possible. Estimating or approximating an answer helps students decide if they are on the right track.
  • Solve the problem and check the reasonableness of your answer. Reminding students that it is rare to complete a problem correctly on the first attempt encourages them to embrace mistakes and errors (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships ) .
  • Explain your solution method.

Teacher-student interaction will help you differentiate instruction. Ask students to compare and contrast different approaches, and then summarize their responses for them. Students should understand what works and does not work (and why); which methods are more efficient; and how models differ. It is critical that teachers elicit, value, and celebrate approaches that are different but nonetheless arrive at the correct solution. Encourage your students to use pictures, diagrams, charts, expressions, and equations as part of the problem-solving process. Discuss with them how their picture, diagram, chart, expression, or equation relates to the situation in the problem. Ask them to explain why they chose it and why they think it is a good mathematical expression to use for the problem they are tackling.

There are many technology tools and resources that can support students as they work to understand problems and expand their repertoire of appropriate models.

Virtual manipulatives can be used in addition to (or as an alternative to) the physical manipulatives that are already found in most mathematics classrooms. The following short video, Virtual Manipulatives , below provides an overview of how to make use of virtual manipulatives.

There are also many websites that offer lesson plans for teachers. ReadWriteThink , for example, provides a number of high-quality materials, including several that focus specifically on developing reading comprehension through mathematical problem solving. Look for links to other suggested materials on PowerUp’s Pinterest page.

As the end of the school year approaches, almost all of Mr. Garcia’s Grade 3 students are proficient at multiplying and dividing numbers up to 100. Most are able to apply their skills to solve word problems, but several students are still struggling — in particular, they have difficulty articulating explanations for their solutions. Throughout the year, Mr. Garcia’s students have been building a class website, through which they share useful resources with other third-grade students and show parents their progress in class.

Mr. Garcia decides that his next lesson will reinforce their understanding of problem-solving strategies in alignment with the CCSS on mathematical practice (see above). Students will create their own word problems and write the solutions to those problems. The final product will be a presentation that can be shared on the class website.

While Mr. Garcia will rely heavily on his interactive whiteboard to communicate visually with the class, he will also encourage his students to use a variety of technology tools, including:

  • The Thinking Blocks applet to demonstrate multiplication and division models
  • Software for creating presentations (e.g., PowerPoint, Keynote , Prezi )
  • A platform for sharing presentations on the class website (e.g., SlideShare , Prezi)
  • Digital organizers that students can use to collect personal notes and reference material
  • A polling tool to elicit student feedback

Mr. Garcia decides to begin the class by reviewing the problem-solving process. He works with the entire class to solve a multiplication problem from Thinking Blocks :

Thinking Blocks

Students then work in pairs to create their own problems. When the class comes back together later in the lesson, Mr. Garcia will invite a few pairs to present their problems and solutions, specifically choosing students who are able to provide clear explanations. All students will then write up their problems and solutions to share on the class website. To finish the lesson, students will write summaries that describe how to determine whether a word problem requires multiplication or division.

Mr. Garcia’s lesson plan is divided into three sections — launch, learning task, and closure — and is outlined in the chart below.

Lesson Plan

This article draws from the PowerUp WHAT WORKS website, particularly the Understanding Problems Instructional Strategy Guide . PowerUp is a free, teacher-friendly website that requires no log in or registration. The Instructional Strategy Guide on Understanding Problems includes a brief overview of the topic with an accompanying slide show; a list of the relevant mathematics Common Core State Standards; evidence-based teaching strategies to differentiate instruction using technology; short videos; and links to resources that will help you use technology to support mathematics instruction. If you want to dig deeper into the research foundation behind best practices in the use of virtual manipulatives, take a look at our Tech Research Brief on the topic. If you are responsible for professional development, check out the PD Support Materials for helpful ideas and materials for using the resources. Want more information? Go to PowerUp WHAT WORKS .

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IMAGES

  1. Learning task 3: Solve the following problems. Write your solutions and

    solve the following word problem learning task 3

  2. Learning task 3: Solve the following problems. Write your answers in

    solve the following word problem learning task 3

  3. learning task 3 read and solve the following problems. write your

    solve the following word problem learning task 3

  4. Learning Task 3: Solve the given problems. Write your answers in your

    solve the following word problem learning task 3

  5. Answered: E Learning Task 3. Analyze and solve…

    solve the following word problem learning task 3

  6. Learning task 3 :Solve the problem carefully by answering the questions

    solve the following word problem learning task 3

VIDEO

  1. Learning Task 3:Read the following naming words twice

  2. Word Problems Part 2

  3. A Nice Algebra Problem

  4. Learning Task 3: In your answer sheet, copy and answer

  5. Word Problem 1 to practice your Problem Solving Strategies

  6. Tricky Linear Word Problem

COMMENTS

  1. Solved Learning Task 3. Solve the word problems. 1. The

    1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 160, how long is each side? 2. Inzo is 10 years older than Migz. Five years ago Migz is one-third as old as Inzo. What are their present ages? 3. An express train travels 100 kph from station A to station B. A local train travelling at 45 This problem has been solved!

  2. Word Problems Calculator

    To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to ...

  3. 7 Fun Activities For Teaching Word Problems That Actually Work!

    STEM Box Activities$ Classroom Behavior Management Tool$ Word problems are an important math skill for students to master. Here are some fun activities for teaching word problems that actually work!

  4. Strategies for Solving Word Problems

    1. Read the Entire Word Problem Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too. 2. Think About the Word Problem

  5. Word Problem Strategies : Analyzing Word Problems with Free Organizers/Mats

    Teaching Word Problem Strategies with Word Problem Organizers. These word problem graphic organizers/mats help walk students through the thinking and analyzing process that is automatic for us. Through this analysis, the students have a better chance of comprehending the word problem, choosing the correct operation to solve it, and determining ...

  6. Solved Learning Task 3 Solve the following problems. 1.

    1. | Chegg.com Math Statistics and Probability Statistics and Probability questions and answers Learning Task 3 Solve the following problems. 1. Rhian likes to wear colored shirts. She has 15 shirts in the closet. Five of these are blue, four are in different shades of red, and the rest are of different colors.

  7. Solving Word Problems: Steps & Examples

    Step 1: Visualize the Problem The first step is to visualize the problem. See if you can picture what is going on. Draw pictures if that will help you. Pinpoint or highlight the important parts...

  8. Illustrative Mathematics

    Task. Many problems can be solved in different ways. Decide if the following word problems can be solved using multiplication. Explain your thinking. Then solve each problem. Liam is cooking potatoes. The recipe says you need 5 minutes for every pound of potatoes you are cooking. How many minutes will it take for Liam to cook 12 pounds of potatoes?

  9. Algebraic word problems

    Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

  10. Solving Word Problems (Grades 3-6)

    Solving Word Problems (Grades 3-6) Our Solving Word Problems lesson plan for grades 3-6 provides students with more advanced strategies for solving word problems. Students learn how to use pictures or diagrams to solve word problems and how to solve word problems involving more advanced operations.

  11. Learning Task 3: Solve the following problems. Show the four steps

    24.01.2021 Math Elementary School verified answered • expert verified Learning Task 3: Solve the following problems. Show the four steps and the complete solutions. Write your answer in your notebook. 1. Mr. Villa bought 91.25 inches of plastic labeling tape. He will use 1.25 inches long to label each. How many labels can he make? 2.

  12. Grade 3 word problems with equations and variables

    These worksheets formulate problems involving variables. These are relatively simple word problems requiring addition, subtraction, multiplication or division to solve; however, the problems are expressed in terms of a stated variable, and the student is asked to write an equation using that variable, before solving the problem.

  13. Solved: Learning Task 3: Solve the following word problems involving

    Click here 👆 to get an answer to your question ️ Learning Task 3: Solve the following word problems involving Pythagorean theorem. 4. A ladder 13m long is pl

  14. Apply a Problem-Solving Strategy to Word Problems

    Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers. Write the equation. 18= 1 2p 18 = 1 2 p. Multiply both sides by 2. 2⋅18=2⋅ 1 2p 2 ⋅ 18 = 2 ⋅ 1 2 p. Simplify. 36=p 36 = p.

  15. Learning Task 3: Solve the following word problem.

    1. Find the perimeter and area of a rectangle with a length of 6 cm and a wide of 4 cm. 2. A square table cloth has a side of 5 m. What are its perimeter and area? m. 3. The area of a rectangular fence is 500 square feet. If the width of the fence is 20 feet, then find its length. What is its perimeter? 4.

  16. The 3 Step Method to Teaching Word Problems

    by Jennifer Van Blair | Sep 30, 2022 | Math Word problems are difficult. Most adults surveyed can recall struggling with word problems in school, some even saying that they STILL struggle with word problems. That's why I developed this 3 step method for teaching word problems.

  17. Apply a Problem-Solving Strategy to Basic Word Problems

    Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers. Write the equation. 18= 1 2p 18 = 1 2 p. Multiply both sides by 2. 2⋅18=2⋅ 1 2p 2 ⋅ 18 = 2 ⋅ 1 2 p. Simplify. 36=p 36 = p. Step 6. Check the answer in the problem and make sure it makes sense.

  18. Understanding Word Problems in Mathematics

    The first Common Core State Standard (CCSS) for mathematical practice focuses specifically on problem solving: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Proficient students are able to explain the meaning of a problem and look for entry points to its solution. They are able to analyze givens, constraints ...

  19. Solved Learning Task 4: Solve the following word problems ...

    Final answer. Learning Task 4: Solve the following word problems. 1. Mr. Pablo bought a residential lot. The lot is in the shape of a trapezold as shown in the lustration. What is the area of the lots 12 m 10 m 20 m 2. Maria Alyn bought a lot in a parallelogram shape. Ils bases 24 meters and its height is 16 meters.

  20. Learning Task 3. Answer the following word problems. 1. It took Jose

    1. It took Jose two-thirds of an hour to complete his - Brainly.ph devillajohnrico 21.09.2021 Math Senior High School verified answered • expert verified Learning Task 3. Answer the following word problems. 1.

  21. Solved Learning Task 3 Solve the following problems. 1. A

    Question: Learning Task 3 Solve the following problems. 1. A die is rolled once. Find the probability that a) the number is even or a multiple of 3; b) the number is a multiple of 2 or multiple of 3; c) the number is an odd number or a multiple of 2. 2. A card is drawn at random from a deck of 52 playing cards.

  22. Learning Task 3: Solve the following problems. Show the four steps

    Word Problems The four steps in solving word problems include understand, plan, solve, and check and look back. Let us now answer the word problems using these steps. 1. Understand Asked: The number of labels that Mr. Villa can make. Given: 91.25 inches and 1.25 inches Plan Operation: Division Solve 73 125 √9125 - 875 375 - 375 0 Check and ...

  23. Learning Task 3: Solve the following problems. Write your ...

    Answer 8 people found it helpful shahanabarretto report flag outlined Word Problems 1. What is the quotient if 24 is divided by 48? Solution Divide 24 by 48. 24 \div 48 = 0.524÷48=0.5 Answer