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Teaching math problem solving strategies, teaching math problem solving strategies in middle school.
There are many math problem solving strategies out there and some are very beneficial to upper elementary and middle school math students. Before we jump into them, I’ll share a little bit of my experiences in teaching math problem solving strategies over the past 25+ years.
During my second year of teaching ( in the early 90s) , I was teaching 5th grade, and our state math testing began to include a greater focus on problem solving and writing in math.
Over the next several years, the other math teachers and I used standard sentence starters to help math students practice explaining their problem solving process. These were starters like:
- “In this problem, I need to….”
- “From the problem, I know….”
- “I already know…”
- “To solve the problem, I will…”
- “I know my answer is correct because…”
Benefits of Sentence Starters
By using these sentence starters, students ended up with several paragraphs (some short, some long) to explain how they approached and solved the math problem, AND how they knew they were correct .
Sometimes this process took quite a long time, but it was helpful, because:
- It made many students slow down and think a bit more about what they were doing mathematically.
- Students took a little more time to analyze the problem (rather than picking out the numbers and guessing at an operation!).
I was teaching 5th grade in elementary school at this time, and we had a full hour for math every day. So, fitting in problem solving practice a few times a week was pretty easy, after students understood the process.
I really liked spending the time on these types of math problems, because they often led to discussion of other math concepts, and they reinforced concepts already learned. I used math problems from a publication that focused on various strategies, like:
- Guess and Check
- Work Backwards
- Draw a Picture
- Use Logical Reasoning
- Create a Table
- Look for a Pattern
- Make an Organized List.
I LOVED these…I really did (do)! And the students I taught during those years became very good at reasoning and solving problems.
Teaching Math Problem Solving in Middle School
When I moved to 6th grade math in middle school, I tried to keep teaching these strategies, but our math periods are only 44 minutes.
- I tried to use the problem solving as warm-ups some days, but it would often take 30 minutes or more, especially if we got into a good discussion, leaving little time for a lesson.
- I found that spending too many class periods using the problem solving ended up putting me too far behind in the curriculum (although I’d argue that my students became better thinkers:-), so I had to make some alterations.
- highlight/underline the question in the problem
- shorten up the writing to bullet points
- highlight/underline the important information in the problem
Math Problem Solving Steps
Now, when I teach these problem solving strategies, our steps are: Find Out, Choose a Strategy, Solve, and Check Your Answer.
Find Out When they Find Out, students identify what they need to know to solve the problem.
- They underline the question the problem is asking them to answer and highlight the important information in the problem.
- They shouldn’t attempt to highlight anything until they’ve identified what question they are answering – only then can they decide what is important to that question.
- In this step, they also identify their own background knowledge about the concepts in that particular math problem.
Choose a Strategy This step requires students to think about what strategy will work well with the question they’ve been asked. Sometimes this is tough, so I give them some suggestions for when to use these particular strategies:
- Make an Organized List: when there are many possible answers/combinations; or when making a list may help identify a pattern.
- Guess and Check: when you can make an educated guess and then use an incorrect guess to help you decide if the next guess should be higher or lower. This is often used when you’re looking for 2 unknown numbers that meet certain requirements.
- Work Backwards: when you have the answer to a problem or situation, but the “starting” number is missing
- when data needs to be organized
- with ratios (ratio tables)
- when using the coordinate plane
- with directional questions
- with shape-related questions (area, perimeter, surface area, volume)
- or when it’s just hard to picture in your mind
- Find a Pattern: when numbers in a problem continue to increase, decrease or both
- when the missing number(s) can be expressed in terms of the same variable
- when the information can be used in a known formula (like area, perimeter, surface area, volume, percent)
- when a “yes” for one answer means “no” for another
- the process of elimination can be used
Solve Students use their chosen strategy to find the solution.
Check Your Answer I’ve found that many students think “check your answer” means to make sure they have an answer (especially when taking a test), so we practice several strategies for checking:
- Reread the question; make sure your solution answers the question.
- Redo the math problem and see if you get the same answer.
- Check with a different method, if possible.
- If you used an equation, substitute your answer into the equation.
- Ask – does your answer make sense/is it reasonable?
Teaching the Math Problem Solving Strategies
- Students keep reference sheets in their binders, so they can quickly refer to the steps and strategies. A few newer reference math wheels can be found in this blog post .
- For example, I often find that a ‘Guess and Check’ problem can be solved algebraically, so we’ll do the guessing and checking together first, and then we’ll talk about an algebraic equation – some students can follow the line of thinking well, and will try it on their own the next time; for others, the examples are exposure, and they’ll need to see several more examples before they give it a try.
Using Doodle Notes to Teach Problem Solving Strategies
This year, I’m trying something new – I created a set of Doodle Notes to use during our unit.
- The first page is a summary of the steps and possible strategies.
- There’s a separate page for each strategy, with a problem to work through AND an independent practice page for each
- There’s also a blank template, so I can create problem solving homework for students throughout the year, using the same format. I’m hoping that using the Doodle Notes format will make the problem solving strategies a little more fun, interesting, and easy to remember.
This was a long post about teaching math problem solving strategies! Thanks for sticking with me to the end!
ELA Review Game: Unveiling the Power of Truth or Dare
Grammar Instruction: the Potential of ELA Wheels / Doodle Notes
Figurative Language Doodle Wheels: Unlocking Literary Magic
Connecting Math Skills Through the Magic of Cross-Disciplinary Learning
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October 16, 2019
There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.
1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.
Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.
Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?
2. Guess and check
Teach students the same strategy research mathematicians use.
With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly. By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.
Find two numbers that have sum 11 and product 24.
Try/guess 5 and 6 the product is 30 too high
adjust to 4 and 7 with product 28 still high
adjust again 3 and 8 product 24
3. Make a table or a list
Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.
To make sure you are listing all the information correctly read the problem carefully.
Find the common factors of 24, 30 and 18
Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.
Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?
A table or list is useful in solving logic problems.
Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.
Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.
Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.
5. Find a pattern.
Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.
The “rule” can then be used to find the answer to the question and complete the table/list.
Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?
6. Working backward
Problems that can be solved with this strategy are the ones that list a series of events or a sequence of steps .
In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.
Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.
For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.
The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.
8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took
8+31+5+4= 48 Answer: The box came with 48 pieces of candy.
Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.
Print and digital activities
I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.
How to use the activity cards
Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.
Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.
For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.
Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.
Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions
There are 2 versions of the resource
70 google slides with explanations + 70 printable task cards
70 google slides with explanations + 11 worksheets
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Strategies for Solving Word Problems – Math
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:
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:
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:
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:
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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Maneuvering the Middle
Student-Centered Math Lessons
Math Problem Solving Strategies
How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem? For me, the answer is too many to count. Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for . There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!
C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.
- Why I like it: Gives students a very specific ‘what to do.’
- Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem. None of the steps emphasize reading the problem but maybe that is a given.
R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence.
- Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence. This is a great strategy to teach when you are tackling various types of problems.
- Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.
3. U.P.S. CHECK
U.P.S. Check stands for understand, plan, solve, and check.
- Why I like it: I love that there is a check step in this problem solving strategy. Students having to defend the reasonableness of their answer is essential for students’ number sense.
- Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.
4. Maneuvering the Middle Strategy AKA K.N.O.W.S.
Here is the strategy that I adopted a few years ago. It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)
UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!
- Know: This will help students find the important information.
- Need to Know: This will force students to reread the question and write down what they are trying to solve for.
- Organize: I think this would be a great place for teachers to emphasize drawing a model or picture.
- Work: Students show their calculations here.
- Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.
Ideas for Promoting Showing Your Work
- White boards are a helpful resource that make (extra) writing engaging!
- Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
- Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.
Show Work Digitally
Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work.
If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more.
Students who plan succeed at a higher rate than students who do not plan. Do you have a go to problem solving strategy that you teach your students?
Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.
Problem Solving Posters (Represent It! Bulletin Board)
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October 4, 2017 at 7:55 pm
As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!
October 4, 2017 at 8:59 pm
Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!
December 15, 2017 at 7:57 am
Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:
1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.
This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.
October 5, 2017 at 6:27 am
Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)
I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….
October 5, 2017 at 9:46 am
Great idea! Thanks so much for sharing with our readers!
October 8, 2017 at 6:51 pm
LOVE this idea! Will definitely use it this year! Thank you!
December 18, 2019 at 7:48 am
I would love an anchor chart for RUBY
October 15, 2017 at 11:05 am
I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.
April 20, 2018 at 7:36 am
I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.
June 22, 2018 at 12:19 pm
That’s brilliant! Thank you for sharing!
May 31, 2018 at 12:15 pm
Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?
June 22, 2018 at 10:46 am
Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.
July 28, 2018 at 6:53 pm
I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.
February 3, 2019 at 3:56 pm
This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.
March 7, 2019 at 6:59 am
Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution
September 2, 2019 at 11:18 am
Going off of your idea, Natalie, how about the following?
K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)
I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.
March 16, 2020 at 4:44 pm
I’m doing this one. Love it. Thank you!!
September 17, 2019 at 7:14 am
Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.
I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!
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14 Effective Ways to Help Your Students Conquer Math Word Problems
If a train leaving Minneapolis is traveling at 87 miles an hour…
Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.
1. Solve word problems regularly
This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.
Learn more: Teaching With Jennifer Findlay
2. Teach problem-solving routines
There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.
Learn more: Word Problems Made Easy
3. Visualize or model the problem
Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.
Learn more: Math Geek Mama
4. Make sure they identify the actual question
Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed.
Learn more: Robert Kaplinsky
5. Remove the numbers
It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking.
Learn more: Where the Magic Happens Teaching
6. Try the CUBES method
This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.
Learn more: Teaching With a Mountain View
7. Show word problems the LOVE
Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use.
8. Consider teaching word problem key words
This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.
Learn more: Book Units Teacher
9. Determine the operation for the situation
Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.
Learn more: Solving Word Problems With Jennifer Findlay
10. Differentiate word problems to build skills
Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.
Learn more: Differentiating Math
11. Ensure they can justify their answers
One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.
Learn more: Madly Learning
12. Write the answer in a sentence
When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.
Learn more: Multi-Step Word Problems
13. Add rigor to your word problems
A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.
Learn more: The Routty Math Teacher and Alyssa Teaches
14. Use a problem-solving rounds activity.
Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.
Learn more: Teacher Trap
Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .
Plus, 60+ Awesome Websites For Teaching and Learning Math .
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35 Math Questions For 5th Graders: Answers With Worked Examples
In 5th grade math, the toughest questions are often the reasoning questions. In this article, we’ve put together a collection of math questions for 5th graders, organized by the different kinds of reasoning questions that students may encounter on standardized tests and beyond.
Why Focus On Math Reasoning Questions?
Most fifth graders find reasoning questions to be the most difficult. Unsurprisingly, we teach thousands of students in the weeks leading up to standardized tests. Teaching them math reasoning skills at the elementary level is a big part of what we do here at Third Space Learning.
We even recently made the decision to restructure our elementary lessons to introduce math reasoning questions earlier in their learning journey as the difficulty level was just too high at the end of the lesson. We definitely feel fifth grade teachers’ pain!
Whatever level your students are currently achieving in math, math reasoning questions will appear from elementary to high school, so it is an essential skill for the future.
If you find you have children in your class with a lot more catching up to do than others, then we may be able to support them with some personalized one-on-one tutoring if you get in touch.
Common Core Practice Test Grade 5
Want more math questions for 5th graders? Try our Grade 5 practice assessment for Common Core or state equivalents, including 40 questions covering a range of topics.
35 Math Questions For 5th Graders
There are 7 types of math reasoning questions that fifth graders are likely to encounter:
For each of these types we’ll examine an example problem, looking at the question, the correct answer, and how to go about answering this problem.
We’ll also look at further examples of each type of math reasoning question and answer, again with worked examples and an explanation of how to answer each.
Our aim is to provide you with a sample of the types of math reasoning questions and how to teach the reasoning and problem solving skills they’ll need to solve them.
For more word problems like this, check out our collection of 2-step and multi-step word problems . For advice on how to teach children to solve problems like this, check out these math problem solving strategies.
Math Question Type 1: Single step word problems
The simplest type of reasoning question students are likely to encounter, single step problems are exactly that: students are asked to interpret a written question and carry out a single mathematical step to solve it.
Take a look at the question below:
Reasoning Question 1
A relatively easy question to interpret–the first step will be to rewrite the amounts given so that they can properly line up the place values in order to solve. From here the simple mathematical step is subtraction i.e. $2.00 – $1.35 = 0.65.
The most crucial skill for grade schoolers in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.
Below are several more examples:
Reasoning Question 2
Answer : 7 hours 24 minutes
Students need to understand that one hour is equal to 60 minutes. From here the single mathematical step is division: 444/60, to find a whole number answer with a remainder.
Reasoning Question 3
Answer : 48 cm 3
Students must multiply length by width by height, using the amounts provided by the question.
Reasoning Question 4
Answer : 1,488 cubic cm
A simple enough calculation (multiplying) if students are aware that the volume of a rectangular prism can be found by multiplying the area of the base by the height.
Reasoning Question 5
Answer : 7,590
A single, relatively simple rounding problem – students should recognize that ’94’ is the place they should focus on for this problem.
Math Question Type 2: Multiple step worded problems
A more complex version of the single step word problem, multi-step problems require students to interpret a written problem, but solving it then requires the use of two or three math skills.
For example, consider this question below:
This question encompasses three different math skills: multiplying (and dividing) decimals, addition and subtraction. Students can choose to work out the multiplication or division first, but must complete both before moving on.
Once these values have been worked out the next steps are relatively simple – adding the two values together, and subtracting the total from $5.
Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of math language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.
Answer : $5,520
There are two steps to this problem, but both are multiplication. The first is to work out how much money is made per day – 92 x $15. This product is then multiplied by 4 – the number of days – to get to the answer.
Answer : 1360 miles
Another two step problem. The first step is to work out 4 of 3,400 miles. Then divide this by 10 to solve for 4/10 of 3,400.
Answer : $153
There are four steps involved in solving this problem: multiplication (doubling $51), division (dividing $51 in half), multiplication again (doubling half of $51–which some students may recognize those last two steps were unnecessary as that brings us back to $51), and addition (putting the two costs together).
Given the number of steps involved it can be easy for students to make arithmetic mistakes.
Answer : 11.45 lbs
A two-step problem again: multiplying 3.45 lbs by 4, then subtracting 2.35 lbs from the total.
Math Question Type 3: Problems involving measurements
As their name suggests, these questions ask students to solve a problem that includes one or more units of measurement.
Answer: 40 washes
This is a two step problem; students must first be able to read and convert kilograms to grams (and therefore know the relationship and conversions between the two units- 1,000 grams to 1 kilogram), multiply 2.6 by 1,000 which equals 2,600, then divide 2,600 by 65. The quotient is the number of washes possible.
Answer : 50g
A relatively simple division problem, relying on students having knowledge that 200g is one fifth of a kilogram.
Answer : 5.12 miles
Another three step problem, and this requires students to subtract and divide decimals – subtracting 12.63 miles from the total amount, taking the difference, 13.91, and subtracting 3.67 miles, and then dividing that difference, 10.24, in half to obtain the distance the other two friends ran.
Answer : 84 inches/7 foot
To find 8 feet in inches, students must multiply 8 by 12. This gives the answer 96 inches. Students must then divide 96 by 40 to find the height of one box: 2.4 inches. Multiply 2.4 by 5 and minus this from the original 96 inch tower.
Interesting to note that the units for the answer may or may not be specified – an answer given in inches or feet will be accepted, however sometimes the unit will be specified in the answer box. This is why we encourage students to keep an eye on whether units are provided in the answer box.
Answer : 0.05 lbs
As with the running question there are three steps involved to solve this problem: subtracting the heaviest car from the total amount (3.85 – 1), figuring out the weight of the remaining three cars (2.85/3) and subtracting 0.95 from 1 to get the remaining amount of 0.05 lbs.
Question Type 4: Problems involving drawing
Problems involving drawing require students to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling.
Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.
This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.
A lot of work for a single point!
Some further examples:
Answer : Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.
Answer : An accurately drawn angle.
This question demands students to have an understanding of and ability to accurately use a protractor. Often, a mark scheme allows some room for error – “between 34 and 36 degrees” is acceptable.
As with the question above, a small amount of room for error is given as it acceptable to be between 139 and 141 degrees.
Answer : Points drawn at (2,1), (5,1) and (2,4).
Math Question Type 5: Explanation questions
These problems ask children to explain a mathematical statement or error.
As an example:
Answer: If the distance from P to R is 800 yards and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640 yards. Therefore Olivia is wrong.
More than most problems, this type requires students to actively demonstrate their reasoning skills as well as their mathematical ones. Here students must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.
Further examples below:
Answer : No; 20/100 is the same as 20 divided by 100, which equals 0.2
Answer : No; multiplication and division have the same priority in the order of operations, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.
Answer : No
Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0,” “Not if the number is less than 1” etc.
Answer : Any answer that refers to the fact that there is a 5 in the hundredths place, AND a 9 in the thousandths place, so that the number has to be rounded up as far as the ten-thousands place.
Math Question Type 6: Sequence questions
Another relatively simple kind of reasoning question, sequence problems involve students completing mathematical sequences.
Consider this example:
Answer: 35 , 42, 49, 56 , 63, 70
The question’s instructions point clearly to the solution: figure out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.
Higher achieving students might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer – this should be encouraged so long as they then check their answer in the normal method to ensure they haven’t made a mistake.
Answer(s) : 5/8 and 2 1/8 (OR 17/8)
Both answers must be correct to receive the point. Students must recognize that 3/4 is the same as 6/8, so that the following number must be three eighths higher. They then must be able to add and subtract fractions to obtain the answers.
Answer(s) : 4.2 and 7
Answer(s) : 128, 135 and 156.
Answer(s) : 0 and 24
This number line question can be a little tricky; students need to figure out that the marks on the line represent increments of 1½, and count backwards and forwards in 1½’s to obtain the missing numbers.
Math Question Type 7: Ordering questions
A slightly more complex variation of the sequence question, ordering problems require students to put a set of numbers, fractions or measures in the correct order.
A good example is this fifth grade math question below:
Answer: 3/5, 3/4, 6/5
This question throws a wrench in things by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers, decimal numbers, and fractions all mixed into one problem.
A good knowledge of the fundamentals of fractions is essential here: students must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.
Answer : D,C,A,B
Encourage students to convert all the fractions to one denominator value to make ordering easier.
Answer : (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th
Students could use many strategies to solve this problem. The most time consuming would be to rewrite all the fractions with a common denominator. More efficient strategies would include reasoning about the size of the fractions in comparison to ½ or 1. For instance, a student may notice that ⅜ is the only fraction less than ½, putting Ben in 5th place. 4/8 is exactly ½ whereas the others are greater than ½, putting Michael in 4th place. Then the student may recognize that 10/12 is closer to 1 than ¾, completing the rest of the table.
Answer : C, B, D, A
Answer : D, A, C, B
7 Top Tips For Answering 5th Grade Math Reasoning Questions
Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in standardized tests. They may not all be applicable to every single question, but will apply to at least two, usually more.
- Get students in the habit of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
- Ask students to ‘spot the math’ in a question – which operations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
- Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so students should work to give their answer in that unit.
- In a similar vein, remind students to convert different units of measurement in a question into the same unit to make calculations easier e.g. lbs to oz.
- Encourage numerical answers where possible. Even in explanation questions demonstrating the mathematical equation is a better explanation than trying to write it out.
- The bar model can be a useful way of visualizing many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
- Check your work! Even if the work is ultimately irrelevant to the question, you can lose points if it is wrong.
Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade – 3rd grade – 4th grade – 5th grade – 6th grade Why not learn more about how it works ?
The content in this article was originally written by Anantha Anilkumar at Third Space Learning and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.
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Math and Special Education Blog
8 problem solving strategies for the math classroom.
Posted by Colleen Uscianowski · February 25, 2014
Would you draw a picture, make a list possible number pairs that have the ratio 5:3, or guess and check?
Explicit strategy instruction should be an integral part of your math classroom, whether you're teaching kindergarten or 12th grade.
Teach students that they can choose from a list of strategies to solve a problem, and often there isn't one correct way of finding a solution.
Demonstrate how you solve a word problem by thinking aloud as you choose and execute a strategy.
Ask students if they would solve the problem differently and praise students for coming up with unique ways of arriving at an answer.
Here are some problem-solving strategies I've taught my students:
Below is a helpful chart to remind students of the many problem-solving strategies they can use when solving word problems. This useful handout is a great addition to students' strategy binders, math notebooks, or math journals.
How do you teach problem-solving in your classroom? Feel free to share advice and tips below!