· 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. |