# 4.3 - Decimals

The student will

a)   read, write, represent, and identify decimals expressed through thousandths;

b)   round decimals to the nearest whole number;

c)   compare and order decimals; and

d)   given a model, write the decimal and fraction equivalents.*

*On the state assessment, items measuring this objective are assessed without the use of a calculator.

### BIG IDEAS

• When given a model, I can see that fractions, and decimals represent the same quantity in different forms

• So that I can understand that the use of decimals is important when I count money, look at price tags, read an odometer, and see the remaining time in sports

• If you work as a carpenter or a builder, you will need to use decimals when measuring or  cutting materials as well as completing home projects

### UNDERSTANDING THE STANDARD

• Decimal numbers expand the set of whole numbers and, like fractions, are a way of representing part of a whole.
• The structure of the base-ten number system is based upon a simple pattern of tens, where each place is ten times the value of the place to its right.  This is known as a ten-to-one place value relationship (e.g., in 2.35, 3 is in the tenths place since it takes ten one-tenths to make one whole).  Use base-ten proportional manipulatives, such as place value mats/charts, decimal squares, base-ten blocks, meter sticks, as well as the ten-to-one non-proportional model, money, to investigate this relationship.
• A decimal point separates the whole number places from the places that are less than one.  A number containing a decimal point is called a decimal number or simply a decimal.
• read the whole number to the left of the decimal point;
• read the decimal point as “and”;
• read the digits to the right of the decimal point just as you would read a whole number; and
• say the name of the place value of the digit in the smallest place.
• Any decimal less than 1 will include a leading zero. For example 0.125 which can be read as “zero and one hundred twenty-five thousandths” or as “one hundred twenty-five thousandths.”
• Decimals may be written in a variety of forms:
• Standard:  26.537
• Written:  twenty-six and five hundred thirty-seven thousandths
• Expanded:  20 + 6 + 0.5 + 0.03 + 0.007.
• Strategies for rounding whole numbers can be applied to rounding decimals.
• Number lines are useful tools when developing a conceptual understanding of rounding with decimals.  When given a decimal to round to the nearest whole or ones place, locate it on the number line.  Next, determine the two whole numbers it is between. Then, identify to which it is closer.
• Base-ten models concretely relate fractions to decimals (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, decimal circles, money).
• Decimals and fractions represent the same relationships; however, they are presented in two different forms. The decimal 0.25 is written as 1/4.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Read and write decimals expressed through thousandths, using base-ten manipulatives, drawings, and numerical symbols. (a)

• Represent and identify decimals expressed through thousandths, using base-ten manipulatives, pictorial representations, and numerical symbols (e.g., relate the appropriate drawing to 0.05). (a)

• Identify and communicate, both orally and in written form, the position and value of a decimal through thousandths (e.g., given 0.385, the 8 is in the hundredths place and has a value of 0.08. (a)

• Investigate the ten-to-one place value relationship for decimals through thousandths, using base-ten manipulatives (e.g., place value mats/charts, decimal squares, and base-ten blocks). (a)

• Round decimals expressed through thousandths to the nearest whole number. (b)

• Order a set of up to four decimals, expressed through thousandths, from least to greatest or greatest to least. (c)

• Compare two decimals expressed through thousandths, using symbols (>, <, =, and ≠) and/or words (greater than, less than, equal to, and not equal to). (c)

• Represent fractions for halves, fourths, fifths, and tenths as decimals through hundredths, using concrete objects. (d)

• Relate fractions to decimals, using concrete objects (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, decimal circles, money). (d)

• Write the decimal and fraction equivalent for a given model (e.g.,  1/4 = 0.25 or 0.25 = 1/4 ; 1.25 =  or 1 1/4). (d)

### KEY VOCABULARY

Updated: Oct 09, 2018