emphasis on number sense
Every number that emerges during a math class, in every lesson, is an opportunity to support the development of number sense.

 Teachers relentlessly build and reinforce students’ number sense by integrating key activities (e.g. mental math, calendar math, number blocks) that develop their comfort with the relative size of numbers, the value of numbers, the sequence of numbers, the base 10 system, and place value. Teachers often connect equivalent values (ex: fractions, decimals, percent) and ask students to use number sense to estimate before solving a problem.
more on number sense
"Our students with number sense understand the relationship between and among numbers. They think flexibly about numbers, are able to break numbers and put them together in a variety of ways. They are also familiar with the properties of singledigit numbers and can use this information to calculate efficiently using larger numbers. Students with number sense also understand the effects operations have on numbers. They see connections between the different operations and have a firm grasp on which operation or series of operations to employ in a given situation. Another component of number sense is mental computation. Students with number sense can manipulate numbers in their head. They have strategies they use to think about numbers and operations. They do not rely solely on paper and pencil, their fingers, or calculator. Also, students with number sense have effective ways to estimate. They can approximate calculations and use familiar benchmarks to gauge unknown amounts."
Developing Number Sense by Rusty Bresser and Caren Holtzman (Math Solutions, 1999).
Developing Number Sense by Rusty Bresser and Caren Holtzman (Math Solutions, 1999).
start now
Strong number sense doesn't happen with one activity or one lesson. It has to be strengthened with daily exercise, which demands a commitment to emphasize number sense (the magnitude of numbers and relationship among numbers) with each lesson, with each day. This can be done outside of the math block, too!
There isn't one way or one route to build number sense, but here are some ways to get started:
There isn't one way or one route to build number sense, but here are some ways to get started:
 Make a time to talk about numbers (K5), even if it's quick.
 Incorporate mental math into your instruction.
 Ask kids to estimate and check for reasonableness every day.
 Encourage multiple ways to solve problems, even simple operations, and have students share strategies. (An overlap with two other core components: multiple representation and real and meaningful discourse! Teacher bonus points!)
TIME TO TALK ABOUT NUMBERS
Implement or strengthen a start of day/class routine that asks students to explore a 'number of the day' to make connections with numbers (visually, verbally, equivalent representations), decompose numbers (ex: 62 is six tens and two ones), and compare that number to other numbers (ex: what does this fall between, is this more than or less than ___). This can be done through "calendar math" or as part of your warm up, morning meeting, etc.
In the top left picture, you see a teacher that keeps track of the days of school in a tens/ones chart. This means everyday students are asked to make sense of the place value. Ex: "Today is day sixty two. Can someone write 62 on the board in standard form? How many tens are in 62? How do you know? How could we represent 6 tens with our rods? (Count 6 rods into the bag) How could represent the 2? What does the 2 mean? How do we know? Would we use the rods? (No, 2 unit cubes go in the bag). Having this quick discussion every day can be very valuable, in all grades.
In the top left picture, you see a teacher that keeps track of the days of school in a tens/ones chart. This means everyday students are asked to make sense of the place value. Ex: "Today is day sixty two. Can someone write 62 on the board in standard form? How many tens are in 62? How do you know? How could we represent 6 tens with our rods? (Count 6 rods into the bag) How could represent the 2? What does the 2 mean? How do we know? Would we use the rods? (No, 2 unit cubes go in the bag). Having this quick discussion every day can be very valuable, in all grades.
SOME ACTIVITIES YOU COULD USE OR MODIFY DURING YOUR "NUMBER TIME"
These have been downloaded from the Virginia Department of Education (2012).
These have been downloaded from the Virginia Department of Education (2012).






"NUMBER TIME" IS A GREAT TIME TO REINFORCE PLACE VALUE CONCEPTS, EVEN IF THEY ARE TAUGHT IN SEPARATE LESSONS.
mental math
Emphasize number sense by requiring some mental math each day. This is something you can implement today!
 Mental math doesn't just mean factual recall or "solve this in your head."
 It's not about "doing it faster" or "because we won't always have a pencil at the store."
 It's about strengthening your flexibility and portability with numbers.
 As students proceed through elementary school, they should develop an increasing repertoire of mental strategies to help with calculating and estimating mentally  first with whole numbers and later with money and fractions.
First, read this helpful, short document, detailing the progression of elementary mental math, created by Columbia Public Schools (PreK5th grade)
Progressions of Mental Math  
File Size:  55 kb 
File Type: 
Then, explore these materials. Heartland Area Education Agency has K5 Mental Math activities available on their website; the files are below, ready to download.





more mental math resources
To the right, you'll find a Prince Edward Island DOE (Canada) sponsored third grade booklet of explanations and activities for mental math / number sense. Check it out and adapt some of the strategies to your grade level.


To the right, you'll find a Explorations in Math document with games and activities for math, including some for mental math. It's created for fifth graders, but could be adapted to any grade level. Start your class off with a mental math game tomorrow!


multiple ways to solve problems, using number sense
Students who can manipulate numbers, because they understand their magnitude and relationship (number sense), can solve operations and make sense of the process. Watch some examples below. What can you do to encourage this flexible thinking and to strengthen your students number sense? Start by encouraging students to access problems in different ways and share how they solved with the class. Also, commit to teaching and highlighting strategies to solve (ex: making friendly numbers or turning into a 10).
Some strategies to solve operations using number sense, as explained by second graders: Watch students at Springhurst Elementary school decompose numbers to solve operations.

Check out these first graders (left) from Terry Fox Elementary solving operations, by using mental strategies. Then, read the document (below) provided by this school, about the strategies they teach in first grade math.

Check out the firstgrade students at Terry Fox Elem on the right solving problems using different strategies. 

why it matters
Number Sense ability in first grade predicts future mathematical success. One in five Americans are not fluent with basic middle school math and that has a strong connection to their elementary math understanding of numbers and how they work together:
Read the article here.
Read the article here.

Watch why Ms. Saul prioritizes mental math for her third graders and how shes does it. (Also available on EMath video page) 