INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
State Resources:
TEA STAAR Mathematics Resources: http://www.tea.state.tx.us/student.assessment/staar/math/
TEA STAAR Released Test Questions: http://www.tea.state.tx.us/student.assessment/staar/testquestions/
TEXTEAMS: Rethinking Elementary Mathematics Part I: Multiple Towers;
What’s in Each Box?; Marissa’s Garden; Marissa’s Garden Again
IFD Legend
Bold, italic black; Knowledge and Skills Statement (TEKS)
Bold black; Student Expectation (TEKS)
Strike through: Indicates portions of the Student Expectation that are not included in this unit but are taught in previous or future units
Bold, italic red: Student Expectation identified by TEA as a Readiness Standard for STARR
Bold italic green: Student Expectation identified by TEA as a Supporting Standard for STARR
Blue: Supporting Information / Clarifications from CSCOPE (Specificity)
Italic blue: provides unit level clarification
UNIT TEST
Mathematics Grade 05 Unit 06: Factors and Primes
Matemáticas Grade 05 Unit 06: Factores y números
primos
EITG
Mathematics Grade 05 Unit 06: Possible Lesson 01
Matemáticas Grade 05 Unit 06: Possible Lesson 01
INSTRUCTIONAL RESOURCE(S)
Mathematics Grade 05 2nd 6 Weeks Spiral Review
Matematicas Grade 05 Spanish 2nd 6 Weeks Spiral
Review
Mathematics Grade 05 Transition Alignment Guide (TAG)
Tool
RATIONALE:
This unit bundles student expectations that address finding factors and prime numbers to support numerical understanding and operations.
Prior to this unit, in Grade 5 Units 03 – 05, operations were addressed including multiplication and its connection to division and data relationships. During this unit, students draw on the
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page 1 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
operational skills of multiplication of prior units and the role of factors in multiplication and connect it to finding factor pairs and prime numbers. The concepts of factors and primes
include using various representations such as arrays, area models, and patterns in factors. After this unit, in Grade 5 Unit 07, students will generate equivalent fractions built from the
ability to understand and identify factor pairs and prime numbers.
Identifying common factors, and prime and composite numbers are STAAR Supporting Standards 5.3D and 5.5B and are building blocks to the conceptual understanding of the Grade 5
Texas Response to Curriculum Focal Point (TxRCFP): Developing proficient use of whole-number division algorithms.
According to National Council of Teachers of Mathematics (NCTM), “students should understand numbers, ways of representing numbers, relationships among numbers, and number
systems. If students understand the structure of numbers and the relationships among numbers, they can work with numbers flexibly” (2000, p. 149). Also, the “understanding of, and
fluency with, whole-number multiplication and division, recognizing and generating factors and multiples, [is a foundational component for] understanding fractions and fraction
equivalence” (NCTM, 2010, p. 45).
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2010). Focus in Grade 6: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency. (2009). Texas response to curriculum focal points. Austin, TX: Author.
MISCONCEPTIONS/UNDERDEVELOPED CONCEPTS:
MISCONCEPTIONS:
Some students may think that there is only one way to represent factor pairs. Factor pairs can be represented multiple ways: factors pairs of 12 are (1,12),
(2,6), (3,4), list of factors: (1,2, 3, 4, 6, 12), multiplication (1 x 12, 2 x 6, 3 x 4), factored tree pairs (
Some students may think that 0 and 1 are prime numbers.
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), and/or T-charts or tables.
page 2 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
Some students may think that all odd numbers are prime numbers.
Some students may think that if two numbers have a factor in common, then that is the only factor they have in common. That may be true for some
numbers but not all. When finding common factors of two numbers, students need to complete the list of factors for each number and then find all common
factors.
PERFORMANCE INDICATORS
CONCEPTS
Numerical Understanding – Factors; Prime/Composite
Grade 05 Mathematics Unit 06 PI 01
KEY UNDERSTANDINGS FOR LEARNERS
When a counting number can be described by several
factor pairs, then it is composite; when a counting number
Select three numbers greater than 50, where two of the
Underlying Processes and Mathematical Tools –
can be described with only by one factor pair, then it is
numbers are three-digits and only one of the numbers is
Observations; Mathematical Language and Symbols
prime.
prime (e.g., 61, 123, 276). Create a flip book that includes
a pictorial model (e.g., area model, factor rainbow, factor
The numbers 0 and 1 are considered neither prime nor
tree, etc.) identifying all the factors of each number. Write
composite since there are an infinite number of factor
an explanation to show whether: (1) each number of the
pairs that have the product of 0 and 1 has only one factor
set as prime or composite, (2) a common factor(s) exists
pair – itself.
among the set of numbers, and (3) the following
statement is true or false: “All prime numbers are odd and
Prime and composite numbers can be even or odd.
all composite numbers are even”.
Factors can be expressed as either prime or composite
Sample Performance Indicator:
Use the following three numbers to create a
flip book that includes a pictorial model
(e.g., area model, factor rainbow, factor
tree, etc.) that identifies all the factors of
numbers.
Numerical Understanding – Factors; Prime/Composite
composite can be made and justified by using concrete
Underlying Processes and Mathematical Tools –
objects, pictorial models, patterns in factor pairs and
Problem-Solving Plan or Strategy; Tools to Solve
verbal descriptions.
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Generalizations about whether a number is prime or
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Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
PERFORMANCE INDICATORS
each of the following numbers in the set:
SUGGESTED DURATION : 7 days
CONCEPTS
KEY UNDERSTANDINGS FOR LEARNERS
Problems; Observations; Mathematical Language and
Symbols; Generalizations; Justification of
61 123 276
Reasonableness
Write an explanation to show whether: (1) each number of
the set is prime or composite, (2) a common factor(s)
Numerical Understanding – Factors; Prime/Composite
A variety of problem solving strategies can be used to find
the factors, both prime and/or composite, of a set of whole
exist(s) among the set of numbers, and (3) the following
statement is true or false: “All prime numbers are odd and
Underlying Processes and Mathematical Tools –
all composite numbers are even”.
Problem-Solving Plan or Strategy; Observations;
Standard(s): 5.3D , 5.5B , 5.14C , 5.14D , 5.15A ,
5.15B , 5.16A , 5.16B
ELPS ELPS.c.1A , ELPS.c.5E , ELPS.c.5G
Mathematical Language and Symbols
Numerical Understanding – Factors
numbers.
A set of whole numbers can be described by its factors
and common factors.
Underlying Processes and Mathematical Tools –
Observations; Mathematical Language and Symbols
KEY ACADEMIC VOCABULARY SUPPORTING CONCEPTUAL DEVELOPMENT
Common factor(s) – a factor or set of factors shared by two or more numbers
Composite number – a number with more than two factors
Divisibility – the ability for a number to be divided without a remainder
Factor – a number multiplied by another number to find a product
Prime number – a number with exactly two factors, 1 and the number itself
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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page 4 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
5.3
Number, operation, and quantitative reasoning. The student adds, subtracts,
multiplies, and divides to solve meaningful problems. The student is expected
to:
5.3D
Identify common factors of a set of whole numbers.
Supporting Standard
Identify
COMMON FACTORS OF A SET OF WHOLE NUMBERS
Including, but not limited to:
Common factors
Prime factors
Composite factors
All common factors of a given set of numbers
Methods or strategies for finding common factors of
the set
Arrays
Area models
Diagrams
Number lines
Note:
Grade 5 introduces identifying common factors of a set
of whole numbers.
Grade 5 introduces the difference between prime and
composite numbers.
Grade 6 is responsible for teaching prime factorization.
Grade 6 continues finding common factors but will
include greatest common factor and least common
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page 5 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
multiple given a set of positive integers.
5.5
Patterns, relationships, and algebraic thinking. The student makes
generalizations based on observed patterns and relationships. The student is
expected to:
5.5B
Identify prime and composite numbers using concrete objects, pictorial
models, and patterns in factor pairs.
Supporting Standard
Identify
PRIME AND COMPOSITE NUMBERS USING MODELS AND
PATTERNS
Including, but not limited to:
Representations of prime and composite numbers
Concrete objects
Area model (tile arrangements)
Pictorial models
Factor trees
Tables
Diagrams
Patterns in factor pairs
Lists
Ex: 24: (1, 24), (2, 12), (3, 8), (4, 6)
Differences between prime and composite numbers
including examples and nonexamples
2 is the only even prime number
1 is the only common factor in all of the factor pairs of
prime numbers
Ex: (1, 3), (1, 2), (1, 13), etc.
1 is neither prime nor composite (1 is not prime
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page 6 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
because the factors of 1 are 1 x 1; the factor pairs of a
prime number are whole numbers greater than 1 that
only have themselves and the number 1 as factors)
0 is neither prime nor composite (0 cannot be
expressed as a product of primes; 0 x 0 and/or 0 x any
number yields an infinite number of factors pairs that
have the product of 0 - meaning it is not prime)
Note:
Grade 5 introduces prime and composite numbers.
Grade 5 can use factor trees to distinguish between
prime and composite numbers. However, Grade 6 is
responsible for teaching prime factorization.
5.14
Underlying processes and mathematical tools. The student applies Grade 5
mathematics to solve problems connected to everyday experiences and
activities in and outside of school. The student is expected to:
5.14C
Select or develop an appropriate problem-solving plan or strategy, including drawing a
picture, looking for a pattern, systematic guessing and checking, acting it out, making a
table, working a simpler problem, or working backwards to solve a problem.
Select, Develop
PROBLEM-SOLVING PLAN OR STRATEGY
Including, but not limited to:
Drawing a picture
Looking for a pattern
Systematic guessing and checking
Making a table
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page 7 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Solve
PROBLEM SITUATIONS INVOLVING MATHEMATICS
Including, but not limited to:
Everyday real-life situations
Classroom created activities
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
with content standards.
5.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
Use
TOOLS
Including, but not limited to:
Real objects
Manipulatives
Solve
PROBLEM SITUATIONS INVOLVING MATHEMATICS
Including, but not limited to:
Everyday real-life situations
Classroom created activities
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page 8 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
with content standards.
5.15
Underlying processes and mathematical tools. The student communicates
about Grade 5 mathematics using informal language. The student is expected
to:
5.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
Explain, Record, Communicate
OBSERVATIONS
Including, but not limited to:
Objects
Words
Pictures
Numbers
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
with content standards.
5.15B
Relate informal language to mathematical language and symbols.
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Relate, Communicate
LANGUAGE
Including, but not limited to:
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Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Informal language to mathematical language and
symbols
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
with content standards
5.16
Underlying processes and mathematical tools. The student uses logical
reasoning. The student is expected to:
5.16A
Make generalizations from patterns or sets of examples and
nonexamples.
Make
GENERALIZATIONS
Including, but not limited to:
Patterns
Sets of examples and nonexamples
Use
LOGICAL REASONING
Including, but not limited to:
Justification of thinking
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
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page 10 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
with content standards.
5.16B
Justify why an answer is reasonable and explain the solution process.
Justify
REASONABLENESS OF AN ANSWER
Including, but not limited to:
Objects
Words
Pictures
Numbers
Logical reasoning
Explain
SOLUTION PROCESS
Including, but not limited to:
Verbally
Words
Pictorially
STAAR Note:
The process skills will be incorporated into at least
75% of the test questions and will be identified along
with content standards.
TEKS#
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Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
UNDERLYING PROCESSES AND MATHEMATICAL TOOLS TEKS: USE APPROPRIATE PROCESSES AND TOOLS TO SUPPORT INSTRUCTION.
SE#
5.14
Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
5.14A
identify the mathematics in everyday situations
5.14B
solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for
reasonableness
5.14C
select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
5.14D
use tools such as real objects, manipulatives, and technology to solve problems
5.15
Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language. The
student is expected to:
5.15A
explain and record observations using objects, words, pictures, numbers, and technology
5.15B
relate informal language to mathematical language and symbols
5.16
Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to:
5.16A
make generalizations from patterns or sets of examples and nonexamples
5.16B
justify why an answer is reasonable and explain the solution process
ELPS#
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English
language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement
ELPS as an integral part of each subject in the required curriculum.
School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated commensurate with
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page 12 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
ELPS#
TITLE : Unit 06: Factors and Primes
SUGGESTED DURATION : 7 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.
School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the ELPS in a
manner that is linguistically accommodated to help the student acquire English language proficiency.
http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4
ELPS.c.1
Cross-curricular second language acquisition/learning strategies
ELPS.c.1
The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In
order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction
delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the
student's level of English language proficiency. The student is expected to:
ELPS.c.1A
use prior knowledge and experiences to understand meanings in English
ELPS.c.5
Cross-curricular second language acquisition/writing
ELPS.c.5
The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content
areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In
order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered
in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level
of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student
has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5E
employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such
as:
ELPS.c.5E.i
using correct verbs, tenses, and pronouns/antecedents
ELPS.c.5E.ii
using possessive case (apostrophe s) correctly
ELPS.c.5E.iii
using negatives and contractions correctly
ELPS.c.5G
narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is
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page 13 of 14 INSTRUCTIONAL FOCUS DOCUMENT
Grade 5 Matematicas,Mathematics
UNIT : 06
TITLE : Unit 06: Factors and Primes
ELPS#
SUGGESTED DURATION : 7 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
acquired.
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