Count On Strategy is a powerful strategy students can use when problem solving. On today’s episode we will jump into what a math strategy is and how the count on strategy can help students develop as a mathematician. 

In this episode we’re chatting about the count on strategy is one way your students can improve in problem solving real world math problems

In this episode you will chat about: 

• questions to ask students to improve their strategy communication
• examples of the count on strategy
• how the count on strategy can be effective and efficient for solving 

Links Mentioned in the Episode: 

🤍Guide to Engaging Math Discussions

Books I love & mentioned often: 

📗Adding it Up https://amzn.to/3FzM4as 

📘Children’s Mathematics Cognitively Guided Instruction  https://amzn.to/3FzLMQU 

📙Principles to Action: Ensuring Mathematical Success for All https://amzn.to/42o816h 

📕5 Practices for Orchestarting Math Discusions https://amzn.to/3zagEEl 

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Want to read more about count on strategy?

Let’s talk about strategies today. Strategies are the WAY we reason about the problem to arrive at a solution. Sometimes our strategies are effective and get us a correct answer… 

Sometimes our strategies are effective and we make some calculation errors and we don’t’ get a correct answer 

Sometimes our strategies are efficient and sometimes they are not.

Whenever I talk with my students about strategies we use those two words– effective and efficient.

So today we are going to focus on one type of strategy: a counting strategy. 

What is a counting strategy? 

A counting strategy is when students COUNT to figure out the problem. So, the way they count is going to be the focus of our conversation today.

But before we dive into this type of strategy let’s talk about HOW you know what a students’ strategy is… 
It is difficult to know what goes on inside people’s heads, right? Sometimes if our students are good at representing their thinking we will see it on their paper or in their manipulatives. However, they might be keeping it all inside their head. 

That’s why YOU must get good at asking questions and most importantly at listening.
When you ask the right, open-ended question you can get your students to really share their strategy with you… and that is the goal. You want students to be able to describe what they are doing– their strategy. So the goal is to use the grapple time (also known as productive struggle time). Use that time when your students are working to ask students about their strategy.

When you ask students, “How’s it going? Tell me what you’re up to.” You keep it open ended and you are asking students to tell you their strategy.
You want them to describe what’s in their head so you can listen closely and be curious to find out about their strategy.

You’ll want to stay neutral- in your stance (how you approach your student- your body language) and in your tone of voice.
You’ll also want to avoid the urge to jump in and show them the “right” way of doing things. Instead, allow your students this luxury to have your undivided attention to describe their math brilliance! Use this as an opportunity to build their excitement and skills of communication of their math ideas 

So, back to counting… 

We are going to talk about two ways students can COUNT to solve.

They can count all 

They can count on 

Students can count all… if the problem is 34 + 89. They represent the 34 and the 89 and count it all up to add. This could mean they use blocks or drawings to keep track of 34 and then 89. 

They count each individually and then start over at 1 once they’ve combined. They count all to get the total.

A student can count on… they might put 34 in their head. This is called conserving a number. Then, they would count up 89 more.
A bit more efficient would be a  student that conserves 89 in their head and counts up 34.

The way they keep track of this might be with blocks (counting out 34 blocks on the table). Then putting the 89 in their head and counting up by ones as they move the 34 block from their left to their right.

Now, Base 10 understanding also comes into play here.
When counting all or counting up students can employ their understanding of Base 10 and start to count in groups! 

Let’s consider the student who was counting by ones and making each quantity with manipulatives or drawings and then starting over again at 1 when combining…

What about the student that was conserving 89 and counting up 34 more? A student might count 89, 99, 109, 119, then switch to ones and count up by 1s 4 times.

You see that is much more complex and requires more mathematical understanding.

So when are you conferencing with students? What are you looking for? 

1. Are student counting up– are they holding one number in their head or are they starting from one number 
2. Which number are they starting from?
   1. You’ll want to notice which number they are starting from… is it the first number that appears in the problem or the number that is most efficient to start from? 
3. How are students counting up? By 1s? By groups? By 10s and 1s? 
4. Then, how are students representing their thinking on paper? It is amazing to have these strategies to do this mental math… in fact that’s what we’re striving for. Our students are able to solve those adding tax and tip when splitting a check with friends on the fly in their head without calculator problems. But we’re starting this from Kindergarten… so mental math may or may not play a factor at this point. 

Why is it an important strategy? 

Think for a moment the last time you’ve used the count on strategy. This is a strategy that stays with us. So, it is important that students understand this strategy. Even if it isn’t one they choose for themselves, being able to explain it and seeing how to use it is important.

Now, do I think you should stand at the front and talk students through HOW to use the count by strategy No.

I firmly believe in exploration & explanation. Which means…. Students have a chance to explore and grapple with a worthy task and then they have time to explain their strategy and discuss the strategies of others. While you, the facilitator, ask important questions to guide students toward conjecture or math truths. 

How can we support students in counting on? 

You can ask questions that help students see how this strategy is effective: 

• Why did you start at 89 instead of 34? 
• How did you count that? Can you show us again and tell us why you did it that way? 
• Why did you choose to count up by 10s? 
• What in the problem told you to start at 89? 

There is so much you COULD ask students. But the goal here is to get your students to explain WHAT they did and WHY they did it. That is essential to explaining math reasoning. 

Your Guide to Student Centered Math