Topic Nine: Understanding Fractions Pacing (Duration of Unit):

Desired Results

Transfer: Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Established Goals: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and portioning 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.

3.NF.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Prerequisite Standards: 3.OA.2 Interpret a whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of share when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X ?=48, 5 =?÷ 3, 6 X 6=?

Big Ideas:

Numbers and the Number Line
The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique pot on the number line.

Estimation
Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally. Some measurements can be approximated using known referents as the unit in the measurement process.

Practices, Processes, and Proficiencies
Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in a table.

Essential Questions:

What are different interpretations of a fraction?

Students will know...

A region can be divided into equal-sized parts in different ways. Equal sized parts of a region have the same area but not necessarily the same shape.

A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.

Finding a unit-fractional part of a whole is the same as dividing the whole by the denominator of the fraction.

Some points between the whole numbers on a number line can be labeled with fractions or mixed numbers. The denominator of the fraction can be determined counting the number of equal part between two consecutive whole numbers.

Fractions can be approximated by other fractions that are close.

Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in the table.

identifying regions that have been divided into equal-sized parts in different ways. Equal-sized parts of a region have the same area but not necessarily the same shape.

associating the model, symbol, and words used to describe a fractional a whole region.

associating the model, symbol, and words used to describe a fractional part of a set.

finding a fractional part of a set.

identifying fractional parts and mixed numbers on a number line.

estimating fractional parts by using benchmark fractions.

associating the model, symbol, and words used to describe a fractional part of the length of an object.

identifying patterns to solve a problem by making a table.

Assessment Evidence

Performance Assessment:

Other Evidence:

Learning Plan

Learning Activities: 9-1 A region can be divided into equal-sized parts in different ways. Equal sized parts of a region have the same area but not necessarily the same shape.

9-2 A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.

9-3 A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.

9-4 Finding a unit-fractional part of a whole is the same as dividing the whole by the denominator of the fraction.

9-5 Some points between the whole numbers on a number line can be labeled with fractions or mixed numbers. The denominator of the fraction can be determined counting the number of equal part between two consecutive whole numbers.

9-6 Fractions can be approximated by other fractions that are close.

9-7 A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.

9-8 Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in the table.

Topic Nine: Understanding FractionsPacing (Duration of Unit):

Desired ResultsTransfer:Standards for Mathematical Practices1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.

4

. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Established Goals:3.NF.1Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.3.NF.2.aRepresent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and portioning 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.3.NF.2.bRepresent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.3.OA.3Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.Prerequisite Standards:3.OA.2Interpret a whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of share when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.3.OA.3Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.3.OA.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X ?=48, 5 =?÷ 3, 6 X 6=?Big Ideas:Numbers and the Number LineThe set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique pot on the number line.

EstimationNumbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally. Some measurements can be approximated using known referents as the unit in the measurement process.

Practices, Processes, and ProficienciesSome problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in a table.

Essential Questions:Students will know...Vocabulary:Students will be skilled at...## Assessment Evidence

Performance Assessment:Other Evidence:## Learning Plan

Learning Activities:9-1A region can be divided into equal-sized parts in different ways. Equal sized parts of a region have the same area but not necessarily the same shape.9-2A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.9-3A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.9-4Finding a unit-fractional part of a whole is the same as dividing the whole by the denominator of the fraction.9-5Some points between the whole numbers on a number line can be labeled with fractions or mixed numbers. The denominator of the fraction can be determined counting the number of equal part between two consecutive whole numbers.9-6Fractions can be approximated by other fractions that are close.9-7A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fractions tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole.9-8Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in the table.Resources:Home School Connection: