Unit 5
Overview:
In this unit, students will:
● Develop an understanding of fractions, beginning with unit fractions.
● View fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole.
● Understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one.
● Solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
● Recognize that the numerator is the top number (term) of a fraction and that it represents the number of equal-sized parts of a set or whole; recognize that the denominator is the bottom number (term) of a fraction and that it represents the total number of equal-sized parts or the total number of objects of the set
● Explain the concept that the larger the denominator, the smaller the size of the piece
● Compare common fractions with like denominators and tell why one fraction is greater than, less than, or equal to the other
● Represent halves, thirds, fourths, sixths, and eighths using various fraction models.
In this unit, students will:
● Develop an understanding of fractions, beginning with unit fractions.
● View fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole.
● Understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one.
● Solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
● Recognize that the numerator is the top number (term) of a fraction and that it represents the number of equal-sized parts of a set or whole; recognize that the denominator is the bottom number (term) of a fraction and that it represents the total number of equal-sized parts or the total number of objects of the set
● Explain the concept that the larger the denominator, the smaller the size of the piece
● Compare common fractions with like denominators and tell why one fraction is greater than, less than, or equal to the other
● Represent halves, thirds, fourths, sixths, and eighths using various fraction models.
Standards
MGSE3.NF.1 Understand a fraction 1 𝑏
as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction 𝑎 𝑏 as the quantity formed by a parts of size 1 𝑏 . For example, 3 4 means there are three 1 4 parts, so 3 4 = 1 4 + 1 4 + 1 4 .
MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1 𝑏 on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1 𝑏 . Recognize that a unit fraction 1 𝑏 is located 1 𝑏 whole unit from 0 on the number line. b. Represent a non-unit fraction 𝑎 𝑏 on a number line diagram by marking off a lengths of 1 𝑏
(unit fractions) from 0. Recognize that the resulting interval has size 𝑎 𝑏 and that its endpoint locates the non-unit fraction 𝑎 𝑏 on the number line.
MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, e.g., 1 2 = 2 4 , 4 6 = 2 3 . Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6 2 (3 wholes is equal to six halves); recognize that 3 1 = 3; locate 4 4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
MGSE3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
MGSE3.NF.1 Understand a fraction 1 𝑏
as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction 𝑎 𝑏 as the quantity formed by a parts of size 1 𝑏 . For example, 3 4 means there are three 1 4 parts, so 3 4 = 1 4 + 1 4 + 1 4 .
MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1 𝑏 on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1 𝑏 . Recognize that a unit fraction 1 𝑏 is located 1 𝑏 whole unit from 0 on the number line. b. Represent a non-unit fraction 𝑎 𝑏 on a number line diagram by marking off a lengths of 1 𝑏
(unit fractions) from 0. Recognize that the resulting interval has size 𝑎 𝑏 and that its endpoint locates the non-unit fraction 𝑎 𝑏 on the number line.
MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, e.g., 1 2 = 2 4 , 4 6 = 2 3 . Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6 2 (3 wholes is equal to six halves); recognize that 3 1 = 3; locate 4 4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
MGSE3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.