Unit3MultiplyDivideFractions

=Unit 3 Multiplication and Division with Fractions=

Home Activities are all provided from the Teacher's Guide for the 5th Grade CCSS Math Expressions Teacher's Guide.

3-1 Basic Multiplication Concepts
This is now covered in fourth grade CCSS so they should remember most of it.

__Overall Target__: I can multiply a whole number by a **unit fraction** where the product is a whole number.
 * I can multiply a **unit fraction** by a whole number where the product is a whole number.
 * Examples: draw pictures
 * I can write multiplication and division equations for comparison problems with **unit fractions**.
 * Examples: comparison bars, called tape diagrams in CCSS

__Tutorial Resources:__
 * Anchor Chart with Examples from the Classroom


 * How can I enrich my child's understanding of the math topic?**

__Review Vocabulary__:
 * //What is a// **//product//**? Answer: the answer to a multiplication problem. 4 x 3 = 12, 12 is the product.
 * //What is an **equation**?// Answer - an equation is a math sentence with an equal sign: 5 + 4 = 9, it has to have an "=" sign! Often they have a variable as the kids get older: 1/4 + 2/3 = n
 * //What is a **unit fraction**?// Answer - a fraction where the numerator (top number) is one: 1/3 or 1/7
 * //What is a **comparison problem**?// Answer - set up the fraction problem using comparison bars (they should remember this from fourth grade).

__Home Activity: Family Letter__
 * Review the Family Letter that we sent home with your child. "This letter explains how multiplication and division work fractions are developed in Math Expressions. It will give you a better understanding of the learning that goes on in math class and creates a bridge between school and home." A Spanish translation is provided. Discuss with your child what they will be learning about. Make any connections you can to what you know about the topic. Do you use this in your work? Hobbies? Home life?

3-2 Multiplication with Non-unit Fractions
(Under CCSS, this is covered in fourth grade so this will be review for 5th grade, they should remember most of it.)

__Overall Target__: I can multiply a whole number by a **non-unit fraction** where the product is a whole number.
 * I can multiply a **non-unit fraction** by a whole number where the product is a whole number.
 * Examples: number lines
 * I can write multipliciation and division equations for comparison problems with **non-unit fractions**.

__Tutorial Resources:__
 * Anchor Chart with Examples from the Classroom

__Review Vocabulary:__
 * How can I enrich my child's understanding of the math topic?**
 * //What is a **non-unit fraction**?// Answer - a fraction with a numerator (top number) more (larger) than one: 3/4 or 5/6

__Home Activity: Science Connection__
 * **Weather Trends**. Have your child record the weather trends over a one-week period. Ask them to find the fraction of days that:
 * were sunny
 * were cloudy
 * had precipitation (rain, snow, sleet, etc.)
 * Then ask them to calculate the number of days that correspond to the same fractions in a two-week period.

3-3 Multiplication with Fractional Solutions
__Overall Target:__ I can multiply a whole number by a fraction where the product is a fraction.
 * I can multiply a whole number by a unit fraction where the product will be a fraction.
 * Examples: area models
 * I can multiply a whole number by a non-unit fraction where the product will be a fraction.
 * Examples: number lines

__Tutorial Resources__:
 * Anchor Chart with Examples from the Classroom Part 1
 * Anchor Chart with Examples from the Classroom Part 2

__Online Tutorials__: Why do I have several different methods here? Sometimes one method will click with a child where another one won't. If your child is struggling, have them watch a couple of these and see if one of them will click with your child.
 * Using the area model to multiply a fraction by a whole number
 * Multiply a fraction by a whole number - rectangle method
 * Multiply a fraction by a whole number using the area model (2).
 * Multiply a fraction by a whole number using a sequence of operations.

Online Practice and Games:
 * IXL - Multiplying fractions with models


 * How can I enrich my child's understanding of the math topic?**

__Home Activity: Language Arts Connection__
Example: "Emily of New Moon" - 14 letters.
 * Words from a Fraction of Total Letters**
 * Have your child write out the title of a book they like. Ask them to use a fraction of the letter in the title to make new words. They should try it first with a unit fraction and then with a non-unit fraction.
 * unit fraction: 1/7 x 14 = 14/7 = 2 letters possible words: me, on, in, on
 * non-unit fraction: 2/7 x 14 = 28/7 = 4 letters, possible words: mile, mine, nine, none, lone

__Overall Target:__ I can multiply two fractions.

 * I can use fraction bars to model (show) multiplying fractions.
 * I can use area models to model (show) multiplying fractions.
 * I can use the rule for multiplying fractions and show how I know it works.

__Tutorial Resources:__
 * Anchor Chart with Examples from the Classroom

**How can I enrich my child's understanding of the math topic?**
__Review Vocabulary__
 * **area model for multiplication -**
 * see examples on the anchor chart
 * **fraction bar model for multiplication**
 * see the examples on the anchor chart

__Home Activity: Physical Education Connection__ Have your child walk 1/2 mile. Then have them walk 3/4 mile. Ask them how they think 1/2 of 3/4 compares to 3/4 of 1/2 miles. You can also have them do the same for other pairs of distances, such as 7/10 mile and 4/5 mile. In each pair, both distances will be the same. Children can see this by calculating each distance.
 * Compare Walking Distances**

3-5 Multiplication Strategies
__Overall Target__: I can compare and apply strategies for multiplying fractions.

__Tutorial Resources:__
 * Anchor Chart with Examples from the Classroom

Internet Games: __Review Vocabulary:__
 * Math-Play.com
 * Multiplying Fractions Millionaire - the second to the last option
 * Multiplying Fractions Game - Third to last option - requires a lot of simplication
 * How can I enrich my child's understanding of the math topic?**
 * How can I enrich my child's understanding of the math topic?**
 * **Multiply and Simplify method**
 * Set up the fraction multiplication using the rule.
 * Multiply the numerators and denominators.
 * Simplify.
 * **Simplify and Multiply method**
 * Set up the fraction multiplication using the rule.
 * Simplify by dividing by common factors for the numerator and denominator.
 * This simplifies the multiplication that the child has to do.
 * Multiply the numerators and denominators.
 * **unit fraction method**
 * This is what we did in lessons 3-1 and 3-2.
 * Multiply the whole number by the unit fraction related to the fraction in the problem.
 * Multiply the resulting product by the numerator in the initial fraction.
 * Does this sound complicated? See the examples, it's not that bad.
 * **//Factor//**: you multiply factors to get a product: 2 x 3 = 6, 2 and 3 are factors.

__Home Activity: Art Connection__
 * Draw Fractions of a Group**
 * 1) Children collect 12 or 24 objects such as buttons, marbles, or game pieces.
 * 2) They sort the objects in any way they wish and choose one of the sorted groups.
 * 3) Ask them to express the number of objects in that group as a fraction of the whole.
 * 4) Have them find a way to show their fraction in a drawing.
 * 5) Repeat for an equivalent fraction.
 * 6) Now, ask the child to find 2/3, 3/4 and 4/5 of their original fraction or the equivalent fraction.

3-6 Multiply Mixed Numbers
__Overall Target__: I can multiply with mixed numbers.
 * I can multiply mixed numbers using area models.
 * I will practice multiplying mixed numbers by converting mixed numbers to improper fractions and multiplying.


 * How can I enrich my child's understanding of the math topic?**

__Review Vocabulary__
 * **//Factor//**: you multiply factors to get a product: 2 x 3 = 6, 2 and 3 are factors.

__Home Activity: Real World Connection__
 * Adjusting Recipes**
 * 1) Ask your child to imagine that they must prepare a dish that serves 9 people.
 * 2) Students should find a recipe that serves 6 people.
 * 3) Ask them to adjust the ingredients lists in order to make enough for 9 people. This requires multiplying the quantity of each ingredient by 1 1/2.

3-7 Relate Fraction Operations
__Overall Target__: I can relate operations with fractions and whole numbers, and discuss properties of arithmetic.
 * I can draw and compare the results of different fraction operations.
 * Examples use fraction bars.
 * I can explain the Commutative, Associative and Distributive properties with fractions.
 * I can solve numerical and word problems with fractions.


 * How can I enrich my child's understanding of the math topic?**

__Review Vocabulary:__
 * //**Associative Property**//:
 * //**Commutative Property**//
 * //**Distributive Property**//

__Home Activity: Social Studies Connection__ a) the fraction of state names that begin with a vowel? b) the fraction of state names that end with a vowel? Your child can then make up other comparison problems using state names. Examples:
 * Use Fractions to Compare State Names**
 * 1) Have your child find a list of the 50 states.
 * 2) Use the list to answer the following questions:
 * 3) Which is greater?
 * What fraction of state names both begin and end with a vowel?
 * What fraction of state names have more than one word?
 * What fraction of state names begin with a vowel and have more than one word?

3-8 Solve Real World Problems
__Overall Target__: I can add, subtract, and multiply fractions to solve word problems.
 * I can compare the results of different fractions operations.
 * I can solve word problems with mixed numbers.


 * How can I enrich my child's understanding of the math topic?**

__Home Activity: Real World Connection__ Ask your child to keep track, for one week, of the amount of time they spend reading each day. Have them record the number as a fraction of an hour. Have them answer these questions:
 * Track Reading Time**
 * On which day did you read for the greatest amount of time?
 * How many hours more did you read on that day than on the day you read for the least amount of time?
 * How many hours in total did you spend reading?
 * If you only read for 3/4 of the time each day, what would the new total be?

3-9 Make Generalizations
__Overall Target__: I can predict the size of a product relative to the size of one factor based on the size of the other factor.
 * I can predict how a product will compare to one factor based on the size of the other factor.
 * I can predict the size of a solution to a word problem and then solve the problem.

__Home Connection: Real World Connection__
 * How can I enrich my child's understanding of the math topic?**
 * **Sale Price**. Tell your child that a store is having a "1/3 off" sale. Ask how they could compute the sale price of an item that has a regular price or $18. Discuss both of these methods:
 * **Two Step Method**: Find 1/3 of $18 and subtract the result from $18.
 * **One Step Method**: Recognize that if you get 1/3 off, then you pay 2/3. To find the sale price, find 2/3 of $18.
 * Have your child write and solve a problem about purchasing an item at a "1/4 off" sale.

3-10 When Dividing is also Multiplying
__Overall Target__: I can relate division by a unit fraction or whole number to multiplication.
 * I can divide a whole number by a whole number to produce a fraction.
 * I can divide a unit fraction by a whole number.
 * I can divide a whole number by a unit fraction.

Tutorial Resources:
 * Anchor Chart from the Classroom


 * How can I enrich my child's understanding of the math topic?**

__Review Vocabulary:__
 * **//Decimal Fraction//**

__Home Activity: Math-to-Math Connection__ A quarter is about 1/16 or an inch thick. Your child should measure their own height and the heights of two other people in inches. Then they can figure out how many quarters tall each person is and write appropriate division and multiplication equations as part of their solutions.
 * Measurement:**

__Overall Target__: I can write and solve division problems.

 * I can describe situations and make diagrams that represent division problems.
 * I can solve division word problems.

__Home Activity: Music Connection__
In many songs, a whole note gets 4 beats. The names of the other notes are based on what fraction they are of a whole note. Students should copy and label the notes shown above and indicate how many beats each note gets if the whole note gets 4 beats. (Hint: What is 1/8 or 4?)
 * Fractions in Music**

3-12 Distinguish Multiplication from Division
__Overall Target__: I can determine whether solving a word problem requires multiplication or division.
 * I can distinguish (tell the difference) between division and multiplication situations in word problems.
 * I can analyze equations and situations to predict whether the result will be greater or less than the starting number.


 * How can I enrich my child's understanding of the math topic?**

__Review Vocabulary:__
 * dividend
 * divisor
 * quotient

__Home Activity: Real World Connection__
 * Fractions of a Book**
 * Have your child choose their favorite book that they have at home.
 * The book must have page numbers.
 * Invite your child to find:
 * What page they would be on if they had read 1/2 of the book?
 * What page they would be on if they had read 3/4 of the book?
 * Come up with other fractions and find the page that relates to that fraction.

__Home Activity: Real World Connection__ Have your child look for sale ads or sales at stores in their community to find examples that use fractions. Encourage them to compare fractions to identify the best deal on an item.
 * How can I enrich my child's understanding of the math topic?**
 * Items on Sale**

3-14 Focus on Math Practices (Math Smarts) (The way we think about Math.)
__Overall Target__: I can use Common Core Standards and Practices in a variety of real world problem solving situations.
 * I can compute fraction products and quotients.