It never fails. Just when I feel students are confident graphing linear equations and have a clear understanding of how the table relates to the graph and the equation relates to slope and y-intercept, they freeze. At least one student will stare at the paper as if they’ve never seen a table or graph in their life. Then they’ll look at me like, “How in the world am I supposed to know what a slope is?!” Sigh.

If you occasionally get that “deer in headlights” look from students when they need to graph a linear equation, I hope you’ll enjoy this set of puzzles. Though they do require a little prep up front, you can keep them on hand for an easy math center or math station whenever you feel students need a ‘refresher.’

Graph Linear Equations Puzzles: Prep-Work

To begin, I recommend you print all 16 puzzles on card stock paper for durability.

NOTE: The first 8 puzzles include equations written in slope-intercept form. The last 8 puzzles can either be easily re-written in slope-intercept or they are written in standard form.

If your students are not ready for the more challenging equations yet, you can print the first 8 puzzles only.

Once printed, laminate the puzzles so you can use them again and again, then cut out the pieces of each puzzle. There are 3 pieces for each puzzle (an equation, a table and a graph).

Once all pieces and puzzles are cut out, mix them up really well and share with students!

Plus, to make checking the solutions super easy for you (or students!), a single page ‘quick check’ answer key is included of all 16 puzzles.

Print this page as well if you’d like to use it for a quick scan of their matches.

Ideas for Using the Linear Equation Puzzles in Class:

• Math Center: If you have regular math center or stations in your class, this makes a great center option.
• Choice Board: If you provide students with a choice board, you could include the puzzles as a choice board option.
• Small Groups: If you would like all students in the class to work on the puzzles together, you can create 3-4 sets of puzzles and they let students work in small groups to match the pieces and discuss together.
• Bulletin Board Display: Lastly, you can print the puzzles on plain white paper, cut out the pieces and scatter the tables/graphs around the room. Give each student (or pair of students) an equation and let them ‘hunt’ for the matching table and graph. Once you confirm they have a matching puzzle set, they can glue the completed puzzle onto construction paper to hang on a bulletin board or around your classroom.

If you’re looking for resources to teach & explore linear functions, check out Math Geek Mama+, our ad-free option that includes inquiry lessons, games, digital activities & more to help students make sense of algebra topics like this one.

Plus, you’ll find more engaging and easy to use math center ideas like this one!

LEARN MORE ABOUT MATH GEEK MAMA+ HERE

Ideas for Class Discussion of the Graphing Equations Puzzles:

The goal of this activity is to help students see the connections between an equation, a table and the graph of the equation. So ideally, this activity doesn’t end when students complete the puzzles. If possible, give time for students to share their thinking & strategies for finding matches.

Here are some additional discussion question ideas:

• Where do you see the intercepts in the table? On the graph?
• What is the slope? Where do you see the slope in the table? In the equation? On the graph?
• Would you say the graph is increasing or decreasing? Why?
• What does it mean to be a solution of the equation? Where do you see solutions in the table? On the graph?

Although this seems like a very simple activity, my hope is that it’s a springboard for meaning math conversations, connections and ‘light bulb’ moments for students.

Ready to grab this freebie for your classroom? Use the link below to head to my shop where you can get it free.

{Click HERE to go to my shop and grab the FREE Graph Linear Equations Puzzles Set!}

Looking for more ideas for teaching & exploring linear functions? Check out these:

• Graph Linear Equations: Cut & Paste Pages
• Solve Equations Error Analysis – DIGITAL
• Silly Christmas Riddles: Solve Linear Equations

The post {FREE} Graph Linear Equations Puzzles: Match Equation, Table & Graph appeared first on Math Geek Mama.

I find that a lot of textbooks barely skim the surface when it comes time to solve linear inequalities. After all, once students are comfortable solving linear equations, this is just more of the same, right? Wrong! Inequalities are more complex and have greater depth of meaning than equations, and although the algebra involved in solving them may look similar, it takes a lot of work to actually understand what’s going on. Plus, students have to know when to “flip the inequality symbol.” What does that even mean, and why do we do it? But once you’ve done the hard work of sense-making and students are ready to practice, grab these silly riddle pages for Low-Prep Solve Inequalities Practice.

Understanding the Solution to Inequalities:

One of the biggest differences between a linear equation and an inequality is the solution.

In both cases, the solution is the value(s) that make(s) the statement true.

However, most students are used to solving an equation in which exactly one number makes the equation true. (Yes, a linear equation can also have no solution or infinite solutions, but in early middle school students are solving an equation to find exactly one number that makes it true).

An inequality, on the other hand, will have a whole range of numbers that make the statement true.

For example, if the solution is x < 2, that means that the solution is not 2. The solution is ANY number that is less than 2. So it could be 1.9. It could be 0. It could be -100.

It’s important that as students solve inequalities they model the solution on a number line so they can visualize the entire set of numbers that makes the inequality true.

Although this set of riddles practice pages do not include number lines, you may want to have students sketch a number line next to each solution as well so they can show you they understand the solution and what set of numbers is part of the solution.

Solve Inequalities Practice Pages: Easy to Differentiate

This download includes 3 practice pages, gradually increasing in difficulty.

You will find the following inequalities to solve:

• Solve one-step inequalities (use with 6th or 7th grade)
• Solve two-step inequalities (use with 7th or 8th grade)
• Solve multi-step inequalities (use with 8th or 9th grade)

If you have students who are struggling or need to get back to the basics, start with the first page of one-step inequalities.

But if you have more advanced students who are ready for a challenge, let them try the multi-step page! This page includes variables on both sides of the inequality symbol as well as the distributive property.

Plus, as students solve each inequality they can self-check as they look for the solution at the bottom of the page to determine the answer to the silly riddle!

If you’re looking for resources to teach solving inequalities, check out Math Geek Mama+, our ad-free option that includes inquiry lessons to help students make sense of algebra topics such as solving inequalities.

There are visual lessons to help students see and understand what inequalities mean and WHY the inequality symbol flips.

Plus, you’ll find more engaging and easy to use practice pages like this one!

LEARN MORE ABOUT MATH GEEK MAMA+ HERE

Ready to use these riddle pages with your students? Just use the link below to grab it in my shop.

{Click HERE to go to my shop and grab the FREE Solve Inequalities Practice with Silly Riddles!}

Plus, find more resources for solving equations and inequalities at the links below:

• Summer Algebra Review: Solve Equations Practice
• Writing Algebraic Expressions: FREE Practice Pages
• DIGITAL Solving Linear Equations Error Analysis {FREE}

The post Solve Inequalities Practice – Silly Riddles for 7th-8th Grade appeared first on Math Geek Mama.

One of the most challenging topics in middle school math is making sense of rational numbers in all their forms-fractions, decimals, repeating decimals-and knowing how to convert between various forms. Throw in positive and negative signs and things get really crazy! In this simple rational numbers activity, students will use lots of different math skills and strategies to compare rational numbers.

What Are Rational Numbers?

Rational numbers is a set of numbers that includes any number that can be written in fraction form. Thus, every rational number can also be written as a repeating decimal or a terminating decimal (meaning it stops, such as 0.5). Rational numbers also include integers, meaning both positive and negative numbers.

That means rational numbers include many different forms or sets of numbers, such as:

• Positive and negative whole numbers
• Positive and negative fractions and mixed numbers
• Positive and negative decimal values, as long as they either repeat or terminate

Although students begin comparing fractions and decimals as early as 4th grade, 7th or 8th grade students look at much more complex rational numbers. More challenging comparisons are what’s included in this sorting challenge.

Compare Rational Numbers Sorting Activity

This printable activity includes 12 rational number comparisons.

This means students are trying to determine less than, greater than or equal to with each pair of rational numbers.

Some of the problems compare two fractions, some compare a fraction to a decimal, and some compare two decimal values.

Adding to the challenge, some of the numbers are positive and some are negative.

Students should use a variety of strategies to compare the quantities, such as:

• Are both positive or both negative? If one is positive and one negative, they know right away which is larger, regardless of the number forms
• If the numbers are both fractions, they might rewrite them to have common denominators or use other strategies such as comparing each to a benchmark such as 1/2 or one whole
• If the numbers are both decimals, they should pay attention to place value
• If the numbers are in different forms, they can rewrite one so they are in the same form (such as both decimals) or they can compare the a benchmark, or consider place value
• If they’re looking for a visual, they could put the numbers on a number line

The goal is for students to find ways to compare the quantities and then determine how to correctly complete the comparison statement (<, > or =).

How to Use the Rational Number Sort:

This is designed to be a printable cut and paste activity, however there are other options as well depending on what will work best for your students.

Printable Cut and Paste Activity:

To use as a cut and paste activity, print the sorting mat (one per student or one per pair–this works well as a partner activity).

Then print the page of comparison problems. There are two sets per page, so print enough so you have a complete set for each student or pair of students.

Students then cut out each expression, compare the rational numbers and determine if it goes in the “Less Than,” “Equal To,” or “Greater Than” column on the sorting mat.

Encourage them to sort all problems first and then let you check it before they glue the final answer down.

Once students have corrected sorted each comparison statement, they glue them down and they’re done!

Math Center Option:

If you would prefer to prep this one time and use it again and again, you can print the sorting mat on colored card stock paper and laminate for durability.

Then print the comparison statements on another color of card stock paper and laminate. Cut out all the comparison statements to go along with the sorting mat.

Students then work sort the statements onto the mat, but don’t glue them down.

Then store the comparison statements in a ziplock bag along with the sorting mat for another group to use later!

Lastly, one final option is to print the sorting mat and cards on card stock paper. Laminate the sorting mat or place it in a page protector and give students a dry erase marker.

Then students can simply write the comparison statements onto the sorting mat, no cutting or pasting required.

(You can also do it this way as an individual review. Just print a page for each student on regular paper and let them write in their comparisons to turn into you). 

When they finish, be sure they erase their answers from the mat and store the mat and comparison statements for another day.

I hope this provides a helpful challenge as your students learn to work with & compare rational numbers.

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

Learn more about Math Geek Mama+ right HERE.

If you’re ready to grab it, use the link below to head to my shop to get a free copy!

{Click HERE to go to my shop and grab the FREE Compare Rational Numbers Sort for 7th & 8th Grade!}

Looking for more rational numbers resources? Check out the links below!

• {FREE} Get Them in Order: Comparing Fractions Game
• Adding and Subtracting Integers {FREE Lesson!}
• Multiply & Divide Integers Lesson {FREE}
• Compare Decimals Cut & Paste Sort {FREE!}

The post Compare Rational Numbers Sorting Challenge – Grades 7-8 appeared first on Math Geek Mama.

Multiplying and dividing integers seems like such a straightforward process at first. If both integers are positive or both integers are negative, the result is positive. If the integers are opposite signs (one positive and one negative) the result is negative. Easy, right? Of course I’m about to complicate things, LOL. What about when you’ve got more than two integers? What about when the numbers get really large or really small? What if you’re dealing with exponents?? To help students tackle more complicated expressions without getting bogged down in the numbers (or relying on a calculator), use this Multiply & Divide Integers Sort.

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

Setting Up the Integers Sorting Challenge

IN order to complete this challenge, students do have to have some prior knowledge of the ‘rules’ for multiplying and dividing integers. I recommend using this guided lesson to walk them through an introduction to multiplying & dividing integers. Then they’re ready for this sorting challenge!

This is a very simple activity to set up, but will hopefully prove especially useful for students.

To begin, you will need to print the sorting mat & expression cards (included in the download).

I recommend printing on card stock paper and laminating for durability.

Then cut out the expression cards (there are 24 expressions altogether) and you’re all set!

Reasoning with Integer Operations

Once you have the materials ready for students, they simple use their reasoning skills to determine if each expression will result in a positive value or a negative value without doing any calculations.

The goal here is for students to internalize the ‘rules’ for integer multiplication and division and also look for patterns (such as with exponents).

The post {FREE} Multiply & Divide Integers Sorting Challenge appeared first on Math Geek Mama.

If you have taught middle school math, you likely know how tricky it is to teach integer operations, particularly addition & subtraction of integers. But a lot of times, multiplication and division of integers gets rushed or skimmed through because it’s “easier” than addition and subtraction. The problem then is students don’t have a solid understanding of the WHY behind the integer “rules” and then something that’s “easy” is mixed up or forgotten not long after.

Rather than simply telling students the rules and giving them a worksheet to practice, I want to share a simple, visual math lesson to help students think about the WHY behind these operations and what happens with the sign. Will students still need lots of exposure, practice and repetition? YES. But hopefully this visual lesson is a good starting point and a good reference to refer back to when kids get stuck later.

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

Goal of the Multiply & Divide Integers Lesson:

The post Multiply & Divide Integers Lesson {FREE} 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.

A lot of times, pre-algebra or algebra textbooks begin exploring functions by telling students that functions are rules that determine an output from a given input. Then it shows you how to create a function table with a given rule. Then students practice. When I was preparing to explore functions with my 8th and 9th graders, I wanted to give them a more open-ended challenge to help them think about and make sense of functions on their own before we used formal math language or tables. And so I created this very simple game called, “What’s my rule?”

Understanding Functions & Function Rules

You can read directions for the game below, but basically the idea of the game is for one partner to guess different inputs (x-values) while the other partner tells them the outputs (y-values) based on the secret rule.

The object of the game is for the first player to try and figure out the rule (the function).

I had a couple of goals in mind by giving this to my students to play.

First, I wanted them to think about and make sense of inputs and outputs and how they might keep track of that information.

I did not give instructions on how to create a function table. I simply gave them a white board and encouraged them to keep track of their guesses and answers. Some students tried to play without keeping track, but quickly realized they needed to keep their information organized in some way so they could look for patterns (i.e. the function rule).

Second, I wanted students to begin to make sense of how a function rule determines the output for a given input, that the inputs might change, but the rule does not change, and that order of operations matters.

If they can see function rules in action, they are more likely to internalize what they are and how to use them with given inputs to find outputs.

It was also my hope that this would provide a foundation or help them see the relationship between a linear equation and it’s table and graph.

Writing a function rule (or linear equation) given a description, table or graph can be an incredibly abstract and challenging concept, especially if we just ask kids to jump right to writing equations.

My hope was that this playful game would help bridge the gap from concrete to abstract.

So let’s start playing!

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!

What’s My Rule? Function Rules Game:

Materials Needed for Each Pair/Small Group:

• Set of ‘rule’ cards (I printed on colored card stock paper)
• Small white board & dry erase marker (or scrap paper & pencil)
• Calculator (optional)

How to Play What’s My Rule?:

First, one player chooses a ‘rule’ card and does not show the others.

The other players then choose ‘input’ or ‘start’ values to see what happens to it with the given rule.

The player with the rule card then applies the rule to their number and tells them the ‘output’ or ‘result.’

The player(s) trying to guess the rule keep offering input values (keeping track of the inputs/outputs on their white board) until they are able to correctly guess the rule.

The game really is very simple, but can definitely be confusing to start. I highly recommend you choose a rule and act this out with the whole class before you put them into small groups.

So it might look like this:

1. You choose the rule “Add 3”

2. Invite students to provide a ‘start’ number (you don’t need to use function language such as ‘input’ or ‘x-value’ yet)

3. Let’s say they choose 10. You then tell them, “Ok the result after using my rule is 13.”

4. Keep track of their inputs/outputs on the board in some way so they can see and remember what has already been done (or better yet, ask a student to keep track at the front of the room so everyone can see), and ask for another start value.

5. Let’s say this time they choose 8. You then tell them, “This time the result after using my rule is 11.”

At this point (because ‘add 3’ is a pretty easy rule to spot), students will probably guess that the rule is ‘add 3.’

You may way to caution them of a few things, however, before letting them loose to play on their own.

1. The rule does not change. It has to work for every single start/result pair that comes up in the round, otherwise they’ve not found the correct rule.

2. They can pick ANY number for their start values. Encourage them to try out values such as ‘0’ or negative numbers, especially if they are feeling stuck.

3. Make sure students know that there can be more than one step in the rule, such as “multiply by 2 then add 10”

Once students understand the object of the game and how to play, give each small group a set of materials and let them play. If students are having trouble finding the result (or you don’t want them bogged down in computations), allow them to use a calculator (if they provide the wrong output value, no one will be able to determine the rule).

If students want to keep score or are very competitive, the student who correctly guesses a rule keeps that card. Whoever has guessed the most rules correctly when time’s up, wins.

While students play, wander throughout the class listening to their choices, their conversations, the rule guesses, etc. Step in if you notice a student not correctly using the rule & address it.

Or if you hear a particularly insightful comment/idea, share & celebrate that.

Once it’s time to stop, spend a few moments unpacking the function rules game with your class.

• What did they notice as they played?
• What strategies did they use to try and guess the rule?
• How did they keep track of their start/result values and why?
• What was the most challenging rule to guess? What was the easiest?

I hope this provides a meaningful challenge for your students and gives them a fun way to think about functions, function rules and how they relate to inputs, outputs and tables.

Want to try this out with your students? Click the link below to go to my shop & grab it for FREE!

{Click HERE to go to my shop & grab the FREE Function Rules Game for 8th Grade!}

Looking for more middle school resources? Try this additional freebies:

• Equivalent Expressions Cut & Paste Activity {FREE}
• DIGITAL Solving Linear Equations Error Analysis {FREE}
• {FREE} Would You Rather…? Ratio & Percent Tasks | DIGITAL
• Graphing Systems of Equations Activity {FREE}

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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!

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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.

One of my biggest goals when teaching Algebra–whether it is in the classroom with middle schoolers, reviewing with high school students or teaching my own kids as we homeschool–is to help kids visualize Algebra and see the connections between words, tables, graphs and equations. The last thing I want is for students to think of graphing a linear equation as an independent skill, devoid of meaning and unrelated to everything else that they’re learning. Because it’s not! Understanding the graph of a linear equation and how it relates to a particular context, then seeing the points in a table and tying all that to the equation leads to deep understanding. Not just rote memorization. Not just following steps mindlessly so they can get by. But actual understanding that shows how we see and use Algebra in the real world everyday.

So to that end, I like to do a lot of matching activities and sorting challenges to force students to consider how all these pieces fit and work together. This set of super low-prep cut and paste worksheets is just one example, but I hope it helps your kids practice graphing linear equations while also looking for connections between the equation and the graph.

Materials Needed:

• Linear Equations Worksheets
• Scissors for each student
• Glue sticks

Prep Work:

To get ready to use this, simply print out the worksheets you want to assign to students. There are three included in the download (link at the end of this post), so feel free to use them however you like.

Print enough worksheets for all your students, pass out scissors and glue sticks and you’re all set!

Easy peasy!

Using the Graphing Linear Equations Worksheets:

To begin, students cut out the graphs at the bottom of the page. They then glue the graphs above the corresponding linear equation.

Before your students start, you might want to discuss strategies together as a group. For example:

• Make a table of values for each equation, then match those to the corresponding graphs
• Look at the slopes to determine if they’re positive or negative and narrow down possible graphs
• Use the y-intercept to narrow down the possible graphs

If your students are unsure of where to begin, provide some blank graph paper and encourage them to graph one of the equations on their own.

Although creating a table of values and then plotting each point on a separate graph until you see a matching graph may seem tedious to you, this might be where some students are most comfortable.

Give them time to make the connections between the y-intercept and slope seen in the equation with where and how those values are seen in the graph.

With more practice and exposure, they will eventually grow in confidence and be more comfortable with using the y-intercept as a starting point!

Ideas for Incorporating These Practice Pages:

Although you can use these however you want, here are some ideas of when to assign these low-prep practice pages.

• A warm-up for 3 days in a row
• Extra practice
• Review before a test
• Homework assignment
• Simple sub plans to keep on hand

You will also find answer keys for all three pages in the download, making it super easy for you to check students’ work, or for them to check their graphs themselves.

I hope this is useful for you and enjoyable for your students!

To grab your free printable, use the link below to grab the download in my shop.

{Click HERE to go to my shop and grab the FREE Graphing Linear Equations Worksheets}

More Resources to Explore Linear Equations:

• Linear Equations Puzzles: Free Practice Set
• DIGITAL Solving Linear Equations Error Analysis {FREE}
• Christmas Graphing Challenge: Graphing Linear Equations

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