Using Efficient Math Strategies

You know that math kid.  That one who draws pictures to solve his math problem.

Every. Single Day.

And no matter what you say, she keeps drawing bubbles.

Do you have that math kid in your room too?  Cause some years I've had like 10 of them!

Maybe your kids aren't counting all anymore, but you can't get them to quit counting on, or drawing tens and ones...the concept is still the same...and still as frustrating!

How do we get kids to quit direct modeling or drawing pictures, or whatever we want them to quit doing and move on to more appropriate math strategies?  Let's talk about how I use the word EFFICIENT to help kids move beyond drawing bubbles!

What Does It Mean To Be Efficient?

An efficient math strategy is the quickest way to solve a problem that I understand.  In first grade, we start off by generating strategies.

Throughout the year, we chart strategies as they are shared during math talks or during story problems.  We learn from the very beginning how to identify and name a strategy. (Note this chart is one from several years ago and we had not added strategies like tens and ones yet.)

We start the second half of the year practicing using multiple strategies.  I encourage kids to have more than one strategy ready to share during math talks.  And during our story problem time, I have them show me two ways to solve the same problem instead of showing one strategy for 4 different problems.

The next week, our focus is on picking the best strategy for each story problem and number set.  We read a digital book called Finding Bingo.  (The dog is lost and we are generating ways to find him and deciding which way is the best.)  Then, we introduce the word EFFICIENT.  We talk about what it means and chart some synonyms.

What Are Efficient Math Strategies?

Once we understand what efficient means, we go back to our "Model With Math" chart and evaluate our strategies.

Is this strategy efficient? Why or why not?

Then, we color code our strategies.  This works best if you add strategies to your "Model With Math" chart on index cards from the beginning of the year.  Then, use tape to add them to your chart.

Once you are ready to categorize them into efficient and inefficient, it will be easy to move and you won't have to rewrite them!

In first grade, at the beginning of the year, all strategies are welcome as long as it fits the story.  Any strategies you share that result in the correct answer are "green strategies."

Any strategy that doesn't fit the story, is inefficient and we call a "red strategy."  A red strategy is a strategy that will not ever result in the correct answer.  That could be doing nothing.  Or subtracting on an addition story, etc.

In upper grades, move strategies to red when students are "not allowed" to use these anymore.  And if you see a red strategy as you conference, you simply mark through it with a red crayon and have them choose another strategy.  Be careful not to move strategies to red too quickly.  We don't want to take away strategies that build understanding for kids who need them too soon!

By January (at the latest), we don't want students counting all anymore.  So, once we discuss why counting all is inefficient, we move that strategy from green to yellow.

"Yellow strategies" result in the correct answer, but are a much SLOWER way to solve.  When I am assessing story problems, these would be a "2" on my rubric or below basic.  Notice that yellow strategies include drawing and counting all AND drawing all, but counting on.

If you are in second grade, you may start out with these as yellow strategies at the beginning of the year, and move more over as your year progresses.  This is super easy to differentiate between grade levels, but keep the same language for kids throughout the school!

"Green strategies" are the ones that quickly get us the correct answer.  But they also are strategies that we understand and could teach to a friend.  For example, decomposing 10s and 1s is efficient for the kid who understands it, but for a kiddo who doesn't understand 10s and 1s, it is not an efficient strategy.

This is where it gets tricky.  Not all green strategies are appropriate for every kid.  They have to be able to find a strategy that makes sense to them, and makes sense with the problem or number set.

These strategies are posted with our Model With Math chart so that we can use them during share time.

How Can I Use This With Small Groups?

If you follow my Guided Math Workshop Curriculum, you share during your small group time.  This makes it very easy to differentiate and only add green strategies that each group is ready for.

And it makes total sense to have a different green chart for each group!

As you share your strategies, have kids color a yellow, red or green bubble next to each of their strategies to determine if it is efficient or not.


For the yellow strategies that we find, we talk as a group about how to improve the strategy to make it efficient.

What is inefficient about this? (Reference the efficient chart)
How can we make it more efficient?

Make the word efficient part of your sharing routine helps move our kids beyond those strategies we need them to "drop."

You can find this lesson and materials in my Guided Math Workshop Plans.

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