# 5.2 - Fractions and Decimals

The student will

a) represent and identify equivalencies among fractions and decimals, with and without models; * and

b) compare and order fractions, mixed numbers, and/or decimals, in a given set, from least to greatest and greatest to least.*

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

### BIG IDEAS

• So that I can follow (or double) a recipe when baking a birthday cake
• So that I can measure items more precisely during a scientific experiment
• So that I can share and divide things equally with my friends
• So that I can understand decimals better

### UNDERSTANDING THE STANDARD

• Students should focus on determining equivalent decimals of familiar fractions with denominators that are factors of 100 making connections to tenths and hundredths. (e.g., 2/5 = 4/10 or 0.4) and (e.g., 7/20 = 35/100 or 0.35).
• Students should have experience with fractions such as 1/8 , whose decimal representation is a terminating decimal (e. g., 1/8 = 0.125) and with fractions such as 2/3 , whose decimal representation does not end but continues to repeat (e. g., 2/3 = 0.666…). The repeating decimal can be written with an ellipsis (three dots) as in 0.666… or denoted with a bar above the digits that repeat as in 0. 6̅.
• 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-ten blocks, meter sticks, number lines, and money.
• Proper fractions, improper fractions, and mixed numbers are terms often used to describe fractions. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is equal to or greater than the denominator. An improper fraction may be expressed as a mixed number. A mixed number is written with two parts: a whole number and a proper fraction (e.g., 3 5/8 ).
• An amount less than one whole can be represented by a fraction or by an equivalent decimal.
• Base-ten models (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, money) demonstrate the relationship between fractions and decimals.

### ESSENTIALS

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

• Represent fractions with denominators that are thirds, eighths, and factors of 100 in their equivalent decimal form with concrete or pictorial models. (a)
• Represent decimals in their equivalent fraction form (thirds, eighths, and factors of 100) with concrete or pictorial models. (a)
• Identify equivalent relationships between decimals and fractions with denominators that are thirds, eighths, and factors of 100 in their equivalent decimal form without models. (a)
• Compare and order from least to greatest and greatest to least a given set of no more than four decimals, fractions (proper or improper), and/or mixed numbers with denominators of 12 or less. (b)
• Use the symbols >, <, =, and ≠ to compare decimals through thousandths, fractions (proper or improper fractions), and/or mixed numbers, having denominators of 12 or less. (b)

### KEY VOCABULARY

Updated: Nov 16, 2018