Last updated: 8/15/2021 ## Grade 3 - Numbers and Operations - Fractions

 Subject: Mathematics (NYS P-12 Common Core)
 Unit Title: Grade 3 - Numbers and Operations - Fractions
 Approx. Number of Weeks: 1-10 weeks

#### Unit Summary:

Develop an understanding of fractions and fraction equivalence.

Develop understanding of fractions as numbers.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Represent and interpret data. Collaboration & Communication Creativity & Innovation Critical Thinking & Problem Solving Research & Information Fluency Social & Emotional Intelligence

### 1. What will students know and be able to do?

#### Standards:

 3.NF.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.2 - Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.3 - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.MD.1 - Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 3.MD.2 - Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. 3.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. 3.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.

#### Essential Understandings:

Students will understand that…

Quantities can be described using part to whole relationships.

#### Essential Questions:

How do the parts relate to the whole?

How many ways can I represent it?

#### Students will know:

The size of a fractional part is relative to the size of the whole.

Fractions represent numbers that are equal to, less than or greater than 1.

Graphing representations organize collections of data for analysis.

#### Students will be able to:

Number and Operations—Fractions

Develop understanding of fractions as numbers.

• Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; (3.NF.1)

• Understand a fraction a/b as the quantity formed by a parts of size 1/b.

• Understand a fraction as a number on the number line; (3.NF.2)

• Represent fractions on a number line.

a.Represent a fraction 1/ b on a number line  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 and that the endpoint of the part based at 0 locates the number 1/b on the number line. (defines the unit as a point of reference)

b. Represent a fraction a/b on a number line by marking off a lengths 1/b from 0.(naming fractional parts on the partitioned number line)

Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. ( 1/3, 2/3, 3/3 )

• Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (3.NF.3)

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, 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 = 3/1; recognize that 6/1 = 6; 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.

Measurement and Data

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

• Tell and write time to the nearest minute and measure time intervals in minutes.(3.MD.1)

Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line.

•  Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (3.MD.2)

Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Represent and interpret data.

• Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. (3.MD.3)

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.

• Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. (3.MD.4)

Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Color Code Key: Gaps, Major Clusters, Supporting Clusters, Additional Clusters

### 3. What learning activities will students participate in?

#### Discipline Specific Considerations:

Vocabulary – Specialized and High Frequency

Numerator, denominator, whole number, halves, quarters (fourths), thirds, equivalent fractions, numberline,  arrays, unit fraction, compare,  , equivalent, partitioned, interval, grams, kilograms, liters, liquid volume, mass, bar graph, picture graph, scale, line plot, data, category, endpoint, justify

In graphing representations the scale must start at zero. (true)

In a bar graph the distance between the bars must be uniform. (true)

Common Core State Standards:  Standards for Mathematical Practice

Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning 