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## Problem Structures for Addition & Subtraction

Quick pop quiz. How many problem structures are there for addition and subtraction problems?

If you said somewhere around 15 structures, you’re in the right ballpark. Unfortunately, students are often exposed to only the simplest structures. As teachers, we need to have an understanding of all the structures and teach them to our students in a methodical way.

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“…teachers who are not aware of the variety of situations and corresponding structures may randomly offer problems to students without the proper sequencing to support students; full grasp of the meaning of the operations.” (Van de Walle et al)

The charts below were adapted from Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle et al), a phenomenal book for developing your own understanding of math.

The addition/subtraction structures are grouped into three main types: Change, Part/Part/Whole, and Comparison. For each type, there are multiple structures, depending on what information is known and unknown.

## Change Problems

One of the first things you might notice is that the structures are not designated as addition or subtraction. While we typically think of joining as addition and separating as subtraction, you’ll see from the chart that is not always the case. Result Unknown is the simplest and most familiar structure. You might think of these as classic addition and subtraction problems. As we move across the chart, the problems become increasingly complex, and we see that the Change Unknown and Start Unknown structures can be interpreted as either addition or subtraction.

An appropriate way to introduce the problems is to start with the simplest, Result Unknown , problems. Start with Join problems and allow students to practice solving just that type of problem. Help students focus on the meaning of each number in the problem, in terms of Change , Start , or Result . Drawing models is a good strategy for helping students analyze and visualize each problem. Next, introduce Separate problems, again giving them practice with just that type. Then it’s time to mix them up, so students have to determine the appropriate structure, based on the problem.

Now start to move across the chart, using the same process. Introduce the next structure (Join, Change Unknown ), practice the structure, and then mix it in with the others they already know. Keep in mind that this process takes time. If you’re a second-grade teacher, make a schedule for introducing the structures throughout the school year. Use numbers appropriate to the students’ computation skills.

## Part-Part-Whole

Part-Part-Whole problems are very similar to Change. The subtle difference is that often there is no action in these problems, which makes them a little more abstract for students. The Whole Unknown structure is a very simple addition problem. In the One Part Unknown structure, we know the total and one of the parts, but we are missing the other part. This is also commonly called a Missing Addend problem. We often solve this type of problem using subtraction, but a counting-up strategy works well also. A really interesting structure is Both Parts Unknown. It’s a word problem application of knowing all the combinations for a number !

As students are introduced to more of the structures, remember that it’s just as important that they generate problems as solve them. I love an activity I call You Write the Story . Give students an equation and have them write a story to go with it and draw a model for their story.

One other note about Change and Part-Part-Whole problems, while these examples all have two addends, you can also use more than two addends to provide more of a challenge. Think: There are 425 students in the cafeteria. One hundred twenty-seven students are 5th graders, 146 are 4th graders, and the rest are 3rd graders. How many 3rd graders are in the cafeteria?

Finally, we have Comparison problems, which involve comparing two quantities–a larger quantity and a smaller one. They can also be written using either more or fewer. Fewer is by far more difficult for students. We want to make sure we introduce comparison subtraction using manipulatives to help students understand the structure. See this pos t for more information.

There you have it! All the structures for addition and subtraction problems. You can download your own copy of the tables showing the structures using the button below.

I look forward to hearing how you will teach these structures in your classroom, so be sure to leave a comment!

## Resources for problem structures

Morrow-Leong, K., Moore, S. D., & Gojak, L. (2021). Mathematize it!: Going beyond key words to make sense of word problems , grades K-2 or grades 3-5 . Thousand Oaks, CA: Corwin.

Carpenter, Thomas P., et al. (2015) Children’s Mathematics: Cognitively Guided Instruction . Heinemann.

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Great post! I’ve been reading the Mathematize IT: Making Sense books also.

Do you have a post for Problem Structures of multiplication and division?I saw the book, but I was hoping you had something more like this post for multiplication and division.

I follow all your posts! Thank you for helping me become a better teacher❤️

Thanks for your kind comments! I don’t have a post, but I do have a document with all the structures for all operations . Enjoy!

This is a great visual! Thanks for sharing.

Awesome blog and charts! I did notice that “amount” is misspelled in the last chart in the red boxes.

Well, yes it is! Thanks so much for calling it to my attention. I’ll get it corrected straight away.

Late to the game but I LOVE THIS!

What are your thoughts on multistep problems as it relates to these structures?

That would be another, and trickier, step! Being able to comprehend what’s happening in the problem is key. Check out this post on the 3 Reads Protocol for a great strategy for improving comprehension.

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## Addition and Subtraction Word Problems Worksheets

What makes our pdf worksheets on addition and subtraction word problems indispensable is the fact that they give students tons of practice in the real-life application of key math aspects. Children in kindergarten through grade 5 will wrap their head around the given scenarios and identify the operation required. Choose from 1-digit, 2-digit, 3-digit, and multi-digit addition and subtraction; instantly review the work using the included answer key. Our free worksheets help build a liking for the topic!

Addition and Subtraction Word Problems | Within 10

Ready to redefine your practice sessions involving finding sums and differences? This section will make a great addition to your repertoire. Begin your addition and subtraction within 10 here!

- Download the set

Addition and Subtraction Word Problems | Within 20

Get printable word problems for kindergarten, 1st grade, and 2nd grade students here. Work through engaging situations involving addition and subtraction of numbers within 20.

2-Digit Addition and Subtraction Word Problems | Without Regrouping

A wealth of addition and subtraction word problems without regrouping await! Test the knowledge acquired and review skills in finding the sum or difference of double-digit numbers.

2-Digit Addition and Subtraction Word Problems | With Regrouping

Ride on our printable worksheets that help children practice regrouping through a solid mix of real-life scenarios. Practice borrowing and carry forwarding while performing both operations.

3-Digit and 2-Digit Addition and Subtraction Word Problems

Watch how grateful the aspiring mathematicians in grade 2 and grade 3 are to word problems for helping them ease into this topic. Mastery in adding and subtracting 3-digit and 2-digit numbers begins here!

3-Digit Addition and Subtraction Word Problems

Put passion into your practice sessions with our addition and subtraction word problems within 1000. The carefully-chosen scenarios provide tons of support so skills thrive in no time.

Multi-Digit Addition and Subtraction Word Problems

There's no such thing as 'enough practice' when it comes to solving addition and subtraction word problems. The key is to continue the prepping with our pdfs for the 4th grade and 5th grade students.

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## Comparison Word Problem Worksheets

Related Pages Math Worksheets Lessons for First Grade Free Printable Worksheets

Printable Word Problem Worksheets for 1st Grade: Addition Word Problems Addition/Subtraction Word Problems Comparison Word Problems

Tape diagrams, also known as bar models, are visual representations that can be used to solve comparison word problems. These diagrams help students organize information and visualize the relationships between quantities.

- Read and Understand the Problem: Identify the key information: numbers, quantities, and relationships. Understand what the problem is asking you to find.
- Draw the Tape Diagram: Use rectangles to represent the quantities being compared. Label each rectangle clearly with the quantity it represents. Align the rectangles to make visual comparisons easier.
- Fill in the Known Information: Write the given numbers inside the appropriate rectangles. Use question marks for unknown quantities.
- Solve for the Unknown: Break down the problem into smaller, easier steps. Use addition or subtraction to find the missing information. Write the answers in the appropriate places on the diagram.
- Write the Answer: Clearly state the answer to the problem using a complete sentence.

Encourage students to draw their own tape diagrams and explain their thinking. Practice with different types of comparison problems to solidify understanding. Tape diagrams provide a visual and concrete way to represent comparison problems, making them easier to understand and solve for students.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Comparison Word Problem Worksheets .

## More Comparison Word Problem Worksheets

(Answers on the second page.) Comparison Word Problem Worksheet #1 (subtraction) Comparison Word Problem Worksheet #2 (subtraction) Comparison Word Problem Worksheet #3 (addition/subtraction) Comparison Word Problem Worksheet #4 (addition/subtraction) Comparison Word Problem Worksheet #5 (addition/subtraction) Comparison Word Problem Worksheet #6 (addition/subtraction)

## Related Lessons & Worksheets

Comparison Word Problems

Word Problems (Addition & Subtraction) Word Problems (Multiplication & Division)

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## Addition & Subtraction Word Problem Types

Word problems are often a teacher’s biggest struggle in math. Have you said things like “The kids don’t understand them.” and “They grab the numbers out and do a random operation.” We try so many different methods to try and help, and they fall short. Because often, our focus isn’t on teaching students the operations explicitly. And teaching them explicitly is what we need to do! The Common Core State Standards lay out the different addition & subtraction word problem types that students should know. By teaching them explicitly, we give students the tools they need to be successful problem solvers. We connect how the math they’re learning is relevant to their real life. We help them truly understand the mathematical operation and how and when it’s used. By focusing on the word problems and their types, we’re focusing on what makes addition and subtraction what they are.

This post takes an in-depth look at each of the addition & subtraction word problem types. I also give some helpful links at the bottom that discuss Cognitively Guided Instruction, or CGI problem types. They use slightly different vocabulary than the CCSS but are the same set of skills. An important note- when I talk about teaching the addition & subtraction word problem types explicitly, I don’t mean that they’re only practiced during a specific unit, or that we teach specific keywords for each problem type. Students need to read the problem and understand the context. Recognizing the problem type can support that work, but it’s not focused on keywords. I also do a daily word problem outside of our focused unit work. I firmly believe in spiraling the standards in word problems so students have to focus on context to solve. For more support with problem solving, check out my Why Your Students Struggle with Word Problems, and What You Can Do About It post.

## PART-PART-WHOLE

Probably the most common addition and subtraction type in most teachers minds is part part whole. We use number bonds and bar models to model and represent part/whole relationships. We model addition as two sets of objects coming together. We introduce subtraction as separating our total number of objects into smaller parts. And it’s the foundation for future work with fractions and multiplication and division. Part-part-whole is such a critical concept for our students’ mathematical understanding. It’s important that we connect this work to our language in word problems. Many word problems can be thought of as part-part-whole scenarios (even many in the start-change-end types described next).

Total unknown problems are typical addition problems. There are two sets that come together. Often, these are not the same exact subject. For example, it could be red apples and green apples coming together. Or cats and dogs. When it’s the same object, it’s often, but not always, a start-change-end scenario because the change is those two sets joining. The word problem below demonstrates a total unknown that has the same subject- people.

Part unknown problems are subtraction. We know the total number of items, but we don’t know the number in one of the sets. Through our work with part unknown problems, we reinforce the inverse relationship between addition and subtraction. We can write the similar equation 5 + ? = 8 to connect the two operations. It’s important to work with unknowns in any position and part unknown problems are where I like to spend some work on inverse operations and fact families.

Both Parts unknown problems are less common. They are scenarios with multiple solutions. Students know the total number of items and they give a possible arrangement for how those items are broken up. Both parts unknown scenarios are my favorite way to introduce the unknowns to the right of the equal sign 8 = ? + ?. This helps students to know they don’t just solve from left to right and what the equals sign means.

For more information on Part Part Whole , I have an in-depth blog post that shows the hands on strategies I use to introduce and practice part/whole relationships.

## START-CHANGE-END

While part-part-whole is the most common addition & subtraction problem type in many teacher’s minds, it’s probably not the most common in story problems. In real-world scenarios, addition and subtraction is most often demonstrated through start-change-result. In start change result scenarios, something joins or leaves the others. These are the problem types where someone got more of something, or something broke. If we’re not intentional with our word problems, we tend to default to “result unknown” problems. These problem types often have questions such as “how many are left?” and “how many are there now?”. The action has already happened.

I use the term “end” instead of “result” because “end” is the opposite of “start” and I think think students have a clearer understanding than with result. It’s also the same language I use with elapsed time problems in 3rd grade and I like to keep my language as consistent as possible.

The table below gives examples for each of the 6 start change end problem types. They’re pretty straightforward so I’m not going to explain each one in depth. Whether it’s addition or subtraction, the language indicates the location of the unknown: the subjects at the start, the subjects that changed, or the subjects at the end.

It’s important that we give students practice with unknowns in all positions. It is through these start-change-end problem types that students see that they can be asked to identify how many of something there was in the beginning. Or, what the change/action was. With start-change-end problems students get to build their understanding of unknowns being in all positions, and build their competence with addition and subtraction being inverse operations. Through unknowns in any location, students model and solve using the inverse operation.

If start-change-end is a new concept for you, I give you tools and strategies in an in-depth post on teaching Start Change End .

## COMPARISONS

Comparisons are the most complex word problems for students. They aren’t naturally what we think of when we think of the operations. For this reason, we need to teach them and practice them. A lot!

Difference Unknown problems are typically solved with subtraction. Regardless of the question being how many more or how many fewer, the question wants to know the amount between them. The word “more” can throw students off here because they want to add. You can use the addition equation to demonstrate it as presented, but ultimately subtraction is the easiest way to solve it. My favorite way to model these problems is on a number line because I can demonstrate both question types by counting forwards or backwards.

The Bigger Unknown and Smaller Unknown questions are where things get a bit more complicated. For me, as with any problem, I ask students to start by focusing on the unknown in the question. With these problems, I think it’s best to work on them together because they can be easily confused.

In my Addition & Subtraction Word Problem Type Posters I combine by known information. In both situations above, we’re told that someone has more and they both have the same question. By focusing on what “more” indicates, we’re showing students the differences in question types, and the subtly between the two. You can download my Addition & Subtraction Word Problem Type Posters by signing up below.

Bigger Unknown problems in the table both have the question, “How many birds does Raina have?”. Due to the table placement, we understand that Raina has more birds than Sara. But let’s take a closer look at the problems.

Sara has 3 birds. Raina has 2 more birds than Sara. How many birds does Raina have?

In this problem, it tells us that Raina has more than Sara. This is a pretty easy addition problem adding Sara’s number plus the number more- the comparison- to find Raina’s total.

Sara has 3 birds. She has 2 fewer birds than Raina. How many birds does Raina have?

This problem is not as straightforward. It tells us that Raina has more by telling us that Sara’s 3 is 2 fewer than Raina’s. When students see “fewer” they want to subtract but the bigger number is unknown. We can model that subtraction equation as the unknown – 2 gives us Sara’s 3.

Smaller Unknown problems both ask how many Sara has in the table since Sara has the smaller amount. Again, let’s take a closer look at the problems.

Raina has 5 birds. She has 2 more birds than Sara. How many birds does Sara have?

In this problem, the word “more” can make students feel like they need to add. But subtraction is the better operation. If Raina has 2 more than Sara, we can subtract 2 from Sara’s to Raina’s. Or, as addition, Sara’s + 2 = Raina’s 5.

Raina has 5 birds. Sara has 2 fewer than Raina. How many birds does Sara have?

This problem is more straightforward than the last. Sara has 2 less than Raina so students will naturally subtract.

For these scenarios, I find it most helpful to start with the question. The unknown. If I need to know how many birds Sara has, I keep that in mind as I go back to the word problem a second time and restate it. Raina’s 5 is 2 more than Sara’s. Sara has 2 less than Raina’s 5. By starting with the unknown I’m solving for, I can better understand what the question is asking me to do by connecting it to the known.

I teach my students to read each word problem closely. I connect it with the close reading we do during ELA class. Because truly, both what we read in ELA and the word problems we do, are complex texts. I use a 3 Reads Routine . The first read is to get a general understanding- the gist- the context. The next reads walk through the word problem focusing on the unknowns and the question. You can read more about my 3 Reads Routine in that blog post.

## Addition & Subtraction Word Problem Types

I have posters for each of the addition & subtraction word problem types. You can use these as part of an anchor chart as you write your own word problems together for each problem type. You can display them as you introduce them. You can print several to a page and give students their own individual ones as reference.

I also have a Addition & Subtraction Word Problem Types Reference Sheet for you. This one-page printable is a nice reference sheet for you to keep at your side. Or, students can keep a copy in their math reference folder if you have one. The word problems included are the same as what’s on this site, and not the ones on the posters linked above.

Complete the form below to sign up to receive my Addition & Subtraction Word Problem Type posters.

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I also have Addition & Subtraction Word Problem Types Digital Task Cards . They are organized by word problem type and practice addition and subtraction within 20. The Part-Part-Whole and Start-Change-End sets both have specific practice differentiating between them where students match the unknown and given equation to the given scenarios.

Each of the sets give students specific practice on each of the addition & subtraction word problem types. Students use the built-in tools to write equations with variables or symbols for the unknowns. After writing the equation, students use the manipulatives to model the problem on a number line and tens frames. The format allows students to practice several of the Standards for Mathematical Practice as they model and solve the problem, and check their work.

In addition to part-part-whole, start-change-end, and comparison problem types, there’s also an Adding 3 Numbers Word Problems set. This set is presented in part/whole, or part-part-part-whole scenarios. The set is free and can be downloaded from my TpT store by clicking the cover below.

I hope this post has given you ideas and resources for teaching each addition & subtraction word problem type with your students. The more practice and exposure students get, the more successful they will be. You may also be interested in my post on Games to Build Addition & Subtraction Fact Fluency .

For more reading on CGI Word Problem Types, this post from Langford Math is quite detailed and this wiki has a bunch of sample word problems.

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## Differentiated Math Fact Practice

## 4th Grade Resources

## Problem Solving: Comparing Problems

## What are Comparing Problems?

## Three Types of Comparing Problems

- Comparing when the difference is unknown
- Comparing when the smaller part is unknown
- Comparing when the larger part is unknown

## Comparing When the Difference is Unknown

Comparing when a part is unknown .

## Larger Part Unknown

## Smaller Part Unknown

## Practice Comparing Problems

## Wrapping Up . . .

- Teach students to VISUALIZE what is happening
- Provide students with a variety of STRATEGIES to use when solving
- Celebrate that we can solve problems in DIFFERENT ways and still get the same answer
- Focus on the CONTEXT
- PRACTICE, practice, practice by starting with concrete, hands-on opportunities and slowly moving more abstract.

## The Problem Solving Series

- The 11 Types of Addition and Subtraction Problems
- How I Teach Problem Solving & The Joining Problems
- The Separating Problems
- Part-Part-Whole Problem Solving Group
- Comparing Problems and Wrap-Up

## Save these Problem Solving Tips and Strategies

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## Word Problems Involving Addition and Subtraction

Word problems involving addition and subtraction are discussed here step by step.

There are no magic rules to make problem solving easy, but a systematic approach can help to the problems easily.

Word problems based on addition are broadly of two types: (a) When objects of two or more collections are put together. For example:

Amy has 20 lemon sweets and 14 orange sweets. What is the total number of sweets Amy has? (b) When an increase in number takes place.

For example:

Victor has 14 stamps. His friend gave him 23 stamps. How many stamps does Victor have in all? The key words used in problems involving addition are:

s um; total; in all; all together.

Word problems based on subtraction are of several types: (a) Partitioning : Take away, remove, given away.

(b) Reducing : Find out how much has been given away or how much remains.

(c) Comparison : More than / less than.

(d) Inverse of addition : How much more to be added. The key words to look out for in a problem sum involving subtraction are: take away; how many more ; how many less ; how many left ; greater ; smaller.

1. The girls had 3 weeks to sell tickets for their play. In the first week, they sold 75 tickets. In the second week they sold 108 tickets and in the third week they sold 210 tickets. How may tickets did they sell in all? Tickets sold in the first week = 75

Tickets sold in the second week = 108

Tickets sold in the third week = 210

Total number of tickets sold = 75 + 108 + 210 = 393

Answer: 393 tickets were sold in all.

2. Mr. Bose spent $450 for petrol on Wednesday. He spent $125 more than that on Thursday. How much did he spend on petrol on those two days. This problem has to be solved in two steps.

Step 1: Money spent for petrol on Thursday

450 + 125 = $575 Step 2: Money spent for petrol on both days

450 + 575 = $1025

Examples on word problems on addition and subtraction:

1. What is the sum of 4373, 4191 and 3127? Solution: The numbers are arranged in columns and added.

Therefore, sum =11,691

2. What is the difference of 3867 and 1298?

Solution: The numbers are arranged in columns and subtracted:

Therefore, difference = 2569

3. Subtract 4358 from the sum of 5632 and 1324. Solution: Sum of 5632 and 1324

Difference of 6956 and 4358

Therefore, 2598 is the answer.

4. Find the number, which is

(i) 1240 greater than 3267.

(ii) 1353 smaller than 5292. Solution: (i) The number is 1240 more than 3267

Therefore, the number = 3267 + 1240 or = 4507 (ii) The number is 1353 less than 5292

= 5292 – 1353 or

5. The population of a town is 16732. If there are 9569 males then find the number of females in the town. Solution:

6. In a factory there are 35,675 workers. 10,750 workers come in the first shift, 12,650 workers in the second shift and the rest come in the third shift. How many workers come in the third shift? Solution: Number of workers coming in the first and second shift

= 10750 + 12650 = 23400

Therefore, number of workers coming in the third shift = 35675 - 23400 = 12275

Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Multiply a Number

● Estimating Products

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Dividing Numbers

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

4th Grade Math Activities From Word Problems Involving Addition and Subtraction to

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## Additive Comparison – Definition with Examples

What is additive comparison, additive comparison: definition, additive comparison of decimal numbers, solved examples on additive comparison, practice problems on additive comparison, frequently asked questions on additive comparison.

Word problems that compare two amounts by stating how much more (or less) one amount is than the other are included in the additive comparison.

In math, checking if a number is smaller, greater, or equal to another number is known as comparison.

For example, Zyna has $\$16$ and Diana has $\$20$.

Since $20 \gt 16$, we can say that Diana has more money.

We find the relation between two amounts by asking how much more or less one amount is compared to the other. In other words, an additive comparison problem is a problem in which:

- Two verbal statements are used to compare two sets of items, and
- Further, an additive equation is determined.
- The equation includes numbers and the alphabet, or the variable.

An example of an additive comparison problem using the equation is given below:

Daisy takes 20 minutes to reach school from her home. Ryan takes 15 more minutes than Daisy and Sheryl takes 5 more minutes than Ryan. How much time does Sheryl take to reach school?

Time taken by Daisy to reach school $= 20$ minutes

Time taken by Ryan $= 5$ minutes more than Daisy $= 20 + 15 = 35$ minutes

Time taken by Sheryl $= 35 + 5 = 40$ minutes

Therefore, Sheryl takes 40 minutes to reach school.

Words used in additive comparison are:

- How many more
- How many less
- More than (8 more than 42 miles)
- Less than (6 less than 32 liters)

## Related Worksheets

## What Is a Bar Model?

In math, a bar model is defined as a pictorial representation of a number in the form of bars used to solve number problems. It helps us to attain an understanding of how a problem needs to be solved and calculated.

For instance, one rectangle of the bar model represents a value of 6. We have to find 3 times the value of one bar. So, the value of bar model $= 6 \times 3 = 18$.

It helps us understand which arithmetic operations are used to solve a word problem. Here’s how we can represent different operations using bar models.

In the image (A), the first bar is of 60 and the second is of 30. The bar given below will give us $60 + 30 = 90$.

We are aware of the fact family.

$60 + 30 = 90$, so the subtraction equation will be: $90 \;–\; 30 = 60$

## Comparison Word Problems

There are three types of additive comparison word problems:

- Difference is unknown

Connie has 12 red marbles and 23 blue marbles. How many more blue marbles than red marbles does Connie have?

This is a subtraction problem.

$23 \;-\; 12 = 11$

- Unknown quantity is big

Connie has 12 red marbles and some blue marbles. She has 15 more blue marbles than red ones. How many blue marbles does Connie have?

This is an addition problem.

$12 + 15 = 27$

- Unknown quantity is small

Connie has 20 blue marbles. She has 17 more blue marbles than red ones. How many red marbles does Connie have?

$20 \;–\; 17 = 3$

Let’s solve a few additive comparison problems using bar models.

Example 1: Kate has 7 stamps. Sara has 5 more. How many stamps does Sara have?

Stamps with Kate $= 7$

Stamps with Sara $= 7 + 5 = 12$.

Therefore, Sara has 12 stamps

Example 2 : Jack scored 22 points in a game. Jim scored 6 less points than Jack. How many points did Jim score?

Points scored by Jack $= 22$

Points scored by Jim $= 6$ less than Jack $= 22 \;–\; 6 = 16$

Therefore, Jim scored 16 points.

Decimal numbers are the numbers whose whole part and fractional part are separated using a decimal point. For example: 2.34.

Finding the additive comparison of decimal numbers is the same as finding the additive comparison of whole numbers.

Marie has $\$2.45$ and Myra has $\$1.14$ more than Marie. How much money does Myra have?

Amount of money with Myra $= \$2.45 + \$1.14 = \$3.59$

1. In a basketball game, Peter scored 22 baskets on Monday. He scored 13 more baskets on Tuesday. Find the number of baskets he scored on Tuesday using the bar model.

Solution:

Baskets scored on Monday $= 22$

Baskets scored on Tuesday $= 13$ more baskets than Monday

The bar model is given by:

Number of baskets scored on Tuesday $= 22 + 13 = 35$

2. Sophie has 45 marbles and Mia has 32 marbles. Who has more marbles?

Since $45 \gt 32$, Sophie has more marbles.

Difference $= 45 \;–\; 32 = 13$

Sophie has 13 more marbles than Mia.

3. There were 12 less girls than the number of boys in a summer camp. If the number of boys were 58, how many girls were there? (Use the bar model.)

Number of girls $= 58 \;–\; 12 = 46$

4. On Monday, the temperature was $65.6^{\circ}\text{F}$ and on Tuesday, the temperature was $6.2^{\circ}\text{F}$ more than Monday. What was the temperature on Tuesday?

Solution: Temperature on Monday $= 65.6^{\circ}\text{F}$

Temperature on Tuesday $= 65.6^{\circ}\text{F} + 6.2^{\circ}\text{F} = 71.8^{\circ}\text{F}$

## Additive Comparison - Definition with Examples

Attend this quiz & Test your knowledge.

## What will replace “?” in the given model?

## Oliver has 25 books. Peter has 7 more books. How many books does Peter have?

Cayla did 72 sit ups in the morning. nekira did 48 sit ups at night. how many more sit ups did cayla do than nekira, kitty has $\$450$ out of which she used $\$215$ to buy a scooter. how much money is she left with, adam has 15 lollipops less than hope. if adam has 29 lollipops, how many lollipops does hope have.

What is the difference between addition and additive comparison?

Addition means to add two or more numbers and to find the sum. Whereas additive comparison is to find the relation between two amounts by identifying how much more or less one amount is one compared to the other.

What is the difference between additive comparison and multiplicative comparison?

Additive comparison is to find the relation between two amounts by asking or telling how much more or less one amount is one compared to the other. Multiplicative comparison is to compare two quantities such that when one is multiplied by a specified number, the other is produced.

What is comparison subtraction?

In comparison subtraction, we subtract to find out how much bigger (or how much smaller) one set is compared to another. It is the same as additive comparison.

How does additive comparison work in fraction?

We divide the bar into equal parts which is the denominator of the first fraction and then shade the numerator. Then, we convert the same bar as per the denominator of the second fraction and delete the bars as per given in the numerator of the second fraction.

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## Addition & subtraction word problems

Mixed addition and subtraction.

These word problems worksheets involve addition and subtraction of two or three addends or subtrahends with up to 4 digits. The last question on each worksheet asks the student to write an equation using a variable (" X ") for the unknown quantity.

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## The Lesson Study Group

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## Addition and Subtraction, Part 1: Story Problems

In this resource, we discuss the teaching and learning of addition and subtraction. Often, students’ understanding of this topic is heavily grounded in rote computation of numbers, separated from any real-life context. Unfortunately, this can leave gaps in their understanding of the concepts that underlie those computations. This resource shows how the use of context—story problems—can help students develop a real grasp of addition and subtraction.

## Key Concepts

A story problem introduces addition and subtraction not as a mathematical procedure, but as a hypothetical real-life problem in context. The student then must take the conceptual leap of turning the real-life problem into a mathematical problem—providing some of their earliest experiences with the important mathematical practice of “modeling.”

## Story Situations

There are several different kinds of mathematical relationships that students must infer from story problems. These are known as “situation types.” The Common Core State Standards (CCSS) expects K-1 students to understand four situation types:

- Put-together/take-apart

Teachers who understand the situation types (and what is new and challenging about each one) are better able to select and sequence problems that help students build their conceptual understanding of addition and subtraction.

## Building Conceptual Understanding of Addition and Subtraction

The ability to add and subtract are widely recognized to be fundamental mathematical skills. However, we do not always recognize the other important conceptual understandings that students gain through solving story problems, beyond the computational skills gained by practicing addition and subtraction facts without context.

In this problem, we start with the problem in context: we see that there are 5 fish in a tank, and a child is adding 3 more. Next, students must represent this situation mathematically. This can be done with manipulatives (as is shown with the yellow blocks below) and by using the number sentence, 5 + 3 = ?. Students who are newer to solving story problems will rely on the more concrete representation of manipulatives.

As students build fluency of composing and decomposing numbers (and familiarity with story problems), they can jump to representing the problem with a number sentence.

Once students solve the mathematical problem to discover the answer is 8, students must return to the context of the problem and interpret the results. In this case, 8 refers to the total number of fish in the tank.

As we mentioned previously, students develop their understanding of the addition and subtraction operations as they use them to solve story problems. There are several categories of story problems, known as situation types , that describe the relationship among quantities in story problems. The four situation types that the Common Core State Standards (CCSS) require students to learn in grades K-1 are:

Teachers who understand the situation types (and what is new and challenging about them) are better able to support their students in developing a strong conceptual understanding of addition and subtraction. For this reason, we want to spend the rest of this resource familiarizing you with the four addition and subtraction story situations.

## The Addition and Subtraction Story Situations

To get a better idea of what we mean by “situation type,” let’s return to our example addition problem, which represents an add-to situation . In this problem, one quantity (3 fish) is added to an existing quantity (5 fish), resulting in a new quantity (what we discover to be 8 fish). The details of the problem can change (for example, it could involve cookies instead of fish) as can the unknown quantity (for example, perhaps we knew how many fish we had in the end, but not how many we started with), but the relationship among quantities is the same for all add-to problems.

Below, we represent the add-to situation as a diagram, and label each quantity as the CCSS refers to them ( start is increased by change to become result ). We don’t recommend introducing the diagram as a model to students, but it be may be helpful as teachers to see the situation type represented visually.

Another important thing to understand is that the situation type itself isn’t how we know whether to use addition or subtraction . Rather, we determine the needed operation based on which quantity is unknown. In our example above, 3 fish are being added to an aquarium of 5 fish, and the unknown is the total number of fish (5 + 3 = ?)—so this requires addition. But if we added 3 fish to a tank that now has 8 fish, this is still an “add-to” situation: ? + 3 = 8), but we would use subtraction to find the unknown (8 – 3 = ?).

In the table below, we provide an example problem for each type of story situation and a diagram that represents each situation’s relationship among quantities.

## Discussion Questions

After reading this resource, it may be helpful to discuss the following questions as a team.

- What ideas about the teaching-learning of addition and subtraction discussed in this resource strike you as important in your setting?
- How does your curriculum handle addition and subtraction story problems? Which situations does it introduce first? What about it do you like and/or notice that has opportunity for improvement?
- What experiences have your students had that currently inform their understandings of addition and subtraction?
- How do your students represent story problems?
- What do you want to learn more about and what steps can you take to do so?

In our resources linked below, we take a closer look at the situations, and discuss what situations (and which unknown quantities within situations) are challenging for students and how to support them to overcome the difficulties.

First, we take a close look at the situation types that students typically first experience: add-to , take-from , and put-together/take-apart .

Second, we discuss the compare situation.

Finally, we return to add-to and take-from situations to cover how students solve for unknown start or change values .

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## 10 Helpful Worksheet Ideas for Primary School Math Lessons

M athematics is a fundamental subject that shapes the way children think and analyze the world. At the primary school level, laying a strong foundation is crucial. While hands-on activities, digital tools, and interactive discussions play significant roles in learning, worksheets remain an essential tool for reinforcing concepts, practicing skills, and assessing understanding. Here’s a look at some helpful worksheets for primary school math lessons.

## Comparison Chart Worksheets

Comparison charts provide a visual means for primary school students to grasp relationships between numbers or concepts. They are easy to make at www.storyboardthat.com/create/comparison-chart-template , and here is how they can be used:

- Quantity Comparison: Charts might display two sets, like apples vs. bananas, prompting students to determine which set is larger.
- Attribute Comparison: These compare attributes, such as different shapes detailing their number of sides and characteristics.
- Number Line Comparisons: These help students understand number magnitude by placing numbers on a line to visualize their relative sizes.
- Venn Diagrams: Introduced in later primary grades, these diagrams help students compare and contrast two sets of items or concepts.
- Weather Charts: By comparing weather on different days, students can learn about temperature fluctuations and patterns.

## Number Recognition and Counting Worksheets

For young learners, recognizing numbers and counting is the first step into the world of mathematics. Worksheets can offer:

- Number Tracing: Allows students to familiarize themselves with how each number is formed.
- Count and Circle: Images are presented, and students have to count and circle the correct number.
- Missing Numbers: Sequences with missing numbers that students must fill in to practice counting forward and backward.

## Basic Arithmetic Worksheets

Once students are familiar with numbers, they can start simple arithmetic.

- Addition and Subtraction within 10 or 20: Using visual aids like number lines, counters, or pictures can be beneficial.
- Word Problems: Simple real-life scenarios can help students relate math to their daily lives.
- Skip Counting: Worksheets focused on counting by 2s, 5s, or 10s.

## Geometry and Shape Worksheets

Geometry offers a wonderful opportunity to relate math to the tangible world.

- Shape Identification: Recognizing and naming basic shapes such as squares, circles, triangles, etc.
- Comparing Shapes: Worksheets that help students identify differences and similarities between shapes.
- Pattern Recognition: Repeating shapes in patterns and asking students to determine the next shape in the sequence.

## Measurement Worksheets

Measurement is another area where real-life application and math converge.

- Length and Height: Comparing two or more objects and determining which is longer or shorter.
- Weight: Lighter vs. heavier worksheets using balancing scales as visuals.
- Time: Reading clocks, days of the week, and understanding the calendar.

## Data Handling Worksheets

Even at a primary level, students can start to understand basic data representation.

- Tally Marks: Using tally marks to represent data and counting them.
- Simple Bar Graphs: Interpreting and drawing bar graphs based on given data.
- Pictographs: Using pictures to represent data, which can be both fun and informative.

## Place Value Worksheets

Understanding the value of each digit in a number is fundamental in primary math.

- Identifying Place Values: Recognizing units, tens, hundreds, etc., in a given number.
- Expanding Numbers: Breaking down numbers into their place value components, such as understanding 243 as 200 + 40 + 3.
- Comparing Numbers: Using greater than, less than, or equal to symbols to compare two numbers based on their place values.

## Fraction Worksheets

Simple fraction concepts can be introduced at the primary level.

- Identifying Fractions: Recognizing half, quarter, third, etc., of shapes or sets.
- Comparing Fractions: Using visual aids like pie charts or shaded drawings to compare fractions.
- Simple Fraction Addition: Adding fractions with the same denominator using visual aids.

## Money and Real-Life Application Worksheets

Understanding money is both practical and a great way to apply arithmetic.

- Identifying Coins and Notes: Recognizing different denominations.
- Simple Transactions: Calculating change, adding up costs, or determining if there’s enough money to buy certain items.
- Word Problems with Money: Real-life scenarios involving buying, selling, and saving.

## Logic and Problem-Solving Worksheets

Even young students can hone their problem-solving skills with appropriate challenges.

- Sequences and Patterns: Predicting the next item in a sequence or recognizing a pattern.
- Logical Reasoning: Simple puzzles or riddles that require students to think critically.
- Story Problems: Reading a short story and solving a math-related problem based on the context.

Worksheets allow students to practice at their own pace, offer teachers a tool for assessment, and provide parents with a glimpse into their child’s learning progression. While digital tools and interactive activities are gaining prominence in education, the significance of worksheets remains undiminished. They are versatile and accessible and, when designed creatively, can make math engaging and fun for young learners.

The post 10 Helpful Worksheet Ideas for Primary School Math Lessons appeared first on Mom and More .

## IMAGES

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## COMMENTS

How to solve comparison word problems using bar models, tape diagrams, comparison bars, examples and step by step solutions, comparison problems with addition and subtraction, 2nd Grade. Comparison Word Problems. ... Because the part is missing, this is a subtraction problem. Example: Cayla did 88 sit-ups in the morning. Nekira did 32 sit-ups ...

out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more.

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-1st-grade-math/cc-1st-add-s...

Finally, we have Comparison problems, which involve comparing two quantities-a larger quantity and a smaller one. They can also be written using either more or fewer. Fewer is by far more difficult for students. We want to make sure we introduce comparison subtraction using manipulatives to help students understand the structure.

A comparison problem compares one amount to ... We can use the strategy draw a diagram, to solve comparison word problems, that involve addition or subtraction.

2-Digit Addition and Subtraction Word Problems | With Regrouping. Ride on our printable worksheets that help children practice regrouping through a solid mix of real-life scenarios. Practice borrowing and carry forwarding while performing both operations. Download the set. 3-Digit and 2-Digit Addition and Subtraction Word Problems.

Daberculosis. Hi Hannah. To make this easier to understand, you can think of these comparison exercises as a subtraction problem. All of these exercises are subtraction, the only difficult part is knowing what your answer means. I'll go over the first problem in the video. The first problem says "Alexander has 9 marbles and Emily has 5 marbles.

Addition & Subtraction word problems. Practice Worksheets for First Grade. Comparison Word Problem Worksheets. Related Pages Math Worksheets Lessons for First Grade ... also known as bar models, are visual representations that can be used to solve comparison word problems. These diagrams help students organize information and visualize the ...

These grade 1 word problems worksheets involve the addition and subtraction of 1 and 2 digit numbers. Some problems have 3 or more terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6. Similar: Mixed addition / subtraction word problems (single digits) Mixed word problems.

Solving comparison problems (Part 2) ... Addition and subtraction within 20. Start. Q1. Which word problem matches this image? Tom has 5 marbles. Lisa has 3 more marbles than Tom. How many marbles does Lisa have? ... Which addition equation matches this word problem? 12 + 3 = 15 12 + 4 = 16. 2/3. See results. Q3.

Unit test. Test your understanding of with these NaN questions. In this topic, we will add and subtract whole numbers. The topic starts with 1+1=2 and goes through adding and subtracting within 1000. We will cover regrouping, borrowing, and word problems.

For more support with problem solving, check out my Why Your Students Struggle with Word Problems, and What You Can Do About It post. PART-PART-WHOLE. Probably the most common addition and subtraction type in most teachers minds is part part whole. We use number bonds and bar models to model and represent part/whole relationships.

Problem Solving: Comparing Problems Welcome back to the final post in this problem solving series. In this post we are going to talk about the last group of addition and subtraction problem solving problem types - the comparing problems. Before you jump in, I would suggest that you take a few minutes and start at the beginning. ...

How much did he spend on petrol on those two days. This problem has to be solved in two steps. Step 1: Money spent for petrol on Thursday. 450 + 125 = $575. Step 2: Money spent for petrol on both days. 450 + 575 = $1025. Examples on word problems on addition and subtraction: 1.

Model Compare Word Problems. One of the best ways to teach students to solve compare word problems is to model the process for them. Show them how you would approach the problem and think aloud as you work through it. This will help them see that there is a method to solving these types of problems. Write out a few examples on the board and ...

This Go Math 4th Grade video covers the topic of solving word problems by drawing a diagram. Students will learn about the inverse operation of addition and ...

Here is the same freebie I offered last week you can download for your math files: Addition and Subtraction Story Structure Information The six color anchor charts shown below are ... You can also relate knowledge of number bonds to comparison problems. ... Separate and Comparison Problem Solving Structures KG-4th " sarah khan. May 14, 2020 ...

This is an addition problem. $12 + 15 = 27$ Unknown quantity is small; Connie has 20 blue marbles. She has 17 more blue marbles than red ones. How many red marbles does Connie have? This is a subtraction problem. $20 \;-\; 17 = 3$ Let's solve a few additive comparison problems using bar models. Example 1: Kate has 7 stamps. Sara has 5 more.

These word problems worksheets involve addition and subtraction of two or three addends or subtrahends with up to 4 digits. The last question on each worksheet asks the student to write an equation using a variable (" X ") for the unknown quantity. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.

write equations to represent the problem, solve two-step comparison problems. Prerequisites. Students should already be familiar with. multiplication tables to 1 0 × 1 0, addition and subtraction of numbers up to 100. Exclusions. Students will not cover. multiplying by 2-digit numbers apart from 10. Lesson Menu. Lesson. Lesson Plan.

Complete the test and get an award. This is a free online math test for students of second grade math. In this test, the included problems are concerned with the comparison of numbers using addition and subtraction. Students must choose the correct number for which the given statement holds true. Question 1. Which number makes this statement true?

Addition and subtraction story problems are some of the first experiences students will have using the important mathematical practice of modeling. Let's take a look at an example problem to see what this process might look like for Kindergarteners. In this problem, we start with the problem in context: we see that there are 5 fish in a tank ...

This guide elaborates on Table 1: Common addition and subtraction situations in the Massachusetts Curriculum Framework for Mathematics. Grades Pre-K & K: Modeling and Solving Problems Within 10. Pre-kindergarten students begin their study of addition and subtraction situations by modeling real-world situations with concrete objects (PK.OA.A.1).

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). 1, 2 M.1.3 Operations and Algebraic Thinking ...

Addition and Subtraction within 10 or 20: Using visual aids like number lines, counters, or pictures can be beneficial. Word Problems: Simple real-life scenarios can help students relate math to ...

Addition and subtraction of integers. Death Valley is one of the hottest places on earth with a recorded maximum temperature of 57 ° celsius. The lowest temperature ever recorded was − 89 ° celsius in Antartica.