
Unit Map 20112012
P.S. 176 The Ovington School
Collaboration / 2D Grade 4 Math* / Grade 4 (P.S. 176 The Ovington School)
Wednesday, November 2, 2011, 1:22PM


Unit: Fraction Cards and Decimal Squares (Unit 6) (Week 25, 7 Weeks)


The students will understand that:

Fractions are equal parts, equivalent fractions have the same value, even though they may look different, and fractions can be combined with denominators that are the same as well as different

Decimals are an extension of the placevalue system

What is the meaning of fractions and decimals and how do they relate to my life?
How does comparing quantities describe the relationship between them?
What are ways to represent rational numbers when adding?

Common Core Standards and Indicators

CCLS:Mathematics, 4th Grade , Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.
CCLS:Mathematics, 4th Grade , Number & Operations—Fractions
4.NF Extend understanding of fraction equivalence and ordering.

1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or
4.NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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

4c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
4.NF Understand decimal notation for fractions, and compare decimal fractions.

5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

6. Use decimal notation for fractions with denominators 10 or 100

7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or
CCLS:Mathematics, 4th Grade , Measurement & Data
4.MD Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Students will:
A. Understand the meaning of fractions and decimals
B. Comparing the values of fractions and decimals
C. Use representation to add rational numbers

Student will be able to:
A.1 Find fractional parts of a rectangular area and parts of a group using objects
A.2 Interpret the meaning of the numerator and denominator of a fraction
A.3 Represent fractions greater than 1
A.4 Reading and Writing tenths and hundredths through representation of parts of an area
A.5 Identify everyday uses of fractions and decimals
B.1 Identify relationships between unit fractions (Equivalent fractions)
B.2 Comparing the same fractional parts of differentsized wholes
B.3 Ordering fractions and decimals justifying their order through reasoning about fractions equivalencies, representation, relationships and the meaning of numbers
B.4 Representing and comparing fractions using a number line
B.5 Identify decimal and fraction equivalents
C.1 Using representation to add fractions that sun to 1
C.2 Estimating sums of fractions and decimals
C.3 Adding fractions with the same and related denominators
C.4 Adding decimals that are multiples of 0.1 and 0.25
 
Fraction

Numerator

Denominator

Thirds

Sixths

Landmarks

Decimal

Identifying and Comparing Fractions (Investigations)
Other written assessments
Session 1.5 Assessment: Identifying and Comparing Fractions: Students find combinations of fractions that equal one whole rectangle. They are assessed on their ability to identify thirds and sixths of a 5 × 12 rectangle and their understanding of the relationship between and .
Comparing Fractions (Investigations)
Other written assessments
Session 2.6 Assessment: Comparing Fractions: Students continue to order fractions on a number line. They are assessed on comparing pairs of fractions. They discuss strategies and their conjectures about general rules for fraction comparisons.
End of Unit Assessment (Investigations)
Other written assessments
Session 3.7 and EndofUnit Assessment: Students are assessed on the benchmarks of this unit by completing problems that require them to compare and order fractions and decimals.
Dependable Parent Volunteers (Exemplar)
Social Media (Twitter, Blog, Wiki): Self Assessment
Given the fraction of the day each parent volunteers, students determine which parent is spending more time volunteering in the classroom.
NCTM Standards: Numbers and Operations; Geometry and Measurement
Content Standards: Fractions; Time
Decimal and Fraction Multiple Choice (Funaro)
Other (Please Explain): Other written assessments
Decimal and Fraction Open Ended (Funaro)
Other written assessments
Decimal and Fraction Multiple Choice
Dependable Parent Volunteers
Decimal and Fraction Open Ended
Session 1.5 Assessment
Session 2.6 Assessment
Session 3.7 Assessment

Investigations in Number, Data and Space
Investigation 1  Parts of Rectangles
(A.1, A.2) Session 1.1 Introducing Halves and Fourths, Finding Fourths and Eighths (4.NF.1, 4.NF.3, 4.NF.3.a, 4.NF.3.b)
(A.1, B.1) Session 1.2 Finding Thirds and Sixths (4.NF.3, 4.NF.3.a, 4.NF.3.b)
(A.1, A.2) Session 1.3 Fractions of 24, Story Problems About 24 (4.NF.3, 4.NF.3.d, 4.NF.4, 4.NF.4.c)
(A.1, B.2) Session 1.4 (MATH WORKSHOP) Same Parts, Different Wholes (4.NF.3, 4.NF.3.d, 4.NF.4,4.NF.4.c)
(A.1, C.1) Session 15 Combinations That Equal 1 (4.NF.1, 4.NF.3, 4.NF.3.a)
(C.1, C.3) Session 1.6 Introduction to Adding Fractions, (MATH WORKSHOP) Fractions 2(a) Adding Fractions, 2(b) Combinations that Equal 1 2(c) Finding Fractions of a Rectangle 5x12 and 10x10 2(d) Story Problems About a Class (4.NF.3, 4.NF.3.a, 4.NF.3.b)
(C.1, C.2, C.3) Session 1.7 (MATH WORKSHOP) Fractions 2(a) Adding Fractions 2(b) Combinations that Equal 1 2(c) Finding Fractions of a Rectangle 5x12 and 10x10
Investigation 2 Ordering Fractions
(A.1, A.2, A.3) Session 2.1 Making Fraction Cards (4.NF.1, 4.NF.2)
(A.1, A.2) Session 2.2 Making Fraction Cards (4.NF.2)
(A.2, B.1, B.3) Session 2.3 Capture Fractions (4.NF.1, 4.NF.2)
(B.1, B.4) Session 2.4 Comparing Fractions to Landmarks, Fractions in Containers (4.NF.2)
(B.3, B.4) Session 2.5 Introducing Fractions on a Number Line, (MATH WORKSHOP) Comparing Fractions 3a Making a Fraction Number Line 3B Capture Fractions (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3.a)
(B.3, B.4) Session 2.6 (MATH WORKSHOP) Comparing Fractions 2a Making a Fraction Number Line 2b Capture Fractions (4.NF.2)
Investigation 3 Working with Decimals
(A.5, A.4) Session 3.1 Introducing Decimals, Decimals on the 10x10 Square (4.NF.5, 4.NF.6, 4.MD.2)
(A.4, B.3) Session 3.2 Comparing 0.25 and 0.3, Decimal Compare ( 4.NF.6, 4.NF.7)
(B.5, A.4, C.4) Session 3.3 Playing Fill Two (4.NF.5, 4.NF.6, 4.NF.7)
(C.2, C.4) Session 3.4 Introducing Parts of a Mile, Running Distances (4.NF.7, 4.MD.2)
(B.3, A.4, C.4) Session 3.5 (MATH WORKSHOP) Comparing and Combining Decimals 1a Decimal Compare, 1b Fill Two, 1c Making Your Own Running Logs (4.NF.2, 4.NF.6, 4.MD.2)
(B.3, A.4, C.4) Session 3.6 (MATH WORKSHOP) Comparing and Combining Decimals 1a Decimal Compare, 1b Fill Two, 1c Making Your Own Running Logs (4.NF.7, 4.MD.2)

Envisions (These lessons can be supplemented to the Investigations Unit)
Topic 10 (all)
101 Fractions: Regions and Sets
102 Fractions: Fractions and Division
103 Fractions: Estimating Fractional Amounts
104 Fractions: Equivalent Fractions (4.NF.1)
105 Fractions: Fractions in Simplest Form (4.NF.1)
106 Fractions: Improper Fractions and Mixed Numbers
107 Fractions: Comparing Fractions (4.NF.2)
108 Fractions: Ordering Fractions (4.NF.1)
109 Problem Solving: Writing to Explain
Topic 11 (all)
111 Fractions: Adding and Subtracting Fractions with Like Denominators (4.NF.3, 4.NF.3.a, 4.NF.3.b, 4.NF.3.d)
112 Fractions: Adding Fractions with Unlike Denominators (4.NF.3, 4.NF.3.a)
113 Fractions: Subtracting Fractions with Unlike Denominators (4.NF.3, 4.NF.3.a)
114 Problem Solving: Draw a Picture and Write an Equation (4.NF.3, 4.NF.3.b, 4.NF.3.c, 4.NF.4.a, 4.NF.4.a]b, 4.NF.4.c, 4.MD.2)
Topic 12 (all)
121 Decimals: Decimal Place Value
122 Decimals: Comparing and Ordering Decimals (4.NF.7)
123 Decimals:Fractions and Decimals (4.NF.5, 4.NF.6)
124 Decimals: Fractions and Decimals on the Number Line
125 Decimals: Mixed Numbers and Decimals on the Number Line
126 Problem Solving: Draw a Picture (4.MD.2)
Topic 1
15: Using Decimals to Understand Money
16: Counting Money and Making Change
Envisions MATH Exam View Test Generator Topics 1, 10, 11, 12
Envisions MATH Topics 1, 10, 11, 12 Tests
BOOK: HandsOn Number and Operation (Games are attached)
pages 151165
151 Just a Fraction More or Less (Ordering Proper and Improper Fractions)
152Find the Factors, Old Bean! (Finding Factors/Multiples)
153Placing an Order (Improper Fractions)
154Somewhere, in There, Is a GCF! (Finding CCF or LCM)
155A Fraction of an Order (Ordering Fractions with Unlike Denominators)
156Making Order of Fractions (Creating and Ordering Fractions)
157A Round of Rounding (Rounding Fractions)
158Draw, Pardner ( Drawing and Cutting Fractional Pieces)
159Odd Man Out (Finding Equivalent Fractions) (FUNARO)
160Cut it Out (Cut geometric shapes to represent equivalent fractions)
161 If the Fraction Fits (Introduction to Equivalent Fractions)
162 Know When to Fold Them (Reducing Fractions)
163 Make a Buck (Convert Money to Fractional Representation)
164Being Shelfish (Create a storage Unit following specific directions)
165 The Magic of 60 (Adding and Subtracting Fractions)
BOOK: Lessons for Introducing Fractions (Grades 45) Teaching Arithmetic, Marilyn Burns
BOOK: Pattern Blocks (Grades 34) The Super Source
Pages 8689 Wipe Out
BOOK: Math and Literature (Grades 46) Marilyn Burns
Beast of Burden
BOOK: About Teaching Math (A K8 Resource) Marilyn Burns
Pages 223244
Fraction Independent Activities: Fractions Close to 1/2, Building Rectangles, Fraction Riddles (FUNARO), Rod Relationships, Build the Yellow Hexagon,
Decimal Independent Activities: Multiplication Puzzlers, Adding to One, The Place Value Game
Exemplars
CDI
Deluxe Birthday Cake (4.NF.1, 4.NF.2, 4.NF.3.a, 4.MP.5.), Disappearing Cookies, Great Pizza Dilemma (4.NF.1., 4.MP.5.), Is Dan Losing His Marbles? (4.MP.4.)Party Seating (4.MP.4.), Sandbox for Geoffrey, Should We Burst Their Bubble? (4.MP.4.)
CDII
Dependable Parent Volunteers(4.NF.2, 4.NF.3.a.), Feverish Freddy (4.MP.4.), Fun Night, Ollie Owl's Food Court (4.MP.4.), Who Owns the Most Land? (4.MP.4.)
CDIII (We currently do not have this CD)
A Challenge (4.MP.4.), Feeling Hungry (4.MP.4., 4.MP.5.), Lost Spinner (4.MP.4.), Lugging Water I (4.MP.4.), A Puzzle(4.NF.1.), Picture Frames (4.MP.4.), Should Hannah Play? (4.MP.4.), Spinner Fixing (4.MP.4.), Painting Plans, Tiles for a Bedroom (4.MP.4.)
Exemplars35.doc
Deluxe Birthday Cake Given a birthday cake made of three different flavors in
Great Pizza Dilemma What are the ways that a group of friends might share pizzas with one another?
Should We Burst Their Bubble?  Students determine which gum container presents the better deal.
Dependable Parent Volunteers  Given the fraction of the day each parent volunteers, students determ
Feverish Freddy  Students determine the fair market value of real estate lots.
Ollie Owl's Food Court  Students decide how much rent the owl should charge each restaurant owner
Who Owns the Most Land?  Students determine who owns more land and which is the most valuable.








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