Competencies and Objectives:
NUMBER AND OPERATIONS
1. Understand relationships among numbers, use the four basic
operations, compute fluently, and make reasonable estimates.
a. Add and subtract up to five-digit whole numbers with and without
regrouping. (DOK 1)
b. Add and subtract decimals through hundredths. (DOK 1)
c. Explain two or more methods of multiplying whole numbers (one- and two-digits)
with justification. (DOK 2)
d. Explain two or more methods of dividing four-digit dividends by one- and two-digit
divisors, with and without remainders, and justify the processes. (DOK 2)
e. Add and subtract fractions with like denominators. (DOK 1)
f. Model and identify equivalent fractions. (DOK 2)
g. Represent equivalence relationships between fractions and decimals using
concrete materials, diagrams, or other models. (DOK 1)
h. Estimate products and quotients of whole numbers to include strategies
such as rounding. (DOK 2)
i. Recall multiplication and division facts. (DOK 1)
j. Compose and decompose five-digit numbers and decimal numbers
through hundredths, with representations in words, physical models, and
expanded and standard forms. (DOK 1)
k. Determine and use benchmark numbers such as 0, 0.5 (½), and 1 to judge the
magnitude of whole numbers, decimals, and fractions. (DOK 2)
l. Model factors and multiples of whole numbers. (DOK 1)
2. Analyze and represent patterns, number relationships, and functions
using algebraic symbols. Demonstrate an understanding of the
properties of the basic operations.
a. Analyze a given numeric pattern and generate a similar pattern. (DOK 2)
b. Determine the value of variables in equations; justify the process used to make
the determination. (DOK 2)
c. Construct input/output function tables and generalize the rule using words,
models, and symbols. (DOK 3)d. Explain the properties of the basic operations using models, numbers, and
variables: (DOK 2)
• Zero property of multiplication
• Associative properties of addition and multiplication
• Commutative properties of addition and multiplication
• Identity properties of addition and multiplication• Distributive properties of multiplication over addition and subtraction
e. Demonstrate and explain the inverse operations of addition/subtraction
and multiplication/division. (DOK 2)
3. Analyze characteristics, properties, and relationships of two- and threedimensional
geometric shapes. Use coordinate geometry.
a. Analyze and describe the similarities and differences between and among twoand
three-dimensional geometric shapes, figures, and models using
mathematical language. (DOK 2)
b. Identify and analyze the relationships between and among points, lines, line
segments, angles, and rays. (DOK 2)
c. Identify transformations (rotations [turns], reflections [flips], and translations
[slides]) of two-dimensional figures. (DOK 1)
d. Locate ordered pairs in the first quadrant of the coordinate plane. (DOK 1)
4. Evaluate and justify measurable attributes of objects, units, systems,
and processes. Perform measurements.
a. Estimate and measure a given object to the nearest eighth of an inch. (DOK 2)
b. Convert capacity, weight/mass, and length within the English and metric systems
of measurement. (DOK 1)
c. Describe relationships of rectangular area to numerical multiplication. (DOK 2)
d. Use appropriate tools to determine, estimate, and compare units for
measurement of weight/mass, area, size of angle, temperature, length, distance,
and volume in English and metric systems and time in real-life situations.
(DOK 1)DATA ANALYSIS & PROBABILITY
5. Formulate and analyze data. Evaluate inferences and predictions.
a. Draw, label, and interpret bar graphs, line graphs, and stem-and-leaf plots.
b. Find and interpret the mean, mode, median, and range of a set of data. (DOK 1)
c. Compare data and interpret quantities represented on tables and graphs
including line graphs, bar graphs, frequency tables, and stem-and-leaf plots to
make predictions and solve problems based on the information.