Number and Operations (Number Sense) Counting Numbers Number and Operations (Number Sense)
1. A diagram of nested subsets of the Real numbers.
Counting Numbers
Whole Numbers
Integers
Rationals
Reals
2. Definitions of “Number Sense” and “Numeracy”.
What is number Sense?
“Much of school mathematics depends on numbers, which are used to count,
compute, measure, and estimate. Mathematical activity belongs here that centers
primarily on the development of number concepts, on computation with numbers
(addition, subtraction, multiplication, division, finding powers and roots, etc.), on
numerations (systems for writing numbers, including base ten, fractions, negative
numbers, rational numbers, percents, scientific notation, etc.), and on estimation.
At higher levels this strand includes the study of prime and composite numbers, of
irrational numbers and their approximation by rationals, of real numbers, and of
complex numbers.”
Mathematics Framework for California Public Schools, K-12, 1999
“Like common sense, number sense produces good and useful results with the
least amount of effort. It is not mindlessly mechanical, but flexible and synthetic
in attitude. It evolves from concrete experience and takes shape in oral, written,
and symbolic expressions.”
National Research Council, 1989
A person who has Number Sense has some combination of
A.
B.
C.
D.
an ability to represent number in a variety of ways,
an awareness of the relationships between numbers,
a knowledge of the effects of operations,
an ability to interpret and use numbers in real world counting and
measurement.
3. Connections to State Standards.
Number sets through the grade levels
CA Standards
K: Counting Numbers through 30
K: Addition and subtraction for 2 numbers each less
than 10 (Concrete)
1.
Counting Numbers though 100
1.
Addition facts to 20 (and corresponding differences)
Addition and subtraction problems with a one-digit
and a two-digit number.
2.
Counting numbers through 1,000
Fractions – halves, thirds, sixths, eighths, twelfths.
Decimals as related to money.
2.
Sums and differences of 3-digit numbers
Mental Arithmetic for sums and differences of 2digit numbers
Model and solve simple multiplication and division.
3.
Counting numbers through 10,000
Development of Fractions done in 2nd grade
Decimals to the hundredths.
3. Multiplication tables through 10 x 10.
Sums and differences of 4 digit numbers.
Multiply and divide a multi-digit number by 1-digit
number.
Add, Subtract, Multiply, and Divide with money.
4.
Counting numbers through 1,000,000
Decimals and fractions through hundredths
Concepts of negative integers (Number line,
counting, temperature, owing)
4. Estimate and Compute the sums or difference of
whole numbers and positive decimals (2 places).
Multiply or Divide a multi-digit number by a 2-digit
number.
5.
Decimals number from thousandths to millions
Write fractions as percents and decimals
Develop positive and negative integers
5. Add, subtract, multiply, and divide decimals and
negative numbers.
Proficient with multi-digit multiplication and
division.
Add, subtract, multiply, and divide simple fractions
6.
Positive and negative fractions and decimals
Mixed numbers
Pi
All of the above
Differentiate between rationals and irrationals
6.
Calculate (Add, subtract, multiply, and divide with
all types of rational numbers.
7.
All of the above
Use exponents and roots when working with
rational numbers.
7.