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.

I am one of the lucky ones to have an eighty minute math block EVERY. SINGLE. DAY. But I quickly learned that my students could not spend those eighty minutes sitting in their seats. They needed to get up and MOVE, but I also still wanted them to engage in the math. Task Card Math Scavenger Hunts quickly solved this problem. My students love walking into my classroom and seeing the twenty-four task cards hung up around the room. They know that after our mini-lesson, they are in for a treat!

*This is a guest post from Paige at The Math Matrix

How to Use a Math Scavenger Hunts in the Classroom:

Our task card scavenger hunts are a pack of twenty-four task cards that require students to solve problems while “hunting down” their next problem. All students start at a different card – this way, students can complete the activity without everyone being crowded around one single problem.

At each card, students will solve the math problem. After they record their answers on the recording sheet (in the correct box), they need to search the room for the solution, which brings them to the next card with a new problem to solve.

Your students will be going around the room to continue to solve and search for the next answer until they get back to the card they started at – this will ensure they got all of the answers correct!

If they end up at their starting card and yet have missed some problems, they know they’ve made a mistake somewhere.

Or if they can’t find their solution around the room, perhaps it’s because they don’t have the right solution!

Using the scavenger hunt setup, students can self-check and work together to correct mistakes.

Four Benefits of Using Math Task Card Scavenger Hunts:

1. Get Students TALKING

I love when my students talk math in my classroom, and encourage discussions about solution strategies and helping each other with incorrect answers.

2. Get Students MOVING

I hang up my Task Card Scavenger Hunts all over my room and grade level hallway and have my students use their clipboards to get up and MOVE around!

3. Get Students IMMEDIATE FEEDBACK

The nature of Task Card Scavenger Hunts gives immediate feedback because if the student cannot find the answer on another card, they know that they made a mistake.

While introducing this activity, I always make sure to discuss what might happen if we can’t find the answer and to circle back to the card they were working on to troubleshoot their solution.

4. Get Students HELP

When my students are working all over my room, I find it really frees up my time and I can move from student to student to give help to those who need it. I also found that this time is the best to pull small groups of students when I see them making the same mistakes or having the same question!

Trying Task Card Scavenger Hunts in Your Classroom

As you can tell, Task Card Scavenger Hunts really help my students break up their time in my class, while still practicing the important math concepts that they have been learning.

If you are looking for a free sample to see if math scavenger hunts are right for your classroom, CLICK HERE for a free sample covering mixed multiplication and division math facts!

Plus, there are many more task card scavenger hunts over in my store for you to check out!

Once you start with Task Card Scavenger Hunts, you won’t look back (I promise – your students will be BEGGING to do more!)

Find More Math Scavenger Hunts for the Classroom Below:

• Christmas Multiplication Facts Scavenger Hunt – Grades 3-4 {FREE}
• 2-3 Digit Multiplication Christmas Scavenger Hunt – 4th Grade {FREE}
• Area & Perimeter Practice for 3rd Grade – Scavenger Hunt Activity {FREE}
• Virtual Math Scavenger Hunt: Learn About Math in Nature {FREE}

The post Math Scavenger Hunts: Simple Math Practice for the Classroom {with FREE Hunts!} appeared first on Math Geek Mama.

As we gear up for possibly the strangest, hardest back to school season any of us have ever seen, there are unique needs for teachers and students. As I discussed things with a teacher friend, I asked how I could help her prepare and meet the needs of students and one struggle she mentioned (that I’ve heard from so many others!) is that even if students can go back to school in person, they can’t share supplies. There will be no passing around the base ten blocks or fraction tiles. No working together to model problems with ten frames and counting bears. To help overcome this, I created a collection of printable math manipulatives so every child can have their own set.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.

Printable Math Manipulatives for Kids

Why do kids need math manipulatives and visuals? Do these actually help, or does it just create busy work?

First of all, recent research has shown us that our brain uses visual processing portions of the brain when solving math problems. This is true even if we don’t draw a picture or use a visual diagram of some sort.

So I believe the more we can help kids create a library of visuals for their brain to use and draw from, the better they will be able to process, make connections & retain the math they learn.

Second, when kids are just beginning to learn concepts, there are so many math ideas that are very abstract. They’re not yet developmentally ready to jump to abstract ideas. So using a manipulative or visual model to show them the math is a tremendous stepping stone to connecting to the abstract concept.

Depending on the math skill you’re introducing or exploring, there are dozens of different manipulatives you might use.

Sometimes, this might be a large, fancy set of blocks like these.

Other times, it might simply be a number path or number line.

No matter what your needs are, I am sure you will find a printable version that you can use to make sense of math with your students in this printable math manipulatives set.

Included Manipulatives

There are so many resources included here, so you can print only the options you need for your students. This includes:

• Base Ten Blocks
• Number Paths (1-100)
• Hundred Charts
• Number Lines (6 labeled, 2 blank)
• Place Value Mats + Tiles for Whole Numbers
• Decimal Place Value Mat + Tiles (tenths + hundredths)
• Five frame
• Ten frames (2 versions)
• Number Bonds (2 versions)
• Blank Multiplication Tables (2 versions)
• Multiplication Fact Bookmarks
• Fraction Tiles
• Clock

In addition, each page is labeled so you know what the manipulative is and how you might use it with your students.

It also printable name labels in color and black and white so you can label each students’ set. (And no one will be sharing their supplies accidentally!)

Assembling the Printable Math Toolbox

I designed the whole kit so that it can fit into a plastic pencil case. I purchased ours at Target, but they typically have them at the dollar store or Wal-Mart as well.

However, you could just as easily store each individual set in a plastic, zip lock bag.

I recommend printing all materials on card stock paper for durability. Using different colors also makes it easier to find various materials and see what goes together.

You may also want some paper fasteners like these to assemble the clock and multiplication facts bookmarks.

I simply punched holes in the corner of the bookmarks, stacked them together in order, and used the fastener to hold them together. I could then easily flip through the different sets as a reference.

For the clock, I punched a small hole in the center of the clock and the end of each hand and then stacked them on top of each other. Then I inserted the fastener to hold it all together. I was then able to move the hands around the clock easily.

Lastly, there are two multiplication tables included. One is the whole table (12×12), the other is split into 4 sections so that the individual sections will fit in a pencil box. Print whichever version works better for your students.

Also note that I left these tables blank so that students could fill them in (as they learn the facts or as a review). Then, they can keep the table to use as a reference.

Once all the materials are printed and assembled, put it together in a pencil box or zip lock bag and add the students name to it.

This is optional, but it might also be good to add a couple of dice and a set of pencils. Then you’re students are all set to explore any math concept!

I hope this is a useful resource for you!

Of course if you prefer, you might also like this collection of virtual math manipulatives. This includes online manipulatives that students can use on their computer or tablet with nothing to print out.

If you teach geometry, you might like this set of printable 3D shape nets to build a variety of 3D shapes.

Lastly, if you’re looking for recommendations for manipulatives to purchase, see my top picks in this post.

To grab this printable math set, go to my shop at the link below!

{Click HERE to go to my shop and grab the FREE set of Printable Math Manipulatives!}

The post Printable Math Manipulatives | FREE Download appeared first on Math Geek Mama.

How fluent are your kids with math facts and computation skills? Do you want something fun and engaging, yet challenging for their mind when schools are closed? It’s important to keep up mental math skills like adding, subtracting and multiplication or they will be forgotten. It’s also a good workout for the brain to be challenged and to look for new strategies and build number sense as they try to work out different problems.

*Please Note: This post includes affiliate links which support the work of this site. Read our full disclosure here.*

What’s Included in the Download:

This collection of mental math challenges includes a variety so you can use this with multiple ages or easily differentiate.

First, you will find two addition and subtraction challenges.

Next, there are two challenges involving addition, subtraction and multiplication.

For older kids, there are two challenges involving addition and subtraction with integers (positive and negative numbers).

And if that’s not enough of a challenge, or your kids start to get bored with this, the download also includes a blank copy so that kids can design their own mental math challenge for friends or family.

How to Use the Mental Math Challenge:

On each challenge, the “starting number” is left blank, so you or your kids can pick a new number each time.

In this way, you can differentiate for different students using the same math operations by giving larger or more difficult starting numbers.

Although this is a “mental math” challenge, I have left spaces blank in between each operation so that they can write each answer down as they go (to keep track of where they are).

But all the math computing must be done in their head.

If your kids enjoy these challenges, try printing on card stock and then laminating, or slide it into a page protector to easily erase and use over and over.

For an Added Challenge:

If these exercises are too easy for your middle or high school students, there is also a blank challenge card included.

You can use the blank page a couple of ways. First, you can create a page tailored to their specific needs, using larger numbers, more difficult computation or even fractions and decimals.

Or you can give the blank page to your students they can create their own to challenge each other.

Another GREAT challenge for any age is to give them a blank page and see if they can create their own challenge that will always end with the same number (meaning, whatever you choose for your starting number will be your final answer, no matter what number you choose).

This is a great introduction to algebraic thinking and operations.

(HINT: The key to that is to make sure every operation you write in the path gets “canceled out” or “undone” somewhere. So if you start with “add 5”, somewhere along the way you also have to have “subtract 5.”)

{Click here to go to my shop and download the complete set of Mental Math Challenges HERE!}

I hope these are fun and helpful!

If your kids love a fun and unique math challenges, they may also love this set of hands on logic puzzles using pattern blocks! This huge collection will keep their brains busy for hours!

If you’re looking for logic puzzle challenges for older kids, try this collection. A Year of Logic Puzzles includes fun themed grid and sudoku puzzles for the entire year, for ages 9+.

The post {FREE} Mental Math Challenge for Kids: Exercise Your Brain! appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.*

Planning Just Right Number Talks:

Because I try to create and share resources that will be useful to you and make your teaching job easier, I have often thought about creating ready to use number talks. There are other resources like that out there, where all the problems are laid out for you, ready to present.

The problem is that number talks work when they are designed with your students in mind. When the problems are chosen to meet them right where they are and to push and stretch them in ways that are appropriate.

Only you can choose the right problems and move ahead at a pace that is just right for your kids.

Planning number talks requires you to know where students are and then adapt and adjust as you see how they tackle certain problems. It requires adjusting when you’ve presented a problem that’s too difficult. Or jumping ahead because there’s little to no productive struggle.

Pre-planned number talks can never do that for you.

You know your students and their needs are different from the kids you taught last year or the kids you will teach next year.

So what I have for you instead are some simple number talk planning pages that can hopefully help guide you through planning what problems you’ll tackle with your kids and help you think through how you’ll adjust when necessary.

Number Talk Planning Pages:

This download is included in my online course, Meaningful Number Talks.

But if you are already familiar with number talks and use them regularly in your classroom, you might not need the entire course. So I’m sharing this set of planning pages free to help you get started.

This download includes a single page for recording what problem you’ll present to students each day, along with space for extensions or investigations that might come up.

There’s also space for 1-3 backup problems in case you need to pivot on the spot. Having these planned ahead of time will allow you to adjust easily.

Second, this download includes a page for you to think through an individual math problem. What are possible strategies that might come up? What probing questions will you ask students?

Finally, it includes space for you to reflect afterwards so you can continue to grow and improve as an educator.

There are color and black and white versions of each page. I hope this is a useful tool for you as you guide your students through number talks. And I hope these help you to be intentional about the types and sequence of problems you present to your students.

Looking for more in depth understanding of what number talks are, why they matter and how to get started? Check out my course, Meaningful Number Talks. This short course can be completed in a weekend, allowing you to begin number talks by Monday!

Learn more about Meaningful Number Talks here.

Ready to try out the planning pages? Just fill out the form below and they’ll be sent directly to your inbox!

The post {FREE} Number Talk Planning Pages appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.*

What are Number Talks?

First of all, let’s talk about what a number talk is. A number talk is a quick time of mental math practice for your students to focus on developing skills and strategies around math operations (addition, subtraction, multiplication or division).

They should only last about 10-15 minutes, but can (over time) produce deep and meaningful changes in how your students approach and think about numbers and operations.

If this sounds like just another fad or yet another thing to add to your already full plate, I’d encourage you to consider why these brief mathematical conversations will be so beneficial to your students.

Why Incorporate Number Talks in the Classroom:

I could probably go on and on about the benefits of number talks and all the different ways to incorporate them, but today I will just hit on the what I believe are the biggest benefits.

Which of these would be most impactful for your students?

1. Number talks teach kids to think like a mathematician.

Talking about math is essential. It’s what mathematicians do. While students may think that mathematicians simply sit around working out computation problems, that’s not at all an accurate picture.

Mathematicians ask big questions, come up with ideas, look for answers and talk about it with other mathematicians.

We know that scientists come up with theories (or hypotheses) and then test them. Mathematicians do the same thing. Their ideas are called conjectures. They then prove them by reasoning (or talking) about them using logic in order convince other mathematicians.

Related: 10 Things Every Good Mathematician Should Do

2. Number talks help kids develop a conceptual understanding.

All too often, kids focus on formulas and algorithms without actually understanding what or why they do them. By seeing multiple methods of solving the same problem (mentally), kids have a deeper understanding of the math and their own ideas are then solidified.

This is not to say that there’s anything wrong with formulas, they are certainly helpful and efficient. But they don’t show or explain the meaning behind the math that kids are doing.

Developing a conceptual understanding, on the other hand, will help kids to actually understand and make sense of the formal algorithms.

3. Number talks give kids the opportunity to make connections & come up with their own strategies.

When you present a problem to students that is new or just a little ahead of where you are in your current curriculum, it gives kids the opportunity to think about and apply what they already know to something new.

This helps them to bridge the gap and form connections in their brain. It also challenges them to come up with their own strategy because no one has yet told them “this is how you do it.” You might think that kids won’t be able to do that and it will leave them frustrated. But I think you’ll be surprised and just how creative and free kids are when they can approach a problem in their own unique way (I’ve seen it over and over again!)

4. Algorithms and formulas apart from understanding leads to nonsensical reasoning and solutions.

In a number talk, kids are forced to think about not only how to solve the problem, but justify their reasoning and think about whether the answer actually makes sense.

If kids are only shown a particular strategy or formula to follow, they don’t have to give any thought to whether or not it makes sense.

Thus, they will often think of them as arbitrary, and no longer think about what they’re doing or what their final answer is in a logical way. This can lead to answers that are clearly not right or don’t make sense, but kids don’t think about that.

5. Number talks strengthen mental math skills.

This should be fairly obvious, because number talks focus on solving problems mentally, but I’ll mention again here anyway.

Because kids are challenged to solve a problem without pencil, paper or calculator, they have an opportunity to work on mental math skills that often gets neglected.

And by strengthening these skills, kids will gradually work towards more meaningful and efficient strategies that they may never have thought of or solidified in their minds without the opportunity given in a number talk.

And strengthening these skills will only lead to deeper conceptual understanding, which  leads to better understanding of formal algorithms.

Related: Printable Mental Math Game

I’m sure there are many more benefits to regular number talks, but these are some that I have seen in students.

If you are already doing number talks, great! I hope you share my enthusiasm and see the benefits to your students!

Get Started with Number Talks:

If you’ve never tried number talks and want to know more, I’d encourage you to check out my course on Meaningful Number Talks. It walks you through in greater detail all the steps to get started and includes tons of examples. Plus, it includes printables to use in your classroom so you can begin to implement number talks right away.

You can complete the course in a weekend and get started with number talks on Monday!

I’d also encourage you to check out these additional resources on classroom number talks and math conversations. I have found all of these books to be extremely helpful!

Additional Number Talk Resources:

• Making Number Talks Matter by Cathy Humphreys & Ruth Parker
• Number Talks: Whole Number Computation Grades K-5 by Sherry Parrish
• Number Talks: Fractions, Decimals & Percentages by Sherry Parrish
• Intentional Talk by Elham Kazemi

Want a FREE set of planning pages to get started with number talks? Simply fill out the form below!

The post 5 Reasons Number Talks Should be a Regular Part of Your Math Routine appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.*

“The Day the Crayons Quit” Math Writing Prompt:

I’m sure you are familiar with the highly popular book, The Day the Crayons Quit by Drew Daywalt. In this book, the crayons, tired of their typical uses (or neglect), write letters to announce that they have quit the job.

No more being used for mere outlines, cries the black crayon!

Use me for something other than water, cries the blue crayon!

And on and on it goes.

Your kids probably adore this engaging tale, so why not use that as a hook to get them thinking and writing about math.

With the math version, kids replace crayons with their choice of math object or tool.

For example, they might write a letter from the ruler, or the number line. Or maybe the clock or hundreds chart. Or a shape, like a circle or octagon.

As kids brainstorm and write their own letter from the math object that quit, they will have to think about how the object is used and why it might be disgruntled.

They will have to use appropriate math vocabulary.

And then they practice letter writing and can even draw a picture to go along with their letter if they want.

What a great combination of math thinking, letter writing and creativity!

This download is included in my online course, Thinking Deeply: How to Incorporate Meaningful Writing into Math Class. You can learn more about the complete course here.

Included in This Download:

As I mentioned, I saw the idea for this writing activity in Linda Dacey’s book, Why Write in Math Class?

But I thought it would be helpful for you to have some brainstorming pages and ready to use writing pages to help you complete this with your students!

This download includes 2 pages for brainstorming. The first gives kids space to write out all the different math tools they can think of. You may want to complete this as a class so they have a nice long list of ideas to choose from.

Once they have chosen their math object or tool, they have a page to plan why it might be quitting and things to remember about letter writing.

Once they’ve got a plan in place, they can write their letter!

There are 3 different letter writing pages you can print for students, depending on their age. A primary version, for example, includes primary writing lines and space for a picture.

But there are 2 other options for older kids who do not need the primary writing lines.

Or of course, you could use your own writing paper or journal to write the final draft if that is preferred.

I hope your kids have fun thinking about the importance of math in the real world, and the math tools we use everyday!

And most of all, I hope they have fun thinking outside the box!

{Click HERE to go to my shop and grab the FREE Math Writing Prompt: The Day the __ Quit!}

The post {FREE} Creative Math Writing Prompt: The Day the __ Quit! appeared first on Math Geek Mama.

But I also love the visual of number bonds. So this simple apple math lesson combines a fun, hands on tool (apple slices) with this visual to help kids better understand composing and decomposing numbers.

*Please Note: This post contains affiliate links that help support the work of this site. Read our full disclosure policy here.*

When my kids were in Kindergarten and first grade, I tried to combine them for math whenever possible. That’s how this lesson came about.

Rather than simply using a worksheet, however, I wanted to show them in a hands-on way how to decompose numbers and find patterns. And since all my kids love to eat apples, this worked out great because when we were done with math, they got to eat the apples for a snack!

Apple Number Bonds Set up:

To get ready, I cut up several apples into slices.

I wanted to be able to look at several different numbers from 4-10, so I made sure we had enough slices for them to each practice on their own.

Teaching to Decompose Numbers with Number Bonds:

To start, I showed them that I had cut an apple into 8 slices. I then explained that they had to share the slices between the two of them and they had to decide how many each person received.

They quickly decided that they would each get 4 to keep things equal and fair. So we saw that 4+4 = 8.

Then I explained to my son that his sister is not as hungry, so he can have more. She gave him 2 of her slices and we saw that now, he had 6 and she had 2, but it was still equal to 8 apple slices.

We continued mixing up the slices and I let them make observations about ways to make 8, then 9, 10 and so on. It was great fun! {Though I think their favorite part was eating them!}

My daughter caught on pretty quickly and proceeded to find other number bonds without using the apple slices. My son, however, needed to use them to help him find the answer to a pair because he kept wanting to guess. For example, he would say “Seven and…three?” So I would make him count out seven for himself and then see that one was left, and so on. But this was great for him!

Then I let them practice with these fun cut and paste pages that I created!

There are two pages included in the free download that are cut and paste, one with numbers from 1-10, and one with numbers from 11-20.

There are also pages that allow kids to find their own ways to decompose numbers and compare and hopefully recognize patterns.

You could use these pages with actual apple slices (or any other manipulative) and let them record their findings as we did, or just as extra practice or review for older ones.

{Click HERE to go to my shop and download the Apple Slices Number Bonds Pages!}

Want MORE hands on math fun with apples? I’ve expanded this freebie and added a TON of other early math resources in my Apple Math Collection for K-2.

Your kids will use apples to learn about counting and number recognition, addition & subtraction, graphing, measurement, estimation and MORE!

Buy Apple Math HERE!

I hope you can use this to have some fun and playing with numbers and observing patterns! And if you’re looking for another fun Apple activity for back to school, try this FREE “About Me” Math activity!

Or sit and read Ten Apples Up On Top and talk about ways to make ten! Most of all, have FUN!

The post Number Bonds with Apple Slices {FREE Printables!} appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which help support the work of this site. Read our full disclosure here.*

Strategies for Adding & Subtracting Decimals:

In this series, we’ve looked at several different methods and visuals to help kids add & subtract decimals.

This can include using real world problem solving, building the numbers with base ten blocks, solving problems with decimal grids and solving problems on a number line.

I believe all of these tools and visuals are important to help kids make sense of decimal numbers.

But not all are going to be as effective and efficient as they get more proficient at solving problems.

For example, building out every single problem with base ten blocks can get tedious. So using decimal grids to model the same thing on paper is more efficient.

And hopefully, after practicing and exploring with lots of different visuals, kids will begin to feel comfortable solving these problems mentally. So I would encourage you to pair your study with number talks involving addition & subtraction with decimals.

Today, I want to share a partner challenge that focuses on two visual models: number lines and decimal grids.

Adding & Subtracting Decimals Partner Activity

Before I explain this specific example, let me first explain how a “pair-share-check” activity works.

To begin, group kids in pairs. Give one student the “partner #1” page and the other student the “partner #2” page.

Then independently they each solve problem 1 on their worksheet.

The thing is, they are each solving the same problem, but in a different way.

After they each solve it, they share their solutions and methods. Because they’ve solved the same problem, they should each have the same solution.

If not, they need to look at how they solved and compare and discuss to try and determine the error or misunderstanding.

Then they move on to problem #2 and solve and discuss the same way.

The goal with this challenge is to give kids an opportunity to practice using different strategies and also to compare and discuss those strategies (one might work better for a particular problem than another).

In the following example using decimals, kids alternate using a number line and a decimal grid.

So for the first problem, one student will solve it with the help of a number line, and the other will use a decimal grid.

Notice that I used these tools only to help with the decimal portion of the number, and dealt with the whole number part separately. You can encourage kids to do the same, because of limited space on the paper.

Or if your kids prefer to use an open number line, they can always draw one in the space there and solve that way instead.

Adding & Subtracting Decimals Discussion Questions:

After completing the set of problems, I’ve also included a page of discussion questions so kids can think a little deeper about how they’re solving them and why.

Answers to these questions will vary, but they might find that a number line is more useful when adding tenths but the decimal grid is better when adding hundredths.

Or perhaps they prefer one visual for adding and the other for subtracting.

And they might just prefer a different method or visual model altogether! That’s ok.

The important thing is that they’re thinking about how and when they might use a visual model so that they’re making logical choices as they solve problems.

And of course, as they think about the different visual models and discuss with their partner (or together as a class) they’re engaging in meaningful math talk.

So I hope you’re excited to try this out with your students!

This partner activity is included in my complete Add & Subtract Decimals Resource Collection!

Learn more about these visual lessons and games here.

Included in the Adding & Subtracting Decimals Partner Challenge:

Just so you know, this download includes 2 different sets of problems. The first set (with a partner 1 and partner 2 page) includes problems that don’t require regrouping.

This is a much more straightforward set of problems, great for when you’re just beginning to work with decimals.

The second set includes problems that do require regrouping. This is when the use of visual models will be especially important for kids.

And again, it also includes a page of discussion questions.

I suggest printing partner 1 and partner 2 pages (for whichever set of problems you want kids to work on) with the discussion questions on the back.

That way kids will have their set of problems and their extension questions all on one piece of paper.

What do you think? Have you ever paired kids up to compare strategies before? What other tips or ideas do you have?

What other visuals or strategies do you like to use for adding & subtracting decimals? Share in the comments!

I hope your kids have fun but are also challenged with this adding & subtracting decimals partner activity!

Want more low-prep practice? Grab this set of decimal operations mazes!

Or grab this complete activity collection to see and make sense of adding & subtracting decimals.

{Click HERE to go to my shop & grab the Adding & Subtracting Decimals Partner Activity!}

And of course, be sure to check out our complete series of “Teaching Addition & Subtraction with Decimals!”

• Adding & Subtracting Decimals with Base Ten Blocks
• Base Ten Blocks Printable Game
• Adding & Subtracting Decimals on a Number Line
• Adding & Subtracting Decimals with a Decimal Grid

The post Adding & Subtracting Decimals Partner Challenge {FREE!} appeared first on Math Geek Mama.

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Finding Math Gaps:

The most obvious place to start is by figuring out where the math gaps are. What do your kids know and where are they lacking?

What skills have they never been introduced to, or what skills are they just shaky on still?

If you’re a classroom teacher, you likely have a good idea of what skills various kids are struggling with or have no knowledge of altogether, thanks to standardized testing. Not that these types of tests are perfect, or the be-all-end-all of math knowledge, but it gives you a snapshot of a child’s skill level.

You may also create your own pre-assessments before teaching new units or chapters, allowing you to see what skills need to be covered before you proceed.

This is especially important if you have a transient school with a lot of kids coming and going. It’s hard to know what skills a child is lacking if they’ve just shown up from out of state.

If you are a homeschool parent though, you may not know where gaps are. Or you may think that your child has mastered the basics until you move on to more difficult concepts only to discover they are not as confident as you thought.

And if you’re a tutor, it’s essential to do some assessments before you begin working with a new student. This will help guide your lessons to make sure that your time together is productive.

Whatever the case, I suggest doing some informal assessments to see where kids are.

Here are a few assessment options, depending on the age of your kids:

Assess kids’ knowledge of addition and subtraction facts with these simple tests from Kate Snow:

• Addition Facts Quick Test
• Subtraction Facts Quick Test

Give quick grade specific tests:

• Use these skill assessment tests from Basic Mathematics (grades K-12)
• Use the placement tests from Math Mammoth as a quick assessment (grades 1-7)
• Use these pre-assessments from Teaching to Inspire (grades 3-5)

Use Math Standards as a Skills Checklist:

Another option is to look at a set of math standards and see if there are things you have not yet taught (or that you know your kids have not yet learned or mastered).

One thing to note, however, is that every list of math standards is going to be different. Different people hold varying views on what should be taught and when, so you will need to see a particular set of standards as a starting point.

There are lots of options in terms of lists of math standards. One place to start is to look at your state’s standards.

For example, Virginia uses the SOLs or Standards of Learning. You can then go through the standards for a particular grade level and see how your child or student measures up.

Some states use the Common Core State Standards. Before you balk at that, know that this is not a prescription for how to teach math. It’s simply a list of skills that kids should learn by grade level.

Even if you don’t agree with every standard, it can be a good starting point for finding and filling math gaps.

Finally, UT Austin has put together a set of math benchmarks by grade level, which you could also use as a checklist to find math gaps and help kids go back and master essential skills they may have missed.

Filling Math Gaps Starting Point:

No matter what gaps you find in your kids’ learning, I would encourage you to start with a thorough review of place value.

Place value is the foundation of our number system and all math operations, and solving computation problems is infinitely harder without a good and flexible understanding of place value and how to compose and decompose numbers.

Helpful Place Value Tools:

• Place value disks
• Sticky notes (there are lots of ideas for sticky notes in this post, but my favorite way to use them is to model place value)
• Base Ten Blocks
• Grid paper (for place value of decimals)

Printable Place Value Games & Resources:

• Place Value Puzzles
• Sir Cumference Place Value Game
• Build a Snowman Place Value Cards
• Is it Equal? Place Value Sort

Filling Gaps in Addition & Subtraction Skills:

If your kids are younger and still struggling with basic addition & subtraction (or older kids are struggling with large numbers because they never mastered basic facts) I highly recommend these resources from Kate Snow:

• Addition Facts That Stick
• Subtraction Facts That Stick

Initially, I thought this was going to be a program to help kids memorize all the addition and subtraction facts within 10. And since I don’t believe in teaching rote memorization, I assumed I wouldn’t be a fan.

But I purchased them anyway, because from what I know of Kate’s math teaching philosophy, a set of tricks to memorize facts didn’t seem like something she would be advocating.

On the contrary, this set of books teaches addition & subtraction using visuals, games and a systematic approach that help kids develop strategies, not memorize with flashcards.

She’s done all the hard work for you in outlining a simple plan to help kids really understand and increase their fact fluency.

So even if your child is in 2nd or 3rd grade, if they’re still struggling with number sense and addition and subtraction, I recommend grabbing this set to build a solid foundation.

Filling Math Gaps in Upper Elementary:

By the time kids get to upper elementary, math gaps can become more pronounced and more difficult to tackle as math progresses more quickly.

So if after assessing kids you find large gaps, I recommend a few different resources.

First, you can purchase math supplement books from Maria at Math Mammoth. She is resources available for virtually all math topics for grades 1-7.

Even if you don’t use the Math Mammoth curriculum, these are great resources to help kids with specific skills and the prices for pdf downloads range from about $3-7, making them really affordable.

Another option is to use the book, Activities for the AL Abacus, from RightStart. This is a simplified version of the RightStart Math Curriculum, and covers basic math operations for grades K-5.

You can learn more about what it covers and how to use it here.

Finally, if you notice that multiplication facts are tripping up your kids, check out this post on the order to teach the multiplication facts.

Going back through the facts in a way that makes sense and increases kids’ confidence may help them get caught up. And you may like to use this set of hands on lessons and games to help you as you reteach or reinforce these important skills.

Filling Math Gaps in Middle School & Beyond:

Once kids get to middle school or Algebra, it is even more essential that basic operations with whole numbers, fractions and decimals get mastered.

So if kids in middle school are stuck or behind, I would again recommend a quick review of place value to make sure their foundation is sure.

Then, depending on where the gaps are, you may still be able to use the supplemental books from Math Mammoth.

Or you might find these resources from When Math Happens useful.

And finally, I recommend the program Hands On Equations for kids in Pre-Algebra or Algebra (or beyond) to really teach basic Algebra in a way that makes sense.

You can use this program to begin basic Algebra in elementary school, but for middle school or high school students who are still struggling, I highly recommend using Hands On Equations.

It teaches Algebra in a visual, hands on way that is contrary to most Algebra textbooks.

And if there are gaps in an understanding or percents, you may like my comprehensive resource, Practical Percents.

This book begins with a basic understanding of operations with powers of 10 (again, the foundation of place value) and then includes lessons on all types of problems involving percents.

I find this to be one of the least covered concepts in most math textbooks, and yet, one of the most practical in our everyday lives.

Learn more and purchase Practical Percents here.

One final note. If you are a classroom teacher, you may have students with so many learning gaps there just isn’t time to help them with all the things they need and teach your given curriculum.

Or maybe you’re a homeschooling parent whose child has simply surpassed where you feel comfortable teaching, math wise.

If that’s the case, I suggest finding a reliable math tutor. Though a tutor cannot learn the content for them, they can help provide supplements and work with them one on one to fill in those gaps.

Not sure how to find a tutor? Check out this post with ideas and tips.

What would you add? What resources do you find useful? What questions do you still have? Share in the comments!

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