Math Fluency Archives - Tanya Yero Teaching

How To Integrate Number Sense Into Your Math Lessons

November 11, 2018

There are a lot of components to a math lesson. You look for activities with engagement and complexity to assess understanding. Sounds simple enough but there are several layers to each of those factors making it hard to find the perfect balance. So when I work with teachers on implementing number sense during their math class they start to panic.

“How can I add another thing to my math block?”

“I don’t have enough time!”

“I don’t know what type of questions to ask!”

I get it. You’re holding all these reminders in your mental filing cabinet when you’re teaching a lesson. You want to target specific standards and explain key concepts. You want to ask higher order thinking questions. You want your students to really grapple with concepts rather than memorize procedural steps.

But guess what?

Building number sense will ensure you target all those wants. Number sense is not another component to your math block. Instead it is part of everything you say and do in the classroom. Simply put…it’s good teaching.

Questioning

A good math teacher is always looking for ways to sprinkle number sense into lessons, but it can be hard to find and/or write number sense connected questions.

Look for questions that are open ended, require critical thinking, and reinforce the concept that numbers can be manipulated. Be intentional in the types of questions you ask.

Example: When rounded to the nearest hundred, I become 400. What numbers could I be?

This question takes a standard (rounding) that is often taught procedurally in classrooms and requires students to conceptualize the concept of rounding based on the value of specific digits. Students must work backwards starting with a number that has been rounded to the nearest hundred. Students will first share the most obvious answers such as 399. It takes some time for the class to conclude that any number from 351 to 449 rounds to 400 if asked to round to the nearest hundred. This question is far more complex than, “Round 377 to the nearest hundred,” thus reinforcing number sense.

Strategies

Some children have been given opportunities to build number sense at a very young age. Those students will appear to naturally understand how to manipulative numbers and place value for easier computation, while others will struggle. Educate your students on the different number sense strategies. Model these strategies time and time again. Constant repetition will help your struggling students develop number sense. Provide your class with daily prompts to drive the concept home. We learn better when we are asked to apply that knowledge regularly.

Math Talk

Number sense related questions lead to great math discussions. The more open ended you can make a question the better. Open ended tasks increase discussion and collaboration amongst your students. Encourage your students to work in groups or pairs so they communicate their mathematical reasoning.

I use my Grab and Go Number Talks resource to drive home these three components of number sense. It has everything I need for the year.

Math, Math Fluency

Week 1: Teaching Strategies that Focus on Number Sense

October 23, 2017

In order to effectively teach math fluency, we must define fluency. In years past math fluency has simply been defined as the speedy recall of math facts. Thus, the birth of timed assessments. We’re looking for how quickly a student can see a problem and regurgitate the answer. But does this approach support number sense and problem solving?

I built my math block on conceptual understanding, yet my approach to fluency did not support that depth of understanding. My quest for a better way to teach and assess math fluency began. First I evaluated what fluency meant to me now that I was striving for deeper thinking within this subject. I decided I wanted to teach and assess math fluency based on efficiency, accuracy, and flexibility. Efficiency and accuracy is nothing new to fluency. Timed assessments evaluate how fast a child can recall their facts and accuracy is simply if their answers are correct or incorrect. I revamped how I viewed efficiency. I merged efficiency and flexibility together. I stopped using timed assessments and became more flexible with how I assessed efficiency of facts.

When I taught new math standards I fostered the idea of approaching problems in different ways. We celebrated the flexibility of math and how different pathways could be used to solve one problem. Why not teach fluency in the same way? I started to integrate number sense practice so my students could see the flexibility of fluency.
In short number sense is the ability to manipulative numbers. For some students this comes naturally, while others struggle. Number sense starts in kindergarten. From the 10 frame to base ten blocks, number sense strategies are taught early on. Unfortunately these strategies start to take a back seat as students get older. Intermediate teachers need to implement opportunities for number sense development in their math blocks. Number sense needs to be cultivated daily. Here is a list of the number sense strategies I teach my students at the beginning of the year.

Addition:
Making tens – Manipulating numbers to make multiples of 10 or 100 to make addition easier
Friendly Numbers – Manipulating addends to make numbers that are easy to add.
Place Value – Separating addends by their place values (expanded form).
Compensation – Removing one quantity from one addend and adding that amount to the other addend.

Subtraction:
Removal – Decomposing numbers to make subtracting easier.
Place Value – Separating numbers by their place values (expanded form).
Adjustment – Adding or subtracting to make numbers that are easier to compute.
Keeping the same difference – Adding a certain amount to each number to make subtraction easier.

Multiplication:
Friendly numbers – Making a number that is easy to multiply. Next, subtract the amount you added on.
Partial products – Multiplying each digit of one factor by each of the digits in the other factors
Part-part whole – Decomposing or separating into friendlier numbers to make multiplying easier

Division:
Repeated subtraction – Subtracting equal amounts of the divisor from the dividend
Partial Quotients – Using easy multiples of the divisor and subtracting the amounts from the dividend
Part-part whole – Decomposing or separating into friendlier numbers to make dividing easier

I use the questions above to develop number sense with my students.

I have taught 3rd and 4th grade, so I know the struggle is real when it comes to students memorizing x6, x7, and x8 facts. Instead of memorizing these facts, what if we taught them to manipulative an equation to suit their ability? Let’s take 48 ÷ 8. A student with strong number sense could change this fact to 40 ÷ 8 = 5 and 8 ÷ 8 = 1, thus arriving at the quotient of 6. Another could see 24 as half of 48 and divide 24 by 8 twice to arrive at the correct answer. It’s this manipulation of numbers that proves both children have number sense and mastery of certain facts. This is what we should focus on in terms of fluency; strong number sense.

It takes time. A lot of time. There will be moments when you think your students will never get on board. Stick with it. Through modeling and repetition they will catch on.

My Math Fluency Alternative Curriculum has various resources that provide ample practice of the strategies mentioned above.

Want a quick and easy resource to teach your students the different number sense strategies? Check out this FREE flipbook in my TpT store.



Math, Math Fluency

5 Ways to Foster Meaningful Math Fluency

October 19, 2017

I wish I had a time machine. I would go back and change some of my routines I did in my classroom. Without a doubt I would modify the way I taught and assessed math fluency. I was an advocate of timed tests and rote learning of math facts. I sat in parent conferences and defended my stance on the importance of timed fluency tests. Thru professional development and trial and error I modified my fluency curriculum. I came to the conclusion that timed tests and merely recalling math facts did not support the core foundation of my math pedagogy.

I teach math conceptually. I believe that math curriculum is comprised of 30% procedural and 70% conceptual understanding. My main goal is to teach my students to be problem solvers; to work smarter, not harder. But that philosophy wasn’t being used by my students when it came to fluency.

The importance of math fluency hit home one day when I had my students check and grade their own timed tests. I have never noticed how many of them would have to write out 100 minus however many they got wrong to calculate their score. By 4th grade my students should have been able to mentally manipulate numbers within a 100. The time I spent adding rigor to my math block was being wasted if my students couldn’t carry that deep thinking into fluency.

Current trends in education focus on growth mindset, project-based learning, and critical thinking, yet many educators limit student growth by only using timed fluency assessments.

I developed a new process for teaching math fluency. My “5 Steps to Building Meaningful Math Fluency” outlines how I define, teach, and assess math fluency. Each step provides details and examples of how you can start implementing meaningful math fluency in your classroom.

Week 1-Teaching strategies that focus on number sense (CONTAINS A FREEBIE!)