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 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 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. 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.

Other considerations: Reference the Mathematics COVID-19 Implementation Tool Grade 4

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.

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 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 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): I. Numeric Reasoning A2, B1, C1; II. Algebraic Reasoning D1, D2; III. Geometric and Spatial Reasoning C1, D3; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

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 …
• 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 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 Center 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

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE 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.

Specificity 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.
TEKS# SE# TEKS SPECIFICITY
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:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
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:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
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:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
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:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
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:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
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:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
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 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
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 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.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Measuring angles
• TxCCRS:
• I.C. Numeric Reasoning – Systems of measurement
• I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
4.7C Determine the approximate measures of angles in degrees to the nearest whole number using a protractor.

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 4 introduces determining the approximate measures of angles in degrees to the nearest whole number using a protractor.
• TxRCFP:
• Measuring angles
• TxCCRS:
• I.C. Numeric Reasoning – Systems of measurement
• I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
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 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
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 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:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
• III.C.1. Make connections between geometry and algebraic equations.
• III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
• III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.