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Instructional Focus Document
Grade 4 Mathematics
TITLE : Unit 10: Geometry – Measuring Angles SUGGESTED DURATION : 11 days

Unit Overview

Introduction
This unit bundles student expectations that address skills necessary to solve problems involving angles less than or equal to 180 degrees, including drawing and measuring angles with a protractor. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, 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 Unit 09, students identified points, lines, line segments, rays, angles, and perpendicular and parallel lines. They identified angles by type such as right, acute, obtuse, and straight and used that knowledge to identify acute, right, and obtuse triangles. Students explored various methods for labeling angles using symbols and letters and examined the attributes and properties of angles.

During this Unit
Students illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. They also illustrate degrees as the units used to measure an angle, where 1 over 360.png of any circle is one degree and an angle that "cuts" N over 360.png out of any circle whose center is at the angle's vertex has a measure of n degrees. Using a protractor, students determine the approximate measures of angles in degrees to the nearest whole number and draw angles of a specified measure. Given one or both angle measures, students determine the measure of an unknown angle formed by two non-overlapping adjacent angles. The concepts of complementary and supplementary angles are embedded within the study of adjacent angles. Within this unit, all angle measures are limited to whole numbers.

After this Unit
In Grade 6, students will extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle. Students will also model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts.

Additional Notes
In Grade 4, using a protractor to determine the approximate measures of angles in degrees to the nearest whole number is identified as STAAR Readiness Standard 4.7C. Drawing an angle with a given measure, and determining the measure of an unknown angle formed by two non-overlapping adjacent angles, given one or both angle measures are addressed by STAAR Supporting Standards 4.7D and 4.7E. These standards are all included in STAAR Reporting Category 3: Geometry and Measurement. Illustrating the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle, as well as illustrating degrees as the units used to measure an angle, where 1 over 360.png of any circle is one degree and an angle that "cuts" N over 360.png out of any circle whose center is at the angle's vertex has a measure of n degrees are skills that are identified as 4.7A and 4.7B. These two standards are neither Supporting nor Readiness, but are foundational to the conceptual understanding of angles and angle measures. All of the standards within this unit are subsumed under the Grade 4 Texas Response to Curriculum Focal Points (TxRCFP): Measuring angles. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): III.A. Geometric Reasoning – Figures and their properties, IV.A. Measurement Reasoning – Measurement involving physical and natural attributes, VIII. Problem Solving and Reasoning, and IX. Communication and Representation.

Research
According to the National Council of Teachers of Mathematics (2005), “Whatever the context, measurement is indispensable to the study of number, geometry, statistics, and other branches of mathematics. It is the essential link between mathematics and science, art, social studies, and other disciplines, and it is pervasive in daily activities, from buying bananas or new carpet to charting heights of growing children…” (p. 1). Chapin and Johnson (2000), assert that “understanding the concept of angle is a prerequisite for understanding some of the properties of polygons. Students often consider angle measurement to be a static rather than a dynamic one: they think that angle size is fixed and is determined by the length of the rays rather than by the size of the turn. One way to help students better understand the dynamic nature of angle measurement is to have them use a protractor to construct various angles and then compare them” (p. 151).

 

Chapin, S & Johnson, A. (2000). Math matters: Understanding the math you teach. Sausalito, CA: Math Solutions Publications.
National Council of Teachers of Mathematics. (2005). Navigating through measurement in grades 6 – 8. 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/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013


  • Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life.
    • Why is developing geometric, spatial, and measurement reasoning essential?
    • How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Illustrating and analyzing geometric relationships in models and diagrams aid in representing the attributes of geometric figures with quantifiable measures in order to generalize geometric relationships and solve problem situations.
    • In what situations might someone need to measure angles?
    • What relationships exist between …
      • angle measures, 360 degrees, and circles?
      • the number of degrees used to describe the size of an angle and the spread of the rays that form the angle?
      • a protractor and a circle?
    • How can illustrations and/or symbols aid in …
      • measuring angles?
      • solving problems involving angles?
    • What strategies and tools can be used to …
      • measure angles?
      • draw an angle of a given measure?
    • How are angle measures described orally and symbolically?
    • How can angle classifications be used to determine the reasonableness of an angle measurement?
    • What strategies can be used to determine the measure of an unknown angle formed by two non-overlapping adjacent angles given …
      • the measures of both adjacent angles?
      • the measures of one angle and the whole?
      • the measure of the whole when the adjacent angles are congruent?
    • How can understanding …
      • adjacent angles
      • complementary angles
      • supplementary angles
      • congruent angles
      … aid in solving problems involving angles?
  • Geometry
    • Composition and Decomposition of Angles
    • Geometric Representations
      • Two-dimensional figures
  • Measurement
    • Geometric Relationships
      • Angles
    • Measureable Attributes
      • Angles
    • Measure
      • Measurement tools
      • Units of measure
  • Associated Mathematical Processes
    • Application
    • Problem Solving Model
    • Tools and Techniques
    • Communication
    • Representations
    • Relationships
    • Justification
Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may think that the angle size is determined by the length of the rays rather than by the size of the turn.
  • Some students may think that the orientation of the angle on a drawing will affect the measurement of the angle.
  • Some students may not have made the connection between estimating the size of an angle before measuring and the appropriate scale on the protractor.
  • Some students may think that degree measure for angles is read from only one side of a protractor (e.g., An angle with a measure of 30° may be at the markings of 30° and 150° on the protractor).
  • Some students may think that when measuring with a protractor, one of the two rays must always align with zero rather than recognizing that an accurate measure is dependent upon the difference in the beginning and ending measure (e.g., An angle with a measure of 30° can be determined by beginning at 0° and ending at 30° or by finding the difference between other ending and starting points, such as 180° – 150°, 100° – 70°, etc.).

Unit Vocabulary

  • Acute angle – an angle that measures less than 90°
  • Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
  • Angle – two rays with a common endpoint (the vertex)
  • Angle congruency marks – angle marks indicating angles of the same measure
  • Center of the circle – the point equidistant from all points on the circle
  • Complementary angles – two angles whose degree measures have a sum of 90°
  • Congruent angles – angles whose angle measurements are equal
  • Degree – the measure of an angle where each degree represents 1 over 360.png of a circle
  • Obtuse angle – an angle that measures greater than 90° but less than 180°
  • Protractor – a tool used to determine the measure of an angle
  • Ray – part of a line that begins at one endpoint and continues without end in one direction
  • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
  • Straight angle – an angle that measures 180° (a straight line)
  • Supplementary angles – two angles whose degree measures have a sum of 180°

Related Vocabulary:

  • Approximate
  • Circle
  • Congruent
  • Cut out
  • Interval
  • Parallel
  • Perpendicular
  • Rotation
  • Semi-circle
  • Turn
  • Unit
  • Vertex
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Creator if your district has granted access to that tool.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

 

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

 

Texas Education Agency – Mathematics Curriculum

 

Texas Education Agency – STAAR Mathematics Resources

 

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

 

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

 

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

 

Texas Education Agency Texas Gateway – Resources Aligned to Grade 4 Mathematics TEKS


TEKS# SE# Unit Level Taught Directly TEKS Unit Level Specificity
 

Legend:

  • Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
  • Student Expectations (TEKS) identified by TEA are in bolded, black text.
  • Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
  • Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Legend:

  • Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
  • Unit-specific clarifications are in italicized, blue text.
  • Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
  • A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
4.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

  • Mathematical problem situations within and between disciplines
    • Everyday life
    • Society
    • Workplace

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Process Standard

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

  • Problem-solving model
    • Analyze given information
    • Formulate a plan or strategy
    • Determine a solution
    • Justify the solution
    • Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1C 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.
Process Standard

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

Including, but not limited to:

  • Appropriate selection of tool(s) and techniques to apply in order to solve problems
    • Tools
      • Real objects
      • Manipulatives
      • Paper and pencil
      • Technology
    • Techniques
      • Mental math
      • Estimation
      • Number sense

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.


Process Standard

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

  • Mathematical ideas, reasoning, and their implications
    • Multiple representations, as appropriate
      • Symbols
      • Diagrams
      • Language

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Representations of mathematical ideas
    • Organize
    • Record
    • Communicate
  • Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
  • Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Mathematical relationships
    • Connect and communicate mathematical ideas
      • Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
      • Current knowledge to new learning

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

  • Mathematical ideas and arguments
    • Validation of conclusions
      • Displays to make work visible to others
        • Diagrams, visual aids, written work, etc.
      • Explanations and justifications
        • Precise mathematical language in written or oral communication

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.7 Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:
4.7A Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers.

Illustrate

THE MEASURE OF AN ANGLE AS THE PART OF A CIRCLE WHOSE CENTER IS AT THE VERTEX OF THE ANGLE THAT IS "CUT OUT" BY THE RAYS OF THE ANGLE. ANGLE MEASURES ARE LIMITED TO WHOLE NUMBERS.

Including, but not limited to:

  • Ray – part of a line that begins at one endpoint and continues without end in one direction
  • Degree – the measure of an angle where each degree represents of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
  • Angle – two rays with a common endpoint (the vertex)
    • Various angle types/names
      • Right angle, 90°, used as a benchmark to identify and nae angels
        • Acute angle – an angle that measures less than 90°
        • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
          • Notation is given as a box in the angle corner to represent a 90° angle.
        • Obtuse angle – an angle that measures greater than 90° but less than 180°
        • Straight angle – an angle that measures 180° (a straight line)
    • Angle measures limited to whole numbers, 0° to 180°
  • Center of the circle – the point equidistant from all points on the circle
  • Circle
    • A figure formed by a closed curve with all points equal distance from the center
    • No straight sides
    • No vertices
    • No parallel or perpendicular sides
    • A circle measures 360° for one full rotation around the center of the circle.
  • Representation of an angle measure as a “turn” around the center point of a circle “cut out” by the rays of the angle where the vertex of the angle is aligned to the center of the circle.

Note(s):

  • Grade Level(s):
    • Grade 4 introduces illustrating the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers.
    • Foundational for work with central angles in Geometry and radian measures in Precalculus.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • IX. Communication and Representation
4.7B Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers.

Illustrate

DEGREES AS THE UNITS USED TO MEASURE AN ANGLE, WHERE OF ANY CIRCLE IS ONE DEGREE AND AN ANGLE THAT "CUTS" OUT OF ANY CIRCLE WHOSE CENTER IS AT THE ANGLE'S VERTEX HAS A MEASURE OF n DEGREES. ANGLE MEASURES ARE LIMITED TO WHOLE NUMBERS

Including, but not limited to:

  • Degree – the measure of an angle where each degree represents of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
    • Angle measures limited to whole numbers, 0° to 360°
  • Angle – two rays with a common endpoint (the vertex)
  • Center of the circle – the point equidistant from all points on the circle
  • Circle
    • A figure formed by a closed curve with all points equal distance from the center
    • No straight sides
    • No vertices
    • No parallel or perpendicular sides
    • A circle measures 360° for one full rotation around the center of the circle.
  • Representations of the “cuts”  out of a circle as degrees of angle measures

Note(s):

  • Grade Level(s):
    • Grade 4 introduces illustrating degrees as the units used to measure an angle, where of any circle is one degree and an angle that "cuts" out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers.
    • Leads to the development of radian measures in Precalculus.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
4.7C Determine the approximate measures of angles in degrees to the nearest whole number using a protractor.
Readiness Standard

Determine

THE APPROXIMATE MEASURES OF ANGLES IN DEGREES TO THE NEAREST WHOLE NUMBER USING A PROTRACTOR

Including, but not limited to:

  • Degree – the measure of an angle where each degree represents of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
    • Angle measures limited to whole numbers, 0° to 180°
  • Various angle types/names
    • Right angle, 90°, used as a benchmark to identify and name angles
      • Acute angle – an angle that measures less than 90°
      • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
        • Notation is given as a box in the angle corner to represent a 90° angle.
      • Obtuse angle – an angle that measures greater than 90° but less than 180°
      • Straight angle – an angle that measures 180° (a straight line)
  • Protractor – a tool used to determine the measure of an angle
    • Two sets of measures from 0° to 180° going in opposite directions
    • Relationships between a protractor and a circle
      • One protractor is a semi-circle, 180°
      • Two protractors make a complete circle, 360°
  • Measurement or “m” notation indicates the measure of the angle in degrees (e.g., m∠1 = 50°)
  • Measure angles with a ray aligned at zero degrees.
    • When aligning the ray to zero degrees on the right side of the protractor, read the angle measurement using the inner set of measures from right to left.
    • When aligning the ray to zero degrees on the left side of the protractor, read the angle measurement using the outer set of measures from left to right.
  • Measure angles whose rays may lie between numerically marked intervals.
    • Relate to reading unmarked whole number intervals on a number line.
  • Measure angles where a ray of the angle does not lie on zero degrees.
    • Read measure of both rays using either the inner or the outer set of measures, then subtract smaller measure from larger measure to determine angle measure.
  • Measure angles within two-dimensional figures.
    • Treat the sides of the figure that form the angle as rays.
  • Use a right angle, 90°, as a benchmark to determine angle classifications (acute, obtuse, and right) to determine reasonableness of angle measures.

Note(s):

  • Grade Level(s):
    • Grade 4 introduces determining the approximate measures of angles in degrees to the nearest whole number using a protractor.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
4.7D Draw an angle with a given measure.
Supporting Standard

Draw

AN ANGLE WITH A GIVEN MEASURE

Including, but not limited to:

  • Degree – the measure of an angle where each degree represents of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
    • Angle measures limited to whole numbers, 0° to 180°
  • Angle – two rays with a common endpoint (the vertex)
    • Various angle types/names
      • Right angle, 90°, used as a benchmark to identify and name angles
        • Acute angle – an angle that measures less than 90°
        • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
          • Notation is given as a box in the angle corner to represent a 90° angle.
        • Obtuse angle – an angle that measures greater than 90° but less than 180°
        • Straight angle – an angle that measures 180° (a straight line)
  • Protractor – a tool used to determine the measure of an angle
    • Use a protractor to draw an angle of a given measure
      • Use the straight edge of the protractor to draw a ray.
      • Place the vertex of the protractor on the endpoint of the ray.
      • Align the vertex and the 0° mark on the protractor to the ray.
      • Use the scale beginning with 0 and mark the given angle measure.
      • Use the straightedge of the protractor to draw a ray from the vertex to the angle mark.

Note(s):

  • Grade Level(s):
    • Grade 4 introduces drawing an angle with a given measure.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
    • X. Communication and Representation
4.7E Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.
Supporting Standard

Determine

THE MEASURE OF AN UNKNOWN ANGLE FORMED BY TWO NON-OVERLAPPING ADJACENT ANGLES GIVEN ONE OR BOTH ANGLE MEASURES

Including, but not limited to:

  • Degree – the measure of an angle where each degree represents of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
    • Angle measures limited to whole numbers, 0° to 180°
  • Angle – two rays with a common endpoint (the vertex)
  • Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
  • Complementary angles – two angles whose degree measures have a sum of 90°
  • Supplementary angles – two angles whose degree measures have a sum of 180°
  • Congruent angles – angles whose angle measurements are equal
  • Angle congruency marks – angle marks indicating angles of the same measure
  • Decompose and compose angle measures
    • Angle measures up to 360°
    • The angle measure of the whole is the sum of the angle measure of the parts
      • Given the measure of one angle, and the whole, find the measure of the other angle.
      • Given the measure of two angles, find the measure of the whole angle.
      • Given the measure of the whole angle divided equally, find the measure of the equal sized angles
      • Multiple steps to find a missing measure
      • Adjacent angles within two-dimensional figures
      • Angles in context without graphics

Note(s):

  • Grade Level(s):
    • Grade 4 introduces determining the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
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# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
Click here to collapse or expand this section.
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 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
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
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 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 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.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.
Last Updated 08/01/2018
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