S D C S SAN DIEGO CITY SCHOOLS Instructional Module to Enhance the Teaching of H A R C O U R T Math California Edition Grade 5 Module 4 Reorganized Geometry Reorganized 9/03/04 WORK IN PROGRESS
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Grade Five Traditional Calendar 2004-2005 Order of Units and Pacing Guide Month Module Number of Days Module 1: Data and Graphing 11 days September 19 instructional days Module 2: Place Value and Addition and Subtraction of Whole Numbers and Decimals 8 days October 21 instructional days Module 2: Place Value and Addition and Subtraction of Whole Numbers and Decimals 7 days Module 3: Algebra: Use Addition and Multiplication; Integers 14 days November 18 instructional days Module 3: Algebra: Use Addition and Multiplication; Integers 8 days Module 4: Geometry 10 days December 13 instructional days Winter Break 12/20 12/31 January 20 instructional days Module 4: Module 5: Module 5: Geometry Multiply Whole Numbers and Decimals; Percent Multiply Whole Numbers and Decimals; Percent 2 days 11 days 3 days Module 6: Divide Whole Numbers and Decimals 17 days February 17 instructional days Module 7: Number Theory; Fraction Concepts and Addition and Subtraction of Fractions 17 days March 18 instructional days Spring Break 3/21 3/25 Module 7: Number Theory; Fraction Concepts and Addition and Subtraction of Fractions 5 days Module 8: Geometry: Area, Perimeter, and Volume 12 days April 20 instructional days Module 9: Operations with Fractions: Multiplication and Division Module 10: Measurement, Probability and Ratio 11 days 9 days Reorganized 9/03/04 4
May 21 instructional days STAR 4/26 5/17 DMT 5/9 5/13 Module 10 Measurement, Probability and Ratio 12 days June Review Grade 5 concepts 13 instructional days Preview Grade 6 Concepts Grade Five Year Round Calendar 2004-2005 Order of Units and Pacing Guide 13 days Month Module Number of Days September Module 1: Data and Graphing 11 days 19 instructional days Module 2: Place Value and Addition and Subtraction of Whole Numbers and Decimals 8 days October 21 instructional days Module 2: Module 3: Place Value and Addition and Subtraction of Whole Numbers and Decimals Algebra: Use Addition and Multiplication; Integers 7 days 14 days November 18 instructional days Module 3: Module 4: Algebra: Use Addition and Multiplication; Integers Geometry 8 days 10 days December 13 instructional days Winter Break 12/22 1/17 Module 4: Module 5: Geometry Multiply Whole Numbers and Decimals; Percent 2 days 11 days January 10 instructional days Module 5: Module 6: Multiply Whole Numbers and Decimals; Percent Divide Whole Numbers and Decimals 3 days 7days February 17 instructional days Module 6: Module 7: Divide Whole Numbers and Decimals Number Theory; Fraction Concepts and Addition and Subtraction of Fractions 10 days 7 days March 11 instructional days Spring Break 3/16 4/8 Module 7: Number Theory; Fraction Concepts and Addition and Subtraction of Fractions 11 days April 15 instructional days Module 7: Module 8: Number Theory; Fraction Concepts and Addition and Subtraction of Fractions Geometry: Area, Perimeter, and Volume 4 days 11 days Reorganized 9/03/04 5
May 21 instructional days Module 8: Module 9: Module 10: Geometry: Area, Perimeter, and Volume Operations with Fractions: Multiplication and Division Measurement, Probability and Ratio 1 days 11 days 9 days June 22 instructional days STAR 5/27 6/17 DMT 6/13 6/17 July 14 instructional days Module 10: Measurement, Probability and Ratio Review Grade 5 concepts Preview Grade 6 Concepts 12 days 14 days Reorganized 9/03/04 6
San Diego City Schools Instruction and Curriculum Division MATHEMATICS CURRICULUM MAP GRADE 5 MODULE 4 GEOMETRY: PLANE AND SOLID FIGURES Modules represent individual units of study that lead to essential learnings THREADS THROUGHOUT THE YEAR- GRADE 5 The threads represent ongoing learning opportunities in which students should be actively engaged throughout all units of inquiry during the entire school year. These items should not be isolated to any one particular unit of inquiry. Students will: Develop understanding of numbers and the number system and use their understanding to solve problems and recognize reasonable results. Develop understanding of and fluency in basic computation and procedural skills. Use mathematical reasoning to solve problems. Communicate their mathematical thinking by using words, numbers, symbols, graphs and charts and translate between different representations. Use equations and variables to express generalizations of patterns and relationships. Develop logical thinking to analyze evidence and build arguments to support or refute a hypothesis. Make connections among mathematical ideas and between other disciplines Develop and use strategies, skills, and concepts to solve problems. Use appropriate tools, including technology, as vehicles to learn mathematical concepts. These are essential learnings that represent bigger ideas/concepts: Students use ordered pairs to locate and describe locations on a 4-quadrant coordinate grid. Students build their spatial sense through geometric experiences. Students transform shapes in a plane or in space and describe the changes as translations (slides), reflections (flips) and rotations (turns). Students visualize, and draw a three dimensional figure from two-dimensional views. Students test figures for rotational symmetry. Students estimate angle size using benchmark angles and use a protractor to measure angle size more accurately. Students test and generalize the number of degrees in the angles of a triangle. Students relate circumference of a circle to perimeter of polygons. Through measurement and observation, students determine the relationship between the radius and diameter of a circle. These are essential questions that learners ask themselves in order to achieve the essential learnings: How do I describe the parts of a graph on a 4 quadrant coordinate plane, and then identify and plot ordered pairs of integers on the graph? *How can I identify, describe and classify plane and solid geometric figures by their properties, including angles and sides? How can I use estimation and measurement with a protractor to classify angles? *How can I identify the parts of a circle and explain the relationship between radius and diameter? *How do I identify similar and congruent figures? *How do I identify and explain lines of symmetry in a polygon? *How do I test a polygon for rotational symmetry? How can I verify that the total number of degrees in the angles of any triangle is 180? How do I identify and draw solid figures from top, side and front views? * Presented in previous grades Resources: Van de Walle: Chapters 19 & 20 (pp. 329-340 & pp. 360-376); Mathematics Source Book: (pp. 27-30 and pp. 109-114) Reorganized 9/03/04 7
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13 Days Key Mathematical Concepts: Identify and graph ordered pairs of integers in four quadrants of the coordinate plane. Identify, describe and classify plane and solid geometric figures by their properties. Use the number of degrees in a triangle and quadrilateral to solve problems. Classify angles using estimation and measurement with a protractor. Identify and measure the parts of a circle. Identify similar and congruent figures. Day 1 Lesson 24.1 Graph Relationships Day 6 Day 2 Lesson 24.2 Graph Integers on the Coordinate Plane Day 7 Day 3 Lesson 24.3 Use an Equation to Graph Day 8 Day 4 Lesson 25.1 Day 9 Lines and Angles Day 5 Lesson 25.2 Measure and Draw Angles Day 10 Lesson 25.3 Lesson 25.5 Lesson 25.5 Lesson 25.6 Lesson 26.1 Angles and Polygons Circles Congruent and Similar Figures Symmetric Figures Classify Plane and Solid Figures Day 11 Day 12 Day 13 Lesson 26.2 Lesson 26.4 Lesson 26.5 Quadrilaterals Solid Figures Draw Solid Figures from Different Views Reorganized 9/03/04 9
DAY 1 Unit 7: Algebra and Geometry Chapter 24: Geometry LESSON 24.1, pp. 438-441 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. Toothpicks or straws (36 per group) and mini-marshmallows, clay or gumdrops (24 per group). TR43 44, 45 and 46: Grids to add to plastic cover for repeated use with dry erase pens during unit and the rest of the year. Two sheets of consumable graph paper per student. Graph Relationships SDAP 1.4: Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. SDAP 1.5: Know how to write ordered pairs correctly; for example, (x,y).:.:. To graph a relationship shown in a table. To understand the input, x, and the output, y, from a function table can be written as ordered pairs. To understand the first number of an ordered pair gives the horizontal movement. (x-axis) and the second number gives the vertical movement (y-axis). To learn that the intersection of the x-axis and the y-axis is called the origin. Groups of three build the three prisms on pages 438 and 439 using mini-marshmallows, clay or gumdrops and toothpicks. Discuss the properties of prisms in relation to the three prisms they have built. (A prism is a polyhedron that has two congruent bases. All other faces are rectangles.) Use the prisms to surface the meanings of congruent, face, base, and sides on the base. The edges are the toothpicks; the faces are the rectangles formed by the toothpicks; the vertices are represented by the marshmallows. (Vocabulary can be labeled and charted so students can refer to it.) Students will use tables and graphs to analyze the relationship between the number of sides of the base of the prism and the number of vertices of the prism, and then, the number of sides of the base and the number of total faces on the prism. Students label TR44 Grid while teacher models it on large graph paper. Display the table at top of Learn, page 438. Reorganized 9/03/04 10
Learn, p. 438. Record Prism Patterns on board/overhead, and read with students. Model writing and graphing the first ordered pair with the students. Students write and graph the ordered pairs for the second two prisms. Teach, p. 438, Guided Instruction bullets 1 & 2 to guide discussion. Students write and graph the ordered pairs that represent the relationship between the number of sides on the base and the number of faces on the prism. Display the table on page 438. Students use their prisms to verify data for the Y values of the table. Students copy the table, write the ordered pairs and complete the graph on TR 44 grid. (Dry erase or consumable) (Their graphs should look like those on p. 438. Teach, p. 438, Guided Instruction bullet #3 to discuss. EXPLORE: Work with the concept. Focus on students doing mathematics. PRACTICE: Focus on Communication and Representation. Alternative Teaching Strategy T.E. 438B Connect activity to graphing of prism properties. Practice & Problem Solving, p. 439. Graph the ordered pairs for # 4 or 5. Check with a partner. Practice & Problem Solving, p. 439 #8-10 SUMMARIZE: Connect purpose to activities. T.E. ASSESS, p. 439: DISCUSS T.E. ASSESS, p. 439: WRITE HOMEWORK: Practice & Problem Solving, p. 439 #6 Mixed Review, p. 439 Try to write a rule for finding the number of nickels in any number of quarters or the perimeter of any square. Reorganized 9/03/04 11
MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. TR 45 for each student. EXPLORE: Work with the concept. Focus on students doing mathematics. PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. DAY: 2 Unit 7: Algebra and Geometry Chapter 24: Geometry LESSON 24.2, pp. 440-444 TR43, 44, 45 and 46: Grids to add to plastic cover for repeated use with dry erase pens during unit and the rest of the year. One sheet of consumable graph paper per student Graph Integers on the Coordinate Plane SDAP 1.4: Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. SDAP 1.5: Know how to write ordered pairs correctly; for example, (x,y). AF 1.4: Identify and graph ordered pairs in the four quadrants of the coordinate plane.. To identify and graph integers on a coordinate plane To understand that when plotting points, begin at origin (0,0), and move horizontally first, then vertically. To learn the four sections of the coordinate plane are called quadrants. To understand the coordinates can be positive, negative or zero. Number of the Day 24.2, T.E. p. 440A Display transparency of TR46: Students determine how this grid is different from the one used in the last lesson. Learn, p. 440. Write Mapping History on the board/overhead. TEACH, T.E. Pg. 440. Guided Instruction questions to guide discussion. Emphasize use of correct vocabulary (origin, ordered pairs, coordinate plane, quadrants, negative direction, positive direction, x-axis, y-axis) Continue with Graphing Ordered Pairs, p. 441. Discuss with questions top margin TE p. 441. Check, p. 441 #2 4. Discuss. Then, #18 20. Discuss. Use direction clues from ELL Strategy on T.E. p. 440B if your students need the assistance. Practice & Problem Solving, p.442 #41 46. Students work with partners. Discuss. Then, #47 51. Discuss Link Up to Geometry: Pg. 443: Optional: Allow students to identify how the new locations were found (rotation, reflected, translation). Practice & Problem Solving, p. 442 #52. Discuss. T.E. ASSESS, p. 443: WRITE. Share. HOMEWORK: Mixed Review and Test Prep: Pg. 443 Reorganized 9/03/04 12
DAY: 3 Unit 7: Algebra and Geometry Chapter 24: Algebra Integers LESSON 24.3, pp. 444-447 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: Purpose of Lesson: LAUNCH: Introduce students to concepts. EXPLORE: Work with the concept. Focus on students doing mathematics. TR46 Use an Equation to Graph AF 1.5: Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. SDAP 1.5: Know how to write ordered pairs correctly; for example, (x,y). AF 1.4: Identify and graph ordered pairs in the four quadrants of the coordinate plane..:. To use an equation to graph the relationship between numbers. To understand speed is a rate of movement. To understand the equation of a straight line is in the form y = a X x, where a is a constant. Number of the Day 24.3, T.E. p. 444A Modify by clarifying problem: 1 week = 7 days (1,7) Discuss the labels for a graph of the data. (x = weeks; y = days) Can you predict the ordered pair for number of days in 10 weeks? How will the graph change for each week? Alternative Teaching Strategy, T.E. p. 444B Learn, p. 444. Write Slow Start on board/overhead. Read with students. Teach, p. 444, Guided Instruction questions to guide discussion. Continue with More Graphing, p. 445. Discuss using bullets top margin, p. T.E. p.445. Alternative Teaching Strategy: T.E. Pg.446 Practice & Problem Solving, p. 446 #20-25 PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. Science Connection: T.E. 444B Students create a table and a graph to plot the snail s progress. Predict the distance traveled in one hour. Discuss equivalent ways of describing the graph with an equation: D= m+m; D = m x 2; D = 2m Discuss representations for a couple of problems in Practice. T.E. Assess, p. 447: DISCUSS T.E. Assess, p. 447: WRITE HOMEWORK: Mixed Review and Test Prep: Pg. 447 Reorganized 9/03/04 13
DAY: 4 Unit 7: Geometry Chapter 25: Plane Figures LESSON 25.1: Pg. 454-457 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. Literature Connection: Flatland (T.E. 454B) For each student: Ruler and Polygon Worksheet, two toothpicks or Popsicle sticks or straws, poster size paper; markers; magazines per group, one copy of TR56. Lines and Angles MG 2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools. MG 2.3: Use a variety of methods, such as works, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. :. Identify different kinds of angle and line relationships. Understand properties of lines such as: lines in the same plane intersect or are parallel. Learn, Pg. 454: What s the Angle? Teach, Pg. 454: Guided Instruction questions to guide discussion. SE Pg. 454, bottom. Use toothpicks to form angles and move them to show acute, obtuse, right and straight angles. Students might also use them to model intersecting, perpendicular and parallel lines. EXPLORE: Work with the concept. Focus on student s doing mathematics. TR56 PRACTICE: Focus on Communication and Representation. Alternative Teaching Strategy: T.E. Pg. 456 Activity, Pg. 455. Students work individually, but discuss in pairs as they work. Emphasize proper labeling. Check, Pg. 456 #1. Discuss. Practice & Problem Solving, Pg. 456 #19-22. Practice & Problem Solving, Pg. 456-457 #29 36. Students work in pairs. Share thinking and solutions. Reorganized 9/03/04 14
SUMMARIZE: Connect purpose to activities. HOMEWORK: ASSESS, TE Pg. 457: DISCUSS ASSESS, TE Pg. 457: WRITE Link up to Science, Pg. 457. See margin TE Pg. 457 to prepare students for assignment. Mixed Review and Test Prep, Pg. 457 #42-44. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Use tables from Lesson 24.3 and Function Tables from Pg. 437 for patterns and equations. Reorganized 9/03/04 15
DAY: 5 Unit 7: Geometry Chapter 25: Plane Figures LESSON 25.2, Pg. 458-459 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. List mathematical terms that you want students to use when describing their procedures or thinking. Model use of the terms and encourage students to refer to charts when writing and speaking. EXPLORE: Work with the concept. Focus on student s doing mathematics. Protractor for each student; Measure and Draw Angles MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. MG 2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools. : :. Use a protractor to measure angles. Understand the attributes of acute, right and obtuse angles. Understand the length of the ray of an angle does not change the measure of the angle. Ask students to discuss types of angles with a partner. Share responses whole group. Introduce the protractor as a mathematical tool. Explore, Pg. 458. Teach, Pg. 458, Guided Instruction questions to guide discussion. Students do Try It, bottom Pg. 458. Be sure students name angles as well as measure them. Alternative Teaching Strategy, TE Pg. 458B Connect, top SE Pg. 459. Review, practice, discuss with students. Model using a protractor to draw angles of a given number of degrees. Students construct angles of: 40, 125, 95, and 35 degrees. Reorganized 9/03/04 16
PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to Practice, Pg. 459 #1 4. Discuss with students. Practice, Pg. 459 #12, 13, 14. Share thinking. ASSESS, TE Pg. 459: DISCUSS ASSESS, TE Pg. 459: WRITE activities. HOMEWORK: Mixed Review and Test Prep: Pg. 459 #17-20 Trace angles of different sizes from household objects. Classify the angles. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. Reorganized 9/03/04 17
DAY: 6 Unit 7: Geometry Chapter 25: Plane Figures LESSON 25.3, Pg. 460-463 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. Square dot paper Square and triangle dot paper: TR49 and TR50 Angles and Polygons MG 2.1: Measure, identify, and draw angles, perpendicular and parallel llines, rectangles, and triangles by using appropriate tools. MG 2.2: Know that the sum of the angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems. : :. Use angles to classify and measure polygons Understand polygons have the same number of angles as sides. Understand regular polygons have all sides the same length, such as a square. Quick Review: Pg. 460 Learn, Pg. 460: Sign of the Times. Put empty chart on board/overhead. Ask students to copy chart. Fill in as shapes are discussed and have students fill their charts in at the same time. Teach, Pg. 460. Guided Instruction questions to guide discussion. Activity 1, bottom Pg. 460. Discuss. EXPLORE: Work with the concept. Focus on student s doing mathematics. Guiding Question: Challenge groups to determine the sum of the number of degrees of the interior angles in a rectangle and in a triangle. How could we prove it? One Way: Activity 2, top SE Pg. 461. Demonstrate activity as students work through the steps. See bullets top margin TE Pg. 461 to guide discussion. Emphasize Math Idea. Another way to test the number of degrees in the interior angles of a polygon: Discuss what the students discovered about the sum of the angles in triangles. Sketch several quadrilaterals on the board and ask students to sketch some of their own. Draw a diagonal in one quadrilateral to form two triangles. Students determine the total degrees in the quadrilateral using what they know about triangles. Connect conclusions to Activity 2 results. Reorganized 9/03/04 18
PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. HOMEWORK: Practice & Problem Solving, Pg. 462 #10 13. Do together & discuss. Practice & Problem Solving, Pg. 462 463 #21-22, 26-27, 31-32. Students work with partner. Discuss whole group. ASSESS, TE Pg. 463: DISCUSS ASSESS, TE Pg. 463: WRITE Practice & Problem Solving, Pg. 462: Draw 14-17 on dot paper. Mixed Review and Test Prep, Pg.. 463 ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. Reorganized 9/03/04 19
DAY: 7 Unit 7: Geometry Chapter 25: Plane Figures LESSON 25.4, Pg. 464-467 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. EXPLORE: Work with the concept. Focus on student s doing mathematics. Compass, straight edge and protractor for each student. Paper, scissors, cm ruler, TR27. Circles MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. MG 2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools. : :. To draw a circle and identify and measure its parts. Understand the relationship between parts of a circle: diameter, radius, chord. Know the central angles of a circle total 360 degrees. Learn, Pg. 464: Round and Round. Teach, Pg. 464, Guided Instruction questions to guide discussion. Activity 1, p. 464. Using a compass. Model as students do the activity and discuss as they work. Reinforce vocabulary as you discuss. Check, Pg. 465 #1 5. Do with students and discuss. Activity 2: Pg. 465. See bullets top margin TE Pg. 465 to guide discussion. Check, Pg. 466 #11, 12. Do together and discuss. PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. Practice & Problem Solving, Pg. 466 467 #32-37. Students work individually or with partners. Share solutions and discuss. ASSESS, TE Pg. 467: DISCUSS ASSESS, TE Pg.. 467: WRITE. Share solutions. HOMEWORK: Mixed Review and Test Prep, Pg. 467 #38-47. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. Reorganized 9/03/04 20
DAY: 8 Unit 7: Geometry Chapter 25: Plane Figures LESSON 25.5, Pg. 468-471 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAU LAUNCH: Introduce students to concepts. EXPLORE: Work with the concept. Focus on student s doing mathematics. Pattern Blocks for each table. Congruent and Similar Figures MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. : : :. Identify similar and congruent figures. Understand that corresponding parts of congruent figures are congruent. Ask students to discuss in groups what they know about congruent and similar figures and record group responses. Learn, Pg. 468: Double Take. Use transparency of Pg. 468 or put examples on board/overhead to discuss congruent and similar figures. Teach, Pg. 468. Guided Instruction questions to guide discussion. Students each explain to a partner everything they understand about congruent and similar figures and any questions they still have (one minute per partner). Alternative Teaching Strategy: Pg. 468B. Check, p. 468 #1 4. Do with students and discuss. Pattern Blocks PRACTICE: Practice & Problem Solving, Pg. 469 #11-17. Focus on Students work independently or with partners. Communication and Discuss whole group. Representation. SUMMARIZE: ASSESS, TE Pg. 469: DISCUSS: How would you check to see if two Connect purpose to figures were congruent? activities. ASSESS, TE Pg. 469: WRITE HOMEWORK: Mixed Review and Test Prep, Pg. 469. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. Reorganized 9/03/04 21
DAY: 9 Unit 7: Geometry Module 4: Chapter 23: Plane Figures LESSON 25.6, Pg. 470-473 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. Challenge 25.6: 1 copy per student. Pattern blocks. Grid paper. Scissors. Small mirrors to test lines of symmetry. Symmetric Figures MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. : :. To identify multiple lines of symmetry and test for rotational symmetry. Understand turning a figure around a point (vertex) is rotation. Every regular polygon has rotational symmetry. Learn, Pg. 470: Reflect on It. Write HOLLYWOOD on the board/overhead and present the question. Teach, Pg. 470. Guided Instruction questions to guide discussion. Discuss meaning and have students draw the lines of symmetry in the word. Ask students if the whole word has any lines of symmetry since all the letters did? Alternative Teaching Strategy, Pg. 470B. EXPLORE: Work with the concept. Focus on student s doing mathematics. Introduce to students another kind of symmetry, called rotational symmetry. Activity, middle SE Pg. 470. Students discuss in pairs. Share observations. Example, bottom SE Pg. 470. Discuss rotational symmetry. Continue with bullets margin, TE Pg. 470 to guide discussion. To reinforce the concept of rotational symmetry: Trace the blue parallelogram (rhombus) (from the pattern blocks) on the overhead and turn it in its frame to see when it fits back into it. Students test the rest of the pattern blocks for rotational symmetry and line symmetry. Reorganized 9/03/04 22
PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. Practice & Problem Solving, Pg. 471 #13-19. Discuss Challenge 25.6 Students explain the difference between line and rotational symmetry. ASSESS, TE Pg.. 471: DISCUSS HOMEWORK: Practice & Problem Solving, Pg. 471: 10-12. Mixed Review and Test Prep. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. Reorganized 9/03/04 23
DAY: 10 Unit 7: Geometry Chapter 26: Classify Plane and Solid Figures LESSON 26.1, Pg. 478-481 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. EXPLORE: Work with the concept. Focus on student s doing mathematics. TR50: Triangle Dot Paper. Protractors. Centimeter rulers. Challenge 26.1. Posterboard. Triangles MG 2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools. MG 2.2: Know that the sum of the angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems. : :. To classify triangles by the length of their sides, as equilateral, isosceles, or scalene and the measures of their angles, as acute, obtuse, or right. Know the sum of the measures of the interior angles of all triangles is 180 degrees. Quick Review, SE Pg. 478 Learn, p. 478: Side by Side. Display transparency of Pg. 478. Cover the definitions of the three kinds of triangles classified by sides. Ask students to look at the measurements and see if they can recognize the attributes of the three different triangle types. Students then describe the relative sizes of the angles. Discuss the classification by angles. See TEACH, Pg. 478-479, Guided Instruction questions to guide discussion. Check, Pg. 479 #1, 10 12. Discuss whole group. Alternative Teaching Strategy: T.E. Pg. 478B. Posterboard PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. Practice & Problem Solving, Pg. 481 #30, 33, 34. Discuss. Challenge 26.1 Problem of the Day 26.1, Pg. 478A: Discuss the true sentences made from the classifications. ASSESS, TE Pg. 481: DISCUSS. Reorganized 9/03/04 24
HOMEWORK: If necessary, finish: Challenge 26.1. Practice & Problem Solving, Pg. 480: 23-26. Mixed Review, Pg. 481. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg 437. Reorganized 9/03/04 25
DAY: 11 Unit 7: Geometry Chapter 26: Classify Plane and Solid Figures LESSON 26.2, Pg. 482-485 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. TR46: Coordinate Plane Grid. TR49: Dot Paper. TR57: Tangram. Straws cut to the lengths of 3, 4, 5, 6 inches for each student. Modeling clay, or jellied candies, or mini-marshmallows. Markers. Quadrilaterals MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. MG 2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools. : :. To classify quadrilaterals Know quadrilaterals are polygons that have 4 sides and 4 angles. Learn, Pg. 482: Four by Four. Display quadrilaterals on Pg. 482 on board/overhead or transparency and discuss what they all have in common and how they differ. Record attributes as students describe them. Teach, Pg. 482, Guided Instruction questions to guide discussion. Then, draw a trapezoid with one right angle and ask the students to classify it using the chart (quadrilateral, trapezoid). Draw a square and repeat (quadrilateral, rectangle, square, parallelogram). EXPLORE: Work with the concept. Focus on student s doing mathematics. Alternative Teaching Strategy, TE Pg. 482B Early Finishers T.E. Pg. 482B, for all students. Tangrams: TR57 Reorganized 9/03/04 26
PRACTICE: Focus on Communication and Representation. Practice & Problem Solving, Pg. 483: 14-17, 19, 20, 21. Discuss/share reasoning. SUMMARIZE: Connect purpose to activities. ASSESS, TE Pg. 483: DISCUSS ASSESS, TE Pg. 483: WRITE HOMEWORK: Review/Test, Pg. 494: 7-10 ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. Reorganized 9/03/04 27
DAY: 12 Unit 7: Algebra and Geometry Chapter 26: Classify Plane and Solid Figures LESSON 26.4, Pg. 486-489 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. EXPLORE: Work with the concept. Focus on student s doing mathematics. Rectangular prisms and cylinders of different sizes: 1 for every pair Collection of pyramids, prisms that are not rectangular, cones and spheres. Solid Figures MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. AF 1.2: Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. :. Identify solid figures Solids are named according to the shape of the base of the prism or pyramid. Prisms and pyramids have 2 bases that are congruent and parallel. Learn, Pg. 486: Box, Ball, or Can. Use a transparency of the picture of the Rock & Roll Hall of Fame to engage students in identifying shapes. Discuss observed attributes. Use Guided Instruction questions (T.E. Pg. 486-487) but if possible use solids, not just pictures of solids in the book, for students to examine. Model orally giving a description of a polyhedron using the charted vocabulary. As you discuss the vocabulary used, create a class chart of words and sketches to illustrate meaning. Then partners take turns describing a different polyhedron using the math vocabulary. Classify Solid Figures, Pg. 487. See bullets top margin TE Pg. 487 to guide discussion. Discuss examples shown in the pictures. Practice & Problem Solving, Pg. 488 #14-17. Do with students and discuss. Reorganized 9/03/04 28
PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. Practice & Problem Solving, Pg. 488 #26 29. Discuss responses. Ask students to make a table just like the one on Pg. 488, for #22 25. Students work with partners to fill in the table while observing the solid figures. Give each group two or three solid figures to identify, and count bases, faces, edges and vertices. Pass the figures from table to table. ASSESS, TE Pg. 489: DISCUSS ASSESS, TE Pg. 489: WRITE: Sketch it. Share responses and sketches. HOMEWORK: Mixed Review and Test Prep: Pg. 489: 34-45. ROUTINES: o Choose from: o Routines in Harcourt Training and Routines already introduced. o Include ordering positive and negative integers when using a blank number line. o Include addition and subtraction of integers using models or mental math. o Tables from Lesson 24.3 and Function Tables from Pg. 437. o Math Detective, Pg. 496: 8 different problems to use one at a time. Reorganized 9/03/04 29
DAY: 13 Unit 7: Geometry Chapter 26: Classify Plane and Solid Figures LESSON 26.5, Pg. 490-491 MATERIALS: LESSON FOCUS: CALIFORNIA STANDARDS: PURPOSE OF LESSON: LAUNCH: Introduce students to concepts. TR32 Grid Paper connecting cubes for teacher EXPLORE: Work with the concept. Focus on student s doing mathematics. PRACTICE: Focus on Communication and Representation. SUMMARIZE: Connect purpose to activities. TR32 Grid Paper, one piece for plastic cover to be reused and two to be consume by each student. Cubes for students and teacher. Draw and Identify Solid Figures from Different Views MG 2.3: Visualize and draw two-dimensional views of threedimensional objects made from rectangular solids. MG 2.0: Students identify, describe, and classify the properties of, and relationships between, plane and solid geometric figures. : :. Draw and identify solid figures from different views Solids can be recognized from 3 views: front, top and side. Alternative Teaching Strategy: T. E. Pg. 490 Explore, Pg. 490. Ask students to practice the views shown on a piece of grid paper. Try It, Pg. 490. Students may use the same grid paper used for Explore. Connect, Pg. 491. Discuss with students. Practice, Pg. 491. Partners choose two from #1-4 and draw the views. Practice, Pg. 491 #5-9. Students use grid paper to sketch views. Partner Work: Build a figure with fewer than 12 cubes and draw the three views. Trade drawings with a pair from another table and try to build the figure using the drawings of the three views. Discuss Whole Group: What did you discover about the similarities and differences between drawing three views and building figures using the drawings? Which was easier? Why? Discuss strategies they used. HOMEWORK: Mixed Review and Test Prep, Pg. 491 Reorganized 9/03/04 30
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