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4 Ways to Get Your Primary Students Thinking Algebraically

When you hear the word "algebra," you may automatically think middle and high school math. This is when pre-algebra instruction typically begins. We need to rethink this, though. We should introduce our kiddos to algebraic concepts early. I'm talking very early...early as in when we introduce number sense. You're probably wondering how on earth to do that. Here are four ways to get your kids thinking algebraically. 

Read about these 4 ways to get your kids thinking algebraically.

What is Algebraic Thinking?

Learn these 4 fun ways to get your students thinking algebraically even in elementary school.
Algebraic thinking includes many topics, like making generalizations, recognizing and forming patterns, studying relationships, and analyzing how they change. If you think of it in this way then you'll quickly realize that you do, in fact, introduce algebraic concepts in your early elementary classroom. Algebraic thinking introduces a problem-solving approach that is beneficial to students at all levels. It's really a fundamental part of the mathematical process. 

How to Get Your Kids Thinking Algebraically

You may be freaking out at the thought of teaching algebra to your littles. Just the word "algebra" haunts many of us. It may be that one course in high school that you really struggled with. If you aren't comfortable with it, then how in the world will you teach it to your class? It's really not that complicated, though. I'm sure you're already doing some of these things without even realizing it. 

#1 Functions

A function is simply the relationship between an input and an output.  Functions, of course, may be very complex in higher-level math; however, functions may be as simple as adding or subtracting one.   How do you explain the complexity of function to elementary students? Simple. Just use a function machine. Your kiddos will love the visual example of the function machine where they can see what happens to a number when it is put through the machine. I love to play this video as an introduction.  

I love to make teaching functions like a puzzle or a game.  We put a number in, another number comes out.  Then, we have to figure out what happens in the middle.  The more excited I get about these puzzle-like math problems, the more excited my students get.  

I like to introduce functions using pictures, and then gradually move to numbers.  It's also important to use functions rules that correlate to the mathematical operations your students have learned.  This will help them identify the rule and connect it to their prior learning.

#2 Ratio Tables

Ratio tables, like functions, are a fun way to work on algebraic thinking.  Ratio tables are a great way to introduce students to multiplication concepts without teaching multiplication.  Using ratio tables, students can visualize the multiplicative relationship between numbers. ( However, we probably will not use that language to start with.)

With our young students who have not been introduced to multiplication yet, using pictures and circling sets is a great way to help them see this.  

Like functions, I like to treat these like math puzzles.  Students must look at part of a ratio table to determine the rule in order to fill in the rest of the table.  

Ratio tables are great to use as students work on skip counting.  They create a visual representation of skip counting that can help your students "see" what is happening.  

Additionally, having this practice with ratio tables at the lower grades will help students as they begin formal multiplication instruction.

Here's a FREE Functions and Ratio Table resource that I created to help you get started with teaching these activities.  I think both you and your students will find them fun and engaging.  And . . . you'll be building those algebraic thinking skills in no time!

#3 Patterns

Use patterns to begin to teach your class how think algebraically even in elementary schoolPatterns are a huge part of fundamental math. Students need to be able to recognize them, complete them, and create their own. Patterns are a building block of algebraic thinking. 

When introducing patterns, I always start with something visual.  Colors or pictures are a great place to start.  A super simple, yet effective, way to teach patterns is by using color blocks. You can use small manipulative blocks or cut pieces of construction paper. I prefer the construction paper because I can make the pieces bigger and easier to see for whole group instruction. Using the color blocks or paper, you can demonstrate the pattern and have students guess what comes next.  

Once students have the hang of basic patterns, I like to introduce more complicated patterns.  I also give students opportunities to create their own patterns.  Getting students to start identifying and creating patterns is an important part of algebraic thinking. 

Once students have an understanding of visual patterns, you can begin to introduce them to patterns in numbers.  Learning to recognize patterns like our base-ten number system, how the same addition and subtraction rule affects other numbers, and basic multiplication concepts.  Being able to recognize each of these different types of patterns builds algebraic thinking in our students.  

#4 Word Problems

We can't forget about teaching word problems. Word problems put the math in a real-world context.  It is when many of these algebraic thinking skills are put into action.  Word problems are the critical thinking and application part of all of our lessons. 

As we teach our students to put their new thinking skills into action, it's important that we get them thinking in different ways.  This helps them to build fluidity in their mathematical thinking.  For example, don't always have the unknown in the word problem to represent the answer to the equation. Mix it up.  Provide the answer and have students find the start or the change. 

Through word problems and basic equations, it's important to teach students the mathematical symbols and what they mean.  Many kids believe that = means "the answer is" but this will hinder them in the future.  Can you imagine how confusing that will be the first time they see 3x = 2y?  Instead, teach them that the equal sign stands for "equivalent" and "the same as." 

Teacher Tip: Word problems can be difficult for students, especially at the beginning.  Engage them by using topics and themes in your word problems that you've been covering in class. This will pique their interest, give them some prior knowledge to connect to, and you'll get more engagement. 

Mega Math Practice

You're probably thinking that these four ways to get your kids thinking algebraically sound great, but just aren't possible. How in the world are you going to fit all of these things into your daily math lesson? I've got you covered! My Mega Math Practice Bundle for Operations and Algebraic Thinking has everything you need and more! The activities are perfect for morning work, math centers, homework, or even distance learning. Plus they are printable and digital so they are easy to use and assign. 

You'll get over 1,100 pages of fun covering all of the algebraic thinking standards including:
  • All eleven types of word problems 
  • Two-Step Word Problems
  • Properties of Operations
  • Counting On and Counting Back
  • Addition and Subtraction Strategies
  • Balancing Equations-Understanding the Equal Sign
  • Find the Missing Numbers
I know you and your kiddos will love these no-prep activities to get you through the year confidently.  

Try some Mega Math Practice activities for FREE in your classroom.  I want to give you this Mega Math Practice Counting to Add and Subtract Freebie! It'll give you a good taste of what Mega Math Practice is all about. 

Grab this mega math practice freebie to check out my bundle.

Grab the Mega Math Practice Operations and Algebraic Thinking Bundle in my store on Teachers Pay Teachers!  You will have everything you need to help your students learn and practice these important thinking skills.

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