Unit 4 Organizer: - Compton Coaches · Web view2009/08/03 · Recognize reasoning and proof as fundamental aspects of mathematics. Make and investigate mathematical conjectures

Grade 3 Mathematics Frameworks

Unit 4Fractions and Decimals

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Georgia Performance Standards FrameworkThird Grade Mathematics Unit 4 1st Edition

Unit 4FRACTIONS AND DECIMALS

(6 weeks)

TABLE OF CONTENTS

Overview.......................................................................................................................................3 Key Standards & Related Standards.............................................................................................4 Enduring Understandings............................................................................................................. 6 Essential Questions.......................................................................................................................6

Concepts & Skills to Maintain......................................................................................................7

Selected Terms and Symbols........................................................................................................8

Classroom Routines......................................................................................................................9

Strategies for Teaching and Learning...........................................................................................9 Evidence of Learning..................................................................................................................10 Tasks...........................................................................................................................................11

Paper-Folding Fractions..................................................................................................12 Pattern Block Fractions...................................................................................................18 Eating Fractions..............................................................................................................23 A Bowl of Beans.............................................................................................................28 Pizza Party......................................................................................................................35 All in a Line....................................................................................................................41 Trash Can Basketball......................................................................................................46 Sweet Decimal Fraction Bars..........................................................................................51

Culminating Task The Fraction Story Game................................................................................................57

Georgia Department of EducationKathy Cox, State Superintendent of Schools

MATHEMTATICS GRADE 3 UNIT 4: FRACTIONS AND DECIMALSSeptember 19, 2023 Page 2 of 66

Copyright 2009 © All Rights Reserved


OVERVIEW

In this unit students will: Recognize that the numerator is the top number (term) of a fraction and that it represents

the number of equal-sized parts of a set or whole; recognize that the denominator is the bottom number (term) of a fraction and that it represents the total number of equal-sized parts or the total number of objects of the set

Explain the concept that the larger the denominator, the smaller the size of the piece Compare common fractions with like denominators and tell why one fraction is greater

than, less than, or equal to the other Represent halves, thirds, fourths, sixths, eighths, tenths , and twelfths using various

fraction models Recognize the first decimal place to the right of the decimal as the tenths place Add and subtract decimal fractions and common fractions with like denominators using

physical models and/or picturesAlthough the units in this instructional framework emphasize key standards and big ideas at

specific times of the year, routine topics such as counting and ordering numbers, working with calendars and clocks, counting collections of coins, and patterning should be addressed on an ongoing basis through the use of a daily math meeting board, centers, and games. The first unit should establish these routines, allowing students to gradually understand the concept of number and to develop computational proficiency.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.





STANDARDS ADDRESSED IN THIS UNIT

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.

KEY STANDARDS

M3N1. Students will further develop their understanding of whole numbers and decimals and ways of representing them.

a. Identify place values from tenths through ten thousands.b. Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10

of a single digit whole number) and ways to represent them including word name, standard form, and expanded form.

M3N5. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations.

a. Identify fractions that are decimal fractions and/or common fractions.b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3).c. Understand the fraction a/b represents a equal sized parts of a whole that is divided into b

equal sized parts.d. Know and use decimal fractions and common fractions to represent the size of parts

created by equal divisions of a whole.e. Understand the concept of addition and subtraction of decimal fractions and common

fractions with like denominators.f. Model addition and subtraction of decimal fractions and common fractions with like

denominators.g. Use mental math and estimation strategies to add and subtract decimal fractions and

common fractions with like denominators.h. Solve problems involving decimal fractions and common fractions with like

denominators.

RELATED STANDARDS

M3P1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts.c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving.

M3P2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.





M3P3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and

others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

M3P4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a

coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.

M3P5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical

phenomena.





ENDURING UNDERSTANDINGS

Fractional parts are equal shares of a whole or a whole set. The more equal sized pieces that form a whole, the smaller the pieces of the whole

become. When the numerator and denominator are the same number, the fraction equals one

whole. When the wholes are the same size, the smaller the denominator, the larger the pieces. The fraction name (half, third, etc) indicates the number of equal parts in the whole. A decimal point can be used in a number to name a part smaller than one whole. If a whole is divided into ten equal parts, the parts can be named with tenths.

ESSENTIAL QUESTIONS

How can we be sure fractional parts are equal in size? What does each term in a fraction represent? How does the number of equal pieces affect the name of a fraction? What do I know about a fraction that has the same numerator and denominator? What are the important features of a unit fraction? Why is the size of the whole important? How can I write a fraction to represent a part of a group? How can I represent a fraction of a discrete model (a set)? How are multiplication, division, and fractions related? How can I be sure fractional parts are equal in size? What do the numbers (terms) in a fraction represent? How does the number of equal pieces affect the fraction name? How can I write a fraction to represent a part of a group? How are multiplication, division, and fractions related? Why does the denominator remain the same when I add fractions with like denominators? How do we add fractions with like denominators? Why is the number 10 important in our number system? How are tenths related to the whole? How are decimals and fractions related? Why is the number 10 important in our number system? How can I write a fraction to represent a part of a group? When we compare two fractions, how do we know which has a greater value? How can you use decimal fractions to solve addition and subtraction problems? What happens to the denominator when I add fractions with like denominators? How are decimal fractions and common fractions used in problem-solving situations?





CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

Number sense and place value from tenths through ten thousands (comparing, ordering, naming/renaming)

Counting collections of coins and bill, making fair trades for coins and bills Fluency with basic facts: addition, subtraction; developing fluency with multiplication





SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them.

The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

The websites below are interactive and include a math glossary suitable for elementary children. It has activities to help students more fully understand and retain new vocabulary. (i.e. The definition for dice actually generates rolls of the dice and gives students an opportunity to add them.) Note – At the elementary level, different sources use different definitions. Please preview any website for alignment to the definitions given in the frameworks.

http://www.teachers.ash.org.au/jeather/maths/dictionary.htmlhttp://intermath.coe.uga.edu/dictnary/

Common fraction: A number used to name a part of a group or a whole containing a fraction bar, a numerator, and a denominator.

Decimal fraction: A fraction whose denominator is a power of ten (i.e. 1/10, 5/10, 10/10).

Denominator: The number (term) below the fraction bar that represents the number of equal fractional parts into which a whole has been divided.

Equivalent sets: Sets containing an equal number of objects.

Increment: the amount or degree by which something changes.

Numerator: The number (term) above the fraction bar in a common fraction representing the number of equal parts of a whole or group under consideration.

Term: The number in the numerator and denominator of a fraction.

Unit Fraction: Any common fraction with a numerator of one.

Whole number: Zero or any counting number.




http://intermath.coe.uga.edu/dictnary/

http://www.teachers.ash.org.au/jeather/maths/dictionary.html


CLASSROOM ROUTINES

The importance of continuing the established classroom routines cannot be overstated. Daily routines must include such obvious activities such as taking attendance and lunch count, creating and discussing daily graphs, and calendar activities at a math meeting board. They should also include less obvious routines, such as how to select materials, how to use materials in a productive manner, how to put materials away, and how to access classroom technology such as computers and calculators. An additional routine is to allow adequate time for children to explore new materials before attempting any directed activity with these materials. The regular use of routines is important to the development of students’ number sense, flexibility, and fluency, which will support students’ performances on the tasks in this unit and throughout the school year.

STRATEGIES FOR TEACHING AND LEARNING

Students should be actively engaged and developing their own understanding. Mathematics should be represented in as many ways as possible by using graphs, tables,

pictures, symbols, and words. Students should be asked to explain their thinking and defend their opinions through

conversation, demonstration, and by showing their work. Mathematics should be represented in as many ways as possible by using graphs, tables,

pictures, symbols, and words. Appropriate manipulatives and technology should be used to enhance student learning. Students should be given opportunities to revise their work based on teacher feedback,

peer feedback, and metacognition which includes self-assessment and reflection. Students need to write in mathematics class to explain their thinking, to share how they

perceive topics, and to justify their work to others.





EVIDENCE OF LEARNING

By the conclusion of this unit, students should be able to demonstrate the following competencies:

Identify and give multiple representations for the fractional parts of a whole (area model) or of a set, using halves, thirds, fourths, sixths, eighths, tenths and twelfths.

Recognize and represent that the denominator determines the number of equally sized pieces that make up a whole.

Recognize and represent that the numerator determines how many pieces of the whole are being referred to in the fraction.

Represent and compare fractions with denominators of 2, 3, 4, 6, 10, or 12 using concrete and pictorial models.

Model, represent, and solve addition or subtraction problems using decimal fractions or common fractions with like denominators.

Solve problems involving fractions.





TASKS

The following tasks represent the level of depth, rigor, and complexity expected of all third grade students. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. It is important that all elements of a task be addressed throughout the learning process so that students understand what is expected of them. While some tasks are identified as a performance task, they also may be used for teaching and learning (learning task).

Task Name Task TypeGrouping Strategy Content Addressed

Paper-Folding Fractions Learning TaskIndividual/Partner Task Naming fractional pieces, area model

Pattern Block Fractions Learning TaskPartner/Small Group Task Unit fractions, Identifying the whole

Eating Fractions Learning TaskIndividual/Partner Task Naming fractions of a set

A Bowl of Beans Performance TaskIndividual/Partner Task Naming fractional pieces, discrete model

Pizza Party Performance TaskIndividual/Partner Task

Adding, subtracting fractions with like denominators

All in a Line Learning TaskPartner/Small Group Task Create number line, using tenths

Trash Can Math Learning TaskPartner/Small Group Task

Tenths, representing tenths as a decimal fraction and as a decimal

Sweet Decimal Fraction Bars Performance TaskIndividual/Partner Task Sharing equal parts, tenths

Culminating ActivityThe Fraction Story Game

Performance TaskPartner/Small Group Task Create fraction game using story problems





LEARNING TASK: Paper-Folding Fractions

STANDARDS ADDRESSED


a. Identify fractions that are decimal fractions and/or common fractionsb. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e.

0.3)c. Understand the fraction a/b represents a fraction that is a equal sized parts of a

whole that is divided into b equal sized parts.d. Know and use decimal fractions and common fractions to represent the size of parts

created by equal divisions of a whole. e. Recognize and describe a dime as having the value of one tenth of a dollar







phenomena.





ESSENTIAL QUESTIONS

How can we be sure fractional parts are equal in size?

What does each term in a fraction represent?

How does the number of equal pieces affect the name of a fraction?

What do I know about a fraction that has the same numerator and denominator?

MATERIALS

“Paper-Folding Fractions” student recording sheet, copied on light-colored paper

“Paper-Folding Fractions, Paper Strips” student sheet, copied on white

paper or a set of 11 strips (7 inch by inch)

of paper Crayons Dark, thin-point markers Glue stick or tape

GROUPING

Individual/Partner Task

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task students explore fractions by folding strips of paper. They then describe the fractions they created and write its name in fractional form.

Background KnowledgeBefore the activity, be sure the children all understand the concept of equal parts. Use

pieces of different shaped paper (piece of construction paper, coffee filter, 8 ½ inch square cut from a piece of copy paper, 1/2 sheet of copy paper cut vertically, etc.) to demonstrate folding into equal-sized pieces. For some of the students to understand “equal-sized” you may have to cut and match the pieces, demonstrating that they are the same size.





Task DirectionsStudents will follow the directions below from the “Paper-Folding Fractions” student

recording sheet. You will be making fraction pieces using strips of paper. You will need 11 strips of paper. Fold your strips as follows:

2 strips – fold in halves 2 strips – fold in thirds 2 strips – fold in fourths 2 strips – fold in sixths 2 strips – fold in eighths Leave one strip unfolded

Once you have folded your strips, follow the directions below:1. Choose four strips that represent different fractions.2. Mark over the fold lines with a dark marker on each strip.3. Shade in part of the fractional pieces on the strip (For example, shade three

out of four parts).4. Glue each strip on the back of this paper.5. For each strip of paper glued

a. Write a sentence that tells the number of shaded parts and the total number of parts (i.e. I have four pieces and three are shaded).

b. Write the fraction name for the shaded part and the un-shaded part of each strip (i.e. ¾ shaded, ¼ un-shaded).

6. Keep the remaining fraction strips for additional tasks.

CommentsThis lesson is an introduction to fractional pieces, writing fractions, and representing

fractions with folded strips of paper. Copying the student sheet onto a piece of light-colored paper will make it easier to

see the fraction strips when they are glued on the back of the student recording sheet. Be sure students are folding their paper into equal-sized pieces to represent each

fractional piece. Typically, students have some difficulty folding the strips into thirds. Have students help

each other with this. One way to assist with folding thirds is to “roll” the paper so that there are thirds represented, and then crease the paper.

This is an opportunity for students to make sense of the meaning of denominator. They should recognize that as the number of equal parts increases, the denominator increases. Also, when the whole is the same, as the number of equal parts increases, the size of each piece decreases.

This is an opportunity for students to make sense of numerator. The numerator identifies the number of pieces being considered or counted.

Students should also recognize that when the numerator and denominator are the same, one whole is represented.

In addition to the activity above, students can make a fraction page by gluing one of each of the six different strips in order. Students may place the largest fractional pieces at the top and the smaller fractional pieces below. (i.e., 1 whole strip, a strip folded into halves, a strip folded into





thirds, a strip folded into fourths, etc). If they line them up one above the other on the page, they can create a visual representation of how the sizes of different fractional pieces are related.

Questions/Prompts for Formative Student Assessment Are you unfolding your strip of paper to check your work? Is your strip folded into equal parts? How do you know? How many parts did you create? How many are shaded? How do you write that as a

fraction?

Questions for Teacher Reflection Do students recognize that the parts of the fraction (fractional pieces) need to be the same

size? Do students recognize that the numerator for the shaded fraction added to the numerator

for the unshaded fraction equals the total number of fractional pieces in one whole? Do students recognize that folding halves in half makes fourths? Fourths folded in half

makes eighths? Thirds folded in half make sixths?

DIFFERENTIATION

Extension Students can write comparative comments about their fraction strips. (More is shaded

on of a strip than on of a strip. There are more pieces on a strip cut into thirds than

on a strip cut into halves.) Students shade all possible combinations for a fraction (i.e. fourths could have

shaded). Once all combinations are found the strips can be glued and

labeled as above. Students can draw and label additional fractions using sets of objects, e.g. colored

circles. Have students create one whole using a combination of fractional pieces.

Intervention Provide students with paper strips with small marks or dotted lines to indicate fold

lines. Allow students to copy from a sentence frame for the required sentence (e.g., I

have _____ pieces and _____ are shaded. _____ of the strip is shaded; _____ of the strip is unshaded.) Alternatively, provide a photocopy of a student recording sheet that includes the sentence frames.

TECHNOLOGY CONNECTION

http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html?from=category_g_2_t_1.html Allows students to practice naming fractional parts of a whole.




http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html?from=category_g_2_t_1.html


Name _______________________________________ Date_____________________________

Paper-Folding Fractions

You will be making fraction pieces using strips of paper. You will need 11 strips of paper. Fold your strips as follows:

2 strips – fold in halves 2 strips – fold in thirds 2 strips – fold in fourths 2 strips – fold in sixths 2 strips – fold in eighths Leave one strip unfolded

Once you have folded your strips, follow the directions below:1. Choose four strips that represent different fractions.2. Mark over the fold lines with a dark marker on each strip.3. Shade in part of the fractional pieces on the strip (For example, shade three out of

four parts).4. Glue each strip on the back of this paper.5. For each strip of paper glued,

a. Write a sentence that tells the number of shaded parts and the total number of parts (i.e. I have four pieces and three are shaded).

b. Write the fraction name for the shaded part and the un-shaded part of each strip (i.e. ¾ shaded, ¼ un-shaded).

6. Keep the remaining fraction strips for additional tasks.





Paper-Folding FractionsPaper Strips

Cut apart the strips below. Use them for the Paper-Folding Fractions task..





LEARNING TASK: Pattern Block Fractions

STANDARDS ADDRESSED


a. Identify fractions that are decimal fractions and/or common fractionsc. Understand the fraction a/b represents a fraction that is a equal sized parts of a

whole that is divided into b equal sized parts.d. Know and use decimal fractions and common fractions to represent the size of parts

created by equal divisions of a whole.








phenomena.





ESSENTIAL QUESTIONS

What are the important features of a unit fraction? Why is the size of the whole important?

MATERIALS

“Pattern Block Fractions” student recording sheet Pattern Blocks White Paper (copy paper or white construction

paper) Red, blue, yellow, and green markers or crayons

GROUPING

Partner/Small Group Task

TASK DESCRIPTION, DEVELOPMENT, AND DISCUSSION

Students will investigate pattern blocks to explore the significance of identifying the whole.

Background Knowledge Before beginning the lesson, students should be aware that a unit fraction has a numerator of

one. This lesson is important because it gives students an opportunity to explore how the unit

fraction relationship changes when the whole is changed. They will need to recognize that a

green triangle can be or depending on whether the whole is the red trapezoid or yellow

hexagon, respectively. This work also demonstrates, in a different way, the need for fractional pieces to be equal in size.

As an example, students may discover that two red trapezoids make one yellow hexagon. That means a red trapezoid is ½ of a yellow hexagon. Students should be persistent about seeking unit fractions. The following are the possible unit fractions that can be found with pattern blocks:

Green Triangle = Yellow Hexagon

Green Triangle = Red Trapezoid

Green Triangle = Blue Rhombus

Blue Rhombus = Yellow Hexagon

Red Trapezoid = Yellow Hexagon





Green Triangle = Double Yellow Hexagon

Blue Rhombus = Double Yellow Hexagon

Red Trapezoid = Double Yellow Hexagon

Yellow Hexagon = Double Yellow Hexagon

CommentsStudents may be given several options for recording their work.

Trace the shapes and color them in with the appropriate color. Glue die-cut pattern block pieces, if available. Manipulate pattern blocks online and easily print, and then label their work from the

following website. http://gingerbooth.com/flash/patblocks/patblocks.phpStudent responses should show the nine different unit fraction relationships listed above.

Students may need to be given an example using the double yellow hexagon as the whole. The relationships students record should be correct and labeled in words including the unit fraction, also written correctly.

Task DirectionsStudents will follow the directions below from the “Pattern Block Fractions” student

recording sheet.The creators of Pattern Blocks would like to advertise them as tools to help students

understand fractions. But to do that, they need to know how many of the Pattern Block shapes can be made using other Pattern Blocks. For example, they know that two red

trapezoids make one yellow hexagon. Each red trapezoid is of a yellow hexagon. Are

there other similar relationships? Your task is to find as many relationships between Pattern Blocks as you can. For each relationship you find, describe the relationship of the blocks in a sentence; see the example below. Record your findings in an organized way. Be prepared to share your findings with your class.

Questions/Prompts for Formative Student Assessment What represents one whole? How many ____ (i.e. triangles, trapezoids, etc.) do you need to cover one whole ___? What would one of those fractional pieces be called? What is the unit fraction for that whole? How do you know?

Questions for Teacher Reflection Do students recognize that the sections (fractional pieces) need to be the same size?




Each red trapezoid is of a yellow hexagon.

http://gingerbooth.com/flash/patblocks/patblocks.php


Are students able to find the relationship of the fractions without needing to completely cover the whole?

Are students able to move flexibly between different representations of one whole?

DIFFERENTIATION

Extension Have students create a “whole” using a combination of two or three pieces. Then

have students find unit fractions for their whole. Have students find and represent fractions other than unit fractions (i.e., a blue

rhombus is of red trapezoid).

Have students name one pattern block in as many ways as possible (i.e., a blue

rhombus can be of a yellow hexagon, of a red trapezoid, etc.).

Students may try an online pattern block activity that asks about the relationships between pattern blocks at http://math.rice.edu/~lanius/Patterns/

Intervention Students who experience difficulty finding unit fractions may benefit from stacking

the pieces and completely covering one piece with several congruent pieces (pieces that are the same shape and size).

Provide students with pattern block shapes with dotted lines to indicate how the whole could be divided into equal parts. Students would need to match the blocks and identify the unit fraction

Allow students to copy from a sentence frame for the required sentences (e.g., Green Triangle = _______ Yellow Hexagon or _______________= 1/6 Yellow Hexagon). Alternatively, provide a photocopy of a student recording sheet that includes the sentence frames.

Allow students to use die cut pattern blocks to write their sentences (e.g., [Cut out of a Green Triangle] = 1/6 [Cut out of a Yellow Hexagon]).


Technology links discussed above.http://gingerbooth.com/flash/patblocks/patblocks.php.)http://math.rice.edu/~lanius/Patterns/




http://math.rice.edu/~lanius/Patterns/

http://gingerbooth.com/flash/patblocks/patblocks.php

http://math.rice.edu/~lanius/Patterns/


Name _______________________________________ Date_____________________________

Pattern Block Fractions

The creators of Pattern Blocks would like to advertise them as tools to help students understand fractions. But to do that, they need to know how many of the Pattern Block shapes can be made using other Pattern Blocks. For example, they know that two red trapezoids make one yellow hexagon. Each red trapezoid is

of a yellow hexagon. Are there other similar relationships? Your task is to find as many

relationships between Pattern Blocks as you can. For each relationship you find, describe the relationship of the blocks in a sentence; see the example below. Record your findings in an organized way. Be prepared to share your findings with your class.




Each red trapezoid is of a yellow hexagon.


LEARNING TASK: Eating Fractions

STANDARDS ADDRESSED



whole that is divided into b equal sized parts. d. Know and use decimal fractions and common fractions to represent the size of parts

created by equal divisions of a whole. h. Solve problems involving decimal fractions and common fractions with like

denominators.








phenomena.





ESSENTIAL QUESTIONS

How can I write a fraction to represent a part of a group?

How can I represent a fraction of a discrete model (a set)?

How are multiplication, division, and fractions related?

MATERIALS

“Eating Fractions” student recording sheet The Doorbell Rang, by Pat Hutchins or similar

book about sharing a set of items Twenty-four round counters per student Colored pencils or crayons

GROUPING



Students are asked to share a set of cookies fairly, representing a fraction of a set.

Background Knowledge This task gives students an opportunity to explore fractions of a set. Also, students are

able to explore how relationships change when the number of groups changes. Student work should include correct fractional statements such as:

1. There are 3 children and twelve cookies. Each child will get 4 cookies because 3 x 4 = 12 or 12 ÷ 3 = 4. There are 3 children, so

each child will get of the cookies. One third of 12 is 4.

2. There are 6 children and twelve cookies. Each child will get 2 cookies because 6 x 2 = 12 or 12 ÷ 6 = 2. There are 6 children, so

each child will get of the cookies. One sixth of 12 is 2.

CommentsThis task may be introduced by reading The Doorbell Rang by Pat Hutchins or a similar book

about sharing a group of items. After reading the story, discuss the events and how the number of cookies per person changed as more people arrived.

As students are working, observe the strategies they use to solve the problems. Then choose students who solved the problems in different ways to share their work with the class. This provides a variety of strategies to initiate a class discussion, considering and comparing the different strategies used by the students.





While all students may not use them, it is important to have manipulatives available to students so that they can actually move and group the circles and then count the number of cookies for each child. Students can then record their work with the circle manipulatives in a picture on their student recording sheet. Some students may need assistance in making the transition from using manipulatives to solve a problem to using a picture to organize their thinking and solve a problem. While manipulatives should always be available, it is important that students can represent their work using pictures and eventually use pictures to organize their thinking. A later stage is when students are able to organize and represent their thinking abstractly using numbers.

Task DirectionsStudents will follow the directions below from the “Eating Fractions” student recording

sheet.1. Imagine you and your two siblings are going to share a plate of 12

cookies. a. How many cookies will each child get if you share the

cookies equally? b. What fraction of the cookies will each child get?

Show how you know your answers are correct using words, pictures, and numbers.

2. Just as you’re getting ready to eat, your three cousins come to visit. Your mom says you have to share the 12 cookies.

a. How many cookies will each child get if you share the cookies equally? b. What fraction of the cookies will each child get?”


Questions/Prompts for Formative Student Assessment How many children are there at first? How many after the cousins arrive? If the whole is all of the cookies, what fraction of the cookies would you get before

your cousins arrived? After they arrived? How do you know how many cookies each child will get? What happens to the number of cookies each child gets when the cousins arrive?

Questions for Teacher Reflection Are students able to model the redistribution of the cookies between more children

accurately using manipulatives, pictures, or numbers? Are students able to describe what happens to the number of cookies each child

receives as the number of children increases? Are students able to recognize the relationship between the unit fraction and

multiplication/division? (i.e., If there are 6 children, the students will 6 x 2 = 12 or

12 ÷ 6 = 2 because they are trying to find of the cookies.)





DIFFERENTIATION

Extension Have students explain how the number of cookies per person would change if the

number of cookies was increased or decreased. (What if mom baked two batches of cookies?)

Have students work with a number of cookies that is not a multiple of the number of children. (What if 15 or 22 cookies were made?)

Ask students to create a “Doorbell Rang” story of their own, and then solve their problem. These problems can then be shared with a partner or used as an independent activity in a center.

Intervention Before asking students to solve the problem, act out the story using counters and

demonstrating how student solutions would look on the board, giving students some experience before working on their own.

Provide circular pieces of paper that can be arranged and glued on the paper to represent the situation.

Students who are having difficulty may need to be reminded to draw one plate for each person who will be sharing the cookies (i.e., 6 children would need 6 plates) then share the counters equally on each plate.

Use sentence frames, i.e. When 24 cookies are shared with ___ children, each child will get ____ cookies.


http://www.mattnelson.com/dee/fractions/Fractions_Lesson_Plan_2.pdf - More activities about The Doorbell Rang. (Note – use toothpicks instead of the matchsticks referred to in this lesson.)




http://www.mattnelson.com/dee/fractions/Fractions_Lesson_Plan_2.pdf


Name ________________________________________ Date ___________________________

Eating Fractions

1. Imagine you and your two siblings are going to share a plate of 12 cookies.

a. How many cookies will each child get if you share the cookies equally?

b. What fraction of the cookies will each child get?Show how you know your answers are correct using words, pictures, and numbers.

2. Just as you’re getting ready to eat, your three cousins come to visit. Your mom says you have to share the 12 cookies.

a. How many cookies will each child get if you share the cookies equally? b. What fraction of the cookies will each child get?”






PERFORMANCE TASK: A Bowl of BeansAdapted from Riddle Math: Using Student-Written Riddles to Build Mathematical Power (2001) by Carl M. Sherrill

STANDARDS ADDRESSED



whole that is divided into b equal sized parts. e. Know and use decimal fractions and common fractions to represent the size of parts









phenomena.





ESSENTIAL QUESTIONS

How can I be sure fractional parts are equal in size? What do the numbers (terms) in a fraction represent? How does the number of equal pieces affect the fraction name? How can I write a fraction to represent a part of a group? How can I represent a fraction of a discrete model (a set)? How are multiplication, division, and fractions related?

MATERIALS

Clean-Sweep Campers (2000) by Lucille Recht Penner, or similar book about fractions of a set

Each student will need the following materials: “A Bowl of Beans” student recording sheet Handful of mixed beans (red kidney beans,

pinto beans, black beans, black-eyed peas, etc.) Small paper plates Colored pencils or crayons

GROUPING

Individual Task


Students write and solve riddles regarding fractions of a set.

CommentsTo introduce this task read Clean-Sweep Campers (2000) by Lucille Recht Penner, illustrated

by Paige Billin-Frye (A Math Matters book) or a similar book that discusses fractions of a set. Discuss the different solutions the girls devised for cleaning groups and/or discuss possible ways students could be grouped for Sports Day (see page 32).

Other related books that could be used with this task are Jump, Kangaroo, Jump!: Fractions (1999) by Stuart J Murphy, illustrated by Kevin O’Malley and The Wishing Club: A story about fractions (2007) by Donna Jo Naoli, illustrated by Anna Currey.

It is very important that beans are available for students to use. Students can use any type of bean initially, using the total number of beans given in the riddle. Once they find the fraction of the whole, they can trade the correct number of beans for the correct kind of bean.

After reviewing student-created riddles for accuracy, allow students write their riddle on an index card with the solution drawn and explained on the back. Have students share their riddles with others in the class or leave them as an independent activity that is self-checking.





Background KnowledgeBefore assigning the task, students should have had several experiences with finding a

fraction of a set. Also, students should have some degree of fluency with multiplication facts with a product of 24 or less.

Student solutions to the riddles should include a picture of the beans and an explanation using words and numbers. Some possible solutions are shown below.

Riddle #1 I have 8 beans.

of my beans are red.

The rest are pinto beans.Show my set of beans.

Riddle #2


I have 9 beans.

of my beans are black.

Show my set of beans




“I divided 8 beans onto 4 plates because I needed to find of the beans. There were 2 beans on each plate. I made the other six beans red beans. The answer to Riddle #1 is a set of 8 beans, 2 red beans and 6 pinto beans.”

“I divided 9 beans into 3 groups because I needed to find of the beans. There were 3 beans in each group. I know that 3 beans are of

the total beans, so of the total beans must be 2 x 3 or 6 beans. So I made six beans black beans. The answer to Riddle #2 is a set of 9

“I divided 9 beans onto three plates because I needed to find of the beans. There were 3 beans on each plate. I know

that so the rest of the beans must be of the total beans. So I made rest of the beans black beans. The answer to Riddle #2 is a set of 9 beans, 3 red beans and 6 black


Riddle #3

of my beans are black-eyed peas.

of my beans are pinto beans.

The rest are red. I have 12 beans.

Show my set of beans.

Task DirectionsStudents will follow the directions below from the “A Bowl of Beans” student recording

sheet.You will need a bowl of different kinds of dried beans to solve the riddles below. Draw a picture of your set of beans for each riddle. Explain how you solved each riddle using words and numbers.




Riddle #2


I have 9 beans.






“I shared 12 beans in 2 groups because I needed to find of the beans. There were 6 beans in each group. I know that 6 beans are of the total beans, so 6 beans must be black-eyed peas.

Then I shared 12 beans in 4 groups because I need to find of the total beans. There were 3 beans in each group. I know that 3 beans are of the beans, so 3 beans must be pinto beans. The rest of the beans are red beans. If 6 are black-eyed peas and 3 are pinto beans, 6 + 3 = 9 and 12 – 9 = 3, so there are 3 beans left and those are red. The answer to riddle #3 is a set of






Riddle #3





Using beans create your own bean riddle below. Show the answer to your riddle on the back of this paper.

Questions/Prompts for Formative Student Assessment What information in the riddle did you need first? Is there any missing information in the riddle? If you have ___ (i.e., 9) beans in ___ (i.e., 3) equal groups, how many beans are in

each group? How many groups do you need? How do you know?

If we know of the beans are 3 beans, how many beans would be of the beans?

How do you know? How did you know how many ___ (i.e., red) beans to use? How would this set of beans look if there were 12 beans instead of 9 total beans?

Questions for Teacher Reflection Are students able to explain how they found the correct number of beans? Are students fluent in finding the number of beans for a unit fraction? Are students fluent in finding the number of beans for the fraction of a set? Are students able to correctly solve bean puzzles? Are students able to correctly create bean puzzles?

DIFFERENTIATION

Extension Ask students to create riddles with at least three types of beans. Have students explore equivalent fractions represented in a set (i.e., in a set of 9

beans if 1/3 of the set is red, then 3/9 of the beans are red).





InterventionAn alternative activity could be used as follows:

Riddle #1

I have 6 beans. One-half of the beans are black beans. How many beans are black

beans?Riddle #2

I have 8 beans. One-third of the beans are pinto beans. How many beans are pinto

beans?

Riddle #3

I have 12 beans. One-fourth of the beans are red beans. How many beans are red

beans?


http://www.visualfractions.com/Identify_sets.html This website could be used as an intervention. Students determine the fraction of a set.




http://www.visualfractions.com/Identify_sets.html


Name ________________________________________ Date ___________________________

A Bowl of Beans

You will need a bowl of different kinds of dried beans to solve the riddles below. Draw a picture of your set of beans for each riddle. Explain how you solved each riddle using words and numbers.




Riddle #2


I have 9 beans.



Riddle #3





Using beans create your own bean riddle below. Show the answer to your riddle on the back of this paper.





PERFORMANCE TASK: Pizza Party

STANDARDS ADDRESSED


c. Understand the fraction a/b represents a equal sized parts of a whole that is divided into b equal sized parts.

d. Know and use decimal fractions and common fractions to represent the size of parts created by equal divisions of a whole.

e. Understand the concept of addition and subtraction of decimal fractions and common fractions with like denominators.

f. Model addition and subtraction of decimal fractions and common fractions with like denominators.

g. Use mental math and estimation strategies to add and subtract decimal fractions and common fractions with like denominators.

h. Solve problems involving decimal fractions and common fractions with like denominators.







phenomena.





ESSENTIAL QUESTION

What happens to the denominator when I add fractions with like denominators?

Why does the denominator remain the same when I add fractions with like denominators?

How do we add fractions with like denominators?

MATERIALS

“Pizza Party” student recording sheet “Pizza Party, Pizza Dough” student

sheet (each sheet has enough circles for two students)

Colored pencils or crayons Glue stick

GROUPING

Individual Task


Using fraction models divided into eighths (pizzas), students create addition and subtraction story problems.

CommentsOne way to introduce the task is by describing a family tradition of having pizza and a movie

every Friday evening. Explain that the family makes two pizzas for dinner and rents a movie for the family to watch. There is always one cheese pizza and one pepperoni pizza. Each pizza is cut into eight equal slices.

Discuss with the students some possible addition problems that could be done with the pieces of pizza. For example, if the mom ate two slices of cheese pizza and one slice of pepperoni

pizza, how much pizza did she eat? Discuss the whole is cut into 8 equal pieces, so cheese +

pepperoni = of a pizza. Have a student record the number sentence on the board, reminding

students about the correct fraction notation. As a subtraction problem, one example would be discussing the amount of cheese pizza left

after the mom took two pieces. 8/8 – 2/8 = 6/8. Ask students how they might illustrate subtraction with the pizza slices. (Students may suggest crossing out the pieces removed or circling the pieces that are being subtracted.)





Sometimes students find it difficult to understand that the whole can be any shape. Therefore, it may be helpful to provide square pizzas for students to work with in addition to the circle-shaped pizzas used in this task.

Time does not permit all students to share their work with the class. However, students may be afforded the opportunity to share their work in a small group and then one student from each group may share with the whole group. Or students can share their work with a partner and two or three students can be selected to share their work with the class. Teachers need to be thoughtful about who will share during the closing of a lesson. The student(s) whose work is shared needs to add to the class discussion or take the class discussion in a specific direction. A teacher needs to think about what type of conversation will help clarify possible student misconceptions and solidify student understanding of the concepts imbedded in the task.

Background Knowledge The students should have had multiple opportunities with paper-folding fractions. To create

eighths, students can fold the pizza in half, then in fourths, and finally into eighths. Each student’s story problems may be unique. To assess student work, look for an illustration

made with the pizza slices that matches the events in the story, an accurate number sentence for the story, and clear explanations. Student explanations should provide evidence that they understood why the denominator is 8.

Task DirectionsStudents will follow the directions below from the “Pizza Party” student recording sheet.

You will be writing two story problems, modeling with problem using pizzas that you create. Fold this paper in half to create two sections on the back to record your stories.

1. Create two pizzas.a. Cut out two circles of pizza dough and color them to look

like your two favorite types of pizza.b. Fold the pizzas into eighths.

2. Fold this paper in half to create two sections on the back to record your pizza stories.

3. Write an addition story problem on the back of this paper. a. Cut out the correct number of pizza slices for your story.b. Glue down the pizza slices to illustrate your story.c. Explain how you solved the problem using words and numbers.

4. Write a subtraction story problem on the back of this paper. a. Cut out the correct number of pizza slices for your story.b. Glue down the pizza slices to illustrate your story.c. Explain how you solved the problem using words and numbers.

Be prepared to share your story, illustration, and solution with the class.





Questions/Prompts for Formative Student Assessment In your addition story, how many pieces of pizza do you have in all? How many

slices of pizza in one whole? How do you write that as a fraction? In your subtraction story, how many pieces of pizza do you have left? How many

slices of pizza in one whole? How do you write that as a fraction? Why does the denominator stay the same with addition and subtraction? Tell me the story that goes with your picture and number sentence.

Questions for Teacher Reflection Do the students’ illustrations accurately match the story? Can students correctly explain how they solved the problems they created? Do the addition and subtraction problem, illustration, and explanation reflect

understanding of the operations?DIFFERENTIATION

Extension Have students consider the whole to be both pizzas, for a total of 16 slices

equaling one whole. What would happen if the pizza restaurant made a mistake and cut one of the

pizzas into fourths? How does it make finding the answer to an addition or subtraction sentence more difficult if the denominators of your fractions are not the same? Have students write problems where one pizza is cut into fourths, the other is cut into eights.

Intervention Allow students to tell their story and model it with their pieces in a small group

before gluing and labeling it on paper.


http://www.primarygames.com/fractions/question1.htm In this game, students are asked to identify remaining fraction of a pizza. Note this site contains advertising.




http://www.primarygames.com/fractions/question1.ht#m


Name ________________________________________ Date ___________________________

Pizza Party

You will be writing two story problems, modeling with problem using pizzas that you create. Fold this paper in half to create two sections on the back to record your stories.

1. Create two pizzas.a. Cut out two circles of pizza dough and color them to look like

your two favorite types of pizza.b. Fold the pizzas into eighths.

2. Fold this paper in half to create two sections on the back to record your pizza stories.

3. Write an addition story problem on the back of this paper. a. Cut out the correct number of pizza slices for your story.b. Glue down the pizza slices to illustrate your story.c. Explain how you solved the problem using words and numbers.

4. Write a subtraction story problem on the back of this paper. a. Cut out the correct number of pizza slices for your story.b. Glue down the pizza slices to illustrate your story.c. Explain how you solved the problem using words and numbers.

Be prepared to share your story, illustration, and solution with the class.





Pizza PartyPizza Dough





LEARNING TASK: All in a Line

STANDARDS ADDRESSED











phenomena.





ESSENTIAL QUESTION

Why is the number 10 important in our number system?

How are tenths related to the whole?

MATERIALS

“All in a Line” student recording sheet

Adding machine tape Tape, black markers

(narrow point), pencils Color tiles, paper clips

or other manipulatives to use as tenth of unit

GROUPING

Partner/Small Group Activity

TASK DESCRIPTION, DEVELOPMENT, AND DISCUSSION Students will create a number line from 0-10, using increments of tenths.

CommentsEach pair or group will create a number line that begins at 0 and ends at 10 units. (If each

section is equal in length, it is considered a graduated number line.) It can be as long or as short

as the students choose but it must be labeled in tenths using decimal fractions (i.e. etc).

The length of the number line will depend on what manipulative is used to represent one-tenth of a unit.

When students finish the number line, they will write a brief description of how they created it, including the object they used to graduate their line. Students can share their number lines to initiate a conversation of how long the number lines are compared to the length of one-tenth of a unit.

Written explanation should include a description of how they numbered the line and how they knew how many sections to put between the whole numbers. Exemplary work would include regularly spaced, legible numbers. Whole numbers would be indicated either by contrasting color or size.

Background Knowledge





Students should be familiar with number lines, how to write decimal fractions (i.e.

etc.), and how tenths are related to the whole.

Task DirectionsStudents will follow the directions below from the “All in a Line” student recording sheet.

Work with your partner(s) to create a number that begins at 0 and ends at 10 units. Choose an object. (Your teacher will have items such as color tiles, paper

clips, or other objects to use.) Create a number line from 1 to 10. The length of your object should represent

of one unit on your number line.

When finished, write a description below of how you created your number line.

Attached your number line to the bottom of this paper.

Questions/Prompts for Formative Student Assessment What does each section represent? What do ten sections represent? How do you know where to place the whole numbers? How many of the tiles (or whatever manipulative the students chose) would you need

to cover the entire number line? How many between each whole number?

Questions for Teacher Reflection Do students recognize that each section needs to be the same size? Are students able to label the tenths and whole numbers accurately? Do students understand that the label for each section represents the length of each

segment? Do students recognize that the number lines may be of different lengths if the one-tenth

of a unit used was different? Do students understand when the one-tenth of a unit used would cause the number line to be longer or shorter than other number lines?

DIFFERENTIATION

Extension Ask students to look for patterns on their number line. (i.e. How many tenths are between

0 and1? 0 and 2?...0 and 10? How do you know? Did you have to count them?) What other patterns do you notice?

Intervention For students who have difficulty using a manipulative to create tenths, allow them to

create a number line from 0-1 or 0-2 using an object as described above. Then give the student two copies of the “All in a Line, 0-1 Number Lines.” Allow the student to cut, paste number lines together, and then label the scale.





Name ________________________________________ Date ___________________________

All in a Line

Work with your partner(s) to create a number that begins at 0 and ends at 10 units.

Choose an object. (Your teacher will have items such as color tiles, paper clips, or other objects to use.)

Create a number line from 1 to 10. The length of your object should represent of

one unit on your number line. When finished, write a description below of how you created your number line. Attached your number line to the bottom of this paper.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________





All in a Line0-1 Number Lines

Carefully cut along the dotted lines and then glue the segments together to create a number line. Make sure there are not gaps or overlaps between segments.





LEARNING TASK: Trash Can Basketball (Adapted from a 1st grade GPS frameworks task, Trash Can Basketball)

STANDARDS ADDRESSED

M3N1. Students will further develop their understanding of whole numbers and decimals and ways of representing them.

c. Identify place values from tenths through ten thousands.d. Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10

of a single digit whole number) and ways to represent them including word name, standard form, and expanded form.
















phenomena.

ESSENTIAL QUESTIONS

How are decimals and fractions related? Why is the number 10 important in our number

system? How can I write a fraction to represent a part of a

group? When we compare two fractions, how do we know

which has a greater value?

MATERIALS

“Trash Can Basketball” student recording sheet

Each group will need 10 pieces of “trash” (paper balls).

Box, tub, or trash can for a container Crayons or markers and construction paper

for making a poster

GROUPING

Partner/Small Group Activity


Students collect data from playing “Trash Can Basketball.” They use the data to write decimal fractions and decimal numbers.

CommentsThe copy room is a good source of trash paper. Be sure the paper balls are tight. Loosely

packed ones make it really difficult to throw accurately.All solutions reached in this task should be specific to the data collected. All student

work should show both their data and their partner’s data. Tallies should match decimal numbers assigned. Explanations should be clearly stated and specific.

Before beginning the throwing contest, as a class, decide on any rules regarding practice throws.





Background KnowledgeBefore the activity, the class should have had several lessons to demonstrate and practice

understanding and representing tenths. One tenth of a final score is determined by one throw if your final score (the whole) is

determined by ten throws.

Task DirectionsStudents will follow directions below from the “Trash Can Basketball” student recording

sheet. This is your chance to demonstrate your basketball skills! You have been chosen to

participate in a paper-ball throwing contest.

Directions:1. Use the scrap paper to make 10 paper balls per group. (Wad the paper balls up

tightly so they are easier to aim.) 2. Place a trash can (or other large container) 5 feet away. 3. Predict how many paper balls you will be able to get into the basket. Write your

prediction in the chart below.4. Take turns with your partner(s) throwing the ten paper balls into the trash can.

Your partner will collect data using tally marks on the chart below to show how many of the 10 paper balls went into the trash can.

5. Create a poster to display

your group’s results. Your poster should include the following.

a. Represent the number of good throws for each partner as a decimal fraction and express a comparison of decimal fraction scores using a >, <, or = symbol.

b. Represent the number of good throws for each partner as decimal numbers and express a comparison of decimal scores using a >, <, or = symbol.

Example:

Player #1 0.6 of the baskets

Player # 2 0.7 of the baskets

0.6 < 0.7

c. Write to explain the results of the contest. Be prepared to share your poster and results with the class.





Questions/Prompts for Formative Student Assessment How did you determine your score? How many times did you throw the paper

ball? How many times did you “make a basket”? How is your score written as a decimal fraction? How is your score written as a decimal? How do we compare two decimal fractions? How do we compare two decimals?

Questions for Teacher Reflection Can students accurately explain how they determined their decimal and decimal

fraction scores? Do students recognize how decimal fractions and decimals are related? Can students correctly compare the two scores in both decimal fraction and decimal

forms?

DIFFERENTIATION

Extension Repeat the activity as time permits. (Try different types of paper balls, distances,

types of shots, etc.)

Intervention Have the chart pre-made on the poster for student use and/or allow student to write

his/her results on a computer, print, and attach to the poster.


http://www.widro.com/throwpaper.html - Students can play the waste basket basketball virtually. This is very challenging because a virtual fan is blowing. Note – web site contains advertisements.




http://www.widro.com/throwpaper.html


Name ________________________________________ Date ___________________________

Trash Can BasketballThis is your chance to demonstrate your basketball skills! You have

been chosen to participate in a paper-ball throwing contest.

Directions:1. Use the scrap paper to make 10 paper balls per group. (Wad the paper balls up tightly so

they are easier to aim.) 2. Place a trash can (or other large container) 5 feet away. 3. Predict how many paper balls you will be able to get into the basket. Write your

prediction in the chart below.4. Take turns with your partner(s) throwing the ten paper balls into the trash can. Your

partner will collect data using tally marks on the chart below to show how many of the 10 paper balls went into the trash can.

Trash Can Basketball Contest

Player #1

________________

Number of Tosses

Prediction for Number of “Baskets”

Number of “Baskets”

(Use tallies)

Score as a fraction

Score as a decimal

10

Player #2

________________

Number of Tosses

Prediction for Number of “Baskets”

Number of “Baskets”

(Use tallies)

Score as a fraction

Score as a decimal

10

5. Create a poster to display your group’s results. Your poster should include the following.a. Represent the number of good throws for each partner as a decimal fraction and

express a comparison of decimal fraction scores using a >, <, or = symbol. b. Represent the number of good throws for each partner as decimal numbers and

express a comparison of decimal scores using a >, <, or = symbol. Example:

Player #1 0.6 of the baskets

Player # 2 0.7 of the baskets

0.6 < 0.7





c. Write to explain the results of the contest. Be prepared to share your poster and results with the class.





PERFORMANCE TASK: Sweet Decimal Fraction Bars

STANDARDS ADDRESSED


e. Understand the concept of addition and subtraction of decimal fractions and common fractions with like denominators.

f. Model addition and subtraction of decimal fractions and common fractions with like denominators.

g. Use mental math and estimation strategies to add and subtract decimal fractions and common fractions with like denominators.

h. Solve problems involving decimal fractions and common fractions with like denominators.








phenomena.





ESSENTIAL QUESTIONS

How can you use decimal fractions to solve addition and subtraction problems?

What happens to the denominator when I add fractions with like denominators?

MATERIALS

“Sweet Decimal Fraction Bars, Story Problems” student recording sheet

“Sweet Decimal Fraction Bars, Ten-Frames” student recording sheet

GROUPING



In this task, students will be given problems to solve involving a candy bar divided into ten equal sections.

CommentsStudents may use the ten-frames student sheet or the number line created in the “All in a

Line” task to solve these problems. Alternatively, students may choose to use math pictures to solve the problems. Allow students to choose a model that makes sense to them. As students work, look for strategies that students use that may be beneficial to other students. Allow students who used these helpful strategies to share their thinking during the summary part of the lesson.

Background KnowledgeStudents should have experience working with adding and subtracting common fractions and

decimal fractions using a number line, an area model, and a set model. Also, students should be able to record the operation using fractional notation.





Task DirectionsStudents will follow the directions below from the “Sweet Decimal Fraction Bars” student

recording sheet below.

A Sweet Decimal Fraction Bar is a chocolate candy bar that is divided into ten equal sections. Solve the following problems.

1. Hannah had of a Sweet Decimal Fraction Bar. She gave of the candy bar to

Carlos. How much of the candy bar does she have left?

2. Sarah has of a candy bar. Brianna has of the same candy bar. Also, Mika has

of the same candy bar. Together do the girls have enough to equal a whole

candy bar?

3. Marissa gave Paulo of a Sweet Decimal Fraction Bar. Michael gave Paulo of

a Sweet Decimal Fraction bar. How much candy does Paulo have now?

4. Caleb had of a Sweet Decimal Fraction Bar. He gave Mika of the candy bar.

How much of the candy bar does he have left?

Questions/Prompts for Formative Student Assessment Does the story involve combining or taking away? How do you know? How many tenths of a candy bar do you have in all? How many tenths of a candy

bar do you have left? How do you know? Can you show what happened in the story on a number line? Using the ten-

frames? Using a set of counters? In a math picture? How many tenths would you need to equal a whole candy bar? How many tenths

do you have?

Questions for Teacher Reflection Do students use at least one model fluently and accurately to solve addition and

subtraction problems with tenths? Are students able to accurately compute using decimal fractions? Are students able

to explain how they used fractions to solve the problems? Are students able to use decimal fractions efficiently to solve this problem?





DIFFERENTIATION

Extension Ask students to create an addition and a subtraction problem. Have students solve the

problems on the back of the paper.

Give students four numbers and a target number (e.g.

). Ask students to use the number line below to show an addition/subtraction sequence

that would result in the target number.

For this example, students could show the following.

This problem was adapted from the following website.http://nlvm.usu.edu/en/nav/frames_asid_107_g_2_t_1.html?from=category_g_2_t_1.html

Intervention Allow students to act out the problems with a partner or in a small group. Students

may cut the ten-frames and use the fractional pieces when acting out the stories.







Name ______________________________________ Date _____________________________

Sweet Decimal Fraction BarsStory Problems

A Sweet Decimal Fraction Bar is a chocolate candy bar that is divided into ten equal sections. Solve the following problems.




1. Hannah hadof a Sweet Decimal Fraction Bar. She gaveof the candy bar to Carlos. How much of the candy bar does she have left?

2. Sarah hasof a candy bar. Brianna has of the same candy bar. Also, Mika has of the same candy bar. Together do the girls have enough to equal a whole candy bar?

3. Marissa gave Pauloof a Sweet Decimal Fraction Bar. Michael gave Pauloof a Sweet Decimal Fraction bar. How much candy does Paulo have now?

4. Caleb hadof a Sweet Decimal Fraction Bar. He gave Mikaof the candy bar. How much of the candy bar does he have left?


Name ______________________________________ Date _____________________________

Sweet Decimal Fraction BarsTen-Frames





PERFORMANCE TASK: The Fraction Story Game

STANDARDS ADDRESSED




created by equal divisions of a whole.e. Understand the concept of addition and subtraction of decimal fractions and common

fractions with like denominators.f. Model addition and subtraction of decimal fractions and common fractions with like

denominators.g. Use mental math and estimation strategies to add and subtract decimal fractions and

common fractions with like denominators.h. Solve problems involving decimal fractions and common fractions with like

denominators.











M3P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate mathematical ideas.

b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical phenomena.

ESSENTIAL QUESTION

How are decimal fractions and common fractions used in problem-solving situations?

MATERIALS

Materials Required Per Group “The Fraction Story Game, Directions” student

sheet “The Fraction Story Game, Game board”

student sheet Colored pencils or crayons Index cards (about 60) Common classroom materials -

recycled items for game pieces (about 6)

GROUPING

Small Group Task


Students create a game while reviewing all the different aspects of fractions they have studied.

CommentsStudents may not understand what you mean by “common classroom materials.” While

many classrooms have standard dice that can be used, give alternative examples such as, a penny can be flipped to determine how many spaces the players get to move (heads = 2 spaces, tails =1 space). For game pieces, extra marker caps, manipulatives, or coins can be used.

Begin by having students review lessons or activities that have been done during the fraction unit that they think were important. Record their thoughts on chart paper or the board. You may





want to post a list of the elements of the standard covered during the unit and brainstorm tasks and activities you did that addressed each element.

Since a good game should have at least 20-30 questions, you may want the children to work with a partner or in small groups to create enough questions.

This culminating task represents the level of depth, rigor, and complexity expected of all third grade students to demonstrate evidence of learning.

Additional Comments: Students should have had multiple opportunities to write story problems by

this time in the school year. Questions should match a standard/element. Creating questions to match elements of the standard taught is a wonderful

way to review. It is a strategy that can be used from elementary school through college and is very effective.

Index cards may be used for the problem cards. Insist that the students write legibly. All problem cards should have the solutions on the back

Solutions should be accompanied by an explanation/illustration. Game boards, playing pieces, and cards can be stored in large Ziploc bags or

manila folders.The cards students create for their games can be used in a variety of ways. The problem

cards can be used to create a Jeopardy type game which can be played as a review of the unit. Also the problem cards can be reproduced and used as a set of review question before the unit assessment.

Background KnowledgeWhile this task may serve as a summative assessment, it also may be used for teaching and

learning. It is important that all elements of the task be addressed throughout the unit so that students understand what is expected of them.

Task DirectionsStudents will follow the directions below from “The Fraction Story Game, Directions”

student sheet.

Your task is to create a fraction story game using what you learned about common fractions and decimal fractions. Use the fraction game board on “The Fraction Story Game, Game Board” student sheet to create a game that other students will want to play.

Directions: Look at the list of elements of the standard that you studied in class. The

problem cards you create must match those elements. You will need to make approximately 30 problem cards for your game. Most

of the cards should be written in story problem form. Be sure you have some problem cards for each of the elements of the standard

addressed in this unit. Make sure you use both decimal fractions and common fractions in your problem cards.





Each problem card must have the correct answer on the back. Cover each problem card with a blank index card so players cannot see the problems before their turn. See sample below.

Write the rules for your game.

Things to remember: You can only use common classroom materials. You may decorate your game board in a way that makes the game interesting

and fun to play. Be sure to play your game with a partner to be sure it works.

Questions/Prompts for Formative Student Assessment What are the skills you learned during this unit? What kind of problem can you create for ____ (one of the elements of the standard)? How do you know this is the correct solution for your problem?

Questions for Teacher Reflection Do the problem cards accurately reflect the standards taught? Are all of the elements of the standard represented? Is there an appropriate mixture of cards about decimal fractions and common

fractions? Are other children interested in playing the game created?

DIFFERENTIATION

Extension Students can create their own game board format with penalties, rewards, and more

complex rules.

Intervention Allow students to work in a small group so each student will need to make only

one card per element of the standard. For some of the elements of the standard, give the students the problem and

require them to create the solution to the problem.





Students with a significant problem with manual dexterity may need to type their problems, then cut and paste then onto the index cards.






http://jeopardylabs.com/ - This site allows you to create a Jeopardy game on a web-based template.

http://www.jmu.edu/madison/teacher/jeopardy/Create_Jeopardy.pdf - Directions for creating a Jeopardy game using PowerPoint.




http://www.jmu.edu/madison/teacher/jeopardy/Create_Jeopardy.pdf

http://jeopardylabs.com/


Name ______________________________________ Date _____________________________

The Fraction Story GameDirections

Your task is to create a fraction story game using what you learned about common fractions and decimal fractions. Use the fraction game board on “The Fraction Story Game, Game Board” student sheet to create a game that other students will want to play.

Directions: Look at the list of elements for the standard that you studied in class. The problem cards

you create must match the elements of the standard. You will need to make approximately 30 problem cards for your game. Most of the cards

should be written in story problem form. Be sure you have some problem cards for each of the elements of the standard addressed

in this unit. Make sure you use both decimal fractions and common fractions in your problem cards.

Each problem card must have the correct answer on the back. Cover each problem card with a blank index card so players cannot see the problems before their turn. See sample below.

Write the rules for your game.

Things to remember: You can only use common classroom materials. You may decorate your game board in a way that makes the game interesting and fun to

play. Be sure to play your game with a partner to be sure it works.





Name ______________________________________ Date _____________________________

The Fraction Story GameGame Board




Start

Finish

Problem Cards

Documents

Unit 4 Organizer: - Compton Coaches · Web view2009/08/03 · Recognize reasoning and proof as fundamental aspects of mathematics. Make and investigate mathematical conjectures