· Students should recognize, name, and focus on finding equivalent decimals of familiar fractions such as halves, fourths, fifths, eighths, and tenths.
· Students should be able to determine equivalent relationships between decimals and fractions with denominators up to 12.
· Students should have experience with fractions such as, whose decimal representation is a terminating decimal (e. g., = 0.125) and with fractions such as , whose decimal representation does not end but continues to repeat (e. g., = 0.222…). The repeating decimal can be written with ellipses (three dots) as in 0.222… or denoted with a bar above the digits that repeat as in 0.
· To help students compare the value of two decimals through thousandths, use manipulatives, such as place value mats/charts, 10-by-10 grids, decimal squares, Base-10 blocks, meter sticks, number lines, and money.
– Line up the decimal numbers at their decimal points.
– Beginning at the left, find the first place valuewhere the digits are different.
– Compare the digits in this place value to determine which number is greater (or which is less).
– Use the appropriate symbol > or < or the words greater than or less than to compare the numbers in the order in which they are presented.
– If both numbers are the same, use the symbol = or words equal to.
Two numbers can be compared by examining place value and/or using a number line.
· Decimals and fractions represent the same relationships; however, they are presented in two different formats. Decimal numbers are another way of writing fractions. Base-10 models (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, money) concretely relate fractions to decimals and vice versa.
All students should
· Understand the relationship between fractions and their decimal form and vice versa.
· Understand that fractions and decimals can be compared and ordered from least to greatest and greatest to least.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· Represent fractions (halves, fourths, fifths, eighths, tenths, and twelfths) in their equivalent decimal form and vice versa.
· Recognize and name equivalent relationships between decimals and fractions with denominators up to 12.
· Compare and order from least to greatest and greatest to least a given set of no more than five numbers written as decimals, fractions, and mixed numbers with denominators of 12 or less.