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Have you seen my self-paced math stations around Facebook, Pinterest, or TpT and wondered how they could fit into your classroom? I hear from a lot of teachers who have wanted to use them for years, but are unsure of how they will work and if they will fit their needs.

This post is intended to help you understand EXACTLY what is entailed for implementing the math stations in your classroom. Because they are all formatted very similarly to ensure consistency, this post is applicable to all of the first to fourth grade stations for addition, subtraction, multiplication, division, and fractions.

SEE ALL MATH STATIONS HERE.

Ok let’s get started!

GOALS

Although it seems that the goal of these math stations would be to master the math facts, there are actually other goals that are just as important. These are:

• success for all students
• motivation
• confidence

I believe that when students feel successful, smart, and confident, it enables them to learn. How can we expect our students to enjoy math, be confident, and take risks if they are never successful?

THE LEVELS

Each math station consists of a sequence of levels. Each level focuses on one skill, strategy, or set of facts.

For example, in The Multiplication Station, students master one set of facts in each level. For each set of facts, they learn a strategy to make that easier. So in the 4’s level they learn the strategy of “doubling the double.” Or in the 12’s level they learn the strategy of breaking up the 12 into a 10 and a 2, then multiplying the parts.

As another example, suppose we are looking at the First Grade Addition Station. In this station students will move through levels such as Counting On, Doubles, Doubles Plus One, Making Ten, etc. In each level they will master that particular strategy before moving to the next one.

BUT ISN’T IT CONFUSING LEARNING SO MANY STRATEGIES?

NO! These stations incorporate the concepts of isolation and integration. So when a new strategy is learned, it is first ISOLATED from all of the rest. This means that students are only focusing on that one strategy. Later, when it is mastered, they INTEGRATE it with the other strategies that they have learned. The strategies slowly build on each other in a way that makes practical sense.

STRATEGIES AS “TOOLS IN A TOOLBOX”

I like to refer to math strategies as “tools in a toolbox.” We want each of our students to possess the tools that she needs to solve an equation. This does not mean a memorized series of steps that, if forgotten, results in a wrong answer and no other strategy to fall back on.

This means that we want our students to UNDERSTAND what they are doing. Through conceptual understanding, students will be able to solve a problem AND have alternate strategies to fall back on.

HOW ARE THE STATIONS SELF-PACED AND INDEPENDENT?

The independent, self-paced nature of these stations is a huge part of what makes them so successful. All of your students will start at the very first level. The first few levels of every station are meant to be confidence boosters. This means that they are typically fairly simple. You’ll notice your students’ motivation soaring during these levels.

Students will work through the level on their own. They will complete an activity, self-check using the prepared answer keys, complete their “passport,” and then move onto the next activity. The personal tracker that they will each have tells them exactly what they have done, and what they will do next.

Once students are finished all of the activities in a level, they will self-assess. “Do I know the strategy?” “Am I comfortable with this set of facts?” When they feel ready, students will approach you for a very quick, oral assessment. Once the assessment has been successfully completed, students will move to the next level.

After a few days of working with the stations, you’ll notice that your higher-end students start to speed along, and may be a few levels ahead of everyone else. Some other students might be taking a bit longer on the levels, and you may be working with them in small groups to help them understand the concepts.

This is ideal, and exactly what you want.

This means that every student in your classroom is being appropriately challenged. Every student is working to his full potential.

HOW ARE STUDENTS ASSESSED?

Assessment throughout the Math Station is mostly done by students. You already have enough marking to do! When you prepare the Math Station, you will also be laminating answer keys. These answer keys will be stored in the folder for each level. When students have completed an activity, they will get the answer key and self-check.

I’ve heard from some teachers who didn’t think that their students could handle the self-checking, but were later shocked at how easy it was for the students.

The assessment that you WILL be doing as the teacher is the short oral quiz at the end of each level. In most of the stations, I’ve included assessment quick reference cards. These will help you assess your students quickly and effectively. You will take about 1-2 minutes asking the student to solve a series of equations from the level that she finished. This will easily and quickly tell you if she has mastered the skill or strategy or not.

I hear from teachers all the time who tell me that the oral assessment is their favorite part of these stations. You can gain SO much information from talking to your students face-to-face rather than simply reviewing a written test. You can see where your student stumbles, where he is quick to know the answer, and what parts he is still struggling with.

MEETING ALL OF THE NEEDS

These math stations make it easy to meet the needs of all students in your classroom. You will be allowing your high-flyers to work ahead, while allowing your students who need to work more slowly do so.

This also allows you to do mini-lessons or small group instruction with the ones who need it. You might see that three students are struggling with the same level, so you’ll be able to take them aside for some extra practice.

HANDS ON ACTIVITIES

Hands on activities are incorporated throughout the station. In some stations, students will do a hands-on activity after every second or third level. In other stations, such as the Fraction Station, a hands-on activity is completed after every level.

SUMMARY

I hope that I’ve succeeded in helping you understand how these math stations work. In summary, the routine is very simple:

• Student completes an activity.
• Student self-checks and repeats those steps until the level is finished.
• Teacher gives student an oral assessment, and then student moves to the next level.

A NOTE FROM SHELLEY

I first started creating these math stations in 2012. This was an approach that I had used with my own students, and now has been widely used by tens of thousands of teachers.

I know how hard it can be to teach math strategies. Even though you have the best of intentions, there are so many things in your curriculum that it feels like you can’t focus on math strategies all year long.

This is your solution.

If you are committed to once and for all implementing a highly strategic plan for math fact fluency, I believe that you will experience great success with these stations.

Here is the link to all Math Stations. Please be sure to read the hundreds of testimonials from other teachers in the feedback sections to see if this might be something that would work for you.

EXTRA, BUT USEFUL INFORMATION

• These Math Strategy Task Cards can be used as extra reinforcement for students who need it. Most of the task cards align with the levels of the coordinating Math Station. These are also useful to use during guided math groups, mini lessons, or math interventions.

• Make your stations into booklets rather than using the bin/tub approach. You can find free cover pages for your student booklets HERE.

The post Self-Paced Math Stations for Fact Fluency and Mastery appeared first on Shelley Gray.

WHAT IS A FRIENDLY NUMBER?

In this case, we refer to friendly numbers as a number that is easy to work with. For example, multiples of 10 are “friendly” because they are easy to work with when we add or subtract.

USING FRIENDLY NUMBERS AS AN ADDITION STRATEGY

When we use the “friendly number” strategy for addition, it helps us work with big numbers. This is because we are essentially breaking the equation up into more manageable parts.

We begin by getting to a friendly number, which is typically a multiple of 10, 100, or 100 – depending on the numbers that we are working with. Then we add on the remainder.

Let’s take a look at the “using friendly numbers” addition strategy in action.

EXAMPLES

In this example we will add 27+9 using the friendly number strategy.

First, let’s put the number 27 on our empty number line.

Now let’s get to a friendly number. We know that the number 30 is “friendly” or easy to work with, so we can add 3 to get to 30.

Lastly, we add the remaining 6 and get our answer of 36.

Suppose we are solving 265+18.

First we will write 265 on our empty number line.

Then we can add 5 from the 18 to get to a friendly number 270.

We have 13 left, so now we can simply add the 13 to the 270 to get a final answer of 283.

BIG IDEAS

Mental Math is not about following a one size fits all process or procedure. Mental Math involves being able to think flexibly about numbers and manipulate them in different ways.

For the equations shown above, this friendly number strategy worked well. But students also could have used left to right addition, breaking up the an addend, compensation, or even the plus 7,8,9 strategy.

Our goal is to teach our students to think flexibly about numbers so that mental computation comes easily to them.

NEXT STEPS:

• Download a free activity to practice the using friendly numbers addition strategy HERE.

• Find task cards to reinforce the “using friendly numbers” strategy here:
  • Using Friendly Numbers task cards for fourth grade
  • Using Friendly Numbers task cards for third grade

The post Using Friendly Numbers: An Addition Strategy appeared first on Shelley Gray.

Compensation is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve. Some students may prefer this strategy as an alternative to left-to-right addition or the breaking up the second number strategy.

Compensation is a useful strategy for making equations easier to solve. More importantly, it encourages students to think flexibly about numbers.

HOW TO PERFORM THE COMPENSATION STRATEGY

Let’s solve the equation 34+49 using the compensation strategy.

First, since 49 is so close to 50, we will add 34+50. This is easier to solve. Then, since we added one extra to the original equation, we have to subtract one from the final answer.

Let’s suppose that we want to solve the equation 132+64. We can use compensation to add these two numbers. With compensation, there is no one right way to perform the strategy. In this case, let’s begin by taking 4 away from the 64 and add 132+60 to make 192. This is an easy equation to solve. Now, since we subtracted 4 from the original equation, we have to add 4 to the answer. 192+4=196.

NEXT STEPS:

• If you would like full support for teaching addition strategies in your classroom, check out The Addition Station HERE.  These Math Stations are self-paced, student-centered stations for the basic math strategies. Students move through the levels at their own pace, ensuring that they are always challenged, and working to their full potential.
• Read other posts on this website about addition strategies HERE.
• Download a FREE activity for practicing the compensation strategy HERE.

The post Compensation: An Addition Strategy appeared first on Shelley Gray.

Breaking apart an addend is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition.

This strategy involves breaking up one addend in an equation into more manageable parts. Like many other mental math strategies, this strategy encourages students to think flexibly and to manipulate numbers in different ways. This is the big goal of mental math!

As you look at the examples given, you’ll notice that this strategy reinforces place value understanding, as students are breaking apart the addend by place value.

EXAMPLES

Let’s take a look at how to perform this strategy. Whenever you introduce a new strategy in your classroom, be sure to use small, easy to work with numbers. This will ensure that students can focus on the strategy itself rather than struggling with big numbers while trying to master a new strategy.

In this example, we will add 14+12. We will break the 12 into a 10 and a 2.

Now we add. First we add 14+10 to make 24, and then add the remaining 2 to make 26.

Let’s try another example. Here we will solve 35+46. First we break the 46 into a 40 and a 6.

We will add 35+40 to make 75, and then add the remaining 6 to make 81.

FLEXIBLE THINKING

One of the greatest aspects of mental math is that there is not a series of steps to memorize. Really we just want our students to understand what the numbers mean and be able to manipulate them in a way that works for each individual student.

Suppose we have the equation 213+214.

One student might choose to break up the second number and add 213+200+10+4.

Another student might choose to break up the second number into only two parts and add 200+210+4.

A third student might choose to add these numbers using left to right addition.

Here’s a video with more information on how you can teach the break apart strategy using the Concrete Representational Abstract model:

This is one strategy that you definitely will want to incorporate into your math instruction. It can be used in many different ways and you will notice that your students begin using this sort of thinking for other math concepts as well.

NEXT STEPS:

• If you would like full support for teaching this strategy, find my Break Apart for Addition Unit HERE.

• Download a FREE activity for practicing the breaking up an addend HERE.

The post Breaking Apart An Addend: An Addition Strategy appeared first on Shelley Gray.

STUDENT #1

This student is knows that 16+4=20 because she has practiced this fact over and over and over again. 

When the teacher asks her to solve 16+5, she’s stumped. This is a fact she hasn’t learned yet.

After moving on to other math units and focusing less on addition, the fact 16+4 is forgotten and will have to be re-learned next year.

STUDENT #2

This next student hasn’t learned the fact 16+4 yet, but can easily figure it out because he knows that 6+4 is ten and then 10 more is 20.

When the teacher asks him to solve 16+5, he is easily able to visualize it because of all the work their class has done with ten frames. He already knows that 16+4=20, so 16+5 is just one more!

Then he thinks of one other way he could have solved it! He imagines the 16 as a 10 and a 6. He adds the 6 to the 5, which is a doubles plus one fact (11) and then adds on the remaining 10 to make 21.

Opponents of mental math will say this is too confusing, but I’ve simply written it all out so that you can see the steps that happen in a person’s head very quickly. This does not need to be written out like this every time.

Near Doubles

This strategy is a natural progression from the doubles. It includes using a known fact and building on it. For example, to solve 6+7, a student could think, “I know that 6+6 makes 12, and one more makes 13.” This strategy is best modelled with ten frames, which makes it easy to see! Students need to SEE math so they can build their understanding!

 

Here’s a video that explains the near doubles strategy in more depth or find a unit for teaching the near doubles facts HERE.

 

 

Make a Ten

Make a Ten is a mental math strategy where students use the number combinations that make ten to form connections and relationships to other facts. First, students must learn the number combinations that make 10. Then they can confidently use those combinations. For example, to solve 8+5, a student might think, “I can take two from the 5 and give it to the 8 to make a ten, and then add the leftover 3 to make 13.” Ten frames are a fantastic way to illustrate this strategy.

 

Here’s a video that explains the make a ten strategy in more depth.

 

Find a unit for teaching make a ten HERE or find the math mats shown below HERE.

 

 

Making Multiples of Ten

This strategy is a natural follow-up to making ten. To make , we can use the number combinations that make ten (6+4, 7+3, etc.). This helps us recognize that expressions such as 26+4 will make a multiple of ten. Ten frames are an excellent way to model the thinking process. For example, when we model 26+4 with a ten frame, it’s easy to see that we can shift the 4 dots over to completely fill three ten frames and make 30.

 

Find a unit for teaching the making multiples of ten strategy HERE.

Left to Right Addition

Left-to-right addition is a powerful mental math strategy for adding numbers with two or more digits. Place value understanding is key, as students will be grouping the tens and then the ones. For example, to solve 24+53, we will first add 20+50 to make 70, then 4+3 to make 7, and finally 70+7 to make 77. Left-to-right addition is important to teach BEFORE students learn the traditional algorithm. This is because left-to-right addition focuses on conceptual understanding rather than on the memorization of a series of steps.

 

Here’s a video that explains left to right addition in more depth.

 

Find a unit for teaching left to right addition HERE.

 

 

 

 

Break Apart/Decomposing

Breaking apart an addend by place value is a powerful mental math strategy for adding numbers with two or more digits. Although this is similar to left-to-right addition, some students prefer it because only one addend is decomposed by place value, rather than both of them. For example, to solve 43+35, we could first decompose the 35 into 30 and 5. We start by adding 43+30 to make 73, then the remaining 5 to make 78.

 

Here’s a video that explains the break apart strategy in more depth.

Find a unit for teaching break apart HERE.

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