Standards Database Logo
Home | Browse | Search | Purpose | History | Process | Acknowledgment| Reference



 Standard 2.Understands and applies basic and advanced properties of the concepts of numbers
  Level II [Grade 3-5]
   Benchmark 5
Understands the concepts related to fractions (e.g., numerator and denominator, equivalence, relative magnitudes) and decimals (e.g.,relative magnitudes)
    Knowledge/skill statement 2
Understands the concept of fractions
Related assessment item(s):
     Identifies picture model of ¾ (N4)
Determine the diagram with correct number of shaded squares (T1)
Identify the correct representation of a half (T1)
Find the proportion of cake eaten given the total number of pieces (T1)
Use manipulatives and knowledge of fractions to create figures (T1)
Find the number of additional shaded  boxes needed for 4/5 of the boxes to be shaded (T2)
Write and solve an equation, given the information provided and determine which statement is true (T2)
Solve the word problem using knowledge of mulitplying fractions and adding/subtracting whole numbers (T2)
Circle the number of cookies that represents 1/3 (T1)
Identifies correct answer by using knowledge of portions of a whole (T2)
Shade a fraction of a figure (N8)
Identify the square with correct fraction of shading. (T1)
Identify the fractional amount shaded in the figure. (T1)
Identify the same fractional area shaded in a different shape. (T2)
Performance expectation(s):
    Understands fractions as parts of unit whole, as parts of a collection, and divisions of whole numbers (M)

Uses drawings, diagrams, and models to show the concept of fractions as part of a whole and part of a set (C3)

Recognizes simple fractions as instructions to divide (S1)

Identifies and describes different uses for the same numerical representation (e.g., ¼ can represent a fraction, a division problem, or a ratio) (C5)

Common Core Reference:
    3.NF.1; 4.NF.3; 4.NF.4; 4.MD.4; 5.NF.3
3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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

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

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5),
recognizing this product as 6/5. (In general, n ×  a/b) = (n × a)/b.)

4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction
of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

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

Citation reference
BD = benchmark, declarative
BP = benchmark, procedural
BC = benchmark, contextual
K = Knowledge
S = Skill
P = Performance

1st letter/number of each code in parentheses:
*   McREL Report
2   Project 2061: Benchmarks for Science Literacy
AC   ACT, College Readiness Standards
AD   American Diploma Project
B1   International Baccalaureate: Math, Primary
B2   International Baccalaureate: Math, Middle
B3   International Baccalaureate: Math, High
C   CBE: Standards for Excellence
C3   CBE: Standards for Excellence, end of grade 3
C5   CBE: Standards for Excellence, end of grade 5
CB   College Board: College Board Standards for College Success: Mathematics and Statistics
CO   CDE: Building Blocks to Colorado’s Content Standards
D   Department of Defense: Prekindergarten Mathematics
HS   Head Start: Child Outcomes Framework
M   NCTM: Principles & Standards for School Mathematics
MA   MDE (Massachusetts): Early Childhood Standards
N4   NAEP: Released items for grade 4 (2003)
N8   NAEP: Released items for grade 8 (2003)
P   NAEP: Mathematics Assessment Framework
PS   McGraw-Hill: Pre-Kindergarten Standards: Guidelines for Teaching and Learning
S1   New Standards: Elementary School
S2   New Standards: Middle School
S3   New Standards: High School
T   TEA: Texas Prekindergarten Curriculum Guidelines
T1   TIMSS: Population 1 assessed grade 4 (released 1998)
T2   TIMSS: Population 2 assessed grade 8 (released 1998)
T3   TIMSS: Final Year assessed grade 12 (released 1998)
U   Understanding University Success: A Report from Standards for Success
UK   United Kingdom: Desirable Outcomes for Children’s Learning

2nd letter code :
E = Explicitly stated in document
I = Implicit in document

Page number of the cited document