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Math Strategies

How to Create Your Own Word Problems for Math Practice

Math, Story Problems
Blog header for How To Create Your Own Word Problems for Math Practice with a photo of a word problem projected on the board.

Word problems are a great way for students to practice any math skill! Story problems not only build problem solving skills, but also provide opportunities for students to use critical thinking, try out different math strategies, and practice their math communication.

Here’s the thing – you know your students better than anyone. You know the math skills they need more practice with, you know their interests, and you know their ability. Using all of those things can help guide you in creating your own story problems for your math students.

Creating problems for your students may seem like a daunting task, but there are some key things to consider to make it easier. 

Math Skills

Photo of word problem worksheet with words - Pick Your Math Skill.

Word problems are a great way to practice most math skills since it provides context to the math. Before creating problems, think of what specific skills you are wanting your students to practice. If it is start unknown, make sure your story sets up in a way that students have to solve for the first number. If you are working on subtraction, you can create problems that have to do with someone giving something away. 

Interests

Photo of kid playing baseball with words - Use Students' Interests

When I create my own word problems, I always try to tie in my students to the story. I use their names and also their interests. This helps build engagement and makes them more interested in solving the problems.  Students love to see whose name is in the problems. 

If Johnny likes baseball, I try to create a problem about him playing baseball.  If Sara loves to read books, I create a problem about her checking out books from the library. This small step of using your students’ name and interests can be a game changer when it comes to students being excited to solve story problems.

Real-Life Situations

Photo of canned food drive with words - Incorporate Real-Life Situations.

Story problems are an amazing way for students to practice solving real-world problems! Most standards actually tie that language into some of their story problem standards.  Try to tie the word problem into something you are working on in class or something the kids might have participated in during outside school time.  

For example, say your school is having a canned food drive. You could create a word problem where students know how many cans have been collected so far and then a goal number of cans to try to reach. In this problem, you could ask students to figure out how many more cans are needed to reach the goal.

Differentiation

Photo of word problem worksheet with words - Differentiate.

Another thing I take into consideration when creating word problems is differentiation. Most if not all math classrooms have students at a variety of levels with a variety of needs. When creating problems for my class I take that it into account.

By creating my own, I’m able to change up the numbers as needed to make the problems work for my students. I will often use the same problem for all groups, but tweak the numbers. This saves me time and also differentiates for my students so they are able to get the practice they need.

Modifications

Photo of student solving problem with the words - Make Modifications.

When you create your own word problems you are also able to make modifications to the problems. For example, if you have some students who are struggling with reading you could make sure to include words they are able to decode. You could also include a picture with the problem to help them with the context. 

Word Problem FREEBIES

If you are looking for some word problems that are already differentiated and created for you, check out these FREEBIES below!

Word Problems Ready-to-Go

If you’d like further practice for your students that is differentiated and can be used for homework, independent practice, or assessments, click below…

More Word Problem Info

Division Strategies: Building a Strong Foundation for Mathematical Proficiency

Math
Blog header - Division Strategies

Mathematics can sometimes feel like a tricky puzzle, especially when it comes to division strategies. Many students find division challenging and overwhelming, but fear not! There are fantastic division strategies that can make this math operation a whole lot easier and even enjoyable.

We’re going to explore some key division strategies that will help you build a strong foundation for math success. Whether you’re a parent or teacher searching for tools to support young learners, we’ve got you covered.

We’ll start with the basics and gradually move on to more advanced approaches. By mastering these division strategies, students can not only solve division problems accurately but also develop critical thinking skills, problem-solving abilities, and a deeper understanding of number relationships. These strategies lay the groundwork for more advanced mathematical concepts and serve as stepping stones toward mathematical fluency.

Division Strategies

Below you will see five different division math strategies that your students might use.  Each student will be in a different spot with their math strategies. For example, some students need the concrete/manipulatives and equal groups will be best for them.  Other students might be ready for repeated subtraction or related facts.  Students can use a variety of strategies and will move through them at different rates when they are ready. I highly recommend letting them explore these strategies first so they understand the concept of division before having them memorize their division facts.

Equal Groups

Photo of math problem 18/6 = 3. 6 circles are drawn with 3 dots in each circle.

Draw out circles for the number of groups that you have. This problem is 18 divided into 6 groups and we need to figure out how many are in each group. Then, in each group put 1 dot until you get to 18. Finally, students will count how many are in each circle/group. Students can count these in a variety of ways. Some students may count by 1s, 2s, 4s. I recommend having them write the number they are on below each circle to help them keep track. After counting by 1’s, the students came to the answer of 3.

Bar Diagram

Photo of division problem 18/6 = square
Rectangular bar divided into 6 equal groups. 3 dots in each group with the number 3 below each spot.

This is very similar to equal groups just a different way to visually represent the problem. Students will draw out a rectangular bar and then divide that bar into 6 groups. Then, they will put one in each group until they get to the total number they started with – 18. Then, count how many are in each group. Some students might also like the visual with the number 3 instead of the dots depending on where they are in their understanding of division.

Repeated Subtraction

Photo of division problem 18/6 = square
18 - 6 = 12
12 - 6 = 6
6 - 6 = 0
Answer is 3.

Repeated subtraction is exactly like repeated addition except you’re subtracting. For this problem, students would start at 18 and would start subtracting by 6 until they get to 0. For example – 18-6 = 12, 12-6 = 6, and then 6-6 = 0. They had to subtract 6 – 3 different times so 3 is the quotient.

Empty Number Line

Photo of division problem 18/6 = square
Number line with jumps back from 18  taking away 6 each time until it gets to 0.

The empty number line division strategy is similar to repeated subtraction just a different way of visualizing it. For students who like to use empty number lines in math, this strategy might be the best one for them. Students start by drawing their empty number line and placing the starting number 18 on the far right. Then, they subtract 6 until they get to 0. They had to subtract 6 – 3 times so the answer is 3.

Related Facts

Photo of division problem 18/6 = square
6 x what is 18 - 3 is put in the box os 18 /6 = 3.

For math students who have a solid understanding of multiplication and are ready for a more abstract strategy – related facts might work for them. For this strategy, students turn the division problem 18/6 = ___ into a multiplication problem 6 x __ = 18. So now they are trying to figure out what they would multiply by 6 to get to 18 and then using that related fact to solve the division problem.

Division Strategies Exit Ticket FREEBIE

Photo of 3 division exit tickets on top of a desk with a pencil.

Grab this FREE set of exit tickets that will provide your math students with a chance to practice and demonstrate their division strategies. Includes 3 half-page questions that make a great exit ticket, independent practice, or formative assessment. Click HERE for your Division Strategies FREEBIE.

For more info…

Division Tip for Conceptual Understanding

Differentiated Division Word Problems

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Subtraction Math Strategies

Math
Blog header for Subtraction Math Strategies

Math has always been one of my favorite subjects to teach.  I think one of the main reasons why I enjoy teaching math so much is the variety of strategies that can be used to solve a math problem.  After reading this post you’ll learn four different subtraction math strategies that your students could use to help boost their understanding and math problem solving abilities.

Subtraction Math Strategies:

Below you will see four different subtraction math strategies that your students might use.  Each student will be in a different spot with their math strategies. For example, some students need the concrete/manipulatives and place value strategy will be best for them.  Other students might be really good at breaking numbers apart and using them in different ways – then break apart or expanded might be best for them.  With math strategies there is not a one size fits all type of mentality.  Students can use a variety of strategies and will move through them at different rates when they are ready.

Place Value Strategy:

Photo of place value strategy

Draw out how many there are to start with – 95  Then, take away or cross out how many are being taken away – 56.  Start by crossing out the 5 tens for 50.  Then, you have 5 ones and you can’t take away 6 from 5 so, take a ten and regroup it into 10 ones.  (Circle the ten and change it into the ten ones (dots)).  Now, you can take away the 6 ones.  Then, count what is left – 10, 20, 30, and 9 more so 39.

Empty Number Line Strategy:

Photo of empty number line subtraction math strategy

First, draw an empty number line.  Then, start at the number that you’re beginning with – 95.  95 will go on the right side of the empty number line because you are subtracting so your number will be getting smaller.  Then, 56 can be taken away a few different ways. In this example, they first took away 50 and got to 45. Then, took away 5 and got to 40 (friendly number) and one more and got to 39.  Students could also take away all 6 ones.  The 50 could also be broken down into – 20, 20, 10 – 10, 10, 10, 10, 10 – 30, 20 – 40, 10 – etc.

Break Apart Strategy:

Picture of break apart strategy

For break apart, leave the first number together since this is the number that you are starting with.  Then, break apart the number that you are taking away.  So, 56 would break into 50 and 6 (expanded notation).  Then, 95 – 50 = 45 and 45 – 6 = 39.  

Expanded Form Strategy:

Photo of expanded form strategy

First, change each number into expanded notation. 95 = 90 + 5 and 56 = 50 + 6.  Then, subtract the ones from the ones.  You can’t take away 6 from 5.  So, you take ten from the 90 to add to the ones.  When you take ten from the 90, the 90 turns into 80.  Then, add the ten you took to your ones 10 + 5 = 15.  Now, you can subtract.  15 – 6 = 9 and 80 – 50 = 30.  Then put the numbers back together 30 + 9 = 39.

Subtraction Practice:

Photo of subtraction word problem resource

If you’re looking for some subtraction practice pages for your students to practice these strategies – I have worksheets already created for you.  Best part is – they are differentiated into 3 levels! These Subtraction Word Problem Printables are great for independent practice, homework, formative assessments, and more. Check them out here >>> Subtraction Differentiated Word Problem Worksheets.

If you are interested in learning about Addition Math Strategies, check out my blog post>>>HERE.

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Addition Math Strategies

Math
Blog header with photo of addition math strategy.

Math has always been one of my favorite subjects to teach.  I think one of the main reasons why I enjoy teaching math so much is the variety of strategies that can be used to solve a math problem.  After reading this post you’ll learn four different addition math strategies that your students could use to help boost their understanding and math problem solving abilities.

Variety of Math Strategies:

While in math there is typically one right answer – there are many different ways you can get there. When I was in school I was good at math and got the right answer, but had no idea how or why.  For addition, my teacher taught me one way – with carrying over and I did and I got the answer. But, I didn’t really understand the “why” behind the math. What I love about teaching math now is we let kids figure it out for themselves.  We give kids a chance to explore multiple strategies and find the right one for them. There is no more one size fits all.  I wish I had learned math this way when I was younger (and please know I’m not faulting my past teachers – this is just the way it was taught then).

Addition Math Strategies:

Below you will see four different addition math strategies that your students might use.  Each student will be in a different spot with their math strategies. For example, some students need the concrete/manipulatives and place value strategy will be best for them.  Other students might be really good at breaking numbers apart and using them in different ways – then break apart or expanded might be best for them.  

Students can also move through the strategies.  One student might start with place value strategy, but as they become more comfortable in math they then move on to empty number line or one of the others. Students aren’t pigeon holed into their strategy. Think of it almost like a buffet where they can try the different strategies and see which one works best for them.

Place Value Strategy:

Example of place value addition math strategy. Students use base-10 blocks to solve the problem.

Start by drawing out the place value model using base 10 blocks for each number.  Students would draw 3 tens sticks and 9 ones dots to represent 39 and then below 2 tens sticks and 8 ones dots to represent 28.  Then, count the ones.  There are 17 ones.  Since there are more than 10, you would regroup.  Circle the ten ones and draw an arrow to the new ten that you made over in the tens area.  Then count up your tens (10, 20, 30, 40, 50, 60) and 7 ones and your answer will be 67.

Empty Number Line Strategy:

Photo of empty number line strategy.

For empty number line strategy you start with an empty line.  Students have a choice and can either start at 39 or 28.  This is a great learning opportunity to talk about what is more efficient.  It would be easier to count up 28 then 39.  So on the left side of the number line, place the number 39.  Then, for counting there are multiple options.  We want to avoid students counting all 28 by ones so they can break it into tens and ones. Some students might start at 39 and jump 10 to 49 and 10 to 59 and then count up 8 ones to get to 67. Some students might start at 39 and jump 20 to 59 and then 8 ones to get to 67. There are multiple ways students can use the number line to help them solve the problem.

Break Apart Strategy:

Photo of break apart addition math strategy.

For the break apart strategy it is just what it sounds like – students are going to break the numbers apart into tens and ones. 39 breaks into 30 and 9. 28 breaks into 20 and 8.  Students will then add 30 and 20 and get 50. Then, add 9 and 8 and get 17. Then they’ll add 50 and 17 to get 67.

Expanded Form Strategy:

Photo of expanded form addition math strategy.

This is one of my favorite strategies and it is very similar to the break apart strategy.  Students will start by writing both numbers in expanded form.  39 expands to 30 + 9 and 28 expands to 20 + 8. These numbers will be written vertically on top of each other (ones on top of ones, tens on top of tens).  Then students add straight down.  9 + 8 = 17. The student will write down 7 in the ones spot and then move the 10 up to the 10s spot.  Then add 10 + 30 + 20 = 60.  Then, put the numbers back together 60 + 7 = 67.

Addition Practice FREEBIE:

Grab a FREE set of Differentiated Addition Word Problems for your students to use to practice their addition strategies. Click HERE for your FREEBIE!

Even More Addition Practice:

Photo of 3 addition word problem worksheets.

If you’re looking for some addition practice pages for your students to practice these strategies – I have worksheets already created for you.  Best part is – they are differentiated into 3 levels! These Addition Word Problem Printables are great for independent practice, homework, formative assessments, and more. Check them out here >>> Addition Differentiated Word Problem Worksheets.

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Strategies for Multiplying by Multiples of 10

Math

One of the skills we cover in second grade (which I know is often a third grade skill) is multiplying by multiples of 10. This can off scare kids as you are using larger numbers, but I knew my kids could handle it. To make it a little less scary, I introduced it using a story problem. I put the problem below up on the board and read over it with the kids.

Then, I told the kids to solve it on their white boards at their seats. I didn’t give any prompting or suggestions, I wanted to see what they would come up with on their own.  Boy was I pleasantly surprised! They had amazing strategies! As you’ll see below they came up with multiple different ways to come to the answer.  They all understood it was equal groups and they used strategies we had talked about with multiplication – drawing out equal groups, skip counting, repeated addition, breaking apart numbers, etc. I was so proud of them. After giving them time to solve I had students bring their white board up to explain their strategies to the class.

This honestly was the best way I have ever introduced it. Instead of me telling them how to figure it out or only showing them the trick (8 x 3 = 24 so 8 x 30 = 240), they really took them time to try to figure it out for themselves. And it helped because on future problems they knew multiple strategies they could use to solve it.

See their awesome strategies below…