MAJOR CONTENT SUPPORTING CONTENT ADDITIONAL CONTENT€¦ · 8.NS.a Know that there are numbers that...
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GRADE 8 CONTENTS LE SS ONS T OPIC S C L USTE R S 1 2 3 4 5 6 7 8 8.EE.A 8.NS.A 8.EE.B 8.EE.C 8.F.A 8.F.B 8.SP.A 8.SP.B 8.EE.C 8.G.A 8.G.B 8.G.C COMMON CORE DOMAINS 8.NS THE NUMBER SYSTEM 8.EE EXPRESSIONS AND EQUATIONS 8.F FUNCTIONS 8.G GEOMETRY 8.SP STATISTICS AND PROBABILITY MAJOR CONTENT SUPPORTING CONTENT ADDITIONAL CONTENT 6 Grade 8
Transcript of MAJOR CONTENT SUPPORTING CONTENT ADDITIONAL CONTENT€¦ · 8.NS.a Know that there are numbers that...
Grade 8 CONTeNTS
LESSONS
TOPICS
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COMMON COre dOMaINS8.NS THE NUMBER SYSTEM
8.ee EXPRESSIONS AND EQUATIONS
8.F FUNCTIONS
8.G GEOMETRY
8.SP STATISTICS AND PROBABILITY
MAJOR CONTENT SUPPORTING CONTENT ADDITIONAL CONTENT
6 Grade 8
FOCUS COHERENCE RIGOR
Content is developed with focus, coherence, and rigor. The attention to rigor reflects the balances of conceptual understanding, procedural skill and fluency, and applications in the Common Core Standards. See each Topic Overview
FOCUS ON
MAJOR CONTENT8.ee.a Work with radicals and integer exponents.
SUPPORTING CONTENT8.NS.a Know that there are numbers that are not rational,and approximate them by rational numbers.
MAJOR CONTENT8.ee.B Understand the connections between proportionalrelationships, lines, and linear equations.
MAJOR CONTENT8.ee.C Analyze and solve linear equations and pairs ofsimultaneous linear equations.
MAJOR CONTENT8.F.a Define, evaluate, and compare functions.
MAJOR CONTENT8.F.B Use functions to model relationships between quantities
SUPPORTING CONTENT8.SP.a Investigate patterns of association in bivariate data.
MAJOR CONTENT8.ee.C Analyze and Solve linear equations and pairs ofsimultaneous linear equations.
MAJOR CONTENT8.G.a Understand congruence and similarity using physicalmodels, transparencies, or geometry software.
MAJOR CONTENT8.G.B Understand and apply the Pythagorean Theorem
ADDITIONAL CONTENT8.G.C Solve real-world and mathematical problems involvingvolume of cylinders, cones, and spheres.
TOPICS
1 Real Numbers
2 Analyze and Solve Equations
3 Use Functions to Model Relationships
4 Investigate Bivariate Data
5 Analyze and Solve Systems of Linear Equations
6 Congruence and Similarity
7 Understand and Apply the Pythagorean Theorem
8 Solve Problems Involving Surface Area and Volume
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LESSONS
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GRADE 8 CONTENTS (continued)
TOPIC 1 FOCUSES ON
MAJOR CONTENT8.EE.A Work with radicals and integer exponents
SUPPORTING CONTENT8.NS.A Know that there are numbers that are notrational, and approximate them by rational numbers
TOPIC 1 OVERVIEWMath Background: Focus ................................................2AMath Background: Coherence ...................................... 2CMath Background: Rigor .................................................2DMath Practices .....................................................................2ETopic Readiness Assessment ..........................................2FPlanner ..................................................................................2G
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TOPIC 1 Real NumbersTopic Overview ................................................................................... 2ATopic Opener .....................................................................................2–3STEM Project ......................................................................................... 4Review What You Know ......................................................................... 5Math Literacy Activity .........................................................................3–6
Rational Numbers as Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7ACC.2.1.8.E.1, MP.2, MP.3, MP.4, MP.7, MP.8
Understand Irrational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13ACC.2.1.8.E.4, MP.1, MP.3, MP.4, MP.6, MP.7
Compare and Order Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19ACC.2.1.8.E.1, CC.2.1.8.E.4, MP.1, MP.2, MP.4, MP.6, MP.7, MP.8
Evaluate Square Roots and Cube Roots . . . . . . . . . . . . . . . . . . . . . . . . . 25ACC.2.1.8.E.1, CC.2.1.8.E.4, MP.1, MP.3, MP.4, MP.6
Solve Equations Using Square Roots and Cube Roots . . . . . . . . . . . 31ACC.2.1.8.E.1, CC.2.1.8.E.4, MP.2, MP.3, MP.4, MP.7, MP.8
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . . 37
Use Properties of Integer Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . 39ACC.2.1.8.E.1, MP.3, MP.4, MP.7, MP.8
More Properties of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45ACC.2.1.8.E.1, MP.1, MP.3, MP.4, MP.6, MP.7
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51ACC.2.1.8.E.1
Use Powers of 10 to Estimate Quantities . . . . . . . . . . . . . . . . . . . . . . . 55ACC.2.1.8.E.1, MP.1, MP.3, MP.7, MP.8
Understand Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61ACC.2.1.8.E.1, MP.3, MP.4, MP.5, MP.6, MP.8
Operations with Numbers in Scientific Notation . . . . . . . . . . . . . . . . 67ACC.2.1.8.E.1, MP.2, MP.3, MP.6
Topic Review ...................................................................................... 73Fluency Practice Activity ....................................................................... 79Topic Assessment .............................................................................. 79ATopic Performance Assessment ............................................................ 79C
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TOPIC 2 FOCUSES ON
MAJOR CONTENT8.EE.B Understand the connections betweenproportional relationships, lines, and linearequations.
MAJOR CONTENT8.EE.C Analyze and solve linear equations and pairsof simultaneous linear equations.
TOPIC 2 CLUSTER OVERVIEWMath Background: Focus ..............................................80AMath Background: Coherence ....................................80CMath Background: Rigor .............................................. 80DMath Practices .................................................................. 80ETopic Readiness Assessment ....................................... 80FPlanner ............................................................................... 80G
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TOPIC 2 Analyze and Solve Linear EquationsTopic Overview ................................................................................. 80ATopic Opener .................................................................................80–81STEM Project ....................................................................................... 82Review What You Know ....................................................................... 83Math Literacy Activity .......................................................................... 84
Collect Like Terms to Solve Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 85ACC.2.2.8.B.3, MP.2, MP.3, MP.4, MP.6, MP.7, MP.8
Solve Equations with Variables on Both Sides . . . . . . . . . . . . . . . . . . . 91ACC.2.2.8.B.3, MP.2, MP.3, MP.4, MP.7
Solve Multi-Step Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97ACC.2.2.8.B.3, MP.2, MP.3, MP.4, MP.5
Equations with No Solutions and Infinitely Many Solutions . . . . 103ACC.2.2.8.B.3, MP.1, MP.4, MP.6, MP.7, MP.8
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . 111
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113ACC.2.2.8.B.3
Compare Proportional Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . 117A CC.2.2.8.B.3, MP.1, MP.2, MP.4, MP.6, MP.7, MP.8
Connect Proportional Relationships and Slope . . . . . . . . . . . . . . . . 123ACC.2.2.8.B.3, MP.2, MP.3, MP.4, MP.6, MP.8
Analyze Linear Equations: y = mx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129ACC.2.2.8.B.3, MP.2, MP.4, MP.5, MP.7
Understand the y-Intercept of a Line . . . . . . . . . . . . . . . . . . . . . . . . . . . 135ACC.2.2.8.B.3, MP.2, MP.4, MP.6, MP.8
Linear Equations: y = mx + b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141ACC.2.2.8.B.3, MP.2, MP.7, MP.8
Topic Review .....................................................................................147Fluency Practice Activity ......................................................................153Topic Assessment ............................................................................ 153ATopic Performance Assessment .......................................................... 153CCumulative/Benchmark Assessment Topics 1–2 ....................................153E
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LESSONS
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GRADE 8 CONTENTS (continued)
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TOPIC 3 FOCUSES ON
MAJOR CONTENT8.F.A Define, evaluate, and compare functions.
MAJOR CONTENT8.F.B Use functions to model relationships betweenquantitites
TOPIC 3 OVERVIEWMath Background: Focus ...........................................154AMath Background: Coherence ................................. 154CMath Background: Rigor ............................................154DMath Practices ................................................................154ETopic Readiness Assessment .....................................154FPlanner .............................................................................154G
TOPIC 3 Use Functions to Model RelationshipsTopic Overview ............................................................................... 154ATopic Opener .............................................................................154–155STEM Project ......................................................................................156Review What You Know ......................................................................157Math Literacy Activity .........................................................................158
Understand Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 159ACC.2.2.8.C.1, MP.2, MP.5, MP.8
Connect Representations of Functions . . . . . . . . . . . . . . . . . . . . . . . . . 165ACC.2.2.8.C.1, MP.2, MP.3, MP.6, MP.8
Compare Linear and Nonlinear Functions . . . . . . . . . . . . . . . . . . . . . . 171ACC.2.2.8.C.1, MP.1, MP.2, MP.3, MP.4, MP.5, MP.8
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . 177
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179ACC.2.2.8.C.1
Construct Functions to Model Linear Relationships . . . . . . . . . . . . 183ACC.2.2.8.C.1, MP.1, MP.2, MP.3, MP.8
Intervals of Increase and Decrease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189A CC.2.2.8.C.1, MP.1, MP.4, MP.6
Sketch Functions from Verbal Descriptions . . . . . . . . . . . . . . . . . . . . 195ACC.2.2.8.C.1, MP.1, MP.2, MP.6
Topic Review .....................................................................................201Fluency Practice Activity ..................................................................... 205Topic Assessment ............................................................................ 205ATopic Performance Assessment ......................................................... 205C
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LESSONS
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TOPIC 4 FOCUSES ON
SUPPORTING CONTENT8.SP.A Investigate patterns of association inbivariate data.
Supporting Content in 8.SP.A supports Major Content in 8.F.A and 8.F.B.
TOPIC 4 OVERVIEWMath Background: Focus ...........................................206AMath Background: Coherence ................................. 206CMath Background: Rigor ............................................206DMath Practices ................................................................206ETopic Readiness Assessment .....................................206FPlanner .............................................................................206G
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TOPIC 4 Investigate Bivariate DataTopic Overview ............................................................................... 206ATopic Opener .............................................................................206–207STEM Project ..................................................................................... 208Review What You Know ..................................................................... 209Math Literacy Activity ........................................................................ 210
Construct and Interpret Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 211ACC.2.4.8.B.1, MP.2, MP.4, MP.6, MP.7, MP.8
Analyze Linear Associations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217ACC.2.4.8.B.1, MP.1, MP.2, MP.3, MP.5, MP.8
Use Linear Models to Make Predictions . . . . . . . . . . . . . . . . . . . . . . . 223ACC.2.4.8.B.1, MP.3, MP.4, MP.5, MP.6, MP.7
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . 229
Interpret Two-Way Frequency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . 231ACC.2.4.8.B.2, MP.1, MP.2, MP.3, MP.6, MP.7, MP.8
Interpret Two-Way Relative Frequency Tables . . . . . . . . . . . . . . . . . 237ACC.2.4.8.B.2, MP.3, MP.4, MP.7
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243ACC.2.4.8.B.2
Topic Review .....................................................................................247Fluency Practice Activity ...................................................................... 251Topic Assessment ............................................................................ 251ATopic Performance Assessment ..........................................................251C Cumulative/Benchmark Assessment Topics 1–4 ................................... 251E
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LESSONS
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GRADE 8 CONTENTS (continued)
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IN TOPIC 5, FOCUS ON
MAJOR CONTENT8.EE.C Analyze and solve linear equations and pairsof simultaneous linear equations.
TOPIC 5 OVERVIEWMath Background: Focus ...........................................252AMath Background: Coherence ................................. 252CMath Background: Rigor ............................................252DMath Practices ................................................................252ETopic Readiness Assessment .....................................252FPlanner .............................................................................252G
TOPIC 5 Analyze and Solve Systems of Linear EquationsTopic Overview ............................................................................... 252ATopic Opener .............................................................................252–253STEM Project ..................................................................................... 254Review What You Know ..................................................................... 255Math Literacy Activity ........................................................................ 256
Estimate Solutions by Inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257ACC.2.2.8.B.3, MP.2, MP.3, MP.4
Solve Systems by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263ACC.2.2.8.B.3, MP.2, MP.3, MP.6, MP.7
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . 269
Solve Systems by Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271ACC.2.2.8.B.3, MP.1, MP.2, MP.7, MP.8
Solve Systems by Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277ACC.2.2.8.B.3, MP.2, MP.4, MP.5, MP.7
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283A CC.2.2.8.B.3
Topic Review ..................................................................................... 287Fluency Practice Activity ..................................................................... 291Topic Assessment ............................................................................ 291ATopic Performance Assessment ......................................................... 291C
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LESSONS
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TOPIC 6 FOCUSES ON
MAJOR CONTENT8.G.A Understand congruence and similarity usingphysical models, transparencies, or geometrysoftware.
TOPIC 6 OVERVIEWMath Background: Focus ...........................................292AMath Background: Coherence ................................. 292CMath Background: Rigor ............................................292DMath Practices ................................................................292ETopic Readiness Assessment .....................................292FPlanner .............................................................................292G
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TOPIC 6 Congruence and SimilarityTopic Overview ............................................................................... 292ATopic Opener ............................................................................. 292–293STEM Project .................................................................................... 294Review What You Know ..................................................................... 295Math Literacy Activity ........................................................................ 296
Analyze Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297ACC.2.3.8.A.2, MP.1, MP.2, MP.3, MP.4, MP.6
Analyze Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303ACC.2.3.8.A.2, MP.1, MP.2, MP.3, MP.7
Analyze Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309ACC.2.3.8.A.2, MP.1, MP.2, MP.3, MP.4, MP.6
Compose Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315ACC.2.3.8.A.2, MP.2, MP.3, MP.4, MP.7, MP.8
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321ACC.2.3.8.A.2
Understand Congruent Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325ACC.2.3.8.A.2, MP.2, MP.3, MP.4, MP.7
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . .331
Describe Dilations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333ACC.2.3.8.A.2, MP.1, MP.2, MP.3, MP.7
Understand Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339ACC.2.3.8.A.2, MP.2, MP.3, MP.6, MP.7
Angles, Lines, and Transversals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345ACC.2.3.8.A.2, MP.1, MP.2, MP.3, MP.6, MP.7, MP.8
Interior and Exterior Angles of Triangles . . . . . . . . . . . . . . . . . . . . . . 353ACC.2.3.8.A.2, MP.5, MP.6, MP.8
Angle-Angle Triangle Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359ACC.2.3.8.A.2, MP.2, MP.3, MP.7
Topic Review .................................................................................... 365Fluency Practice Activity ..................................................................... 371Topic Assessment ............................................................................ 371ATopic Performance Assessment .......................................................... 371CCumulative/Benchmark Assessment Topics 1–6 ....................................371E
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LESSONS
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GRADE 8 CONTENTS (continued)
TOPIC 7 FOCUSES ON
MAJOR CONTENT8.G.B Understand and apply the Pythagorean Theorem.
TOPIC 7 OVERVIEWMath Background: Focus ...........................................372AMath Background: Coherence ................................. 372CMath Background: Rigor ............................................372DMath Practices ................................................................372ETopic Readiness Assessment .....................................372FPlanner .............................................................................372G
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TOPIC 7 Understand and Apply the Pythagorean TheoremTopic Overview ............................................................................... 372ATopic Opener .............................................................................372–373STEM Project ..................................................................................... 374Review What You Know ..................................................................... 375Math Literacy Activity ........................................................................ 376
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385ACC.2.3.8.A.3
Understand the Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . 381ACC.2.3.8.A.3, MP.2, MP.3, MP.4
Understand the Converse of the Pythagorean Theorem . . . . . . . 387ACC.2.3.8.A.3, MP.1, MP.2, MP.7
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . 393
Apply the Pythagorean Theorem to Solve Problems . . . . . . . . . . . 395ACC.2.3.8.A.3, MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.8
Find Distance in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . 401ACC.2.3.8.A.3, MP.2, MP.3, MP.4, MP.6, MP.7
Topic Review ..................................................................................... 407Fluency Practice Activity ...................................................................... 411Topic Assessment............................................................................. 411ATopic Performance Assessment .......................................................... 411C
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TOPIC 8 FOCUSES ON
ADDITIONAL CONTENT8.G.C Solve real-world and mathematical problemsinvolving volume of cylinders, cones, and spheres.
TOPIC 8 OVERVIEWMath Background: Focus ...........................................412AMath Background: Coherence ................................. 412CMath Background: Rigor ............................................ 412DMath Practices ................................................................412ETopic Readiness Assessment .....................................412FPlanner .............................................................................412G
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TOPIC 8 Solve Problems Involving Surface Area and VolumeTopic Overview ............................................................................... 412ATopic Opener .............................................................................412–413STEM Project ..................................................................................... 414Review What You Know ..................................................................... 415Math Literacy Activity ........................................................................ 416
Find Surface Area of Three-Dimensional Figures . . . . . . . . . . . . . . 417A CC.2.3.8.A.1, MP.2, MP.3, MP.8
Find Volume of Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423ACC.2.3.8.A.1, MP.2, MP.3, MP.6, MP.7, MP.8
Mid-Topic Checkpoint and Performance Task . . . . . . . . . . . . . . . . . . . 423
Find Volume of Cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431ACC.2.3.8.A.1, MP.1, MP.2, MP.3, MP.4, MP.6, MP.7, MP.8
Find Volume of Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437ACC.2.3.8.A.1, MP.3, MP.4, MP.7
3-Act Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443ACC.2.3.8.A.1
Topic Review .................................................................................... 447Fluency Practice Activity ..................................................................... 451Topic Assessment ............................................................................ 451ATopic Performance Assessment ......................................................... 451CCumulative/Benchmark Assessment Topics 1–8 .................................. 451E
Grade 8 15
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