number sense Archives - Tanya Yero Teaching

How To Teach Students To Use Number Sense Strategies

October 22, 2019

I have written several blog posts on number talks (CLICK HERE and HERE to read more) and how to implement this practice in the classroom. This has sparked conversation amongst teachers and myself. Teachers are excited to start building a number sense program in their classroom, but one question keeps making its way back to me…. “BUT HOW DO I TEACH MY STUDENTS TO MENTALLY MANIPULATIVE NUMBERS?!?!?”

Number sense and the confidence to mentally solve equations doesn’t come overnight for students. It takes time, repetition, and lots of exposure. For students that lack math confidence, it’s going to be even harder. More often than not students with strong number sense feel good about math and their skills. They are the sit in the front with their hands raised for every question kind of students, but no one is born with number sense. It is something that is gained – a notion that was supported early on by teachers and/or parents and picked up by the child. But every student is capable of learning number sense and no matter what grade you teach you can implement purposeful practices to build number sense within your students.

At the start of every school year, I implement my game plan for daily number sense practice. I start with teaching my students the number sense strategies.

Here is a list of strategies I teach my students each year. Grab this FREE list below!

Consider the following tips when introducing number sense strategies to your students.

Assume Your Students Lack Exposure

I used to administer timed fluency assessments in my classroom. When my students were done we would collectively grade their tests so they could graph their growth in their math notebook. It would baffle me how many students had to tangibly write out 100 subtracted by however many questions they missed to calculate their scores. They were 4th graders! How could they not mentally calculate an addition/subtraction question within 100?! For some I knew that their comfort level would always lie in writing out the standard algorithm and solving it. But I knew others were fully capable of using mental math. I wasn’t doing my part as their math teacher. My students deserved the opportunity to be taught how to mentally manipulate numbers.

Before I implement number talks in my classroom we spend time looking at each number sense strategy and what it looks like in specific scenarios. They need this exposure to apply this knowledge on their own later on.

I spend a month introducing and reviewing various strategies for addition, subtraction multiplication, and division. Number sense strategies also lend themselves beautifully to place value. In time you’ll start to see your students apply the strategies on their own during your number sense routine and during the introduction of new math skills.

Take a look at the samples below from two students when asked to solve 24 x 9 using an alternative method to the standard algorithm.

Teach Your Students That Number Sense Is Fluid

Mental math is based on a few simple principles: 1.) how the child perceives mental math 2.) their comfort within specific strategies and the actual numbers within the question. It’s subjective. How I see an equation and my preference to manipulate the numbers for easy computation will differ from the next person. Inform your students of this. Number sense strategies can be intertwined together or used individually. There is no WRONG way to mentally manipulate numbers.

PRACTICE, PRACTICE, and PRACTICE

Number sense doesn’t develop overnight. Learning how to mentally compute numbers and how to apply this way of thinking to various math questions is challenging. Combat this difficulty with a set routine of daily practice. I start my math block with number sense practice and after about a month we graduate to number talks. My students expect and enjoy this 5-10 minute conversation that benefits all.

Model Your Thinking And Work

Remember that story about my students calculating their timed test scores by writing the equation out? Every week when we finish grading our tests, I model a strategy for my students.

“If I got 19 questions wrong, that’s only 1 away from 20 so I immediately know I got an 81.”

“I missed 27 questions. 80+20 equals 100 and 80-7 equals 73. I got a 73 on my test.”

I want them to consider using friendly numbers as benchmarks for mental calculations and understand that addition and subtraction are interchangeable. Eventually my students catch on to mentally calculating their scores from my modeling and start doing the same.

Create A Daily Routine

After you have properly introduced mental math to your students, how will you keep up with number sense in your classroom? I use the Number Talks resources I created to launch my math block every day. My students know to expect this routine and it’s something they enjoy doing. There is a set available for grades K-6 and include 250 ready to go prompts for you both in print and digital form.

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Math, number sense

How To Teach Decimals Conceptually

October 13, 2019

Decimals are a huge part of your math curriculum. They are connected to so many standards in various domains; place value, fractions, and measurement. Teaching this topic conceptually will give your students the exposure and confidence they need to see beyond standard algorithms and truly understand the reasoning behind their work. It’s easy to teach the algorithms for adding, subtracting, multiplying, and dividing decimals and breeze through this content, but you’re missing out on an opportunity to bring concrete understanding to these four operations.

Here is a breakdown of how I teach the four operations in connected to decimals in my classroom.

Addition and Subtraction of Decimals:

Adding decimals – the easiest of the four, addition of decimals seems to be a nice starting point for students. Before I start on addition I really want my students to have a strong conceptual understanding of decimal place values, how they relate to one another (the hundredths place is one-tenth the value of the tenths place, but 10 times greater than the thousandths place), and be able to visually represent decimals using models.

We use place value disks and a place value chart to represent the decimals we are adding. Students will regroup disks when needed and see how that act changes the value of their numbers.

We also practice representing addition and subtraction of decimals with hundredth grids. Students will use different colored highlighters to represent the values being combined and cross out values when subtracting.

Multiplication of Decimals:

I think multiplication and division of decimals are far more “fun” than addition and subtraction. There are various ways to model and represent decimals using pattern blocks, fraction tiles, hundredth grids, and base ten blocks.

Here are some examples of the types of questions we review in class.

Our Power Problems have rigorous questions for you to implement in your classroom!

We work on these visual representations long before I introduce any algorithms. With a concrete understanding of multiplication with decimals your students will be able to understand the work behind the formula.

Division of Decimals:

You want to continue modeling and requiring students to conceptually understand this operation, just like the other three. Again, we use models to represent dividing a decimal by a decimal, decimal by a whole number, and a whole number by a decimal. Your students should be able to represent each of these scenarios using a hundredth grid. I integrate word problems anywhere I can so students have practice identifying which operation to use.

If you set your students up with conceptual understanding of decimals, this will help with fraction and measurement standards later on in the year. Next year’s teacher will also appreciate your efforts and you’re building number sense too!

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Math, Math Fluency, number sense

The Power Of Number Sense In The Classroom

September 2, 2019

When I first started teaching I taught “to the test.” I taught 3rd grade which in Florida is a grade level that completes standardized testing. It’s also a retention year, which means if your students don’t reach a specific score or higher they must repeat 3rd grade. The pressure was overwhelming. I wanted to make administration and the families of my students happy. I thought the answer was in covering ALL the math curriculum I knew would be on the test in the FASTEST way possible. I would speed thru lessons so I had enough time to go back the last few weeks before the test and review.

Then my first year turned into my second year and by the time the third year rolled around I realized I was creating robotic math students that were simply trained to take a test. They weren’t problem solvers. They lacked number sense and basic strategies that I knew they would need in the real world. They understood procedural learning more than conceptual understanding.

What REALLY is number sense?

Number sense is a child’s set of skills when working with numbers. More importantly, number sense is one’s ability to see the flexibility in numbers. Children with number sense understand quantities, grasps basic concepts, and understand key operations and symbols. But this all leads to the bigger picture of what number sense really is. A child with a strong foundation in number sense can identify multiple ways to solve problems. Number sense supports the beauty and creativity of each child’s mind and how they interpret a question.

The Questions You Ask (And Don’t Ask) Will Affect Your Students’ Number Sense

It’s not enough to teach your students basic algorithms and train them to memorize the steps. When I teach a new math concept the algorithm is the LAST thing I introduce. Why? I want to strengthen my students’ number sense. Math is designed to be fun and exploratory and more often than not we take the drill and kill approach. This approach leaves out the opportunity for good quality questioning.

At the beginning of the year I introduce strategies for manipulating numbers and equations. Expect your students to come to you lacking number sense tools. You have to teach them this style of math and how it works. The posters below stay up in my classroom all year.

I spend time modeling my own thinking, providing opportunities for peer discussion, and integrating manipulatives whenever I can. With time, students will organically begin to manipulative numbers on their own.

The following pictures are samples that I have pulled from student responses when asked to solve 24 x 9. Students that have the ability to see various ways to solve one problem have strong number sense.

Below is the complete list of strategies we came up with together as a class:

24 x 9 is close to 24 x 10 which I know is 240, so 24 x 9 must be one 24 less than 240. Answer: 216

25 x 10 is 225 so 24 x 9 must be 216.

12 x 9 is 108, so 24 x 9 will be double or 219.

20 x 9 is 180. 4 x 9 is 36. 180 + 36 = 216.

24 x 4 equals 96. 96 + 96 = 192 plus one more set of 24 equals 216.

Area model of 24 x 9

Asking questions such as “Does this mathematically make sense?” And “What does this look like in visual form?” will force your students to justify their answers and use multiple strategies. Never accept only one way of solving a problem. Encourage students to share their methods and celebrate the diversity of strategies. Push student thinking and ask meaningful questions. I used the following questions to steer my students towards the equations above.

“How can we use doubles to solve this problem?”

“How can an area model help us solve a multiplication equation?”

“How can we use multiples of 10 to help us solve this problem?”

What Does Number Sense Practice Look Like In The Classroom?

A class that is heavy in procedural questioning lacks the practice of number sense. Students are relying on the memorization of algorithms to solve problems. I provide questions, especially word problems that are rigorous and deep in conceptual understanding. These sorts of questions lend themselves beautifully to discussions that build number sense.

I also integrate Number Talks into my math block for extra practice that is specifically designed for number sense practice. Number Talks is a quick 5-7 minute discussion that builds mental math and number flexibility. CLICK HERE to read more.