Remember all that x and y stuff from high school algebra class? Did you know the foundation for that type of abstract reasoning begins long before our angsty teen years? Even if kids are still using a sippy cup, they're ready to seek out and use patterns to make sense of things!
Algebraic reasoning is all about identifying relationships and generalizing those ideas to new situations or elements.
Think about your day and how much of it is spent effortlessly following patterns you’ve established--scrambling eggs, filling your gas tank, sorting emails.
Kids have their own patterns, too. Arriving in the classroom, putting away their backpacks, following established classroom schedules and routines—all activities they can probably follow in a predictable and comfortable pattern of muscle memory and brain automaticity.
When they have a substitute teacher, the students are the ones who tell that adult how it's done. They can generalize to the presence of a different grown-up and apply previous experience to a related situation. That’s the type of generalized thinking that’s inherent in algebraic reasoning.
Algebraic Reasoning as We Grow
When children look for, create, and analyze patterns and relationships, they can apply their reasoning processes in increasingly abstract ways.
Here are 4 ways algebra develops in early childhood.
1. Patterns
Algebraic thinking begins in preschool when kids practice recognizing and creating patterns in colors, shapes, sounds, and movements.
2. Numerical Relationships
In kindergarten, they begin to explore numerical relationships like those found in skip-counting.
3. Functional Relationships
Elementary kids explore functional relationships such as the number of bicycles in a bike rack and the corresponding number of wheels.
4. Missing Addends & Place Value
They also use algebra to find missing addends (3 + ? = 9) and explore patterns in place value. For example,
What must we add to 35 to get 45?
To get from 45 to 145?
To get from 145 to 1145?
Repeating Patterns
Repeating patterns are those patterns that have a core that repeats. For example, black-white-black-white-black... We usually start with AB patterns because, well, kids seem to get them pretty easily. They have no trouble supplying the next element in a pattern when you pause and ask. You can do this while you're driving in the car or waiting in line for lunch. "Apple-pear-apple-pear-apple. What comes next?"
Train Tunnel Patterns
Make a repeating pattern with unifix cubes, too. Hide the stick in an empty tissue box with a hole cut in the end. Pull the "train out of the tunnel" slowly and have kids tell the next element in the pattern.
An Order for Teaching Patterns
Don't bog down kids' early experiences by sticking to the old reliable AB pattern. As soon as your kids get the idea, move on. Here's an order that makes sense for introducing and experiencing patterns.
AB
ABC
AAB
AABB
Why do we use letters to name patterns?
One big idea in working with repeating patterns is identifying the core of the pattern--which is also how patterns are named. It's all those ABCs listed above. Kids might be confident telling you it's a black-white-red pattern but when we adults generalize by saying. "Yes, it's an ABC pattern," kids might give us a strange look. There's no A, B, or C there, lady! You’re crazy! Don't worry, Pattern Dance to the rescue!
Here are three patterning activities your kids will love.
Pattern Dance
This is one of my favorite activities to help kids make sense of the letters we use to identify a core or name a pattern and how patterns can be generalized to new elements--in this case, new movements.
How to play Pattern Dance
Children take turns creating a dance using 3 different motions in sequence. For example, in this video I chose kick-stomp-shake. The ABC pattern is repeated many times. Then a new leader suggests three new motions.
Here's a video of me playing Pattern Dance with my sons. It's a quick aerobic algebra activity! (Warning: we aren't very coordinated.)
Important:
Notice that after a few moments, I told my boys, "My mouth is getting tired from saying kick-stomp-shake. I am going to say A-B-C instead because it's shorter." I did this because adults sometimes don't properly connect the abbreviations used to describe patterns to the things they represent. The A-B-C represents the kick-stomp-shake. When the next leader of the activity chooses 3 actions for the pattern (hop-twist-clap, for example), this pattern can also be described with A-B-C.
Where's the algebra?
1. Generalizing mathematical ideas from a set of particular instances. Kick-stomp-shake.
2. Establishing those generalizations. Hey, we can also use hop-twist-clap.
3. Expressing the generalization in increasingly formal and age-appropriate ways. Let's just say A-B-C because it means the same as hop-twist-clap and kick-stomp-shake or any 3 movements in order.
Music Patterns
This is a creative activity that shows how patterns can be made of colors, shapes, and sounds all at the same time! All you need are:
colored stickers
blank music staff paper (or plain paper if you don't want to be fancy)
homemade or store-purchased instruments like shakers, bells, and wood blocks
How to play Music Patterns
Color-code each instrument by placing a colored sticker on it. For example, the shakers could be marked with blue stickers, red for the bells, and green for wood blocks.
Children compose music by creating repeating patterns with the same colors of stickers on musical staff paper.
Each instrument plays in the order indicated by the pattern. For example, each time the blue sticker appears in the pattern, the child with the shaker shakes it. When the red sticker appears in the pattern, the child with the bell rings it. When the green sticker appears, the wood block player claps it.
In this video, my sons have a blast creating the pattern with stickers and then "playing" the pattern. After we turned off the camera, they spent about 30 minutes creating new patterns and playing. They used all my stickers! It was a math success!
Pattern Towers
This activity shows how patterns can be built vertically instead of the traditional horizontal layout.
How to play Pattern Towers
You’ll need
drinking straws cut into 3/4" lengths
chopsticks
playdough
Kids poke a few chopsticks into a glob of dough then slide straw pieces onto the chopsticks to build vertical patterns.
In this video, I let my sons Quinn and Knox be creative with their patterns. If you want to, you can ask kids to create a specific pattern (like AABB) or challenge them to show the same pattern in 3 different ways. Lots of possibilities! And it’s cheap and simple as far as supplies go.
Algebraic reasoning is all about identifying patterns and relationships and generalizing them to new situations and objects.
If you're a parent, talking about patterns around the home helps reinforce the concepts in these activities. For example, when setting the table for dinner we create a pattern: fork, plate, knife, spoon. Patterns can also be made of movements like brushing your teeth--up-down, up-down.
There are lots of ways to make pattern noticing, creating, and completing part of your math-positive classroom! Let me know what you think of these patterning ideas, add your own suggestions in the comment section, or send me a Tweet. I'd love to hear how you are using hands-on tasks to build algebraic reasoning with your kids.
If you like these ideas, hit subscribe. And find many more tips in my book Math-Positive Mindsets: Growing a Child's Mind without Losing Yours.