Example : Algebra Word Problems
Linda was selling tickets for the school play. She sold 10 more adult tickets than childrentickets and she sold twice as many senior tickets as children tickets.
As you can see, this problem is massive! There are 5 questions to answer with many expressions to write.
Physical Measurement Word Problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade
72. Comparing Measurements: Cassandras ruler is 22 centimetres long. Aprils ruler is 30 centimetres long. How many centimetres longer is Aprils ruler?
73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?
74. Adding Measurements: Michas dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Michas dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?
75. Subtracting Measurements: Michas dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Michas dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?
76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?
77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?
78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?
How To Do Algebra Word Problems
When you take a real-world situation and translate it into math, you are actually ‘expressing’ it hence the mathematical term ‘expression’. Everything that is left of the equal sign is considered to be something you are expressing. Everything to the right of the equal sign is yet another expression. Simply stated, an expression is a combination of numbers, variables and operations. Expressions have a numerical value. Equations are sometimes confused with expressions. To keep these two terms separate, simply ask yourself if you can answer with a true/false. If so, you have an equation, not an expression that would have a numerical value. When simplifying equations, one often drops expressions such as 7-7 that equal 0.
A few samples:
|y – 12|
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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!
Mixed Operations Word Problems
Best for: 3rd grade, 4th grade, 5th grade
27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?
28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?
30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?
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Determine The Operation For The Situation
Instead of key words, have kids really analyze the situation presented to determine the right operation to use. Some key words, like total, can be pretty vague. Its 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.
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Underline Anything That Will Be Important For Setting Up The Algebra Equations Or Solving The Word Problem
When you have read through the entire word problem, you will want to go back through and underline anything important. This might include the keywords youve just found and any variables, as well as what your solution needs to be, so that you can set up the proper algebra equations.
When you underline or highlight these important parts, you can quickly reference the things you need to without having to read through the entire problem again. This makes it easier to go back and double check that youve got the right equations and variables set up, without losing your train of thought halfway through solving the algebra word problem.
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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 .
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.
Its 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 Thats When It Gets Especially Tricky
The simple addition of those words ramps up the difficulty 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.
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Real World Problems: How To Write Equations Based On Algebra Word Problems
I know that you often sit in class and wonder, “Why am I forced to learn about equations, Algebra and variables?”
But… trust me, there are real situations where you will use your knowledge of Algebra and solving equations to solve a problem that is not school related. And… if you can’t, you’re going to wish that you remembered how.
It might be a time when you are trying to figure out how much you should get paid for a job, or even more important, if you were paid enough for a job that you’ve done. It could also be a time when you are trying to figure out if you were over charged for a bill.
This is important stuff – when it comes time to spend YOUR money – you are going to want to make sure that you are getting paid enough and not spending more than you have to.
Ok… let’s put all this newly learned knowledge to work.
There are a few rules to remember when writing Algebra equations:
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 its outdated, and prefer to teach word problems using context and situations instead . You might just consider this one more trick to keep in your toolbox for students who need it.
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How To Easily Make Your Own Math Word Problems & Word Problems Worksheets
Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:
- Link to Student Interests: By framing your word problems with student interests, youll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a questions characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a questions key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests — such as football and basketball — can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction, word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.
Ordering And Number Sense Word Problems
Best for:2nd grade, 3rd grade
31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
33. Composing Numbers: What number is 6 tens and 10 ones?
34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?
35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?
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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 theyll get comfortable with the process.
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Math Word Problems To Challenge Students Grades 1 To 8
- Teaching Tools
You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.
A jolt of creativity would help. But it doesnt come.
Whether youre a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.
This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.
There are 120 examples in total. Helping you sort through them to find questions for your students, the resource is categorized by the following skills with some inter-topic overlap:
The list of examples is supplemented by tips to create engaging and challenging math word problems.
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Grade 9 Algebra Word Problems
These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions? Includes various examples and solutions for algebra word problems that you will commonly encounter in grade 9.
Age Problems with two unknowns or variables
Example:Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?
Solution:Let x represent Spensers ageTherefore, Taylors age is 5xx + 5x = 18
Grade 9 Algebra Word Problems – Age
Example 1:A mother is three times as old as her daughter. Six years ago, the mothers age was six tines that of her daughter. How old are they now?
Solution:Let x represent the daughters age.Therefore, 3x is the mothers age.6 = 3x – 6Therefore, the daughters is 10 years old and the mother is 30 years old.
Example 2:A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?
Grade 9 Algebra Word Problems – Rate, Distance, Time
Example:A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?
Grade 9 Rate, Distance, Time Word Problems
Example 1:One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?
Look For Keywords In The Algebra Word Problems That Can Signal Which Operation You Will Be Doing
These keywords can go a long way in helping you determine how to set up the algebra equations. Heres a list of some common keywords to get you started:
- Addition: added to, combined, increased by, more than, sum, total
- Subtraction: decreased by, difference of, less than
- Multiplication: increased by a factor of, multiplied by, times
- Division: out of, per, ratio of
- Equals: are, gives, is, will be
Note that these keywords are not a complete list you will definitely see other words used to mean these operations, but keep in mind how the numbers and variables are positioned and what is being asked, and you should be able to add to this keyword list yourself!
Also, be sure to pay close attention to the relationship of the two variables when it comes to division and subtraction. It matters which variable comes first, and when the algebra word problem asks for the difference between x and y, when you write the algebra out, you will show x y. Likewise, the ratio of x and y written out will show x / y.
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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 . There are lots of ways to do this, but heres what I like to do:
- Circle any numbers youll use.
- Lightly cross out any information you dont need.
- Underline the phrase or sentence which tells exactly what youll need to find.
Comparing And Sequencing Word Problems
Best for: Kindergarten, 1st grade, 2nd grade
53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?
54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?
55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?
56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?
57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?
58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?
59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?
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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.
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.
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What Are Word Problems
A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you’ve ever taken a math class, you’ve probably solved a word problem. For instance, does this sound familiar?
Johnny has 12 apples. If he gives four to Susie, how many will he have left?
You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you’re supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:
12 – 4
12 – 4 = 8, so you know Johnny has 8 apples left.