Translating words and phrases into “math language” is an important skill because it will help them prepare for algebra and higher levels of math. But getting kids comfortable and confident with that takes time and practice. Whether you’ve got 5th graders working on numerical expressions or 6th and 7th graders writing algebraic expressions with variables, this low-prep and engaging partner challenge is a great warm-up!

What are Expressions?

Before jumping into this activity with your students, be sure you (and they) understand what expressions are.

Here’s a short, helpful definition of a numerical expression:

Numerical expressions are number sentences involving one or more operations.

Some examples include: 5 + 7 or 15/8 + 12 or (16 + 3) x 18

Numerical expressions contain NUMBERS and math OPERATIONS.

What about algebraic expressions? What’s the difference?

Algebraic expressions are similar to numerical expressions in that they include numbers and operations, but they also include at least one VARIABLE, which represents an unknown number.

Some examples of algebraic expressions are: 3x or 9 – 12y or (4 + p) – 15r

The key thing to note is that expressions include numbers and math operation symbols but NO EQUALS SIGN.

When you have two expressions that are equal to each other, it forms an equation. But that’s a post for another day. If you’d like to move on to finding equivalent expressions try this cut and paste equivalent expressions activity.

Introducing Expressions to Students

Although I shared some definitions and examples for you above, I would encourage you to NOT start there with your students.

Instead, give them the chance to think about their own way of translating situations, words and phrases into expressions using this partner challenge.

Walk around the room and listen in on student conversations to hear how they think about the wording and the math. Listen to student disagreements and how they justify their answers.

This will give you insights into what students already know, what they may need help with, and any misconceptions that you need to clear up after they finish the activity.

Writing Expressions Activity: Which Version Will You Use?

To use this in your class, all you need to do is choose which version is best (numeric expressions or algebraic expressions) then print a set for each pair of students.

But which version do you need for your students? Option one includes numerical expressions only. This is best for 5th grade students who are not yet ready to work with or think about variables.

But you might also use this version with older students who struggle with word problems, need further clarification on different math operations or who need a refresher before including variables.

Option two is to help introduce students to writing algebraic expressions. This is a fun warm-up for 6th or 7th grade students before you get into your expressions chapter or unit, or as a quick refresher before working on more challenging expressions and word problems.

If you enjoy this activity, become a Math Geek Mama+ member and gain access to the entire ad-free library of engaging math activities like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

How to Use the Writing Expressions Partner Activity

To begin, pair students with a partner and print a worksheet for each partner. One student should have ‘Partner A’ and the other student should have ‘Partner B.’

The post FREE Writing Expressions Activity: Partner Challenge – Grades 5-7 appeared first on Math Geek Mama.

Simplify. Combine like terms. These words can be confusing for early algebra students who don’t have a solid foundation or understanding of what they mean in a math context. Hands on, visual models can help students move from confusing and abstract to sense making. One of my favorite tools for visualizing abstract algebra concepts is algebra tiles. But they can be expensive to purchase, cumbersome to store and a mess to clean up, wasting precious class time. So I prefer using digital pieces that students can move and manipulate in the same way, with no cost, no storage and no clean up! Read on to learn how to simplify expressions with digital algebra tiles and grab the FREE activity for your students.

Laying the Groundwork for Simplifying Expressions:

If your students have no exposure to algebraic expressions (meaning expressions that include variables), you may want to explain a few terms to them before you dive in with the algebra tiles.

I have found that the best way to prepare students to abstract ideas with variables is to remind them of what they know of operations with whole numbers.

For example, you might start with an expression such as “5 + 3 – 1.” They might think this is silly and way too basic, but if they don’t actually, truly understand what addition & subtraction mean, they will not be able to apply it to algebraic expressions.

Then you may want to ask about an expression such as “4 + 8 – 4” to discuss additive inverse. The goal is to move them to the point where they understand “zero pairs,” meaning +1 and -1 are equal to zero.

Lastly, to help them understand “like terms” I give them some expressions such as “4 apples + 3 oranges – 2 apples” and discuss finding the total number of apples and the total number of oranges as two separate quantities.

Another helpful analogy (especially if you have older students who will be working with terms with exponents) is to talk about last names such as Roberts and Robertson. Although they start out in the same way, the ending is different. So you cannot combine Roberts with Robertsons, because they are not in the same family (then relate this to x-values versus x-squared values).

After some initial discussions about zero pairs & like terms, you can dive into the visual lesson with algebra tiles.

Simplify Expressions with Digital Algebra Tiles:

This activity is created for google slides, so you can either project this to the whole class to discuss together or you can share a copy with each student in google classroom.

Ideally, students will be able to have their own copy, so they can move around the pieces and think through each expression on their own. But if they don’t have devices to use, maybe they can take turns while you lead a discussion with the whole class or a small group.

This set includes 10 different google slides to get students started. To simplify each expression, they begin by modeling what’s shown using the algebra tiles.

They can then move pieces around to group like objects or if they are able to simplify just by seeing the tiles together, they can then type the final, simplified answer in the box.

It’s pretty straightforward, but if students get stuck, encourage them to group like pieces together. They might also want to write out notes or additional drawings on scrap paper.

Depending on how you use this in your class, you may want to stop and discuss after each slide, or you might let students work until the end and then check/discuss all ten slides at once.

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

Algebra Tiles Lesson as Intervention:

I like to use this type of activity as an opening activity or warm-up to a lesson to get a sense of students’ understanding and thinking.

However, this could also be a very useful resource for intervention if you have students who struggle or need additional work and review with understanding algebraic expressions.

In this case, I would use this in small group time (or as the “teacher” station if you use math stations), allowing students to slow down & share their thinking with you. This will give you a chance to see where they struggle and address misunderstandings or misconceptions.

Grab the Digital Algebra Tiles Activity for Google Slides:

If you’d like to give this a try with your students, use the link below to grab it FREE in my shop! Here’s what you’ll find in the download:

• Access Link to make a COPY of the slides in your own google drive
• Directions for sharing this with your students in google classroom
• Answer key for all 10 slides

I hope this is a useful resource for you and your students, even if you’ve never used algebra tiles before!

{Click HERE to go to my shop and grab the FREE Simplify Expressions with Digital Algebra Tiles Activity}

The post Simplify Expressions Visually with Algebra Tiles – DIGITAL Activity appeared first on Math Geek Mama.

How do you introduce the idea of functions to middle school students? Most textbooks jump right to a definition such as “a relation in which each element of the domain is paired with exactly one element of the range.” What!? An 8th grade student (especially one who is apathetic towards math) is going to fall asleep hearing that. Rather than telling students math-y definitions, or even showing them lots of examples and talking at them, I prefer to give students problems and tasks that they can explore and discuss on their own. Then I can help clarify or clear up misconceptions as they needs arise.

Exploring functions is no different. So today I’m going to share a variety of tasks and ideas for helping students make sense of functions, function representations, & function rules so they are ready to focus on linear functions in particular.

5 Simple Student-Centered Ideas for Teaching Functions:

1. Relations Sorting Activity

One very simple warm-up idea is to give students a matching sort challenge.

This sort includes 8 different matching sets. Each set includes 3 different representations of functions, such as ordered pairs, tables, graphs, equations & descriptions.

The goal of this activity is to help students see that relations & functions can be represented in different ways. This is important because often students learn algebra in isolated pieces & never get the chance to connect the dots. My goal with this is to help them see that each representation is equivalent, and to show them how visual models (such as tables & graphs) relate to more abstract forms such as descriptions and equations.

Read all the details for how to use this functions sort with your students and grab the download FREE right here.

2. What is a Function: Vending Machine Model

If there is one math concept that I see students mix up more than anything, it is determining whether a relation is a function or not.

They understand that “something can’t repeat” and so they try to memorize (or they simply guess on those questions–since the answer is usually ‘yes’ or ‘no.’).

The problem is that this doesn’t give them a solid conceptual understanding of what makes a function unique. And thus, their attempt to memorize does no good.

Instead, I introduce functions using a vending machine analogy.

Let’s review what it means to be a function: every input has exactly one output.

When we think about what this means at a vending machine, it means that you cannot put $1 into the machine and get both a Sprite AND a Coke.

You can only get ONE drink with your dollar.

On the other hand, I can put in $1 and get a Coke, and then you can also put in $1 and get a Coke.

We can both purchase a Coke, because we are two different people, with two different dollars.

So how does this relate back to functions?

Well, what that looks like with ordered pairs is this: an x-value cannot have two different y-values. For example, you cannot have the points (3, 5) and (3, 7).

But you CAN have these two points: (3, 5) and (7, 5).

Once that basic understanding is laid, I look at what this means on the graph. What we see when an x-value has more than one y-value is that the points are on top of each other.

This leads to a discussion of the ‘vertical line test’ or the ‘pencil test’ that is often taught to help students determine functions.

Once they understand that a single $1 cannot give 2 different drinks, it’s easy to connect that with the visual on the graph, and then this ‘test’ becomes more meaningful as well (and more likely to be remembered).

A simple set of guided notes to introduce functions with the vending machine analogy is included in this Introduction to Functions resource.

3. What’s My Rule? Functions Game

Once students understand what a function is, I like to play this simple game as a warm-up to connect a function rule to the set of inputs and outputs.

This game can be played with 2-3 players and is such a fun challenge.

To begin, one player secretly chooses a function rule (described in words, such as “add 3”).

Then they only players choose inputs (or ‘start’ numbers) and the player with the rule gives them the output. After choosing a few inputs, players must try to determine what the general rule is.

The goal of this game is to help students make connections between a description and the inputs/outputs of a function, to look for patterns and to think about evaluating functions to create a table of values.

Although writing a function rule using algebra (or function notation) can feel intimidating for students, this game helps them see that it’s not as scary (or new & foreign) as they think.

It also allows for some great math discussions and really pushes their algebraic thinking as they try to find a pattern or rule that works for EVERY input in the table.

Learn more about how to play the function rules game and grab the FREE download in this article.

4. Compare Functions with Function Tables

Once students understand what functions are and how to interpret and write function rules, they begin creating tables to prepare for graphing functions.

In this simple math center game, students can work independently to practice evaluating and graphing functions, as well as comparing those that are linear to functions that are not linear.

But it also includes a simple partner game which allows students to compare functions with another student. This will help them to look more closely at equations and how inputs affect the outputs.

One goal of the partner challenge is also to help students think about what the graph of the function will look like without actually graphing it.

What do they notice about the points they generate? Do they seem to be increasing or decreasing? Will the graph be linear or non-linear? How can they tell?

These are the types of questions you can discuss with students as they create function tables and compare functions.

Grab this simple Function Tables Math Center (which also includes 2 sets of guided student notes) right HERE.

5. Functions Scavenger Hunt

Lastly, I want to share a resource that provides a fun review of all the skills discussed above. This classroom scavenger hunt allows students to work with a partner & get up and move as they practice creating tables, writing function rules and comparing linear v. non-linear functions.

This resource also includes 2 pages of additional functions practice, which you can assign independently. Each page includes ‘functions four ways,’ requiring students to represent a given function with 4 different representations.

This is to reinforce all that they’ve seen and learned about functions and to again help them see the relationships between different representations.

Use this as an extra in class assignment, as homework, extra credit or in your sub plans to help students review & deepen their understanding of function representations.

Learn more and grab the Functions Scavenger Hunt Set HERE.

Of course, this list of just a starting point, but hopefully this gives you some new ways to engage your students and some fun ideas for teaching functions.

And maybe it even gives you ideas for more ways to teach and explore functions that you haven’t thought of before.

Did you love the ideas shared here? Each of the resources above (and SO many more!) is included in Math Geek Mama+, an all-access, ad-free membership for teachers in grades 5-8.

LEARN MORE ABOUT MATH GEEK MAMA+ HERE!

Find more resources for making middle school math fun & purposeful:

• Writing Algebraic Expressions: FREE Practice Pages
• Summer Algebra Review: Solve Equations Practice
• Graphing Linear Equations: Cut & Paste Worksheets {FREE}

The post Simple Ideas for Introducing & Exploring Functions in Middle School appeared first on Math Geek Mama.

One of my biggest goals when teaching functions is to help students understand that functions can be represented in multiple ways. To help them make connections between a table, a graph and an equation. That describing a situation in words can then be translated into math language (but still mean the same thing!). A lot of times, I see students get hung up on abstract equations, unsure what to do with them. But if we can help students see how visuals such as tables (and ordered pairs) and graphs relate back to the equation or a very simple description, we can deepen their understanding and build a bridge from the concrete to the abstract. That’s why I use this function representations sort to introduce this idea to students.

Understanding Function Representations

First, it’s helpful to understand different ways to represent functions ourselves. Functions can be represented in many ways, such as:

• List of ordered pairs
• A table
• Graph on the coordinate plane
• Equation
• Description in words

I love thinking about and seeing functions in lots of different ways because it can help me notice something (some pattern or relationship) about that function that would be missed with just one representation.

But I also love to help students make these connections because they can often see each of these representations completely independent of one another, missing out on the patterns and relationships.

So before I ever use the word function or try to explain what it is and what it looks like, I give students this function representations sorting activity to let them notice and explore on their own.

Prepping the Function Representations Sort:

This sorting challenge includes 8 matching sets of relations. Each set includes 3 different representations.

To prep this activity, print the matching sets on card stock paper. I printed multiple sets so I could put students into small groups to sort and discuss.

To help keep track of the different sets and make sure all matches stayed together, I printed each set on different colored paper. That way one group got a blue set, for example, and I know all the blue cards stay together, etc.

After printing the cards (4 pages), cut out all the cards and mix them up.

Then you’re all set to share it with your students!

How to Use the Functions Activity with Students:

Again, I recommend putting students into small groups of 3 or 4 and giving one set to each group.

Then tell students they are looking for sets of 3.

And that’s it! I don’t give them any other information. I don’t tell them what constitutes a match. I don’t explain what any of the representations are. I just tell them to look for sets of 3 and be ready to justify their choices.

As groups work together to look at the different cards & discuss their observations and thoughts, go around the room to listen.

If a group is stuck, encourage them to start with a set of ordered pairs, because that it likely going to be a familiar representation. What do they know then about ordered pairs? (They are points on the coordinate plane). Can you find a card with those points plotted on the plane?

Hearing the way students talk about the different relations with their group will give you a sense of what they already know, how they’re thinking about these things and what misconceptions they might have.

Discuss and Compare Functions Together:

Once all groups have found 8 sets of 3 cards (whether or not they’ve correctly matched them), spend some time discussing their thoughts as a whole class.

As students begin to share their matches, ask them to justify their thinking in some way. How can they explain, show or prove that they did indeed match equivalent representations?

What are some of the things they looked for as they tried to sort the relations?

Here are some additional questions to consider together:

• What do you think they graph would look like? (for the functions that don’t have a graph)
• How would the graph for one of the equations be the same or different than the graphs for the sets of ordered pairs?
• Can you extend one of the tables to list more points? How?
• What do the variables mean in the equations and how do they relate to x and y in the table?

Of course, you can add whatever additional discussion questions come up in your class and extend this to whatever else you want to explore as it relates to functions!

Love this idea? This game was originally created for Math Geek Mama+ members. If you want instant access to games like this and so much more, check it out today!

LEARN MORE ABOUT MATH GEEK MAMA+ HERE!

But I hope this provides a fun and super easy starting point that gets your kids talking and noticing things.

Ready to try this out with your students? Use the link below to grab it FREE in my shop!

{Click HERE to go to my shop and grab the FREE Function Representations Sort Activity}

Looking for more resources for middle school math? Try one of these!

• Equivalent Expressions Activity {FREE}
• Graphing Linear Equations: Cut & Paste Worksheets {FREE}
• {FREE} Would You Rather…? Ratio & Percent Tasks | DIGITAL
• Linear Equations Puzzles: Free Practice Set

The post {FREE} Function Representations Sort: Small Group Activity appeared first on Math Geek Mama.

In today’s fast-paced educational landscape, where every moment counts, fostering effective math communication skills is essential to prepare our students for jobs in the 21st century. 

Picture this – a classroom abuzz with chatter, not just any chatter, but the vibrant symphony of students transforming numbers into lively conversations. Math talk not only strengthens students’ understanding of mathematical concepts but also cultivates a positive and collaborative learning environment. 

In this article, we’ll explore 10 easy and practical strategies to foster productive math talk in your upper elementary classrooms, creating an atmosphere where mathematical discourse becomes second nature. Ready to unleash the power of math talk, where every student’s voice becomes a powerful tool for learning? Let’s dive in!

*This is a guest post from Shametria of The Routty Math Teacher

10 Easy & Productive Math Talk Strategies:

1. Establish a Math Talk Routine: Begin each math session with a dedicated time for math talk. This routine can include a brief discussion of the previous day’s concepts, sharing problem-solving strategies, participating in a number talk, or exploring real-life applications of the upcoming lesson. Consistency is key in building a comfortable space for students to express their mathematical thoughts.
2. Use Open-Ended Questions: Encourage critical thinking and discussion by incorporating open-ended questions into your lessons. Questions that require more than a simple yes or no answer prompt students to articulate their reasoning and engage in meaningful conversations. For example, instead of asking, “Is the answer 4?” try, “How can you verify/prove your answer?”
3. Implement Think-Pair-Share Activities: Provide students with an opportunity to process their thoughts individually before sharing with a partner or the whole class. Think-Pair-Share activities not only build confidence but also promote active listening and collaboration. Students can share their unique perspectives, fostering a diverse range of approaches to problem-solving.
4. Create a Math Talk Community: Establish a classroom culture where students feel comfortable expressing their ideas without fear of judgment. Celebrate and value each contribution, emphasizing that every thought is a step towards a deeper understanding of the material. A supportive community encourages even the most reserved students to participate actively.
5. Incorporate Visual Aids: Enhance mathematical discussions by incorporating visual aids such as diagrams, charts, or manipulatives. Visuals provide a concrete representation of abstract concepts, making it easier for students to articulate their understanding. They can use these aids to explain their reasoning to their peers, reinforcing their own comprehension in the process.
6. Elevate Engagement through Real-World Connections: Connect mathematical concepts to everyday scenarios, inviting students to discuss how they encounter and use mathematical concepts and skills in their everyday lives. Whether it’s calculating discounts during a shopping spree or understanding geometric concepts in architectural structures, linking math to the real world not only sparks enthusiasm but also prompts lively discussions among students. Encourage them to share their experiences, building a bridge between the classroom and the world outside.
7. Encourage Debate and Justification: Foster a healthy debate by encouraging students to justify their answers and challenge their peers respectfully. This not only sharpens their analytical skills but also promotes a deeper understanding of mathematical concepts. Debates can be structured as friendly competitions or collaborative group discussions.
8. Integrate Literature and Storytelling: Infuse math talk with creativity by incorporating literature and storytelling into your lessons. Use math-related stories, puzzles, or scenarios to captivate students’ interest and spark lively discussions. This approach not only makes math more relatable but also connects it to the broader world.
9. Provide Scaffolding: Recognize that students may need support as they develop their communication skills. Offer scaffolding by providing sentence starters, prompts, or specific vocabulary to guide their responses. Gradually, as their confidence grows, encourage more independent expression.
10. Offer Professional Development Opportunities: Empower yourself and your colleagues to deepen your understanding of math talk by exploring resources such as my free Math Talk Toolkit. This toolkit is designed to equip teachers with practical strategies, conversation starters, and activities to seamlessly integrate math talk into daily instruction.

Productive Math Talk: Communication is the Key 

As you embark on this exciting journey of fostering math talk in your upper elementary classrooms, remember that communication is the key to unlocking your students’ mathematical potential. 

By implementing these 10 strategies, you’ll create an environment where math talk becomes a natural and integral part of the learning process. Embrace the power of dialogue, celebrate diverse perspectives, and watch as your students not only become proficient mathematicians but also effective communicators. 

Ready to Learn More about Math Talk in the Classroom?

Read “Math Talks: Sparking Communication in Kids” for a comprehensive guide for mathematical discourse in the classroom and discover strategies to encourage math talk, effective prompts, and ways to differentiate instruction via math talks. Download your Math Talk Toolkit to discover a wealth of resources that will elevate your classroom to new heights of mathematical communication!

If you are especially interested in starting daily number talks, check out the resources below!

• The Benefits of Daily Number Talks
• 3 Simple Number Talk Ideas to Get Started
• FREE On-Demand Training: The Power of Number Talks (with a free starter kit)

The post 10 Easy Ways to Foster Productive Math Talk in the Classroom appeared first on Math Geek Mama.

Have you been wanting to start a number talk routine in your classroom, but aren’t sure where to begin? If you’re just getting started, it can be intimidating. How do you encourage discussion? Will students respond? What is the end goal, and how do you steer the conversation in that direction? In this post, I’ll outline three simple ways to start talking about numbers in your classroom, increasing the confidence of both you and your students when it comes to a number talk routine.

*This is a guest post from Shelley at Shelly Gray Teaching

But first, what is a number talk?

Number talks are short, 5 to 15-minute whole-class or small-group discussions with the goal of building number sense.

Perhaps the most important part is that the discussion focuses on HOW MANY WAYS to solve a problem rather than on the answer itself. This is a major shift from what most students and teachers are used to.

The end goal is to have a productive discussion about a math problem where students share their own strategies, reflect on others’ strategies, and learn to see math in different ways.

Related: 5 Reasons to Incorporate Daily Number Talks

But getting to this point can take some time. So how can we get started making this shift from a focus on correct answers to a focus on deep thinking?

Here are three simple number talk ideas to get started:

1. “Double a Number” Number Talk

The first simple way to get your students talking about numbers is to give them a number and have them double it. The focus is not the answer, but rather on HOW they are thinking about the doubling process.

As students share their thinking, record it on the board to make it visual. This helps students understand each other’s strategies.

For the example shown below, one student might think about adding 125+125. Another student might think about doubling 100, doubling 20, doubling 5, then adding them all together. A third student might think about doubling 120 to make 240, then doubling 5 to make 10, and adding the parts together to make 250.

Having a discussion about these different ways of thinking is a powerful way to help your students build number sense.

This short video on Instagram or on YouTube will help explain the effectiveness of this activity in more detail.

2. “Get to the Next Multiple of Ten” Number Talk

Another simple idea for a number talk is to give students a number and ask them to get to the next multiple of 10 in different ways. In the example shown below, we are trying to get to 240.

One student might know that 7 more are needed because 3+7=10. Another student might think about adding 2 to get to 235 first, then adding 5 more to get to 240. Another student might think about base ten blocks or ten frame images to help them visualize.

To make this activity more difficult, ask students to get to the next hundred or even thousand. The most important part is listening to all the different ways they are thinking about this problem.

3. “How Many Ways?” Number Talk

The third idea is another one of my favorites that I call, How Many Ways?. In this activity, we give students a math problem and see how many ways they can come up with to solve it. In this example, we are asking students to add two numbers using a number line in as many ways as possible.

The image above shows just a handful of possible solutions your students might come up with. Can you think of another way to solve it?

Here’s another video to watch on Instagram or on YouTube that will explain this in more detail.

Final & Best Number Talks Tip: Just Get Started

Although the thought of doing number talks can be intimidating, the most important thing you can do is to just get started. Choose one of the activities above (doubling a number is my top choice) and try it! You don’t need to have all the answers ready; you can take direction from your students and master number talks together.

If you’re looking for more information about number talks, you can read this article with tips for getting started. If you’d simply like resources to get you started, find out more about my no-prep Math Conversations slides here.

And if you are interested in how to use number talks to unpack math operations (and how they might look different in K-2!) sign up for this free “Getting Started with Number Talks” class with Math Geek Mama.

The post 3 Simple Number Talk Ideas to Encourage Deep Math Thinking appeared first on Math Geek Mama.

As students learn the four math operations, it’s imperative that they learn to apply the operations to show higher level thinking.  Students should be able to determine which one to use and apply it to real-life situations, especially considering that our end goal is to create productive thinkers who can change the world.

One way we do this is by providing students with word problems that highlight the math operation and include problems that may happen in the real world.  Let’s explore some common reasons why students struggle with math word problems and learn two word problem strategies to help them overcome these challenges.

*This is a guest post from Jessica at Math with Purpose.

Common Reasons Students Struggle with Word Problems:

1. They’re Developing Reading Comprehension Skills

It’s no surprise that word problems can be a challenge for many students.  After all, many of these students are developing their own reading skills and then being asked to read and interpret informational text in a word problem.

Many word problems include multiple steps which require students to infer what to do first.  In fact, the National Foundation for Educational Research found that poor inferring skills lead to poor comprehension.

It is a skill that students must be explicitly taught and is usually one of the later skills due to its complexity. That means our students are expected to do a higher level of reading comprehension every time they read that short word problem in math class!

2. They’re Relying Only On Keywords (Rather than the Meaning of Operations)

Students can encounter difficulty when translating words into mathematical symbols or equations. They may struggle to identify which mathematical operations are needed to solve the problem and how to represent the problem in a mathematical format.  Many teachers teach students to circle key words and memorize them to determine which operation to use.

Students may learn that addition means to “add to” or “make a total” while subtraction is an action of “taking away”.  Students look for keywords that they can circle to determine whether adding or subtracting.   But what happens when the action is there, but students actually need to solve using a different math operation? Here’s an example:

Gabbi had some stickers.  She earned 12 more stickers for completing her homework.  Now she has 56 stickers.  How many stickers did she have at first?

In this problem, it’s clearly an “add to” situation.  Gabbi is adding to her collection.  However, to solve the problem, a student would need to subtract from the total to find the missing part.

While keywords can help with some problems, they don’t actually work for the variety of word problems students will encounter.

In fact, according to the University of Arizona, students will solve 15 different addition and subtraction problem types by the end of Grade 2 and 9 different multiplication and division problem types by the end of Grade 4.

Read more about the problems with relying on key words in word problems here.

Word Problem Strategies to Help Students Comprehend Operations Before Solving

In order to help students comprehend and solve complicated word problems, math educators have to think like a reading teacher and acknowledge there is a whole set of skills required for students to do the mathematics.

Instead of using basic strategies such as circling key words and plugging in numbers that may work some of the time, teachers can push for greater depth and understanding using two easy word problem strategies.

1. Make connections to prior knowledge and experiences:

One of the first reading strategies students learn is to make a movie of the text in their head and make real-world connections to the story.  The most meaningful connections are text to self connections where students relate the text to their own lives.

Students can do the same thing with a word problem!  They can read the story and make a picture of what’s happening– maybe even act it out with real life objects.

Teachers can also change the nouns in the word problem to be more relatable for each class including student names in the problems and objects that they enjoy doing each day.  This one simple change will help students engage with the text and want to find out more.

2. Visualize the problem by drawing a picture:

Once students are connected to the story of the word problem, it’s time to connect it to mathematics.

Instead of relying on keywords, students can draw visuals of the part-whole, comparison or equal groups models to show what operation will be needed to solve the problem.

Through drawing bar models, students will identify the variable and lay the strong foundation for algebra even beginning in Grade 2.

These visuals aren’t complicated and can be taught easily while students are comprehending the word problem.  You can find out more about these visual models for word problems in this blog post and even snag free posters for each representation for your classroom.

Solving math word problems is a valuable skill that empowers students to apply mathematical knowledge in real-life situations, but it also requires students to use a variety of skills to accomplish.  By thinking like a reading teacher, math educators can employ the skills they use during reading to truly help students master word problems by making connections and visualizing the problem.

If you are looking for more support to help students walk through the variety of word problems they will encounter, consider The Problem Solving Handbook.

It includes 3 video lessons for each problem type, plus practice and challenge problems for students to truly master word problems.

The post How to Tackle Math Word Problems & Make Sense of Operations appeared first on Math Geek Mama.

Teaching math can be a rewarding but challenging endeavor. Whether you’re an experienced educator or a new teacher, the subject of mathematics often elicits a range of emotions from students (and teachers alike!). Some find it exciting and intuitive, while others may feel overwhelmed or anxious.

If you find yourself overwhelmed teaching math, don’t worry—you’re not alone, and there are strategies you can employ to make the experience more enjoyable and effective for both you and your students. In this blog post, we’ll explore 9 tips to help you navigate the world of teaching math through planning and conscious thinking.

*This is a guest post from Kelsey at Wife Teacher Mommy.

1. Stop Comparing Yourself to Other Teachers

As a teacher, you have a ton of responsibilities that pull you in a million different directions. Planning lessons, differentiation, grading papers, collaboration, classroom management, behavior management, IEPs, and parent-teacher conferences, just to name a few.

It makes sense that you’re feeling overwhelmed. And you may be exhausted, like, all the time. You may feel like you can’t do it all but the teacher next door or down the hall can. But you know what? The biggest mistake teachers make is comparing themselves to other teachers who seem to have it all together.

Instead of comparing yourself to the other teachers around you, reframe your mindset and focus on your strengths. You bring a unique set of skills to your job that your students benefit from.

For more help and tips to stop comparing yourself to others, listen to this episode of Wife Teacher Mommy: The Podcast.

2. Understand the Math Fundamentals

Before you can effectively teach math, it’s essential to have a strong understanding of the subject matter. Review the fundamental math concepts, brush up on your skills, and explore different teaching methods.

Just as you need to understand the fundamentals, your students do as well. Try incorporating daily math reviews or math fluency practice to help your students keep their math foundation strong.

3. Set Clear Objectives for Your Students

Establish clear learning objectives for each lesson or unit, in addition to clear classroom rules and expectations. Knowing what you want your students to achieve will not only help you stay focused but also give your students a sense of direction.

Clearly communicate these objectives and expectations to your students to help motivate them. They will appreciate knowing exactly what you expect them to learn from the lesson. For more help with setting up a clear classroom management plan, listen to this podcast episode.

Or listen to this episode for extra help if you struggle with motivating those “lazy” students.

4. Create a Vision Board

Do you have a vision board in your home or classroom? Using a vision board can help you feel more intentional and balanced, instead of overwhelmed, in both your personal and professional lives.

Keep an up-to-date vision board where you can see it daily, then celebrate your accomplishments by removing them from the board and adding new intentions.

Simply spend 3 minutes a day focusing on your vision board to reinforce the connection between your conscious intentions and subconscious mind.

5. Make Math Relevant for Students

“When will we ever use this?” I’m sure you’ve had a student (or ten!) ask you this question.

Mathematics is all around us, and showing your students its real-life applications can make the subject more engaging.

Whether it’s calculating expenses, solving practical problems, or exploring the mathematical principles behind art and architecture, relating math to the real world can make it more relatable and interesting.

6. Declutter Your Mind and Space

Start by organizing your math supplies– worksheets, calculators, extra pencils, rulers, compasses, etc. When everything has a place, it can help reduce clutter and make you feel more organized.

Establish a classroom routine with your students that includes tidying up at the beginning and end of the day.

Often, before you can organize your space, you need to organize your mind. Listen to this episode for tips on how to do that. Whether you are new to the classroom or a veteran teacher, one of the organization tips shared will resonate with you.

7. Foster a Growth Mindset

A great mentor once shared this advice with me- when students asked her the question above and there wasn’t an easy real-life application, she focused on a growth mindset and told her students that they were learning how to learn.

Encourage your students to embrace that growth mindset. Help them learn what to do when faced with a new challenge. Show them how to figure out the answer to a question. Teach them that mistakes are part of the learning process and that perseverance is the key to success in math.

A positive attitude towards challenges and setbacks can help students develop a resilient approach to problem-solving. 

Need help with your own growth mindset? Attend a free Mindset Masterclass to help you!

And check out this list of math tasks that will help students foster a growth mindset.

8. Provide Purposeful Feedback

Another piece of great advice that I got as a new teacher was, “You don’t have to grade everything.” This will save you time and sanity. Plus, grading is not always the best way to provide feedback. Traditional grading puts the focus on scores, or how many answers students got right or wrong.

Instead, either verbally or in writing, provide feedback that focuses on how well the student understands the concept you are working on. Start with what they did well and praise their effort, not talent. Then provide clear steps for how they can improve the next time they try.

Individualized feedback can help your students understand their strengths and weaknesses and motivate them to work on their skills.

9. Seek Support and Resources

Don’t be afraid to ask for help or access available resources. Your colleagues and online communities can offer a wealth of advice and support.

If you are feeling overwhelmed teaching math, check out my Mindset Masterclass to transform that overwhelmed feeling into balance. In this class, I teach the 5-Step Mindset Framework that has been used and proven with thousands of clients.

By following these nine tips, you can create a positive and nurturing learning environment where your students can thrive and develop a deeper appreciation for mathematics.

The post Overwhelmed Teaching Math? 9 Tips to Find Balance & Grow as a Teacher appeared first on Math Geek Mama.

As teachers, we have the power to inspire awe or dread in our budding mathematicians. As a seasoned middle school educator with well over a decade of experience, I’ve learned that one of the keys to making math more enjoyable and accessible is through interactive, engaging activities. Read on to see how I use interactive math notebooks & math crafts two fantastic for creating math magic in the classroom!

*This is a guest post from Crystal at Teaching Principal.

What Are Interactive Notebooks & Why Are They Effective Math Instruction?

Interactive notebooks (or INBs for short) are a versatile engaging tool that can transform any student’s math learning experience. These are customized notebooks students create to record their math journey.

What makes INBs so powerful is the interactive element. Students don’t just passively write information down; they actively participate in constructing their own math resources, allowing for deeper conceptual understanding and synthesis.

Benefits of Interactive Math Notebooks:

As I mentioned, INBs are a powerful tool for engaging students in the learning & exploring of math concepts, unlike ordinary note-taking. Here are some additional benefits of using them in the math classroom.

Interactive Math Notebooks Provide:

• Multi-sensory approach for increased student engagement
• Better organization and study habit formation
• Deeper understanding of mathematical concepts

Being dual certified as an elementary and special educator, I’ve personally witnessed exceptional students become more enthusiastic about math when they take ownership of their notebooks. They show pride in their work, and this pride translates into improved learning outcomes.

Bonus: it’s always nice to bring out the interactive notebooks as a data point for parent conferences and progress monitoring updates!

How to Create Interactive Notebook Pages

Creating effective interactive notebook pages can be both fun and educational. It’s all about designing pages that are visually appealing, interactive, and aligned with your student learning objectives. The key is to make the learning enjoyable.

Need help coming up with ideas?

Check out these 4 simple (and free!) interactive notebook templates!

But the creative fun doesn’t have to stop there. You can include foldable activities, brightly colored pockets, and interactive elements like mini-games or pop-ups in your INBs.

For example: for a lesson on comparing numbers using the <, >, and = symbols, younger students can create a “greater gator” alligator, making their learning more tangible and memorable.

Math Craftivities

Simple math crafts are another engaging approach to teaching and reinforcing math.

These projects allow students to explore mathematical concepts through hands-on, creative activities. Whether students are coloring by code to complete a festive scene or solving expressions on segmented candy corn pieces, simple crafts make abstract math ideas concrete and much more enjoyable.

As an added bonus, some of my favorite math crafts double as colorful classroom displays for the holidays! It makes for festively functional bulletin boards, no matter the season.

Combining Interactive Math Notebooks and Math Crafts

Imagine the magic that happens when you combine interactive notebooks with math crafts. Are you ready for that kind of student engagement and mathematical retention?!

Students can create notebook pages that are part of a larger craft project.

Here’s a good example: when teaching about area and perimeter, students can design their own mini-gardens in their interactive notebooks and then later create a 3D diorama, calculating the area and perimeter of their garden.

This not only reinforces the math concept but also allows for creative expression! Your students will love the real-world application and hands-on approach to learning. I can almost guarantee it!

In the world of education, especially post-pandemic, we often hear about the importance of making learning fun. Today’s 21st-century learners are built differently; they thrive off flashy fun. When it comes to mathematics, interactive math notebooks and simple math crafts are two of the most powerful tools to achieve just that.

By embracing these teaching resources, we can make math engaging, accessible, and memorable for all of our students. Don’t hesitate to try out these creative approaches in your math classroom. Watch with wonder as your students’ enthusiasm for math grows!

Looking for manipulatives that students can include in a pocket of their interactive math notebook? Check out this HUGE free collection of printable math manipulatives to find something just right for your students.

The post Make Math Engaging with Interactive Math Notebooks & Math Crafts appeared first on Math Geek Mama.

Math fact fluency is essential and plays a fundamental role in a student’s mathematical education. For students with learning disabilities, mastering math facts can be particularly daunting, but with the right strategies and support, they can develop strong math fact fluency. Math fact fluency, the ability to recall basic arithmetic facts quickly and accurately, is essential for building a solid foundation in math and progressing to more complex concepts.

This is a guest post from Karla at One Room Schoolhouse.

Why spend time on math fact fluency?

• Efficiency: Fluency in math facts allows students to perform calculations quickly and accurately. This efficiency is crucial in everyday life when making calculations, from shopping to cooking.
• Problem-Solving: Math fact fluency enables students to focus on problem-solving rather than getting bogged down by basic calculations. When students don’t have to spend excessive time on simple math facts, they can tackle more complex and interesting math problems.
• Confidence: Mastering math facts gives students confidence in their mathematical abilities. This confidence extends beyond math class and can positively impact their overall self-esteem and academic performance.
• Reduces Math Anxiety: Math fact fluency can help reduce math anxiety. When students are confident in their ability to perform basic math operations, they are less likely to experience anxiety when faced with math tasks.
• Conceptual Understanding: A strong foundation in math facts enhances a student’s conceptual understanding of mathematics. It helps students see relationships between numbers and operations, making more complex math concepts easier to grasp.

How to Develop Math Fact Fluency in Students with Learning Disabilities

1. Understand Learning Styles and Disabilities

Before diving into strategies, it’s crucial to recognize that each student is unique, and learning disabilities can vary widely. Some common learning disabilities that impact math fact fluency include dyslexia, dyscalculia, and attention deficit hyperactivity disorder (ADHD). Tailoring strategies to the specific needs of the student is key.

2. Multisensory Learning: Engage All Senses

Engaging multiple senses while learning can enhance knowledge retention. For students with learning disabilities, multisensory approaches are especially effective. Use tactile materials like counting beads, number lines, and manipulatives to reinforce concepts and create a multisensory learning experience.

3. Chunking and Patterning

Break down math facts into smaller, manageable chunks. Instead of trying to memorize all addition or multiplication facts at once, focus on subsets like 0-5, 6-10, or specific patterns (e.g., doubles, near-doubles). This approach makes the task less overwhelming and allows students to build confidence gradually.

4. Visual Aids and Memory Aids

Visual aids such as charts, diagrams, and flashcards can help students associate numbers with visual representations. Memory aids like rhymes, acronyms, or mnemonics can make abstract concepts more memorable. For example, “8 times 8 is 64, just like a square!”

5. Regular Practice and Repetition

Consistent practice is vital for building fluency. Use games, apps, or worksheets designed to reinforce math facts. Short, focused practice sessions are more effective than lengthy sessions which may lead to frustration. Encourage students to practice a little bit every day. Practice must be fun or students will not be engaged and will not learn.

6. Use of Technology and Apps

Technology can be a powerful tool to engage and support students with learning disabilities. There are numerous math apps and online platforms that offer interactive and adaptive practice, tailoring challenges to individual skill levels and progress.

Gimkit and Blooket are great for increasing math fact fluency because they combine gamification, immediate feedback, adaptability, competition, customization, and accessibility. These elements create an engaging and effective learning environment that can benefit all students, including those with learning disabilities.

By making math practice enjoyable and dynamic, these platforms help students build strong foundations in math fact fluency while nurturing a love for learning. These sites also keep track of data that allows the teacher to see which facts have been mastered and which facts are still challenging to students.

7. Progress Monitoring and Positive Reinforcement

Keep track of the student’s progress and celebrate their successes, no matter how small. Positive reinforcement boosts confidence and motivation. Setting achievable goals and offering rewards can turn the learning process into a positive experience.

Math fact fluency for students with learning disabilities requires a tailored and holistic approach. By understanding each student’s individual needs, employing multisensory techniques, utilizing visual aids and memory aids, and fostering a positive and supportive environment, educators and parents can help these students build a strong foundation in math.

With patience, dedication, and the right strategies, every student can achieve success in math, regardless of their learning challenges. You can also find some of my favorite products here.

The post 7 Math Fact Fluency Strategies for Students with Learning Disabilities appeared first on Math Geek Mama.