EAST ALLEN COUNTY SCHOOLS

Bundle 3

Grade 5

Math

Big Idea: Parts of a Whole Fractions

Enduring Understandings Essential Questions Fractions can be represented visually and in written form.

Fractions can represent whole numbers.

A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on what is whole.

How do fractions relate to whole numbers and decimals?

Why is it necessary to simplify a fraction to lowest terms?

How does the knowledge of greatest common factor and least common multiple help when comparing fractions?

CC/Learning Targets Core Vocabulary Links to Technology

5.1.5 5.2.2 a-f 5.2.3 a,b

5.2.4 a,b 5.7.1 5.7.2

5.7.3 5.NF.1

5.NF.3 5.NF.4a. 5.NF.5

5.NF.6 5.NF.7

-Math!!! (app)

-Fast Facts Multiplication (app) -Doodle Numbers (app) -Math Practice Lite (app)

Bundle Performance Task(s) Wanted- Party Planner (no experience necessary).

Candidate must have excellent math skills, organizational skills, and creativity.

Job Description-You are in charge of preparing snacks and beverages for a celebration at a local charity. There will be a total of 24 people coming to the

celebration. The charity has supplied the recipes, but the serving sizes vary. Your job will be to look at the recipes and then rewrite them for 24 people (use your superior math skills). There’s not much time left…only a week. You better get busy!

As an extension, you are in charge of making a grocery list for the supplies for this celebration. The charity already has purchased some ingredients for the celebration. You will be given $75.00 to purchase the ingredients not supplied. To make it easier to purchase these items, a grocery store cost sheet has been provided for you. Once again, you will need to consider how much you will need to purchase, based on the serving size of the recipe and people coming to the

celebration. Don’t spend more than necessary; this is a charity. The charity also feels that it is important to have invitations for the celebration, and because of a lack of time on their part, they are asking that as an extra bonus, you create the invitation for the benefit celebration.

See Performance Task Template at the end of the bundle.

Grade 5 Math Bundle 3

Quarter 2 Oct. – Nov.

Recommended Read-Alouds G5 - Bundle 3

Big Idea: Accuracy Title Author Relates to…

Full House : an Invitation to Fractions Dodds, Dayle Ann Fractions

Fractions, Decimals, and Percents Adler, David Fractions, decimals, percents

Pythagoras and the Ratios: a Math Adventure Ellis, Julie Ratios

Math G5 - Bundle 3

CC/Learning Targets Resource of Ideas Evidence of Learning *5.1.5 Explain different interpretations of

fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.

Parts of a whole

Parts of a set

Division of whole numbers by whole numbers

-The Number Devil: A Mathematical Adventure by Hans Magnus --Enzensberger pp. 18-20, 181-187 -Full House an Invitation to Fractions by Dayle Ann Dodds -Pythagoras and the Ratios: a Math Adventure by Julie Ellis -Pizza Fractions (app) *Now $.99 -Fraction Bars -Parts of a Whole -Naming Fractions -Visualizing Fractions -Houghton Mifflin Lesson 9.5

-Houghton Mifflin Math Corresponding Lesson Resources -Student created posters/charts -Think-Pair-Share -I Have/Who Has? -Daily Math Review

*5.2.2

Add and subtract fractions (including mixed numbers) with different denominators. a. List multiples of whole numbers up to 10. b. Identify common multiples of whole numbers up to 10. c. Find equivalent fractions through multiplication or division of numerators and denominators. d. Add and subtract fractions with different denominators. e. Add mixed numbers with different denominators (with and without

-Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp.3-28

-Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod -Too Many Cooks by Andrea Buckless -Adding Fractions -Action Fraction Race Game

-enVisionMATH Topics 9.7-9.9, 10.4-10.6

-enVisionMATH Corresponding Lesson Resources -Quiz -I Have/Who Has? -Teacher observation during practice time -Daily Math Review

Math G5 - Bundle 3

(5.NF.2)

regrouping). f. Subtract mixed numbers with different denominators (with and without regrouping).

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

*5.2.3 (5.NF.7)

Use models to show an understanding of multiplication and division of fractions. a. Represent multiplication of fractions with models. b. Represent division of fractions with models.

Apply and extend previous

-You Tube Video- Multiplying Fractions

-Houghton Mifflin Math Lessons 12.1, 12.4

-Teacher observation during math

Math G5 - Bundle 3

understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit

fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations

Math G5 - Bundle 3

to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

*5.2.4 (5.NF.7)

Multiply and divide fractions to solve problems. a. Multiply fractions to solve problems. b. Divide fractions to solve problems.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit

fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and

-Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp.3-28

-Fraction x Whole Number Game -Multiplying Fractions Jeopardy -Multiply Fractions-Battleship

- enVisionMATH Topics 11.2, 11.4, 11.9, 11.10

-enVisionMATH Corresponding Lesson Resources -Quiz -I Have/Who Has -Teacher observation during practice time -Daily Math Review

Math G5 - Bundle 3

compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

5.7.1

Problem Solving Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing

patterns. Problem Solving Strategies: -Use or Look for a Pattern -Work Backwards -Use Logical Reasoning -Make It Simpler -Write a Number Sentence

-Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp.29-69, 166-168 -The Problem Solver 4: Activities for Learning Problem-Solving Strategies

-See Problem Solving Template in Appendix

Math G5 - Bundle 3

5.7.2 Problem Solving Decide when and how to break a problem into simpler parts. Problem Solving Strategies: -Use or Look for a Pattern -Work Backwards -Use Logical Reasoning -Make It Simpler -Write a Number Sentence

-Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp.29-69, 166-168 -The Problem Solver 4: Activities for Learning Problem-Solving Strategies

-See Problem Solving Template in Appendix

5.7.3

Problem Solving Apply strategies and results from simpler problems to solve more complex problems. Problem Solving Strategies: -Use or Look for a Pattern -Work Backwards -Use Logical Reasoning -Make It Simpler -Write a Number Sentence

-Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp.29-69, 166-168 -The Problem Solver 4: Activities for Learning Problem-Solving Strategies

-See Problem Solving Template in Appendix

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

- enVisionMATH Topic 9-1-9-9, 10-1, 10-4-10-7

5.NF.3 Interpret a fraction as division of - enVisionMATH Topic 11-1

Math G5 - Bundle 3

the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.4a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. 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

- enVisionMATH Topic 11-2, 11-4, 11-6

Math G5 - Bundle 3

(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.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a

product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

- enVisionMATH Topic 11.-3, 11-7, 11-8, 11-11, 11-9, 11-10

5.NF.6 Solve real world problems -Five Easy Steps to a Balanced Math Program for Upper Elementary -See Problem Solving Template in

Math G5 - Bundle 3

involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Grades pp.29-69, 166-168 -The Problem Solver 4: Activities for Learning Problem-Solving Strategies

-Problem Solving Activities

Appendix

Correlating CC/Learning Targets Teacher Notes

5.1.7 5.2.5 5.2.7 5.NBT.7

To access enVisionMATH materials for 2006 Indiana State standards: www.pearsonsuccessnet.com

username: envisionindiana

password: 123456 Indicators from the previous bundles should be incorporated into Bundle 3 (DMRs) to ensure that students continue to build mastery of previous topics.

5th Grade Math Performance Task Bundle 3: Parts of a Whole

Party Planner Description of Task- You are in charge of preparing snacks and beverages for a celebration at a local charity. There will be a total of 24 people coming to the celebration. Your first job will be to look at the recipes and then rewrite them for 24 people (use your superior math skills).

Chex Mix Puppy Chow 9 cups Chex 1 cup chocolate chips ½ cup peanut butter ¼ cup butter ¼ teaspoon vanilla 1 ½ cup powdered sugar Put cereal in large bowl. Melt chocolate chips, peanut butter, and butter. Remove from heat and stir in vanilla. Pour over Chex cereal, put into a large plastic bag with powdered sugar and shake well to coat. Spread mixture evenly on wax paper and allow to cool. Yield: 12 servings

No Bake Peanut Butter Brownies 4 cups graham cracker crumbs 1 cup peanuts, chopped ½ cup powdered sugar ¼ cup peanut butter 2 cups semisweet chocolate chips 1 cup evaporated milk 1 teaspoon vanilla extract Combine first 4 ingredients with a pastry blender. In a small saucepan, melt the chocolate chips with milk over low heat, stirring constantly until smooth. Remover from heat; add vanilla. Remove ½ cup and set aside. Pour remaining chocolate mixture over crumb mixture and stir until well blended. Spread evenly in a greased 9-inch square baking pan. Frost with the reserved chocolate mixture. Chill for about 1 hour. Yield: 2 dozen

Fruit Salad 2 cups watermelon balls 2 cups strawberries, halved 2 cups blueberries 3 medium bananas, sliced 2 cups sliced peaches 2 cups sparkling white grape juice Combine the watermelon, strawberries, and blueberries in a glass bowl, cover and chill until ready to serve. To serve, add the sliced bananas and peaches; pour the white grape juice over the top. Serve with a slotted spoon. Yield: 6 servings

Easy Fruit Punch 3 cans frozen fruit punch 9 cans of lemon-lime soda, chilled Pour fruit punch into a large container pr punch bowl. Slowly add each can of chilled soda. Carefully stir after each addition of soda. Yield: 12 servings

Rewrite the Recipes

Chex Mix

Show Your Work

Chex Chocolate Chips Peanut Butter Butter Vanilla Powdered Sugar

No Bake Peanut Butter Brownies

Show Your Work

Graham Crackers

Peanuts Powdered

Sugar Peanut Butter

Chocolate Chips

Evaporated Milk

Vanilla Extract

Product Original Amount Number Sentence New Amount

Chex

Chocolate Chips

Peanut Butter

Butter

Vanilla

Powdered Sugar

Product Original Amount Number Sentence New Amount

Graham Crackers

Peanuts

Powdered Sugar

Peanut Butter

Chocolate Chips

Evaporated Milk

Vanilla Extract

Easy Fruit Punch

Show Your Work

Fruit Salad

Show Your Work

Graham Crackers

Peanuts Powdered

Sugar Peanut Butter

Chocolate Chips

Evaporated Milk

Product Original Amount Number Sentence New Amount

Fruit Punch

Lemon-Lime Soda

Fruit Punch Lemon-Lime Soda

Product Original Amount Number Sentence New Amount

Graham Crackers

Peanuts

Powdered Sugar

Peanut Butter

Chocolate Chips

Evaporated Milk

Fruit Salad

Watermelon Balls = _________

Strawberries = _________

Blueberries = _________

Sliced Bananas = _________

Sliced Peaches = _________

Sparkling White Grape Juice = _________

Easy Fruit Punch

Fruit Punch = _________

Lemon-Lime Soda = _________

Bundle 3 Extension:

The charity has supplied the recipes, but the serving sizes vary. The charity already has purchased some ingredients for the celebration. Check the supplied ingredients sheet because you will need to go

shopping for the remaining ingredients. You will be given $75.00 to purchase the ingredients not supplied. To make it easier to purchase these items, a grocery store cost sheet has been provided for you. Once again, you will need to consider how much you will need to purchase, based on the serving size of the

recipe and people coming to the celebration. Don’t spend more than necessary, this is a charity.

What’s in the Cupboard?

Chocolate Chips

2 cups

Peanut Butter

1 cup

Evaporated Milk

1 cup

Powdered Sugar

2 cups

Chex Cereal

12 cups

Peanuts

3 cups

Grocery Store Prices

Product Amount Cost

Watermelon 1 $4.99

Vanilla Extract 8 oz. $2.39

Graham Cracker Crumbs 1 box (2 cups) $2.79

Butter 4 sticks $1.89

Powdered Sugar 16 oz. $1.79

Lemon-Lime Soft Drink 12 pack $3.49

Strawberries 2 pkgs. (4 cups) $4.00

Blueberries 2 pkgs. (4 cups) $4.00

Bananas 1 lb. (3 bananas) $0.69

Sparkling White Grape Juice 64 oz. bottle $3.19

Chocolate Chips 12 oz. (1 ½ cups)

$2.89

Peaches 2 peach (1 cup) $1.00

My Grocery List

Grocery Item Amount Needed

Cost Per Unit

Total Cost