Decimal understandings and computation build on whole number and fraction understandings and computations.
See the standards throughout the grades.
See this progression for Number and Operations in Base Ten.
NOTE: This page has three sections: Decimal Values, Decimal Addition and Subtraction, and Decimal Multiplication and Division.
N5.a. Use base-ten blocks to represent ones, tenths, hundredths, thousandths.
N5.b. Represent decimals in word and expanded forms and make connections to the fractional representations of these numbers, e.g. 1/10 = 0.1, 1/100 = 0.01, etc.
N5.c. Understand the density of the number line (there is a decimal between any two given decimals).
Connecting decimals to ideas in place value and fractions helps build a strong mathematical foundation.
Base ten extends infinitely in both directions.
Seeing similarities to whole number structures.
What's the Decimal Point? (Interactive game)
"5 Indicators of decimal understandings." Article in Teaching Children Mathematics vol. 22, issue 3, pgs. 186-195.
NCTM Focus Issue: Between the Wholes: Promoting Fraction and Decimal Understanding, Teaching Children Mathematics vol. 22, issue 3.
"Tracking decimal misconceptions: Strategic instructional choices." Article in Teaching Children Mathematics vol. 22, issue 8, pgs. 488-494.
N5.d. Add, subtract, multiply, and divide decimals to hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations; relate the strategy to a written method and explain the reasoning used.
N5.f. Compare decimals and record the comparisons using the symbols <, =, >.
N5.g. Use place value understanding to round decimals to any requested place value.
Addition and subtraction with decimals is based on the fundamental concept of adding and subtracting the numbers in like position values - an extension from whole numbers.
"Models for initial decimal ideas." Article in Teaching Children Mathematics vol. 16, issue 2, pgs. 106-117.
N5.d. Add, subtract, multiply, and divide decimals to hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations; relate the strategy to a written method and explain the reasoning used.
N5.e. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Multiplication and division with decimals shares similar structures and models with whole numbers.
"Making sense of decimal multiplication." Article in Teaching Children Mathematics vol. 16, issue 7, pgs. 430-437.