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 Instructional Focus DocumentPhysics
 TITLE : Unit 03: Two Dimensional Motion SUGGESTED DURATION : 9 days

#### Unit Overview

Introduction

This unit focuses on accelerated motion in two dimensions.

Prior to this Unit

• 6.8B – Identify and describe the changes in position, direction, and speed of an object when acted upon by unbalanced forces.
• 6.8C – Calculate average speed using distance and time measurements.
• 6.8D – Measure and graph changes in motion.
• 8.6A – Demonstrate and calculate how unbalanced forces change the speed or direction of an object's motion.
• 8.6B – Differentiate between speed, velocity, and acceleration.

During this Unit

Students develop a conceptual understanding of projectiles launched upward at an angle. For projectiles launched horizontally, students develop a conceptual understanding and perform calculations using graphical vector addition. Students describe and calculate the values of circular motion using a given formula.

Streamlining Note

Graphical vector addition was removed from former TEKS P.3F and incorporated into new TEKS P.4C.

After this Unit

Students will recognize two-dimensional motion in their everyday lives and use their understanding to make informed decisions.

Research

“By the end of the 12th grade, students should know that:

• …in matters that can be investigated in a scientific way, evidence for the value of a scientific approach is given by the improving ability of scientists to offer reliable explanations and make accurate predictions.” This unit will give students many opportunities to make predictions and explain both predicted and observed results.

 Scientists investigate natural phenomena in order to understand and explain each phenomenon in terms of systems. How are the components, processes, and / or patterns of systems interrelated?   Scientific investigation is an orderly process to ensure that scientific claims are credible. How is scientific knowledge generated and validated?   Data is systematically collected, organized, and analyzed in terms of patterns and relationships to develop reasonable explanations and make predictions. What gives meaning to data? What is the value of observing patterns and relationships in data?   Scientists analyze, evaluate, and critique each other’s work using principles of scientific investigations in order to build on one another’s ideas through new investigations. How can we know what to believe about a scientific claim?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)

An object’s motion is predictable and measurable using mathematical formulas derived from the laws that govern motion.

• In what ways can the laws that govern two-dimensional motion be calculated and expressed?
• What fundamental understandings of the laws that govern two-dimensional motion can you express from the analysis of scenarios, problems, and experimentation?
• In what ways can the laws that govern circular motion be calculated and expressed?
• What fundamental understandings of the laws that govern circular motion can you express from the analysis of scenarios, problems, and experimentation?

Systems

• Motion

Classifications

• Projectile
• Circular

Properties

• Position
• Distance
• Displacement
• Speed
• Velocity
• Acceleration
• Centripetal acceleration
• Tangential velocity

Patterns

• Unit concept

Models

• Centripetal acceleration formula
• Pythagorean theorem

Constancy

• Horizontal velocity

Change

• Vertical velocity
 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:

• Students may think the horizontal component of projectile motion is dependent on the vertical component.
• Students may think air causes the path of a projectile’s motion to be curved.
• Students may think that objects are “pushed out” into a circular path and therefore use the term “centrifugal force” inappropriately.
• Students may think a projectile is any object with a curved path of motion.
• Students may think an upwardly launched projectile experiences no acceleration at its highest point.

Underdeveloped Concepts:

• Students may have difficulty determining the initial given variables in projectile word problems.

#### Unit Vocabulary

Key Content Vocabulary:

• Centripetal acceleration – acceleration towards the center caused by the centripetal force
• Centripetal force – a force which keeps a body moving with a uniform speed along a circular path and is directed along the radius towards the center
• Parabolic pathway – a curved path followed by projectiles
• Projectile – an object projected through space, traveling in two dimensions, that accelerates vertically due to gravity
• Tangential velocity – the instantaneous velocity of a body moving in a circular path

Related Vocabulary:

 Comes to rest From rest Horizontal Launched upward Path Point Radius Reasonable Uniform Vertical With respect to
Unit Assessment Items System Resources Other Resources

Show this message:

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.

State:

Texas Education Agency – Texas Safety Standards

http://www.tea.state.tx.us/index2.aspx?id=5483 (look under Documents)

Texas Gateway for Online Resources by TEA – Analyzing Two-Dimensional Motion

https://www.texasgateway.org/resource/analyzing-two-dimensional-motion

Texas Gateway for Online Resources by TEA – OnTRACK Scientific Process Skills

https://www.texasgateway.org/binder/ontrack-scientific-process-skills

Texas Gateway for Online Resources by TEA – Projectile Motion

https://www.texasgateway.org/resource/projectile-motion

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.
• 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), and American Association for the Advancement of Science (AAAS) Project 2061 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
P.1 Scientific processes. The student conducts investigations, for at least 40% of instructional time, using safe, environmentally appropriate, and ethical practices. These investigations must involve actively obtaining and analyzing data with physical equipment, but may also involve experimentation in a simulated environment as well as field observations that extend beyond the classroom. The student is expected to:
P.1A Demonstrate safe practices during laboratory and field investigations.

Demonstrate

SAFE PRACTICES DURING LABORATORY AND FIELD INVESTIGATIONS

Including, but not limited to:

• Following classroom safety guidelines, as outlined in the Texas Education Agency Texas Safety Standards
• Handling and wearing appropriate safety equipment
• Equipment

Note(s):

• TxCCRS:
• I. Nature of Science – C3 – Demonstrate skill in the safe use of a wide variety of apparatuses, equipment, techniques, and procedures.
P.2 Scientific processes. The student uses a systematic approach to answer scientific laboratory and field investigative questions. The student is expected to:
P.2D Design and implement investigative procedures, including making observations, asking well defined questions, formulating testable hypotheses, identifying variables, selecting appropriate equipment and technology, evaluating numerical answers for reasonableness, and identifying causes and effects of uncertainties in measured data.

Design, Implement

INVESTIGATIVE PROCEDURES

Including, but not limited to:

• Making observations
• Formulating testable hypotheses
• Identifying variables
• Selecting appropriate equipment and technology
• Evaluating numerical answers for reasonableness
• Identifying causes and effects of uncertainties in measured data
• Instrument errors
• User errors

Note(s):

• TxCCRS:
• I. Nature of Science – A3 – Formulate appropriate questions to test understanding of natural phenomena.
P.2E

Demonstrate the use of course apparatus, equipment, techniques, and procedures, including multimeters (current, voltage, resistance), balances, batteries, dynamics demonstration equipment, collision apparatus, lab masses, magnets, plane mirrors, convex lenses, stopwatches, trajectory apparatus, graph paper, magnetic compasses, protractors, metric rulers, spring scales, thermometers, slinky springs, and/or other equipment and materials that will produce the same results.

Demonstrate

THE USE OF COURSE APPARATUS, EQUIPMENT, TECHNIQUES, AND PROCEDURES

Including, but not limited to:

• Stopwatches
• Trajectory apparatus
• Graph paper
• Protractors
• Metric rulers
P.2F

Use a wide variety of additional course apparatus, equipment, techniques, materials, and procedures as appropriate such as ripple tank with wave generator, wave motion rope, tuning forks, hand-held visual spectroscopes, discharge tubes with power supply (H, He, Ne, Ar), electromagnetic spectrum charts, laser pointers, micrometer, caliper, computer, data acquisition probes, scientific calculators, graphing technology, electrostatics kits, electroscope, inclined plane, optics bench, optics kit, polarized film, prisms, pulley with table clamp, motion detectors, photogates, friction blocks, ballistic carts or equivalent, resonance tube, stroboscope, resistors, copper wire, switches, iron filings, and/or other equipment and materials that will produce the same results.

Use

A WIDE VARIETY OF ADDITIONAL COURSE APPARATUS, EQUIPMENT, TECHNIQUES, MATERIALS, AND PROCEDURES AS APPROPRIATE

Including, but not limited to:

• Computer
• Scientific calculators
• Graphing technology
• Inclined plane
• Motion detectors
• Photogates
P.2G Make measurements with accuracy and precision and record data using scientific notation and International System (SI) units.

Make

MEASUREMENTS

Including, but not limited to:

• Accuracy
• Precision

Record

DATA

Including, but not limited to:

• Scientific notation
• International System (SI) units
• Significant Digits (TxCCRS)

Note(s):

• TxCCRS:
• II. Foundation Skills: Scientific Applications of Mathematics – A2 – Use exponents and scientific notation.
• II. Foundation Skills: Scientific Applications of Mathematics – F2 – Use appropriate significant digits.
P.2I Communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports.

Communicate

VALID CONCLUSIONS SUPPORTED BY THE DATA

Including, but not limited to:

• Lab reports
• Labeled drawings
• Graphic organizers
• Journals (science notebooks)
• Summaries
• Oral reports
• Technology-based reports

Note(s):

• TxCCRS:
• III. Foundation Skills: Scientific Applications of Communication – A1 – Use correct applications of writing practices in scientific communication.
P.2J Express relationships among physical variables quantitatively, including the use of graphs, charts, and equations.

Express

RELATIONSHIPS AMONG PHYSICAL VARIABLES QUANTITATIVELY

Including, but not limited to:

• Graphs
• Charts
• Equations

Note(s):

• TxCCRS:
• II. Foundation Skills: Scientific Applications of Mathematics – 2B – Carry out formal operations using standard algebraic symbols and formulae.
• VIII. Physics – A4 – Understand the concept of density.
P.3 Scientific processes. The student uses critical thinking, scientific reasoning, and problem solving to make informed decisions within and outside the classroom. The student is expected to:
P.3A Analyze, evaluate, and critique scientific explanations by using empirical evidence, logical reasoning, and experimental and observational testing, so as to encourage critical thinking by the student.

Analyze, Evaluate, Critique

SCIENTIFIC EXPLANATIONS, SO AS TO ENCOURAGE CRITICAL THINKING BY THE STUDENT

Including, but not limited to:

• Use
• Empirical evidence
• Logical reasoning
• Experimental and observational testing

Note(s):

• Project 2061: By the end of the 8th grade, students should know that:
• Scientific knowledge is subject to modification as new information challenges prevailing theories and as a new theory leads to looking at old observations in a new way. 1A/M2
• Some scientific knowledge is very old and yet is still applicable today. 1A/M3
• Scientific investigations usually involve the collection of relevant data, the use of logical reasoning, and the application of imagination in devising hypotheses and explanations to make sense of the collected data. 1B/M1b*
• If more than one variable changes at the same time in an experiment, the outcome of the experiment may not be clearly attributable to any one variable. It may not always be possible to prevent outside variables from influencing an investigation (or even to identify all of the variables). 1B/M2ab
• Project 2061: By the end of the 12th grade, students should know that:
• From time to time, major shifts occur in the scientific view of how things work. More often, however, the changes that take place in the body of scientific knowledge are small modifications of prior knowledge. Continuity and change are persistent features of science. 1A/H2
• TxCCRS:
• I. Nature of Science – A1 – Utilize skepticism, logic, and professional ethics in science.
• I. Nature of Science – A4 – Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
P.3B Communicate and apply scientific information extracted from various sources such as current events, news reports, published journal articles, and marketing materials.

Communicate, Apply

SCIENTIFIC INFORMATION EXTRACTED FROM VARIOUS SOURCES

Including, but not limited to:

• Current events
• News reports
• Published journal articles
• Marketing materials
P.3E Express, manipulate, and interpret relationships symbolically in accordance with accepted theories to make predictions and solve problems mathematically.

Express, Manipulate, Interpret

RELATIONSHIPS SYMBOLICALLY IN ACCORDANCE WITH ACCEPTED THEORIES

Including, but not limited to:

• Make predictions
• Solve problems mathematically
• Manipulation of equations algebraically
• Proportional reasoning

Note(s):

• TxCCRS:
• VIII. Physics – B1 – Understand how vectors are used to represent physical quantities.
• VIII. Physics – B2 – Demonstrate knowledge of vector mathematics using a graphical representation.
• VIII. Physics – B3 – Demonstrate knowledge of vector mathematics using a numerical representation.
P.4 Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
P.4C Analyze and describe accelerated motion in two dimensions, including using equations, graphical vector addition, and projectile and circular examples.

Analyze, Describe

ACCELERATION MOTION IN TWO DIMENSIONS

Including, but not limited to:

• Projectile motion
• Launched upwards at an angle (conceptual understanding)
• Path of a projectile comparing velocity and acceleration at any point on the path
• Launched horizontally (conceptual understanding and calculations)
• Path of a projectile comparing velocity and acceleration at any point on the path
• Analyze projectile motion in terms of its horizontal and vertical components
• Use data from one of the components to find time and use that value to find the unknown quantity
• Acceleration = (final velocity)– (initial velocity)/ 2 x (displacement)
• a = vfvi2 / 2∆d
• Circular motion
• ac = vt2 / r
• Centripetal acceleration = (tangential velocity)2 / radius
• Direction of acceleration and velocity
• Graphical vector addition in two dimensions
• Pythagorean Theorem
• Sine, cosine, tangent functions

Note(s):

• The STAAR Physics Reference Materials include the formulas for centripetal acceleration as listed above.
• TxCCRS:
• VIII. Physics – C1 – Understand the fundamental concepts of kinematics.
DEVELOPING TEKS

TEKS that need continued practice, improvement, and refinement, but do not necessarily need 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.
• 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), and American Association for the Advancement of Science (AAAS) Project 2061 is labeled.
TEKS# SE# TEKS SPECIFICITY
P.1 Scientific processes. The student conducts investigations, for at least 40% of instructional time, using safe, environmentally appropriate, and ethical practices. These investigations must involve actively obtaining and analyzing data with physical equipment, but may also involve experimentation in a simulated environment as well as field observations that extend beyond the classroom. The student is expected to:
P.1B Demonstrate an understanding of the use and conservation of resources and the proper disposal or recycling of materials.

Demonstrate

AN UNDERSTANDING OF THE USE AND CONSERVATION OF RESOURCES AND THE DISPOSAL OR RECYCLING OF MATERIALS

Including, but not limited to:

• Use and conservation of resources
• Disposal or recycling of materials
P.2 Scientific processes. The student uses a systematic approach to answer scientific laboratory and field investigative questions. The student is expected to:
P.2A Know the definition of science and understand that it has limitations, as specified in subsection (b)(2) of this section.

Know

THE DEFINITION OF SCIENCE AND UNDERSTAND THAT IT HAS LIMITATIONS

Including, but not limited to:

• Science, as defined by the National Academy of Sciences, is the “use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process”.
• …”some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.”
P.2B Know that scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence.

Know

THAT SCIENTIFIC HYPOTHESES ARE TENTATIVE AND TESTABLE STATEMENTS THAT MUST BE CAPABLE OF BEING SUPPORTED OR NOT SUPPORTED BY OBSERVATIONAL EVIDENCE

Including, but not limited to:

• Tentative and testable statements
• Supported or not supported by observational evidence

Note(s):

• TxCCRS Note:
• I. Nature of Science – A3 – Formulate appropriate questions to test understanding of natural phenomena.
• I. Nature of Science – A4 – Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
P.2C Know that scientific theories are based on natural and physical phenomena and are capable of being tested by multiple independent researchers. Unlike hypotheses, scientific theories are well established and highly reliable explanations, but may be subject to change.

Know

SCIENTIFIC THEORIES ARE BASED ON NATURAL AND PHYSICAL PHENOMENA AND ARE CAPABLE OF BEING TESTED BY MULTIPLE INDEPENDENT RESEARCHERS

Including, but not limited to:

• Based on natural and physical phenomena
• Capable of being tested by multiple independent researchers
• Well established, highly reliable explanations
• Subject to change as new areas or science and new technologies are developed

Note(s):

• TxCCRS:
• I. Nature of Science – A2 – Use creativity and insight to recognize and describe patterns in natural phenomena.
• I. Nature of Science – A4 – Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
P.2H Organize, evaluate, and make inferences from data, including the use of tables, charts, and graphs.

Organize, Evaluate, Make inferences

DATA

Including, but not limited to:

• Tables
• Charts
• Graphs

Note(s):

• TxCCRS:
• I. Nature of Science – E1 – Use several modes of expression to describe or characterize natural patterns and phenomena. These modes of expression include narrative, numerical, graphical, pictorial, symbolic, and kinesthetic.
P.3 Scientific processes. The student uses critical thinking, scientific reasoning, and problem solving to make informed decisions within and outside the classroom. The student is expected to:
P.3C Explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society.

Explain

THE IMPACTS OF SCIENTIFIC CONTRIBUTIONS ON SCIENTIFIC THOUGHT AND SOCIETY

Including, but not limited to:

• Historical and contemporary scientists
• Newton
• Einstein
• Galileo
• Maxwell
• Coulomb
• Ørsted
• Ampere
• Lenz
P.3D Research and describe the connections between physics and future careers.

Research, Describe

THE CONNECTIONS BETWEEN PHYSICS AND FUTURE CAREERS

Including, but not limited to:

• How physics is used in various careers
• Possible examples may include:
• Medical physicist
• Astronomer
• Teacher
• Geophysicist
• Equipment designer
• Telecommunications engineer
• Materials designer
• Engineer
P.4 Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
P.4A Generate and interpret graphs and charts describing different types of motion, including investigations using real-time technology such as motion detectors or photogates.

Generate, Interpret

GRAPHS AND CHARTS DESCRIBING DIFFERENT TYPES OF MOTION

Including, but not limited to:

• Linear motion
• Constant velocity
• Accelerated motion (positive and negative acceleration)
• Information illustrated on graphs
• Position-time
• Distance
• Displacement
• Average velocity
• Describe motion
• Velocity-time
• Displacement
• Instantaneous velocity
• Average velocity
• Acceleration
• Describe motion
• Acceleration-time
• Constant acceleration (no slope)
• Describe motion
• Investigation using real-time technology
• Motion detectors
• Photogates
• Ticker timer

Note(s):

• Students in Grade 6 calculate average speed using distance and time measurements, measure and graph changes in motion, and investigate how inclined planes can be used to change the amount of force to move an object (6.8C, 6.8D).
• Students in Grade 8 differentiate between speed, velocity, and acceleration (8.6B).
• TxCCRS:
• I. Nature of Science – A4 – Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
• VIII. Physics – C1 – Understand the fundamental concepts of kinematics.
• VIII. Physics – A1 – Demonstrate familiarity with length scales from sub-atomic particles through macroscopic objects.
P.4B Describe and analyze motion in one dimension using equations and graphical vector addition with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, frames of reference, and acceleration.

Describe, Analyze

MOTION IN ONE DIMENSION

Including, but not limited to:

• Vectors vs. scalars
• Magnitude and direction
• Displacement
• Distance
• Displacement vs. distance
• Velocity vs. speed
• Vector quantities of displacement and vector sum
• Manipulate equations to solve for an unknown
• d = vit + ½a∆t2
• Displacement = (initial velocity)(change in time) + ½ (acceleration)(change in time)2
• vavg = ∆d / ∆t
• Average velocity = displacement / change in time
• Find the average velocity given two or more velocities
• a = (vfvi)  / ∆t
• Acceleration = (final velocity – initial velocity) / change in time
• a = vf2vi2 / 2∆d
• Acceleration = [(final velocity)2 – (initial velocity)2] / [2(displacement)]
• Instantaneous velocity (find initial or final velocity)
• Frames of reference
• Motion with respect to a specified position
• Situations in which velocities add and subtract relative to an observer

Note(s):

• The STAAR Physics Reference Materials include the formulas for average velocity, acceleration, and displacement as listed above.
• Students in Grade 6 calculate average speed using distance and time measurements, measure and graph changes in motion, and investigate how inclined planes can be used to change the amount of force to move an object (6.8C, 6.8D, 6.8E).
• Students in Grade 8 differentiate between speed, velocity, and acceleration (8.6B).
• TxCCRS:
• VIII. Physics – C1 – Understand the fundamental concepts of kinematics.
• VIII. Physics – E1 – Understand rotational kinematics. [Possible Pre-AP Extension]
P.4D Calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects using methods, including free-body force diagrams.

Calculate

THE EFFECT OF FORCES ON OBJECTS

Including, but not limited to:

• Net force
• Fnet = ma
• Net force = (mass)(acceleration)
• Relationship between force and acceleration
• Problems involving force, mass, and acceleration using Newton’s 2nd law
• Friction forces
• The differences between friction-free and friction-inclusive systems
• Law of inertia
• The relationship between mass and inertia using Newton’s 1st law
• Nature of force pairs
• Interpreting real-life situations using Newton’s 3rd law
• Nature of force pairs between objects
• Action-reaction pairs
• Problems involving forces on each object
• Mass vs. weight
• Distinguish between mass and weight
• Calculate the weight of an object
• Fnet = ma (a = g)
• Torque
• τ = Fr
• Torque = (force)(lever arm)
• Compare torque to the net force on an object
• Free-body diagrams of force analysis

Note(s):

• The STAAR Physics Reference Materials include the formulas for net force, torque, and acceleration due to gravity as listed above.
• Students are introduced to the concepts of force in Grades 6 and 8 by observing change in the motion of an object that is acted upon by an unbalanced force (6.8B, 8.6A).
• In Grade 6, students investigate how inclined planes can be used to change the force applied to an object (6.8E).
• In Grade 7, students consider how forces affect motion in organisms (7.7B).
• In Grade 8, students are introduced to Newton’s laws of motion (8.6C).
• TxCCRS:
• I. Nature of Science – A2 – Use creativity and insight to recognize and describe patterns in natural phenomena.
• VIII. Physics – A3 – Understand the concepts of mass and inertia.
• VIII. Physics – A5 – Understand the concepts of gravitational force and weight.
• VIII. Physics – C2 – Understand forces and Newton’s laws.
• VIII. Physics – E3 – Apply the concept of static equilibrium. [Possible Pre-AP Extension]