INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
UNIT OVERVIEW
This unit bundles student expectations that address composing and decomposing numbers up to 100,000, identifying base-10 relationships through the hundred thousands
place, and comparing and ordering these numbers. According to the Texas Education Agency, mathematical process standards including application, tools and techniques,
communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use
mathematics in everyday life, society, and the workplace.
Prior to this unit, in Grade 2, students used concrete objects and pictorial models to compose and decompose numbers up to 1,200. They represented these numbers using
standard form, word form, expanded form, and comparative language, including symbols.
During this unit, students extend their understanding of the thousands period to include the ten thousands and hundred thousands places. Students compose and decompose
numbers through 100,000 as so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using concrete objects (e.g., proportional
objects such as base-10 blocks, non-proportional objects such as place value disks, etc.), pictorial models (e.g., base-10 representations with place value charts, place value
disk representations with place value charts, open number lines, etc.), and numerical representations (e.g., expanded notation, written notation, standard notation, etc.). While
examining the magnitude of 100,000, students begin to describe the mathematical relationship between the digits in a number, such as the value of each place-value position
is 10 times the position to the right. Students continue to build their understanding of the base-10 place value system using multiples of ten and equivalent compositions and
decompositions of numbers of the same value. Students also compare and order whole numbers up to 100,000 and represent the comparisons using words and symbols.
Ordering three or more numbers may include situations involving quantifying descriptors to specify ordering greatest to least or least to greatest and may involve the location of
the numbers on a number line.
After this unit, in Grade 3, students will further examine the role of 10 in the base-10 place value system when rounding to the nearest 10 or 100 to estimate solutions in
addition and subtraction. In Grade 4, students will further extend their understanding of place value up to 1,000,000,000 as well as incorporate decimal understanding through
the hundredths place. Students will further generalize the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its
left.
In Grade 3, number representations and the comparison of whole numbers are identified as STAAR Readiness Standards 3.2A and 3.2D, and mathematical relationships found
in the base-10 place value system is identified as a STAAR Supporting Standard 3.2B. All of these standards are subsumed under the Grade 3 STAAR Reporting Category
Numerical Representations and Relationships and the Grade 3 Texas Response to Curriculum Focal Points (TxRCFP): Understanding and applying place value and properties
of operations to solve problems involving addition and subtraction of whole numbers within 1,000. This unit is supporting the development of the Texas College and Career
Readiness Standards (TxCCRS): I. Numeric Reasoning and IX. Communication and Representation.
According to Van De Walle (2004), “For children to have good concepts of numbers beyond 1,000, the conceptual ideas that have been carefully developed must be extended.
This is sometimes difficult to do because physical models for thousands are not commonly available. At the same time, number sense ideas must also be developed. In many
ways, it is these informal ideas about very large numbers that are the most important” (p. 195). The National Council of Teachers of Mathematics (2006) recognized the need
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
for relating large numbers to the real world. Van De Walle also suggested, “?Really big’ numbers are best understood in terms of familiar real­world referents. It is difficult to
conceptualize quantities as large as 1,000 or more. However the number of people that will fill the local sports arenas is, for example, a meaningful concept for those who have
experienced that crowd” (p. 178).
National Council of Teachers of Mathematics. (2006). Focus in grade 2: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from
http://www.thecb.state.tx.us/collegereadiness/crs.pdf
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from
http://projectsharetexas.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson Education, Inc.
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
Numeric Reasoning
A number can vary in representation as long as the total value of each
representation remains unchanged (whole numbers up to 100,000).
Mathematics Grade 3 Unit 01 PA 01
Analyze the situation(s) described below. Organize
and record your work for each of the following tasks.
Using precise mathematical language, justify and
explain each mathematical process.
1) Parkville Bank was counting their reserve money in
the vault. The bank’s president and chief executive
officer individually counted the money and agreed the
balance was $97,685.
a) Both the bank president and chief executive
officer used expanded notation to represent the
balance. However, their expanded
representations were different. What are two
Base-10 Place Value System
Comparison
Comparison Symbols
Multiple Representations
Numerical Patterns
Order
Standard/Expanded/Written
Notation
Whole Numbers
Algebraic Reasoning
Composition/ Decomposition of
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UNIT UNDERSTANDINGS
What are some ways a number can be represented?
Why can a number vary in representation but the value of the
number stay the same? (e.g., Why do 94 one thousands, 6
hundreds, 32 ones represent the same value as 9 ten
thousands, 4 one thousands, 6 hundreds, 3 tens, 2 ones?)
Numbers can be composed or decomposed in multiple ways to
represent part-whole relationships (whole numbers up to 100,000).
What part-whole relationship exists when a number is
composed or decomposed? (e.g., What relationship can be
described when 94,632 is broken into so many ten thousands,
page 2 of 29 INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
PERFORMANCE ASSESSMENT(S)
possible representations that the president and
the chief executive officer could have used to
record the balance $97,685? In words, describe
why it is possible for their recordings to be
different but the total value to be the same.
b) If Rosewood Bank keeps $98,324 in their vault
and Whisper Hills Bank keeps $98,762 in their
vault, list the three banks by name from greatest
to least amount of money in their vault.
c) Describe, using words and symbols, the
amount of money in the vault at Parkville Bank
compared to the amount of money in the vault at
Rosewood Bank.
Standard(s): 3.1A , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G ,
3.2A , 3.2B , 3.2D ELPS.c.1C , ELPS.c.2D ,
ELPS.c.3B , ELPS.c.3D , ELPS.c.3H , ELPS.c.4H ,
ELPS.c.5E
SUGGESTED DURATION : 6 days
OVERARCHING CONCEPTS
UNIT CONCEPTS
Numbers
Equivalence
Associated Mathematical Processes
Application
Communication
Justification
Relationships
Representations
Tools and Techniques
UNIT UNDERSTANDINGS
so many one thousands, so many hundreds, so many tens,
and so many ones? What relationship can be described when
9 ten thousands, 4 one thousands, 6 hundreds, 3 tens, 2 ones
is composed to form a number?)
A quantity in context is represented by a numeric value and a defining
label (whole numbers up to 100,000).
How can the same number with different labels represent a
small quantity in one context and a large quantity in another
context? (e.g., Why is the number 94,632 small when referring
to pennies but large when referring to dollars?)
The base-10 place value system is based on the relationship where
each place represents a specific multiple of 10 (whole numbers up to
100,000).
What digits make up the base-10 place value system?
What relationships can be found in the base-10 place value
system?
How does the place value change when moving to the left
across the place value positions in a number? (e.g., How does
the place value change when moving from the one thousands
place to the ten thousands place to the hundred thousands
place?)
A digit’s position within a number determines its value (whole numbers
up to 100,000).
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page 3 of 29 INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
PERFORMANCE ASSESSMENT(S)
SUGGESTED DURATION : 6 days
OVERARCHING CONCEPTS
UNIT CONCEPTS
UNIT UNDERSTANDINGS
How is the value of a digit within a number determined? (e.g.,
How is the value of the digit “4” determined in the number
94,632?)
How is the value of a number determined using the position of
the digits? (e.g., How is the value of 94,632 determined?)
When comparing two numbers, the relationship between the numbers
can be that of equality, meaning the two numbers are equal, or
inequality, meaning one number is greater than or less than the other
number (whole numbers up to 100,000).
How is place value used to compare two numbers? (e.g., How
is place value used to compare 94,632 and 49,623?)
How can the comparison of two numbers be described and
represented? (e.g., How can the comparison of 94,632 and
49,623 be described and represented?)
Numbers can be ordered based on their numerical value (whole
numbers up to 100,000).
How is place value used to order a set of numbers? (e.g., How
is place value used to order 94,632; 63,946; and 49,623?)
How are quantifying descriptors used to determine the order of
a set of numbers? (e.g., How do the quantifying descriptors
least to greatest or greatest to least determine the order of the
numbers 94,632; 63,946; and 49,623?)
How can the order of a set of numbers be justified? (e.g., How
can the order of the numbers 94,632; 63,946; and 49,623 be
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page 4 of 29 INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
PERFORMANCE ASSESSMENT(S)
SUGGESTED DURATION : 6 days
OVERARCHING CONCEPTS
UNIT CONCEPTS
UNIT UNDERSTANDINGS
justified?)
MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS
Misconceptions:
Some students may think if two numbers are composed of the same digits, they have the same value even if the digits’ place value locations within the two numbers are
different.
Some students may think if the same digit is in the tens place of the units period and is in the tens place of the thousands period, the value of the digit is the same, not
realizing that the value of each place increases by multiples of ten.
Some students may think a number can only be decomposed one way, when the number can actually be decomposed multiple ways.
Some students may think the total value of a number changes when the number is represented using different decompositions, not realizing that the sum of the addends
in each decomposition remains the same.
Some students may think, when comparing numbers, a number value is only dependent on the largest digit regardless of the place value location within the number (e.g.,
when comparing 13,769 and 24,053, the student may think 13,769 is larger because the digit 6, 7, and/or 9 are/is larger than any of the digits in the number 24,053).
When ordering numbers, some students may incorrectly select the largest number based on the first digit of each number rather than considering the place value location
of the first digit (e.g., 9,632 is smaller than 13,498 even though the digit 9 is larger than the digit 1).
UNIT VOCABULARY
Key Content Vocabulary:
Compose numbers – to combine parts or smaller values to form a number
Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value
Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
Decompose numbers – to break a number into parts or smaller values
Digit – any numeral from 0 – 9
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
Expanded notation – the representation of a number using place value to show the value of each digit (e.g., 56,789 as 50,000 + 6,000 + 700 + 80 + 9 or (5 x 10,000) +
(6 x 1,000) + (7 x 100) + (8 x 10) + 9)
Numeral – a symbol used to name a number
Open number line – an empty number line where tick marks are added to represent landmarks of numbers, often indicated with arcs above the number line (referred to
as jumps) demonstrating approximate proportional distances
Order numbers – to arrange a set of numbers based on their numerical value
Period – a three­digit grouping of whole numbers where each grouping is composed of a ones place, a tens place, and a hundreds place, and each grouping is separated
by a comma
Place value – the value of a digit as determined by its location in a number, such as ones, tens, hundreds, one thousands, ten thousands, etc.
Standard notation – the representation of a number using digits (e.g., 56,789)
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Written notation – the representation of a number using written words (e.g., 56,789 as fifty­six thousand, seven hundred eighty­nine)
Related Vocabulary:
Ascending
Hundred thousands place
Position
Base-10 place value system
Hundreds place
Same as
Comparative language
Largest
Smallest
Descending
Less than (<)
Ten thousands place
Equal to (=)
Magnitude (relative size)
Tens place
Equivalent representations
Ones place
Thousands period
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
Greater than (>)
SUGGESTED DURATION : 6 days
One thousands place
UNIT ASSESSMENT ITEMS
Mathematics Grade 3 Unit 01: Foundations of
Number 2014-2015
Units period
SYSTEM RESOURCES
OTHER RESOURCES
Mathematics Grade 3 Implementation TAG Tool
Texas Education Agency:
Texas Education Agency - Revised Mathematics
TEKS: Side-by-Side TEKS Comparison
Project Share Gateway at
www.projectsharetexas.org (click on the
Resource Index; search for Side by Side)
Texas Education Agency - Revised Mathematics
TEKS: Vertical Alignment Charts
Project Share Gateway at
www.projectsharetexas.org (click on the
Resource Index; search for Vertical Alignment)
Texas Higher Education Coordinating Board and
Texas Education Agency:
Texas College and Career Readiness Standards
(beginning on page 59 or a11)
TEKS#
SE#
3.1
TEKS
UNIT LEVEL SPECIFICITY
Mathematical process standards. The student uses
mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
3.1A
TEKS
Apply mathematics to problems arising in
everyday life, society, and the workplace.
UNIT LEVEL SPECIFICITY
Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Note(s):
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
X. Connections
3.1C
Select tools, including real objects,
manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental
math, estimation, and number sense as
appropriate, to solve problems.
Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND
TECHNOLOGY AS APPROPRIATE, TO SOLVE PROBLEMS
Select
TECHNIQUES, INCLUDING MENTAL MATH, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE
PROBLEMS
Note(s):
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page 8 of 29 INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
VIII. Problem Solving and Reasoning
3.1D
Communicate mathematical ideas, reasoning,
and their implications using multiple
representations, including symbols, diagrams,
graphs, and language as appropriate.
Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE
REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE
Note(s):
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
IX. Communication and Representation
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
3.1E
TEKS
Create and use representations to organize,
record, and communicate mathematical ideas.
UNIT LEVEL SPECIFICITY
Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Note(s):
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
IX. Communication and Representation
3.1F
Analyze mathematical relationships to connect
and communicate mathematical ideas.
Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Note(s):
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
X. Connections
3.1G
Display, explain, and justify mathematical ideas
and arguments using precise mathematical
language in written or oral communication.
Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN
WRITTEN OR ORAL COMMUNICATION
Note(s):
The mathematical process standards may be applied to all content standards as appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
Solving problems with multiplication and division within 100
Understanding fractions as numbers and representing equivalent fractions
Describing characteristics of two-dimensional and three-dimensional geometric figures,
including measurable attributes
TxCCRS:
IX. Communication and Representation
3.2
Number and operations. The student applies
mathematical process standards to represent and
compare whole numbers and understand
relationships related to place value. The student is
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
TEKS
SE#
UNIT LEVEL SPECIFICITY
expected to:
3.2A
Compose and decompose numbers up to 100,000
as a sum of so many ten thousands, so many
thousands, so many hundreds, so many tens, and
so many ones using objects, pictorial models, and
numbers, including expanded notation as
appropriate.
Readiness Standard
Compose, Decompose
NUMBERS UP TO 100,000 AS A SUM OF SO MANY TEN THOUSANDS, SO MANY THOUSANDS,
SO MANY HUNDREDS, SO MANY TENS, AND SO MANY ONES USING OBJECTS, PICTORIAL
MODELS, AND NUMBERS, INCLUDING EXPANDED NOTATION AS APPROPRIATE
Including, but not limited to:
Whole numbers (0 – 100,000)
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Numeral – a symbol used to name a number
Digit – any numeral from 0 – 9
Place value – the value of a digit as determined by its location in a number such as ones, tens,
hundreds, one thousands, ten thousands, etc.
Hundred thousands place
Ten thousands place
One thousands place
Hundreds place
Tens place
Ones place
Base-10 place value system
A number system using ten digits 0 – 9
Relationships between places are based on multiples of 10.
Moving left across the places, the values 10 times the position to the right.
The magnitude (relative size) of one hundred thousand
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Compose numbers – to combine parts or smaller values to form a number
Decompose numbers – to break a number into parts or smaller values
Objects
Proportional models – a visual representation that demonstrates the relative size of each
place value using models with proportional dimensions, meaning the model of each
place value is exactly 10 times larger than the place value model to the right (e.g., the
base-10 long is exactly 10 times as big as the unit showing that one 10 is equal to ten
ones)
Base-10 blocks for values up to 9,999 (proportional representation of the
magnitude of a number with a 1-to-10 relationship)
Non­proportional models – a visual representation that does not maintain the proportional
relationship of size, meaning the size of each place value model is not 10 times larger
than the place value model to the right (e.g., the value of each place value disk is
indicated by the numerical label and color but does not change in size)
Base-10 blocks for values over 9,999 (repetition of ones, tens, hundreds in each
period)
Place value disks (non-proportional representation with a 1-to-10 relationship)
Pictorial models
Base-10 block representations for values up to 9,999 (ones, tens, hundreds, one
thousands)
Base-10 block representations for values over 9,999 (repetition of ones, tens, hundreds
in each period)
Place value disk representations
Open number line – an empty number line where tick marks are added to represent
landmarks of numbers, often indicated with arcs above the number line (referred to as
jumps) demonstrating approximate proportional distances
Multiple concrete and pictorial representations
Compositions and decompositions as a sum of so many ten thousands, so many
thousands, so many hundreds, so many tens, and so many ones
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Expanded notation – the representation of a number using place value to show the value of
each digit (e.g., 56,789 as 50,000 + 6,000 + 700 + 80 + 9 or (5 x 10,000) + (6 x 1,000) + (7 x
100) + (8 x 10) + 9)
Zero may or may not be written as an addend to represent the digit 0 in a number (e.g.,
98,075 as 90,000 + 8,000 + 0 + 70 + 5 or 90,000 + 8,000 + 70 + 5).
Standard notation – the representation of a number using digits (e.g., 56,789)
Period – a three­digit grouping of whole numbers where each grouping is composed of a
ones place, a tens place, and a hundreds place, and each grouping is separated by a
comma
Thousands period is composed of the one thousands place, ten thousands place,
and hundred thousands place.
Units period is composed of the ones place, tens place, and hundreds place.
The word “thousand” after the numerical value of the thousands period is stated when
read.
A comma between the thousands period and the units period is recorded when written
but not stated when read.
The word “unit” after the numerical value of the units period is not stated when read.
The word “hundred” in each period is stated when read.
The words “ten” and “one” in each period are not stated when read.
The tens place digit and ones place digit in each period are stated as a two-digit number
when read.
Zeros are used as place holders between digits as needed to maintain the value of each
digit (e.g., 91,075).
Leading zeros in a whole number are not commonly used in standard form, but are not
incorrect and do not change the value of the number (e.g., 037, 564 equals 37,564).
Written notation – the representation of a number using written words (e.g., 56,789 as fifty­six
thousand, seven hundred eighty-nine)
The word “thousand” after the numerical value of the thousands period is stated when
read and recorded when written.
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Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
A comma between the thousands period and the units period is not stated when read
but is recorded when written.
The word “unit” after the numerical value of the units period is not stated when read and
not recorded when written.
The word “hundred” in each period is stated when read and recorded when written.
The words “ten” and “one” in each period are not stated when read and not recorded
when written.
The tens place digit and ones place digit in each period are stated as a two-digit number
when read and recorded using a hyphen, where appropriate, when written (e.g., twentythree, thirteen, etc.).
The zeros in a whole number are not stated when read and are not recorded when
written (e.g., 91,005 in standard notation is read and written as ninety-one thousand, five
in written notation).
Multiple numerical representations
Standard notation to expanded notation in numerals and expanded notation in numerals
to standard notation
Standard notation to expanded notation in words and numerals and expanded notation in
words and numerals to standard notation
Standard notation to written notation and written notation to standard notation
Expanded notation in numerals to expanded notation in words and numerals and
expanded notation in words and numerals to expanded notation in numerals
Expanded notation numerals to written notation and written notation to expanded
notation in numerals
Expanded notation in words and numerals to written notation and written notation to
expanded notation in words and numerals
Expanded notation in numerals given out of place value order to standard notation or
written notation
Expanded notation in words and numerals given out of place value order to standard
notation or written notation
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
TEKS
SE#
UNIT LEVEL SPECIFICITY
Equivalent compositions of numbers with the same value
Equivalent decompositions of numbers with the same value
Note(s):
Grade Level(s):
Grade 2 used concrete and pictorial models to compose and decompose numbers up to
1,200 in more than one way as a sum of so many one thousands, hundreds, tens, and
ones.
Grade 2 used standard, word, and expanded forms to represent numbers up to 1,200.
Grade 4 will represent the value of the digit in whole numbers through 1,000,000,000 and
decimals to the hundredths using expanded notation and numerals.
Grades 1 and 2 student expectations refer to expanded, standard, and word form,
whereas Grades 3, 4, and 5 student expectations refer to expanded notation.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
TxCCRS:
I. Numeric Reasoning
IX. Communication and Representation
3.2B
Describe the mathematical relationships found in
the base-10 place value system through the
hundred thousands place.
Supporting Standard
Describe
THE MATHEMATICAL RELATIONSHIPS FOUND IN THE BASE-10 PLACE VALUE SYSTEM
THROUGH THE HUNDRED THOUSANDS PLACE
Including, but not limited to:
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Place value – the value of a digit as determined by its location in a number, such as ones, tens,
hundreds, one thousands, ten thousands, etc.
Hundred thousands place
Ten thousands place
One thousands place
Hundreds place
Tens place
Ones place
Base-10 place value system
A number system using ten digits 0 – 9
Relationships between places are based on multiples of 10.
Moving left across the places, the values are 10 times the position to the right.
Note(s):
Grade Level(s):
Grade 4 will interpret the value of each place-value position as 10 times the position to
the right and as one-tenth of the value of the place to its left.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
TxCCRS:
I. Numeric Reasoning
IX. Communication and Representation
3.2C
Represent a number on a number line as being
between two consecutive multiples of 10; 100;
Represent
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
TEKS
SE#
1,000; or 10,000 and use words to describe relative
size of numbers in order to round whole numbers.
Supporting Standard
UNIT LEVEL SPECIFICITY
A NUMBER ON A NUMBER LINE AS BEING BETWEEN TWO CONSECUTIVE MULTIPLES OF 10;
100; 1,000; OR 10,000
Including, but not limited to:
Whole numbers (0 – 100,000)
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Characteristics of a number line
A number line begins as a line with predetermined intervals (or tick marks) with
positions/numbers labeled.
A minimum of two positions/numbers should be labeled.
Numbers on a number line represent the distance from zero.
The distance between the tick marks is counted rather than the tick marks themselves.
The placement of the labeled positions/numbers on a number line determines the scale
of the number line.
Intervals between position/numbers are proportional.
When reasoning on a number line, the position of zero may or may not be placed.
When working with larger numbers, a number line without the constraint of distance from
zero allows the ability to “zoom­in” on the relevant section of the number line.
Number lines extend infinitely in both directions (arrows indicate the number line
continues infinitely).
Numbers increase from left to right on a horizontal number line and from bottom to top
on a vertical number line.
Points to the left of a specified point on a horizontal number line are less than
points to the right.
Points to the right of a specified point on a horizontal number line are greater than
points to the left.
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Points below a specified point on a vertical number line are less than points
above.
Points above a specified point on a vertical number line are greater than points
below.
Characteristics of an open number line
An open number line begins as a line with no intervals (or tick marks) and no
positions/numbers labeled.
Numbers/positions are placed on the empty number line only as they are needed.
When reasoning on an open number line, the position of zero is often not placed.
When working with larger numbers, an open number line without the constraint of
distance from zero allows the ability to “zoom­in” on the relevant section of the number
line.
The placement of the first two numbers on an open number line determines the scale of
the number line.
Once the scale of the number line has been established by the placement of the
first two numbers, intervals between additional numbers placed are approximately
proportional.
The differences between numbers are approximated by the distance between the
positions on the number line.
Open number lines extend infinitely in both directions (arrows indicate the number line
continues infinitely).
Numbers increase from left to right on a horizontal number line and from bottom to top
on a vertical number line.
Points to the left of a specified point on a horizontal number line are less than
points to the right.
Points to the right of a specified point on a horizontal number line are greater than
points to the left.
Points below a specified point on a vertical number line are less than points
above.
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Points above a specified point on a vertical number line are greater than points
below.
Landmark (or anchor) numbers may be placed on the open number line to help locate
other numbers.
Consecutive – a pattern or sequence of numbers in order without interruption
Number lines representing multiples of 10
Number lines representing multiples of 100
Number lines representing multiples of 1,000
Number lines representing multiples of 10,000
Numbers between two consecutive multiples of 10 on a number line
Begin with the original tens place value within the number and then consider the next
highest value in the tens place to determine the next consecutive multiple of 10.
Numbers between two consecutive multiples of 100 on a number line
Begin with the original hundreds place value within the number and then consider the
next highest value in the hundreds place to determine the next consecutive multiple of
100.
Numbers between two consecutive multiples of 1,000 on a number line
Begin with the original thousands place value within the number and then consider the
next highest value in the thousands place to determine the next consecutive multiple of
1,000.
Numbers between two consecutive multiples of 10,000 on a number line
Begin with the original ten thousands place value within the number and then consider
the next highest value in the ten thousands place to determine the next consecutive
multiple of 10,000.
Numbers between two consecutive multiples of 10 on an open number line
Begin with the original tens place value within the number and then consider the next
highest value in the tens place to determine the next consecutive multiple of 10.
Numbers between two consecutive multiples of 100 on an open number line
Begin with the original hundreds place value within the number and then consider the
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
TEKS
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UNIT LEVEL SPECIFICITY
next highest value in the hundreds place to determine the next consecutive multiple of
100.
Numbers between two consecutive multiples of 1,000 on an open number line
Begin with the original thousands place value within the number and then consider the
next highest value in the thousands place to determine the next consecutive multiple of
1,000.
Numbers between two consecutive multiples of 10,000 on an open number line
Begin with the original ten thousands place value within the number and then consider
the next highest value in the ten thousands place to determine the next consecutive
multiple of 10,000.
3.2D
Compare and order whole numbers up to 100,000
and represent comparisons using the symbols >,
<, or =.
Readiness Standard
Compare, Order
WHOLE NUMBERS UP TO 100,000
Including, but not limited to:
Whole numbers (0 – 100,000)
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Place value – the value of a digit as determined by its location in a number such as ones, tens,
hundreds, one thousands, ten thousands, etc.
Compare numbers – to consider the value of two numbers to determine which number is greater
or less or if the numbers are equal in value
Relative magnitude of a number describes the size of a number and its relationship to
another number.
Compare two numbers using place value charts.
Compare digits in the same place value position beginning with the greatest place
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
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TEKS#
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TEKS
UNIT LEVEL SPECIFICITY
value.
If these digits are the same, continue to the next smallest place until the
digits are different.
Numbers that have common digits but are not equal in value
(different place values)
Numbers that have a different number of digits
Compare two numbers using a number line.
Number lines (horizontal/vertical)
Proportionally scaled number lines (pre-determined intervals with at least
two labeled numbers)
Open number lines (no marked intervals)
Order numbers – to arrange a set of numbers based on their numerical value
Numbers increase from left to right on a horizontal number line and from bottom to top
on a vertical number line.
Points to the left of a specified point on a horizontal number line are less than
points to the right.
Points to the right of a specified point on a horizontal number line are greater than
points to the left.
Points below a specified point on a vertical number line are less than points
above.
Points above a specified point on a vertical number line are greater than points
below.
Order a set of numbers on a number line.
Order a set of numbers on an open number line.
Quantifying descriptors (e.g., between two given numbers, greatest/least,
ascending/descending, tallest/shortest, warmest/coldest, fastest/slowest,
longest/shortest, heaviest/lightest, closest/farthest, oldest/youngest, etc.)
Represent
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page 22 of 29 INSTRUCTIONAL FOCUS DOCUMENT
Grade 3 Mathematics
TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
COMPARISONS OF WHOLE NUMBERS UP TO 100,000 USING THE SYMBOLS >, <, OR =
Including, but not limited to:
Whole numbers (0 – 100,000)
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Comparative language and symbols
Inequality words and symbols
Greater than (>)
Less than (<)
Equality words and symbol
Equal to (=)
Note(s):
Grade Level(s):
Grade 1 represented the comparison of two numbers to 100 using the symbols >, <, or
=.
Grade 2 used place value to compare and order whole numbers up to 1,200 using
comparative language, numbers and the symbols >, <, or =.
Grade 4 will compare and order whole numbers to 1,000,000,000 and represent
comparisons using the symbols >, <, or =.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxRCFP:
Understanding and applying place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000
TxCCRS:
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page 23 of 29 INSTRUCTIONAL FOCUS DOCUMENT
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
I. Numeric Reasoning
IX. Communication and Representation
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 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
Choose appropriate ELPS to support instruction.
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.1B
monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C
use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and
grade-level vocabulary
ELPS.c.1D
speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
ELPS#
SUGGESTED DURATION : 6 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
ideas by defining or describing when exact English words are not known)
ELPS.c.1E
internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept
and language attainment
ELPS.c.1F
use accessible language and learn new and essential language in the process
ELPS.c.1G
demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one
commensurate with grade-level learning expectations
ELPS.c.1H
develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and
analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2
The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly
acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language
acquisition in listening. 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.2A
distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B
recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant
clusters
ELPS.c.2C
learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D
monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E
use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F
listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language
attainment
ELPS.c.2G
understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and
contexts are familiar to unfamiliar
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
ELPS#
SUGGESTED DURATION : 6 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
ELPS.c.2H
understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I
demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken
messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3
The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary
with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced
high stage of English language acquisition in speaking. 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.3A
practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce
English words in a manner that is increasingly comprehensible
ELPS.c.3B
expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing
people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using
routine language needed for classroom communication
ELPS.c.3C
speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as
more English is acquired
ELPS.c.3D
speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E
share information in cooperative learning interactions
ELPS.c.3F
ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and
expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended
speaking assignments
ELPS.c.3G
express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a
variety of social and grade-appropriate academic topics
ELPS.c.3H
narrate, describe, and explain with increasing specificity and detail as more English is acquired
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
ELPS#
SUGGESTED DURATION : 6 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
ELPS.c.3I
adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J
respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and
language attainment.
ELPS.c.4
The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the
beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. 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. For Kindergarten and Grade 1,
certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A
learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as
recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B
recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C
develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used
routinely in written classroom materials
ELPS.c.4D
use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to
enhance comprehension of written text
ELPS.c.4E
read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F
use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm
understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly
challenging language
ELPS.c.4G
demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding
to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H
read silently with increasing ease and comprehension for longer periods
ELPS.c.4I
demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of
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ELPS#
SUGGESTED DURATION : 6 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with
content area needs
ELPS.c.4J
demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between
ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content
area needs
ELPS.c.4K
demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and
performing critical analyses commensurate with content area and grade-level needs.
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 gradelevel 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.5A
learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B
write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C
spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English
is acquired
ELPS.c.5D
edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses
commensurate with grade-level expectations as more English is acquired
ELPS.c.5E
employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F
write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in
increasingly accurate ways as more English is acquired
ELPS.c.5G
narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
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TITLE : Unit 01: Foundations of Number - ABILENE ISD
SUGGESTED DURATION : 6 days
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