Unit Map 2011-2012 P. S. 176 The Ovington School

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Unit Map 2011-2012

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)

Big Ideas

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 place-value system

Essential Questions

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


Skills / Strategies

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 different-sized 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

Key Terms / Vocabulary

  1. Fraction

  2. Numerator

  3. Denominator

  4. Thirds

  5. Sixths

  6. Landmarks

  7. 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 End-of-Unit 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 1-5- 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)

10-1 Fractions: Regions and Sets

10-2 Fractions: Fractions and Division

10-3 Fractions: Estimating Fractional Amounts

10-4 Fractions: Equivalent Fractions (4.NF.1)

10-5 Fractions: Fractions in Simplest Form (4.NF.1)

10-6 Fractions: Improper Fractions and Mixed Numbers

10-7 Fractions: Comparing Fractions (4.NF.2)

10-8 Fractions: Ordering Fractions (4.NF.1)

10-9 Problem Solving: Writing to Explain


Topic 11 (all)

11-1 Fractions: Adding and Subtracting Fractions with Like Denominators (4.NF.3, 4.NF.3.a, 4.NF.3.b, 4.NF.3.d)

11-2 Fractions: Adding Fractions with Unlike Denominators (4.NF.3, 4.NF.3.a)

11-3 Fractions: Subtracting Fractions with Unlike Denominators (4.NF.3, 4.NF.3.a)

11-4 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)

12-1 Decimals: Decimal Place Value

12-2 Decimals: Comparing and Ordering Decimals (4.NF.7)

12-3 Decimals:Fractions and Decimals (4.NF.5, 4.NF.6)

12-4 Decimals: Fractions and Decimals on the Number Line

12-5 Decimals: Mixed Numbers and Decimals on the Number Line

12-6 Problem Solving: Draw a Picture (4.MD.2)


Topic 1

1-5: Using Decimals to Understand Money

1-6: 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: Hands-On- Number and Operation (Games are attached)

pages 151-165

151- Just a Fraction More or Less (Ordering Proper and Improper Fractions)

152-Find the Factors, Old Bean! (Finding Factors/Multiples)

153-Placing an Order (Improper Fractions)

154-Somewhere, in There, Is a GCF! (Finding CCF or LCM)

155-A Fraction of an Order (Ordering Fractions with Unlike Denominators)

156-Making Order of Fractions (Creating and Ordering Fractions)

157-A Round of Rounding (Rounding Fractions)

158-Draw, Pardner ( Drawing and Cutting Fractional Pieces)

159-Odd Man Out (Finding Equivalent Fractions) (FUNARO)

160-Cut 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)

164-Being Shelfish (Create a storage Unit following specific directions)

165- The Magic of 60 (Adding and Subtracting Fractions)


BOOK: Lessons for Introducing Fractions (Grades 4-5) Teaching Arithmetic, Marilyn Burns


BOOK: Pattern Blocks  (Grades 3-4) The Super Source

Pages 86-89- Wipe Out


BOOK: Math and Literature (Grades 4-6) Marilyn Burns

Beast of Burden


BOOK: About Teaching Math (A K-8 Resource) Marilyn Burns

Pages 223-244

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



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.)

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.)


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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