Math - 2019-20
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.
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
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.
- To read decimals,
- 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).
and fractions represent the same relationships; however, they are presented in
two different forms. The decimal 0.25 is written as 1/4.
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)