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
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.
A. Understand the meaning 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
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 .
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)
(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)
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.)
CDIIDependable 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.)
Exemplars3-5.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.