How to Teach Number Sense

Elementary school is the most critical time for students to develop a strong number sense. It impacts not only the rest of their math education, but also the rest of their life. Read below to learn more!


This blog post will...
  • explain why teaching number sense is important
  • identify the essential understanding of number sense organized by grade level
  • describe the common misconceptions surrounding it 

WHY IS LEARNING ABOUT NUMBER SENSE IMPORTANT?
You should always provide your students with a purpose for learning. This can be done by explaining to them why number sense is important and giving them examples of how we use number sense in the real world.

Number sense is how children conceptualize and manipulate numbers using both mental math and written expression. Children with a strong number sense understand the relationships between numbers, the ascending and descending value system in order, and why basic arithmetic works. It is important because it gives children the confidence to tackle more complex problems and allows them to flexibly work with numbers. 

Relating the concept to your students’ own real-life experiences makes their work more interesting and meaningful. Real world examples of number sense include comparing heights, counting snacks, and comparing prices. I encourage you to create a number sense anchor chart with your students and record these examples and more.

ESSENTIAL UNDERSTANDINGS of NUMBER SENSE
Essential understandings, also known as enduring understandings, are the big ideas we want our students to master. They help you focus your teaching on what you want your students to know, understand, and do. These “big ideas” derive from standards and serve as the foundation for designing all of your number sense lessons and activities. 

FIRST GRADE
In first grade, students should be able to...
  • understand and apply addition and subtraction properties.
  • understand how addition and subtraction relate.
  • understand the relationship between counting and addition and subtraction.
  • use addition and subtraction strategies (e.g. counting on and making ten).
  • count up to 120 starting at any number.
  • represent a number of objects with a numeral.
  • understand tens and ones.
  • compare two two-digit numbers.
  • add within 100 using strategies.
  • mentally find 10 more or 10 less than a given two-digit number.
  • subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90.

SECOND GRADE
In second grade, students should be able to...
  • fluently add and subtract within 20 using mental strategies.
  • understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
  • count within 1,000 and skip-count by 5s, 10s, and 100s.
  • read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.
  • compare two three-digit numbers.
  • fluently add and subtract within 100 using strategies.
  • add up to four two-digit numbers.
  • add and subtract within 1,000 using strategies.
  • mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
  • explain why addition and subtraction strategies work.
  • select appropriate measurement tools.
  • estimate lengths of objects.
  • represent whole numbers on a number line.

THIRD GRADE
In third grade, students should be able to...
  • understand how multiplication and division relate.
  • fluently multiply and divide within 100.
  • round whole numbers to the nearest 10 or 100.
  • fluently add and subtract within 1,000 using strategies.
  • multiply one-digit whole numbers by multiples of 10 in the range 10-90.
  • understand fractions as parts of a whole.
  • represent fractions on a number line.
  • compare fractions.
  • estimate liquid volumes and masses of objects.

FOURTH GRADE

In fourth grade, students should be able to...
  • interpret a multiplication equation as a comparison.
  • recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
  • compare two multi-digit numbers based on meanings of the digits in each place.
  • round multi-digit whole numbers to any place.
  • fluently add and subtract multi-digit whole numbers.
  • multiply a whole number of up to four digits by a one-digit whole number using strategies.
  • multiply two two-digit numbers using strategies.
  • find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies.
  • compare two fractions with different numerators and different denominators and explain why they are or are not equivalent.
  • understand that fractions with a numerator greater than one can be built by unit fractions.
  • expand fractions with denominators of 10 to denominators of 100.
  • convert fractions with denominators of 10 or 100 to decimals.
  • compare two decimals to hundredths.
  • know relative sizes of measurement units within one system of units.

FIFTH GRADE

In fifth grade, students should be able to...
  • recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • explain patterns in the number of zeros of the product when multiplying a number by powers of 10.
  • explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
  • read, write, and compare decimals to thousandths.
  • round decimals to any place.
  • fluently multiply multi-digit whole numbers.
  • find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies.
  • add, subtract, multiply, and divide decimals to hundredths using strategies.
  • add and subtract fractions with unlike denominators.
  • interpret a fraction as division of the numerator by the denominator.
  • interpret multiplication as scaling.

COMMON STUDENT MISCONCEPTIONS ABOUT NUMBERS
In order to effectively teach your students about numbers you must anticipate, identify, and correct and misconceptions or misunderstandings they have developed. To help you, I have listed some of the most common number sense misconceptions your students are likely to make. 
  • The student does not understand that numbers represent quantities. (Example: A child can rote count to 100 orally, but cannot count 20 objects using one-to-one correspondence.)
  • The student does not understand the ascending number system. (Example: A child can rote count starting from 1, but cannot count up from a given number.)
  • The student does not understand the descending number system. (Example: A child can count forward, but not backward.)
  • The student thinks estimating is a random guess. (Example: A child is asked about how many kids are in the school and he or she says 5 million.)
  • The student thinks the smallest number is 0. (Example: A child is asked what the smallest number in the world is and he or she says 0.)




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