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More Lessons for Grade 1
Common Core for Grade 1
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Common Core: 1.OA.1 and 1.OA.2
Suggested Learning Target
- I can model addition and subtraction word problems using objects, drawings, and equations with unknown numbers in different positions.
- I can solve addition and subtraction word problems using objects, drawings, and equations.
- I can solve word problems with unknown numbers in different positions (e.g., 6 + ? = 8, ? + 2 = 8, 6 + 2 = ?).
- I can represent a problem in multiple ways including drawings and or objects/manipulatives (e.g., counters, unifix cubes, Digi-Blocks, number lines)
- I can take apart and combine numbers in a wide variety of ways
- I can make sense of quantity and be able to compare numbers
- I can use flexible thinking strategies to develop the understanding of the traditional algorithms and their processes
- I can solve a variety of addition and subtraction word problems
- I can use _ or ? to represent an unknown in an equation
- I can model addition and subtraction word problems using objects, drawings, and equations with unknown numbers in different positions.
- I can add three whole numbers whose sum is less than or equal to 20.
- I can solve word problems with three whole numbers using objects, drawings, and equations.
- I can add numbers in any order and be able to identify the most efficient way to solve the problem
Addition Examples:
Result Unknown
Two bunnies sat on the grass. Three more bunnies hopped there.
How many bunnies are on the grass now?
2 + 3 = ?
Change Unknown
Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first?
2 + ? = 5
Start Unknown
Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?
? + 3 = 5
Subtraction Examples:
Result Unknown
Five apples were on the table. I ate two apples.
How many apples are on the table now?
5 – 2 = ?
Change Unknown
Five apples were on the table. I ate some apples. Then there were three apples.
How many apples did I eat?
5 – ? = 3
Start Unknown
Some apples were on the table. I ate two apples. Then there were three apples.
How many apples were on the table before?
? – 2 = 3
Word Problems. Addition with pictures (up to sum 20)
Example:
Lily had 5 apples and her aunt gave her 9 apples later. How many apples did Lily have finally?
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Subtraction by counting back — word problems with pictures
Example:
There are 5 books on the desk. Betty took 2 away. How many books are left on the desk?
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Word problems — subtraction with pictures — cross out — 1 digit
Example:
There are 9 cars in the shop and 8 of them are sold. How many cars are left?
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Word problems — Subtraction with pictures — cross out (numbers to 20)
Example:
Mary had 11 toys and she gave 5 of them to Emma. How many toys did Mary have finally?
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Word problems — adding multiple one-digit numbers
Example:
A furniture store sold 6 tables, 2 bookcases and 1 bed. How many pieces of furniture did the store sell in all?
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Addition word problems that add up multiple values to sums less than or equal to ten.
Example:
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Laurem gave Troy two yellow pencils, three blue pencils and one green pencil. How many pencils did Lauren give him in all?
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Ms. Ellis gave Lauren and Troy some cookies. Lauren ate two sugar and two chocolate chip cookies. Troy ate three oatmeal raisin and two sugar cookies. How many cookies did they eat in all?
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Subtraction Strategies
This video gives suggestions for solving subtraction story problems using a math mountain, equation, and circle drawing.
Example:
I have 8 peanuts. Then I eat 5 of them. How many peanuts are left?
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In today’s post, we are going to see a selection of Second Grade word problems that usually appear at the end of a Smartick session for children with a second-grade level. You will also get a chance to see the solution for each problem.
Ready? Let’s go!
How To Correctly Solve Any Problem
- Read the word problem carefully! You should understand what is being asked very clearly.
- Write down the data.
- Complete the operations and always write down the results for each.
- Write the solution very clearly and respond to what the problem asks.
Second Grade Word Problems
Let’s practice with a selection of Second Grade word problems from Smartick.
Word Problem 1
Solution 1
For this word problem, Smartick has given us the solution and it is up to us to select the correct question.
The answer is: ”They were planting 38 chestnut seeds.” Let’s take a look at each option to see which would work with this answer, we’ll use the process of elimination.
- How many more chestnut seeds than oak seeds were they planting? This is asking us about the different types of seeds, but the solution is only asking about chestnuts so this question is not what we are looking for.
- Are fewer chestnut trees or fewer oak trees expected to grow? This answer isn’t the one we are looking for because the answer only gives us information about chestnut seeds.
- How many more poplar seeds than oak seeds were they planting? Nothing was mentioned in the word problem or the answer about poplar trees.
- How many chestnut seeds were they planting? Here were are being asked about the number of chestnut seeds that were planted and the solution tells us the amount that was planted. This is the question that we are looking for.
Word Problem 2
Solution 2
This word problem is asking how many tablespoons of oil have been added to a stew, and we know that there were 20 tablespoons more added than the 9 tablespoons that the recipe called for. So we need to know how many tablespoons in total were added to the stew.
9 + 20 = 29
29 tablespoons of oil were added to the stew.
Word Problem 3
Solution 3
Here, we are being asked to calculate the total number of clocks. To help us solve it, we can create a drawing using the information from the word problem. It tells us that there are 2 clocks on each shelf, and there are 6 shelves.
Word Problem 4
Solution 4
First, we are asked which operation we need to use to solve the problem and are provided with the options of addition and subtraction. Let’s read the word problem carefully to see which would work best…
There were 6 oranges before Diego added more, and now there are 10. Therefore, the difference between the amount in the bowl now, and the amount there was before, is the amount that Diego added. If we add the numbers, adding the larger quantity to the lesser quantity, it does not give us the number of oranges Diego added to the bowl. However, if we subtract the smaller quantity from the larger quantity, we should find the difference.
The answer to the first question would be: 10 – 6.
And the solution to the word problem: 10 – 6 = 4.
Diego added 4 oranges.
I hope you have learned something new from this selection of second grade word problems that appear during our daily Smartick sessions. If you would like to learn more about other primary school math topics, register with Smartick and try it for free.
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A Picture is Worth a Thousand Words
“Today, we are going to solve math word problems.” When students hear this from their math teacher, their faces drop, sweat starts to form on their foreheads and they refuse to make eye contact. As a math teacher, I understand. I understand the anxiety and want to make the learning process with word problems more enjoyable. This is where reading, writing and, math collide and the real world of math begins. Let’s talk about how to solve word problems with pictures.
When students struggle with word problems in school, they also have difficulty tackling them for homework. Most students want the “one-size-fits-all” formula for word problems but unfortunately, that does not exist. However, drawing a picture will help students visualize the problem and will start advancing their learning stage from the concrete to the abstract. Let’s take a look at how to solve a word problem using pictures:
Steps for Solving Word Problems using Pictures
- Read the entire problem: Get all the facts – Underline key word
- Answer the question: What am I looking for?
- Draw a picture or diagram: Visualize as a real world situation
- Solve the problem: Set up the equation and solve
- Check your solution: Is this answer reasonable?
Word Problem Examples – Example A
Cody has 6 pencils on his desk, Jonah has 4 more than Cody and Vinny has three less pencils than Jonah. How many pencils are there in all?
- Read the entire problem √
- What am I looking for? How many pencils do Cody, Jonah and Vinny have altogether? √
- Draw a picture or diagram √
- Solve the problem √
6 + 10 + 7 = 23 pencils
- Check your solution √
This answer is reasonable
Example B
There are 3 fish tanks labeled X, Y, and Z. Y weighs 6 times as much as X and twice as much as Z. If Z is 36 lbs. heavier than X, find the total weight of X, Y and Z.
- Read the entire problem √
- What am I looking for? What is thetotal weight of fish tanks X, Y and Z? √
- Draw a picture or diagram √
- Solve the problem √
18 + 108 + 54 = 180 pounds
- Check your solution √
This answer is reasonable
Visualizing a word problem with pictures is a strategy that will help motivate many students to begin the process of solving them. This works especially for students that may become bored by the excess amount of words instead of numbers or for those students who become overwhelmed by the information and want to break it down into a simpler form. Another benefit of using pictures when solving word problems involves communicating the results. The pictures act as justification for answers, make the problems easier to understand and therefore, secure the learning process.
Meet our Guest Blogger: Jan Rowe
Jan is one of Educational Connections’ top tutors. She has twelve years of classroom teaching experience and holds a Virginia and Florida teaching license in middle school mathematics and elementary education. Jan has been with Educational Connections for over a year, working with over twenty students. Her tutoring goal is to help each student understand their learning style so they can improve the speed and quality of that learning. When she is not tutoring or teaching, Jan loves to play scrabble, go hiking and play Frisbee with her new puppy.
What’s the first thing that comes to mind when you hear the phrase Word problems?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
For some, it’s a chance to solve a real-world example, so there’s a level of excitement and sense of wonder. For others, it’s groaning, and frustration on where to even begin.
Well, in this lesson we’re going to make Solving Linear Equation Word Problems manageable with easy to follow tricks and steps.
We already know how to solve all different types of equations. Yay!
And we also know how to translate algebraic expressions and equations. Double Yay!
Now it’s time to bring both of these together.
Solving equations and word problems Example
But, what about the tricks and steps?
Yes, there are some easy to follow steps that we are going to use to solve linear word problems.
- Read the problem carefully and determine what is being asked.
- Create a sidebar! Using different colors, symbols and diagrams and write an equation the relates all the information given.
- Solve your equation and check your answer(s).
Now, these steps might not seem all that remarkable, but once you see them in action I guarantee that writing equations from word problems and solving them will become like second nature!
Again, the secret to success is your Sidebar. This is where you will write down all the information you’ve gleaned from the problem, and formulate a solution by writing an equation to model the situation, as Khan Academy accurately states.
Together we will walk through 9 examples in detail ranging from finding consecutive integers to finding hourly wages, profit and cost, distances for rectangles and triangles, and people’s ages.
Linear Word Problems (How-To) – Video
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You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don’t know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.
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1
Read the problem carefully.[1]
A common setback when trying to solve algebra word problems is assuming what the question is asking before you read the entire problem. In order to be successful in solving a word problem, you need to read the whole problem in order to assess what information is provided, and what information is missing.[2]
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2
Determine what you are asked to find. In many problems, what you are asked to find is presented in the last sentence. This is not always true, however, so you need to read the entire problem carefully.[3]
Write down what you need to find, or else underline it in the problem, so that you do not forget what your final answer means.[4]
In an algebra word problem, you will likely be asked to find a certain value, or you may be asked to find an equation that represents a value.- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.
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3
Summarize what you know, and what you need to know. Likely, the information you need to know is the same as what information you are asked to find. You also need to assess what information you already know. Again, underline or write out this information, so you can keep track of all the parts of the problem. For problems involving geometry, it is often helpful to draw a sketch at this point.[5]
- For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don’t know the price of the first book.
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4
Assign variables to the unknown quantities. If you are being asked to find a certain value, you will likely only have one variable. If, however, you are asked to find an equation, you will likely have multiple variables. No matter how many variables you have, you should list each one, and indicate what they are equal to.[6]
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5
Look for keywords.[7]
Word problems are full of keywords that give you clues about what operations to use. Locating and interpreting these keywords can help you translate the words into algebra.[8]
- Multiplication keywords include times, of, and factor.[9]
- Division keywords include per, out of, and percent.[10]
- Addition keywords include some, more, and together.[11]
- Subtraction keywords include difference, fewer, and decreased.[12]
- Multiplication keywords include times, of, and factor.[9]
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1
Write an equation. Use the information you learn from the problem, including keywords, to write an algebraic description of the story.[13]
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2
Solve an equation for one variable. If you have only one unknown in your word problem, isolate the variable in your equation and find which number it is equal to. Use the normal rules of algebra to isolate the variable. Remember that you need to keep the equation balanced. This means that whatever you do to one side of the equation, you must also do to the other side.[14]
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3
Solve an equation with multiple variables. If you have more than one unknown in your word problem, you need to make sure you combine like terms to simplify your equation.
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4
Interpret your answer. Look back to your list of variables and unknown information. This will remind you what you were trying to solve. Write a statement indicating what your answer means.[15]
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1
Solve the following problem. This problem has more than one unknown value, so its equation will have multiple variables. This means you cannot solve for a specific numerical value of a variable. Instead, you will solve to find an equation that describes a variable.
- Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
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2
Read the problem carefully and determine what you are asked to find.[16]
You are asked to find how much money Robyn and Billy will give to the cat shelter. -
3
Summarize what you know, and what you need to know. You know that Robyn and Billy will make money from selling cups of lemonade and from getting tips. You know that they will sell each cup for 75 cents. You also know that their mom and dad will double the amount they make in tips. You don’t know how many cups of lemonade they sell, or how much tip money they get.
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4
Assign variables to the unknown quantities. Since you have three unknowns, you will have three variables. Let
equal the amount of money they will give to the shelter. Let equal the number of cups they sell. Let equal the number of dollars they make in tips.
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5
Look for keywords. Since they will “combine” their profits and tips, you know addition will be involved. Since their mom and dad will “double” their tips, you know you need to multiply their tips by a factor of 2.
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6
Write an equation. Since you are writing an equation that describes the amount of money they will give to the shelter, the variable
will be alone on one side of the equation.
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7
Interpret your answer. The variable
equals the amount of money Robyn and Billy will donate to the cat shelter. So, the amount they donate can be found by multiplying the number of cups of lemonade they sell by .75, and adding this product to the product of their tip money and 2.
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Question
How do you solve an algebra word problem?
Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary’s College.
Academic Tutor
Expert Answer
Carefully read the problem and figure out what information you’re given and what that information should be used for. Once you know what you need to do with the values they’ve given you, the problem should be a lot easier to solve.
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Question
If Deborah and Colin have $150 between them, and Deborah has $27 more than Colin, how much money does Deborah have?
Let x = Deborah’s money. Then (x — 27) = Colin’s money. That means that (x) + (x — 27) = 150. Combining terms: 2x — 27 = 150. Adding 27 to both sides: 2x = 177. So x = 88.50, and (x — 27) = 61.50. Deborah has $88.50, and Colin has $61.50, which together add up to $150.
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Question
Karl is twice as old Bob. Nine years ago, Karl was three times as old as Bob. How old is each now?
Let x be Bob’s current age. Then Karl’s current age is 2x. Nine years ago Bob’s age was x-9, and Karl’s age was 2x-9. We’re told that nine years ago Karl’s age (2x-9) was three times Bob’s age (x-9). Therefore, 2x-9 = 3(x-9) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob’s current age is 18, and Karl’s current age is 36, twice Bob’s current age. (Nine years ago Bob would have been 9, and Karl would have been 27, or three times Bob’s age then.)
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Video
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Word problems can have more than one unknown and more the one variable.
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The number of variables is always equal to the number of unknowns.
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While solving word problems you should always read every sentence carefully and try to extract all the numerical information.
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About This Article
Article SummaryX
To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x — 10. To learn how to solve an equation with multiple variables, keep reading!
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