What to do When Math Worksheets Don’t Work

What is it about math worksheets that make that kid cringe? A well-formatted, cutely decorated math worksheet screams to us to complete it (or maybe I am just weird), but for that kid, it screams boredom.

Do you have one of these kids? I happen to have three of them.

I loved worksheets as a kid, especially cute ones. I couldn’t understand why these worksheets weren’t enticing for my kids.

My kids love to learn. They love to read. They love art. They love storytelling but you can keep those worksheets. They don’t want anything to do with them.

After years of drudging through workbooks and textbooks, I came across an alternative. It was at the Gattengo Conference that I learned the neatest game that would change our math class forever.

The Substitute Game

In this clever game, I found that I didn’t have to have my kids drudge through math worksheets. My kids could create their own problems, but not your everyday worksheet problems. My kids went on to create the most interesting equations that left me sharpening my own math skills.

Today, I am going to introduce you to the simplest version of this game by using PDL’s Number Building Play Mats (free when you subscribe) as a back drop.

The Basic Rules

You begin with one rod.

Then you substitute the rod for two rods.

Next, you pick one rod and substitute it for two rods again.

This game continues until all the rods are white.

This is by far the simplest version of the game. Children gain an understanding of number building by deconstruction each rod throughout the game. You can even play this game in reverse by starting with all white rods. 

Math Worksheets Lack Engagement

Math worksheets can not provide children this opportunity for creativity and autonomy.  You can play this game several times and while the end result is the same, the path to get there will be different every time.  

With Math Worksheets, there is only one answer and one right way.   I am certain that it blocks children from really seeing all the patterns and relationships that exist.  

I couldn't believe how many worksheets my kids filled out and still, they completely missed all the patterns.  ​I honestly believe that math worksheets don't engage the mind in the same way as the substitution game, but don't take my word for it.   Check out some active learning theories articles to see what I am talking about. 

A child playing the substitution game has autonomy to decide which rod to substitute.  They are actively engaged to find the right rods to substitute. ​

Isn't this Game as Limiting as Math Worksheets?

Of course, this simple version of the Substitution game is limited in the relationships children can explore and demonstrate understanding. What about subtraction and division? Fractions and multiplication?

In Gattegno’s Textbook 1 (Free HERE), children are walked through the variety of ways you can describe a rod. A red rod is one half of a purple rod. A red rod is also 2 white rods. A red rod is also described as a yellow minus a green rod. A tan rod is divided four times by a red rod.

As children learn to describe the rods in a variety of ways, the substitution game gets more interesting. Instead of saying, a dark green rod plus a purple rod equals an orange rod, the child can describe the purple rod as 2 red rods or one half of tan.   

Moving the Child to the Abstract

At this point, the child is seeing with their mind.  We aren't substituting rods but substituting the description of the rods.  This is a very pivotal point for a child. How does one go from substituting physical rods to substituting the description of the rods?  

Through specific tasks, Gattegno guides student to see the many relationships that exist between numbers.   The substitution game now becomes the playing field by which to practice describing these relationships. 

Think of parroting Spanish phrases.  It is one thing to parrot and it is a whole other thing to know when and how to use those phrases.   Real conversations challenge us to substitute and manipulate those phrases in order to be real and authentic.  The Substitution game provides an conversational platform for children to move beyond parroting to gain a comfortable level of understanding.  

Tips on Playing the Substitution Game

Because children choose to describe rods in a way that they are most comfortable with, this game is a good gauge to see where to extend a child’s comfort zone.

When my kids first started playing this game, they rarely used fractions to describe a rod, so when it was my turn in the substitute game, I described my rod by its fractional relationship to another rod. I also planned a lesson later that week to practice naming those relationships.

Another tip: Keep a math journal page handy to record student's comfort levels.  Record those successes and note opportunities for extension.  

Write about those moments you had to challenge their understanding.  How did you challenge them?  How could you have done it differently?   How did the student react?   Keeping a math journal helps you plan and improve over time. 

We have played this game in the Facebook group, and time and time again, parents have noted their child's delight in their ability to make interesting equations.  There is nothing like having your child grinning ear to ear with pride over the fascinating equation they built through the game.  

Math Worksheets Lack Differentiated Learning

Kids from diverse levels of understanding can play this game together. Children build upon each other and naturally stimulate each other to create more interesting equations. It is one of the features of the game I love most.  

Trying to teach math class three times a day to three different kids tires me out and often leaves me frazzled. We play this game as a family and I am confident we are all learning and growing at just the right level.

The rigidness of a math worksheet can create roadblocks because they don't stimulate new learning.  Instead, they merely reinforce learning.  

A child can be frustrated by filling out worksheets that they feel are just the same thing.  We know the importance of practice to create fluency, but we have to balance that with the needs of children to be stimulated with new material and autonomy.  

If you have students bored with typical math fact practice, they might find this game a great alternative. In fact, you may be surprised by what they come up with. 

Math Worksheets Get Old

No amount of clip art and fidget spinners can take away the boring rigidness of a math worksheet.  Because a lot of math is really just a substitute game of fancy counting, you can extend this game in many directions.

In another post, I will talk about more ways you can play this game. What about you? What is your favorite way to avoid math worksheets and still get meaningful work done?