5.4.6Ma


 * Grade: 5 Unit: 4 Week 6 Content: Math CC.5.NF.4a 5.NF.4b Dates: 1/28-2/1 **


 * Theme Essential Question: **


 * Essential Questions: **
 * How can you find the product of a fraction and a whole number without using a model?
 * How do you multiply fractions?
 * How can you use an area model to show the product of two fractions?
 * How can you use a unit tile to find the area of a rectangle with fractional sides?


 * Standards: **

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
 * 5.NF.4a **

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 * 5.NF.4b **


 * Objectives: **


 * 5.NF.4a **


 * TSW model the product of a fraction and a whole number.


 * TSW multiply fractions and whole numbers.


 * TSW use a model to find the fractional part of a group.


 * TSW Use visual models to show the multiplication of two fractions (Ex: 1/2 of 1/4)


 * TSW Multiply a fraction by a whole number. (EX: 2/3 x 4 is 4 sets of 2/3 or 8 sets of 1/3)


 * 5.NF.4b **


 * TSW multiply fractions using models.
 * TSW use a model to multiply two mixed numbers and find the area of a rectangle.


 * TSW understand the meaning of multiplication of a whole number by a fraction and a fraction by a fraction.
 * TSW understand that area of a rectangle is measured in unit squares.


 * TSW understand that area is the number of square units in a figure.


 * Assessment: **
 * Product: **

Make a visual model to solve this problem: George drank 3/4 of 1/2 gallon of milk. How much of the gallon did he drink? How much of the gallon is left?
 * NF.4.a **

Use tiles to find the area of a rug that is 3-1/2 feet by 2-1/2 feet. Mr. Brown is building a sandbox that is 6-1/2 feet by 4-1/2 feet. Draw a model of the sandbox, labeling all dimensions. Find the total area of the sandbox. Explain your answer.
 * NF.4.b **


 * ** Key Questions (match Standard) **


 * For **5.NF.4a** and **5.NF.4b** – How can the application and extension of your previous understanding of multiplication help you multiply a fraction or whole number by a fraction?


 * ** 5.NF.4a **
 * How can you use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation? (a x q divided by b)


 * 5.NF.4b **
 * How can you find the area of a rectangle with fractional side lengths by using tiles to cover the fractional area?
 * How is this the same as would be found by multiplying the side lengths?


 * Observable Student Behaviors (Performance) **


 * ** 5.NF.4a **


 * Students will be able to create a story context for an equation of the form (a/b) x q.
 * Students can use area models to represent multiplication of a fraction by a whole number and a fraction by a fraction.
 * Students can represent problems with visual fraction models.
 * When multiplying a problem such as 3/5 x 6, the operations can be thought
 * of in more than one way. Examples:
 * 3 x (6 ÷ 5) or (3 x 6/5) OR (3 x 6) ÷ 5 or 18 ÷ 5 (18/5)
 * Represent problems such as: 1/3 x 5 as finding 1/3 of 5 or 1/2 x 1/2 as finding half of a half.
 * Students create a story context for 3/5 x 6. Examples:
 * Isabel had 6 feet of wrapping paper. She used 3/5 of the paper to wrap
 * some presents. How much does she have left?
 * ** 5.NF.4b **


 * Students can use concrete manipulatives (fraction tiles) to demonstrate area.
 * Students can use graph paper/dot paper to make pictorial representations of area.
 * Students can use graph paper/dot paper to show fraction products as rectangular areas, e.g., show 16/25 square units by creating a rectangle of 25 square units (the whole) and coloring in 16 square units (the part) and then determining the fractional side lengths of the resulting rectangle.


 * ** Mathematical Practices **
 * Make sense of problems and persevere in solving them.
 * Reason abstractly and quantitatively.
 * 3. Construct viable arguments and critique the reasoning of others.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Attend to precision.
 * Look for and make use of structure.
 * 8. Look for and express regularity in repeated reasoning. ||


 * Vocabulary **

Partition Factors Products Numerator Denominator Fraction Whole number Area Length Width A=LW Square units X means of Array Dimension


 * Suggested Activities ** [see Legend to highlight MCO and HYS]

Gizmos: Multiplying Fractions Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. Teacher Guide & Student Exploration Sheet Available

On Core Mathematics, TE pages 67-70, Students pages 127-134.

// Read It, Draw It, Solve It! // By Elizabeth D. Miller Grade 4-5 Lessons on Fractions and Measurement

// Investigations in Number, Data, and Space for the Common Core State Standards, Sessions // for **NF.4a** //4A.1, 4A.2, 4A.3, 4A.4, 4A.5, 4A.6, 4A.7// for **NF.4b** 4A.6, 4A.7,4A.9 and 4A.10

Odyssey Lessons –

For 5.**NF4.a** 5th grade Math MA5429 and MA54210 (Multiplying Fractions with Quiz)

For 5.**NF.4b** 5th grade Math MA5643 and MA5643 (Area of a Rectangle with Quiz)

Fraction Works – Grade 5 – Multiply and Divide Fractions, T-3.


 * Homework **


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers || ||
 * ||  ** Multicultural Concepts **

Resources

************************************************************************************************************
 * Resources **
 * Professional Texts **

For **NF.4a** and **NF.4b**

School Mathematics, Teaching Developmentally, Third Edition; John A. Van de Walle


 * Literary Texts **

This website has suggestions for literature that teaches fractional concepts. []


 * Informational Texts **


 * Art, Music, and Media **


 * Games: **

Manipulatives


 * NF.4a and NF.4b **

__ [] __

__ [] __ __ math/5 __

// Fraction Works - Templates //

Multiplying Mixed Numbers Multiply a mixed number by a mixed number; multiply a whole number by a mixed number. Apply to solve contextual problems
 * Smartboard Lessons, Promethean Lessons **
 * AEGOM Lesson G6M008 **

[]...

[]

[]

Fractions, Decimals and Percents Review [] Students will review how to find a number of a fraction, turn a fraction to a percent and a decimal, reduce fractions, and order fractions.

Finding a Fraction of a Whole Number [] Students will find parts of wholes.

[|Fractoins - Parts of a Set] [] This lesson reviews finding a part of a set by using manipulatives and the algorithm.

Everyday Math - Grade 5 - Unit 5 - Lesson 1

[] Fraction Review. Review key fraction concepts; and to provide practice with solving parts-and-whole problems and finding fractional parts of whole numbers.

Everyday Math 8.5 Fractions of Fractions [] Students solve fraction-of problems using number lines and the folded-paper manipulatives/Fill Effects

Area of Parallelograms [] Covers how to find the area of a parallelogram. Describes how a parallelogram can turn into a rectangle. Uses formula LxW and BxH. Provides a few practices problems and a high level thinking game at the end.


 * Other Activities, etc. **

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