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What Is It?
Number sense involves understanding numbers; knowing how to write and represent numbers in different ways; recognizing the quantity represented by numerals and other number forms; and discovering how a number relates to another number or group of numbers. Number sense develops gradually and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating to them in different ways.
In the primary and intermediate grades, number sense includes skills such as counting; representing numbers with manipulatives and models; understanding place value in the context of our base 10 number system; writing and recognizing numbers in different forms such as expanded, word, and standard; and expressing a number different ways—5 is "4 + 1" as well as "7 - 2," and 100 is 10 tens as well as 1 hundred. Number sense also includes the ability to compare and order numbers—whole numbers, fractions, decimals, and integers—and the ability to identify a number by an attribute—such as odd or even, prime or composite-or as a multiple or factor of another number.
As students work with numbers, they gradually develop flexibility in thinking about numbers, which is a distinguishing characteristic of number sense.
Why Is It Important?
Number sense enables students to understand and express quantities in their world. For example, whole numbers describe the number of students in a class or the number of days until a special event. Decimal quantities relate to money or metric measures, fractional amounts describing ingredient measures or time increments, negative quantities conveying temperatures below zero or depths below sea level, or percent amounts describing test scores or sale prices. Number sense is also the basis for understanding any mathematical operation and being able to estimate and make a meaningful interpretation of its result.
Number sense develops as students understand the size of numbers, develop multiple ways of thinking about and representing numbers, use numbers as referents, and develop accurate perceptions about the effects of operations on numbers (Sowder 1992).
How Can You Make It Happen?
In teaching number sense, using manipulatives and models (e.g., place-value blocks, fraction strips, decimal squares, number lines, and place-value and hundreds charts) helps students understand what numbers represent, different ways to express numbers, and how numbers relate to one another.
When students trade with place-value blocks they can demonstrate that the number 14 may be represented as 14 ones or as 1 ten and 4 ones. They can also demonstrate that 10 hundreds is the same as 1 thousand. By recording the number of each kind of block in the corresponding column (thousands, hundreds, tens, or ones) on a place-value chart, students practice writing numbers in standard form.
Using fraction strips, students find that 1/4 is less than 1/3 and that it names the same amount as 2/8.
Using decimal squares, students see that 8 tenths can be written as 0.8 or 8/10. By pairing up counters to identify even numbers and marking these on a hundreds chart, primary-grade students discover that, beginning with 2, every other number is an even number.
Intermediate-grade students can mark multiples of 3 and 6 on a hundreds chart and find that every number that has 6 as a factor also has 3 as a factor.
Using a number line, students see how fractions with different denominators relate to the benchmark quantities of 0, 1/2, and 1.
From these concrete experiences, students build the foundation for number sense they will bring to computation, estimation, measurement, problem solving, and all other areas of mathematics.