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PatternBlockLessonsto Meet Common Core State StandardsGrades 3–5Excerpts From Bridges in MathematicsPBLCCSS35

Pattern Block Lessons to Meet Common Core State Standards Grades 3–5The Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel. 1 800 575–8130. 2012 by The Math Learning CenterAll rights reserved.Prepared for publication on Macintosh Desktop Publishing system.Printed in the United States of America.PBLCCSS35 QP1277 P0412The Math Learning Center grants permission to classroom teachers to reproduce blacklinemasters in appropriate quantities for their classroom use.Bridges in Mathematics is a standards-based K–5 curriculum that provides a unique blendof concept development and skills practice in the context of problem solving. It incorporates the Number Corner, a collection of daily skill-building activities for students.The Math Learning Center is a nonprofit organization serving the education community.Our mission is to inspire and enable individuals to discover and develop their mathematicalconfidence and ability. We offer innovative and standards-based professional development,curriculum, materials, and resources to support learning and teaching. To find out more,visit us at www.mathlearningcenter.org.

Table of ContentsGrade 3Activity 1 Pattern Block Fractions*1Meets CCSS: 3.NF.1, 3.NF.3, 3.G.2Format: Whole GroupActivity 2 Creating Symmetrical Snowflakes5Meets CCSS: 3.G.2, 4.G.3Format: Whole GroupActivity 3 Sorting Snowflakes by Symmetry11Meets CCSS: 3.G.2, 4.G.3Format: Whole GroupGrade 4Activity 1 Pattern Block Symmetry*17Meets CCSS: 4.G.2, 4.G.3Format: Whole GroupActivity 2 Mosaic Game23Meets CCSS: 4.G.2, 4.G.3Format: CenterGrade 5Activity 1 Pattern Block Angles*31Meets CCSS: 4.MD.5, 4.MD.6, 4.MD.7, 4.G.1, 5.G.3, 7.G.5Format: Whole GroupActivity 2 Angle Measures in Triangles & Quadrilaterals*43Meets CCSS: 4.MD.5, 4.MD.6, 4.MD.7, 4.G.1, 5.G.3, 7.G.5Format: Whole GroupActivity 3 Angle Measure: From Pattern Blocks to ProtractorsMeets CCSS: 4.MD.5, 4.MD.6, 4.MD.7, 4.G.1, 5.G.3, 7.G.5Format: Whole Group* Pattern Blocks are the only manipulative required for this activity.49

Grades 3–5IntroductionIntroductionPattern Blocks and the Common Core State StandardsPattern Blocks are a familiar manipulative available in most elementaryschools. We’ve created this Pattern Block Lessons sampler to help you meetthe new Common Core State Standards (CCSS) and organized it in two gradelevel bands, K–2 and 3–5. The lessons are excerpts from the Bridges in Mathematics curriculum, published by The Math Learning Center. We hope you’llfind the free resources useful and engaging for your students.The Common Core State Standards (2010) define what students should understand and be able to do in their study of mathematics. A major goal of theCCSS is building focus and coherence in curriculum materials. The standardsstrive for greater consistency by stressing conceptual understanding of keyideas and a pacing the progression of topics across grades in a way that alignswith “what is known today about how students’ mathematical knowledge,skill, and understanding develop over time.” (CCSSM, p. 4). In addition to thecontent standards, the CCSSM defines Eight Mathematical Practices that describe the processes—the how teachers will teach, and how students will interact in a mathematics classroom.Bridges in Mathematics helps teachers meet the challenges of the ContentStandards and the Eight Mathematical Practices. During a Bridges lesson,students make sense of mathematics using manipulatives, visual and mental models to reason quantitatively and abstractly. They solve challengingproblems daily that develop their stamina to carry out a plan and to presenttheir thinking to their classmates. Students make conjectures and critiquethe reasoning of others, by asking questions, using tools, drawings, diagramsand mathematical language to communicate precisely. Students develop anduse a variety of strategies to become computationally fluent with efficient,flexible and accurate methods that make use of patterns and the structuresin operations and properties. They use dimensions, attributes, and transformations to make use of the structures in Number and Geometry. Bridges encourages students to estimate a reasonable answer, and continually evaluatethe reasonableness of their solution. This Pattern Block sampler will provideyou with examples of lessons from whole group Problems and Investigationsand centers called Work Places. In many cases there are suggestions for support and challenge to help you meet the CCSS standards and differentiateyour instruction. The Math Learning CenterPattern Block Lessons to Meet Common Core State Standards Grade 3–5 v

Grades 3–5IntroductionBridges in MathematicsBridges in Mathematics is a full K–5 curriculum that provides the tools, strategies, and materials teachers need to meet state and national standards.Developed with initial support from the National Science Foundation, Bridgesoffers a unique blend of problem-solving and skill building in a clearly articulated program that moves through each grade level with common models,teaching strategies, and objectives.A Bridges classroom features a combination of whole-group, small-group, andindependent activities. Lessons incorporate increasingly complex visual models—seeing, touching, working with manipulatives, and sketching ideas—tocreate pictures in the mind’s eye that helps learners invent, understand, andremember mathematical ideas. By encouraging students to explore, test, andjustify their reasoning, the curriculum facilitates the development of mathematical thinking for students of all learning styles.Written and field-tested by teachers, Bridges reflects an intimate understanding of the classroom environment. Designed for use in diverse settings, thecurriculum provides multiple access points allowing teachers to adapt to theneeds, strengths, and interests of individual students.Each Bridges grade level provides a year’s worth of mathematics lessonswith an emphasis on problem solving. Major mathematical concepts spiralthroughout the curriculum, allowing students to revisit topics numeroustimes in a variety of contexts.To find out more about Bridges in Mathematics visit www.mathlearningcenter.orgvi Pattern Block Lessons to Meet Common Core State Standards Grade 3–5 The Math Learning Center

Grade 3Bridges in MathematicsActivity 1MAGNETIC BOARDPattern Block FractionsOverviewStudents use magnetic pattern blocks tomodel the relationships between parts andthe whole and to find equivalent fractions.FrequencyIncorporate this routine into your calendartime two days per week.Skills & ConceptsH Demonstrate an understanding of aunit fraction 1 b as 1 of b equal partsinto which a whole has been partitioned (e.g., ¼ is 1 of 4 equal parts ofa whole) (3.NF.1)H Demonstrate an understanding of afraction a b as a equal parts, each ofwhich is 1 b of a whole (e.g., ¾ is 3 of4 equal parts of a whole or 3 partsthat are each ¼ of a whole) (3.NF.1)H Identify equivalent fractions by comparing their sizes (3.NF.3a)H Recognize simple equivalent fractions(3.NF.3b)H Generate simple equivalent fractions(3.NF.3b)H Explain why two fractions must beequivalent (3.NF.3b)H Demonstrate that fractions can onlybe compared when they refer to thesame whole (3.NF.3d)H Use the symbols , , and to recordcomparisons of two fractions (3.NF.3d)H Explain why one fraction must begreater than or less than another fraction (3.NF.3d)H Partition shapes into parts with equalareas (3.G.2)H Express the area of each equal part ofa whole as a unit fraction of the whole(e.g., each of b equal parts is 1/b ofthe whole) (3.G.2)You’ll needH pattern blocksH magnetic pattern blocks (yellow hexagons, blue rhombuses, green triangles,and red trapezoids, optional)H magnetic surface (optional)H erasable marker (e.g., Vis-à-Vis)Note This activity can be conducted at aprojector if magnetic pattern blocks andsurface are not available.H Write a whole number as a fraction(3.NF.3c)H Recognize fractions that are equivalentto whole numbers (3.NF.3c)H Compare two fractions with the samenumerator (3.NF.3d)H Compare two fractions with the samedenominator (3.NF.3d) The Math Learning CenterPattern Block Lessons to Meet Common Core State Standards Grade 3–5 1

Grade 3Bridges in MathematicsActivity 1 Pattern Block Fractions (cont.)Identifying Fractional Parts of the WholeInvite students to join you in front of the magnetic board. Place a yellowhexagon on the magnetic board and explain that today, this shape has an areaof 1 unit. Write the numeral 1 under the hexagon. Next, display a collectionof blue rhombuses, triangles, and trapezoids, and ask students to considerwhat the area of each of these shapes would be if the hexagon is 1. Invite volunteers to come up to the magnetic board to share their thinking. When students have identified the area of a particular shape, record this informationon the magnetic board.Ginny The red trapezoid is half of the hexagon. I know because when Iput two trapezoids together, it’s the same as 1 hexagon.112Once students have determined the fractional parts represented by eachshape, leave the labeled shapes on the magnetic board for reference in thecoming weeks.1121316Continuing through the MonthAs you continue this workout through the month, invite students to use themagnetic pattern blocks to consider equivalent fractions and determine thefractional value of each shape if the unit is shifted, as described on the next2 Pattern Block Lessons to Meet Common Core State Standards Grade 3–5 The Math Learning Center

Grade 3Bridges in MathematicsActivity 1 Pattern Block Fractions (cont.)page. Follow your students’ lead through the month, and introduce new challenges as they’re ready. For many groups of third graders, considering fractional parts of the hexagon whole will be challenging enough to provide richdiscussions for the entire month. Make sure students have collections of pattern blocks, if needed.Identifying Equivalent Fractions & Combinations of FractionsInvite students to explore equivalent fractional parts by finding a variety ofways to show half (or a third, or two-thirds) of a hexagon, working with theavailable pattern blocks at the magnetic board. If you have enough pieces,leave these equivalent fractions displayed on the magnetic board so studentscan consider them at other times.Teacher Some of you said that when the hexagon is 1 whole unit, thetrapezoid is exactly one-half. Are there other ways to show one-half ofthe hexagon with the other pattern blocks?Sebastian You can also make one-half with 3 triangles. Look, I’ll show you.Teacher Sebastian, I’d like to write what you’ve shown as a numbersentence. I can write one-half equals. Then what? Any ideas about howto complete the number sentence?Emma 3!Tom I don’t get that, Emma. How can one-half equal 3?Emma Well, you have 3 triangles. So 3 equals one-half. Hmm, thatseems a little funny.Rosa There are 3 triangles, but each one is one-sixth. So 3 one-sixths isequal to one-half.Teacher Emma saw 3 triangles, and Rosa explained that each triangleis just one-sixth. So we can say one-half equals three-sixths.12113161 32 6 The Math Learning CenterPattern Block Lessons to Meet Common Core State Standards Grade 3–5 3

Grade 3Bridges in MathematicsActivity 1 Pattern Block Fractions (cont.)Proving EquivalenciesAnother way to approach the concept of equivalent fractions with your classis to write the following number sentences on the board one at a time. Thenask students to think about whether or not the number sentence on the boardis true. Encourage discussion, and then invite volunteers to use magnetic pattern blocks to prove whether the statement is true.21 633 131 2 2 311 76 62 123 1 6 22 1 3 211 43 3Changing the Unit of AreaLater in the month, you could explore with your students what happens ifyou shift the unit. For instance, what if the hexagon is assigned a value ofone-half rather than 1? What would a whole unit look like? What would thevalues of the other pattern blocks be if the hexagon were one-half? Encouragestudents to look for different ways to show the same fractions with differentpattern blocks, for example, by combining a rhombus and a triangle to makeone-fourth.11214161121 1 14 6 12In their explorations and discoveries, students may combine fractions withunlike denominators, as in the example shown above. Because their explorations are both intuitive and visual, there’s no need to do anything but recordtheir findings in fractional terms (e.g., 1/4 1/6 1/12). Be sure to express2/2, 3/3, 4/4, 6/6 and 12/12 as a whole as well.4 Pattern Block Lessons to Meet Common Core State Standards Grade 3–5 The Math Learning Center

Grade 3Bridges in MathematicsActivity 2PROBLEMS & INVESTIGATIONSCreating Symmetrical SnowflakesOverviewYou’ll needExploring the natural world providesstudents with many opportunities toappreciate geometry. Today, you canread a charming book, Snowflake Bentley,to introduce students to the symmetryfound in snowflakes. Students use whitepattern block cutouts to create their ownunique snowflakes.H Snowflake Pattern Blocks, pages 1 and2 (Teacher Masters 1 and 2, class setrun on white paper) or shapes pre-cuton a die cut machineActions1The teacher can opt to read the bookSnowflake Bentley to introduce snowflake forms.2 Students use white paper patternblock cutouts to make their ownsnowflake designs.Skills & ConceptsH Partition shapes into parts with equalareas (3.G.2)H Express the area of each equal part ofa whole as a unit fraction of the whole(e.g., each of b equal parts is 1/b of thewhole) (3.G.2)H Snowflake Bentley by JacquelineBriggs Martin (optional, check thelibrary for availabilty)H poems about snow and snowflakes(optional)H 8″ or 9″ squares of black or blue construction paper (class set plus some extra)H glue sticksNote Wilson A. Bentley was a Vermont photographer who pho