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Grade 4 Unit 5 Geometry Mathematics Unit Goals – Stage 1 Number of Days: 29 Traditional: March 13 – April 28, 2017; Track B: March 23 – June 8, 2017 Unit Description: In Unit 5, students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry. Students use their understanding of equal partitioning and unit measurement to understand angle and turn measure. They apply understanding of shapes to patterns and extend their previous understanding of number sense to geometric and numeric patterns. Materials: protractors, fraction circles, student clocks, pattern blocks, base ten blocks (unit cubes) for building tower patterns, polygons, geoboards, dot paper, AngLegs and Go Math! MathBoard or whiteboard Standards for Mathematical Practice Transfer Goals Students will be able to independently use their learning to… SMP.1 Make sense of problems and • Make sense of never-before-seen problems and persevere in solving them. persevere in solving them. • Construct viable arguments and critique the reasoning of others. SMP.2 Reason abstractly and Making Meaning quantitatively. UNDERSTANDINGS ESSENTIAL QUESTIONS SMP.3 Construct viable arguments and Students will understand that… Students will keep considering… critique the reasoning of others. • Patterns are ordered sets of numbers • Is there a pattern? SMP.4 Model with mathematics. or objects that can be repeated. • Where is geometry found in your everyday world? SMP.5 Use appropriate tools strategically. • Geometric figures can be analyzed and • How are symmetrical figures used in artwork? SMP.6 Attend to precision. classified based on their properties. • How can you relate angles and fractional parts of a circle? SMP.7 Look for and make use of • A line of symmetry divides a shape into structure. two parts that are the same size and SMP.8 Look for and express regularity in shape. repeated reasoning. Acquisition KNOWLEDGE SKILLS Standards for Mathematical Content Students will know… Students will be skilled at and/or be able to… Clusters Addressed • The definitions of the academic • Generate a shape pattern that follows a given rule. vocabulary words such as acute angle, • Measure angles in whole-number degrees using a protractor Operations and Algebraic Thinking clockwise, counterclockwise, degree (°), and use a right angle as a benchmark angle. 4.OA.C Generate and analyze patterns. dimension, geometric pattern, • Solve addition and subtraction problems to find unknown intersecting lines, line, line of symmetry, angles on a diagram in real world and mathematical problems. Measurement and Data line symmetry, obtuse angle, • Draw and identify points, lines, line segments, rays, angles 4.MD.C Geometric measurement: parallelogram, protractor, perpendicular (right, acute, obtuse), and perpendicular and parallel lines understand concepts of angle and lines, ray, repeating pattern, right angle, alone and in two-dimensional figures. measure angles. right triangle, rule, sequence, straight • Classify two-dimensional figures based on the presence or Geometry angle, term, turn, and vertex. absence of parallel or perpendicular lines, or the presence or 4.G.A Draw and identify lines and angles, • A right angle can be used to classify all absence of angles of a specified size. and classify shapes by properties angles. • Recognize and identify right triangles. of their lines and angles. • An angle that turns through 1/360 of the • Recognize a line of symmetry for a two-dimensional figure, circle measures 1 degree. draw lines of symmetry, and identify line-symmetric figures. LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 1 Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Assessed Grade Level Standards Standards for Mathematical Practice SMP.1 SMP.2 SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Standards for Mathematical Content Operations and Algebraic Thinking [a] 4.OA.C Generate and analyze patterns. 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1 generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Use the four operations with whole numbers to solve problems. Measurement and Data [a] 4.MD.C Geometric measurement: understand concepts of angle and measure angles. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. Geometry [a] 4.G.A 4.G.1 4.G.2 4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 2 Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Evidence of Learning – Stage 2 Assessment Evidence Unit Assessment Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in this guide. [a] 4.OA.C • The student generates shape patterns. • The student analyzes a number pattern or shape pattern, showing understanding of the pattern rule and features other than the pattern rule. [a] 4.MD.C • The student uses a protractor to measure angles (composed of one-degree angles) and constructs angles to whole-number degrees. • The student decomposes an angle into smaller non-overlapping parts and adds the measures of these smaller parts to find the measure of the whole angle. • The student solves addition and subtraction problems in real world and mathematical contexts using angle measures. • The student identifies angles of specified measures. • The student relates the concept of an angle to the number of degrees in a circle. [a] 4.G.A • The student identifies and draws points, lines, line segments, rays, and angles both in two-dimensional figures and in isolation. • The student distinguishes between right, acute, and obtuse angles. • The student distinguishes between parallel and perpendicular lines. • The student classifies two-dimensional figures based on presence or absence of parallel/perpendicular line segments. • The student classifies two-dimensional figures based on the presence or absence of angles of a specified size. • The student identifies right triangles. • The student identifies and draws lines of symmetry in line-symmetric figures. • The student distinguishes line-symmetric figures from line-asymmetric figures. (symmetrical vs. asymmetrical) For selected content, students will need to… • Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. • Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Other Evidence Formative Assessment Opportunities • Exit slips • Opening Tasks • Quizzes • Go Math! Show What You Know • Extension Menus • Classroom Challenges • It’s All About the Facts Supplemental materials • Go Math! Performance Task • In-class projects • Homework (Go Math! Standards Practice Book) • Recorded Teacher Observations • Go Math! Getting Ready for the Smarter Balance • Writing activities • Go Math! Chapter 10, 11 Test (Assessment Guide) • SBAC Interim Assessment Block (IAB) • Go Math! Chapter 10, 11 Review / Test – Student Book • Multiple Markers (Use this for 4.OA.C) Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents. LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 3 Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Success Criteria Go Math! http://www-k6.thinkcentral.com Metas de Aprendizaje Days Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet - (Universal Access for SPED, Struggling Students, ELL, GATE) Sabré las operaciones básicas de matemáticas al... • • • Saying facts orally. Writing Fact Families. Using them to play games. • Puedo usar las estrategias matemáticas mentales al... • • Participating in daily Number Talks. Communicating my reasoning. • 90 minutes per week (Schools/ grades with ST Math) Perseveraré en la resolución de problemas al ayudarme a entender las matemáticas al… • • Developing long term problem solving skills. Visualizing math concepts. Making connections between concepts and across grades. Playing interactive games Before the Unit (as needed) I can show what I know about geometry by… • Completing “Show What You Know”. Daily Daily • • LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 • Instructional Tools - Elementary 4th Grade) Maintaining Fluency Through Fact Families, pp.1-10, 13-28 Go Math! Strategies and Practice For Skills and Facts Fluency • Top 10s, 11s, and 12s (Resources - Games) Number Talks Strategies and Problem Sets, Grades 2-5 (also found on intranet in Instructional Tools) • Multiple Marker ST Math Objectives • Exploring Lines and Shapes • Lines of Symmetry • Parallel Lines and Parallelograms • Angles and Triangles ST Math Tips • When a students’ screen is orange use Teacher mode to intervene. • Review teacher mode at trs.stmath.com • Ch. 10-11 “Show What You Know”, pp. 397 & 439 **Use the Diagnostic Table if needed for intervention options: On-level, Strategic, Intensive, and Independent. 4 Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Success Criteria Go Math! http://www-k6.thinkcentral.com Metas de Aprendizaje Days Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet - (Universal Access for SPED, Struggling Students, ELL, GATE) 1 Puedo explorar los ángulos en el entorno del mundo real al… OPENING TASK – G is for Googol • Creating a Geometry Alphabet Book. • Classifying angles. • Locating the three types of angles. • • • G is for Googol Ch. 10-11 “Math Detective”, pp. 397 & 439 Ch. 10-11 “Vocabulary Builder”, pp. 398 & 440 Instructional Tools - Elementary 4th Grade) • • • • 2–3 Puedo describir los ángulos usando el vocabulario geométrico al… • • • 4-6 Puedo explicar cómo medir un ángulo al… • • • • • Identifying, drawing and labeling points, lines, line segments, rays, and angles. Identifying, drawing, and labeling parallel and perpendicular lines. Identifying, drawing and labeling right, acute and obtuse angles. • Placing fraction pieces to create angles on circles. Relating degrees to fractional parts of a circle. Using hands of a clock to show clockwise and counterclockwise. Using circular geoboards to show angles in terms of degrees and turns. Finding example of different kinds of angles in the classroom. • LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 5 • Lessons 10.1: Lines, Rays, and Angles and 10.4: Parallel Lines and Perpendicular Lines (Note: You can skip to the activity on the second page of the lessons because the first page is what the students complete in their Geometry Alphabet Book.) Lesson 11.1: Investigate – Angles and Fractional Parts of a Circle Lesson 11.2: Degrees • • • • • • • See https://www.illustrativemathematic s.org/4 for tasks to be used throughout the unit. Engage, Explore, Evaluate Problems (to use throughout the unit) Notice and Wonder Introduction and Record Sheet (to use throughout the unit, Instructional Tools – Notice and Wonder) String Geometry (Instructional Tools - Normbuilding Activities) Kudos for Geometry Learning Target Posters Line Relationships LBUSD map found under “M” at www.lbschools.net to identify lines and angles in context Time on Your Hands Clock Angles Power Point Problem Solving Grades 3 – 5 pp. 110 – 112; Task 6.3 “Categorizing Letters of the Alphabet” o Categorizing Letters of the Alphabet Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Success Criteria Go Math! http://www-k6.thinkcentral.com Metas de Aprendizaje Days Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet - (Universal Access for SPED, Struggling Students, ELL, GATE) 7–9 Puedo medir y dibujar los ángulos al usar mi transportador al… • Using right angles to determine whether angles are greater than, less than, or equal to right angles. • Using protractors for length measure and angle measure. Sketching given angle measures and check with a protractor. Exploring benchmark angles of 90 and 180 degrees. • • • 10 - 13 14 - 16 17 - 19 Lesson 11.3 Measure and Draw Angles Instructional Tools - Elementary 4th Grade) • • • Good Questions p. 81 # 5-6, p. 82 #1 & p. 83 #7 What is the Shape? Problem Solving Grades 3-5 pp. 88-89; Task 5.4 “Rulers and Protractors” o Rulers and Protractors Good Questions p. 83 #5 Puedo determinar la medida de un ángulo más grande al usar las medidas de un ángulo más pequeño al… Puedo encontrar los ángulos desconocidos usando una variedad de estrategias al… • • • • • Decomposing angles. Adding angle measures. Exploring angles as additive. Cutting paper angles into two parts. Using a protractor. • Lesson 11.4: Investigate – Join and Separate Angles • • • Finding unknown angle measures. Using a symbol to stand for the unknown angle measure. • Lesson 11.5: Problem Solving – Unknown Angle Measures Ch. 11 Performance Task Klee Kat pp. AG179 – 183D • • Daily Homework “For the Win” 3-Acts Lesson o Three Acts Explained (Instructional Tools Modeling) o Three Acts Student Handout (Instructional Tools Modeling) Puedo clasificar los triángulos basado en líneas y ángulos al… • Sorting triangles by the size of their angles. Sorting triangles by the length of their sides. • Lesson 10. 2: Classify Triangles by Angles Lesson 10.3: Classify Triangles by Sides • • Exit Tickets-Triangles Triangles to Classify • LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 6 • • Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Success Criteria Go Math! http://www-k6.thinkcentral.com Metas de Aprendizaje Days Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet - (Universal Access for SPED, Struggling Students, ELL, GATE) 20 - 21 Puedo clasificar los cuadriláteros basado en líneas y ángulos al… • • • Sorting quadrilaterals by the size of their angles. Sorting quadrilaterals by the number of parallel sides. Communicating my reasoning. • • Lesson 10.5: Classify Quadrilaterals Mid-chapter Checkpoint pages 419 - 420 Instructional Tools - Elementary 4th Grade) • • • • 20 – 23 24 - 25 Puedo identificar una línea de simetría en una figura bidimensional al… Puedo usar mi entendimiento de los atributos para analizar las figuras geométricas al… • • • • • • • • Recognizing lines of symmetry. Drawing lines of symmetry. Identifying when a figure is symmetrical and when it is not. Using isometric and square dot paper. FORMATIVE ASSESSMENT LESSON Classroom Challenge: Tile Designs The number and types of angles. The parallel and perpendicular sides. The lines of symmetry. Communicating my reasoning. LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 7 • • Lesson 10.6 Line Symmetry Lesson 10.7: Find and Draw Lines of Symmetry • • • • • • • • FAL, Tile Designs (Intranet Assessment) Chapter 10 Review/Test pp. 433 - 436 (You could assign one page per night for homework) • • • • • Problem Solving Grades 3 – 5 pp. 104 – 107; Task 6.1 “Shape Riddles” o Shape Riddles Good Questions p. 80 # 1-4, p. 83 #9 & p. 86 #4 Sorting Shapes Task Sorting by Attributes Alphabet Symmetry Polygons and Their Lines of Symmetry Symmetry Drawing Stained Glass Task Good Questions page 82 #3 Problem Solving Grades 3-5 pp. 108-110; Task 6.2 “Twin Shapes” o Twin Shapes Tile Designs - FAL, Differentiated Activities Geometry Classroom Challenge with Pattern Blocks Quilt Making Task Geometry Mix Freeze Match Tricky Trapezoids Posted 6/14/16 Grade 4 Unit 5 Geometry Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Success Criteria Go Math! http://www-k6.thinkcentral.com Metas de Aprendizaje Days Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet - (Universal Access for SPED, Struggling Students, ELL, GATE) 26 – 27 Usaré mi entendimiento de los patrones al... • • • • Identifying the rule to extend a pattern. Creating a pattern of towers using baseten unit cubes. Creating a pattern or following a rule to extend a pattern using pattern blocks. Communicating my reasoning. • Lesson 10.8: Problem Solving – Shape Patterns Instructional Tools - Elementary 4th Grade) • • • • • • Double Plus One Task Multiples of Nine Task Pyramid Cup Challenge (Instructional Tools Normbuilding) Video Game Display Squares and Circles Task What is a Trapezoid? (Part 1) Task End of Unit Assessment 28 Ch. 10 Performance Task “Quilting Bee” (Assessment Guide: pages AG174 – AG178D) 29 At this point, all standards addressed in the Grade 4 Interim Assessment Blocks – “Operations and Algebraic Thinking” and “Geometry” have been covered. These blocks may now be administered. We would appreciate feedback on the following: Unit Guide bit.ly/Grade4UnitGuide Assessment and FAL bit.ly/Grade4Assessment LONG BEACH UNIFIED SCHOOL DISTRICT New 2016 – 2017 8 Posted 6/14/16