BRIDGES GRADE 5 SUPPLEMENT Oregon Sets

Transcription

1 BRIDGES GRADE 5 SUPPLEMENT Oregon Sets Activities & Worksheets Introduction 6 Unit Planners 7 4 Materials List 5 6 Set A3 Number & Operations: Estimating to Multiply & Divide A3. A3.6 Set A4 Number & Operations: Long Division A4. A4.8 Set A5 Number & Operations: Adding & Subtracting Fractions A5. A5.2 Set A6 Number & Operations: Fraction Concepts A6. A6.24 Set C Geometry: Triangles & Quadrilaterals C. C.56 Set C3 Geometry: 3-Dimensional Shapes C3. C3.8 Set D2 Measurement: Volume D2. D2.6 Set E Data Analysis: Probability & Technology E. E.6 Bridges Correlations to Oregon Math Standards i viii B5SUPOR-B P2

2 Bridges in Mathematics Grade 5 Supplement Oregon Sets The Math Learning Center, PO Box 2929, Salem, Oregon Tel by The Math Learning Center All rights reserved. Prepared for publication on Macintosh Desktop Publishing system. Printed in the United States of America. QP909 B5SUPOR-B P2 The Math Learning Center grants permission to classroom teachers to reproduce blackline masters in appropriate quantities for their classroom use. Bridges in Mathematics is a standards-based K 5 curriculum that provides a unique blend of 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 mathematical confidence 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

3 Bridges in Mathematics Grade 5 Supplement Oregon Sets Introduction The Bridges Grade Five Supplement is a collection of activities and independent worksheets written to enable teachers in Oregon to fully meet the latest Content Standards in Mathematics. This material is published online as downloadable files on the Math Learning Center website. See The activities included here are designed to be used in place of selected sessions in Bridges Grade Five, starting in Unit Three. All of the activities are listed on pages 2 3 in the order in which they appear in the Supplement. They are listed in recommended teaching order on pages 4 5. On pages 7 4, you ll also find a set of sheets designed to replace the Planning Guides found at the beginning of Units 3, 4, 5, and 6 in the Bridges Teacher s Guides. These sheets show exactly how the Supplement activities fit into the flow of instruction for fifth grade. We suggest you insert these sheets into your Bridges guides so you can see at a glance when to teach the Supplement activities through the school year. The majority of activities and worksheets in this supplement come in sets of three or more, providing several in-depth experiences around a particular grade level expectation or cluster of expectations. Most of the activities will take an hour of instructional time, though some are shorter, requiring minutes. Many of the activities are hands-on and require various math manipulatives and/or common classroom supplies. The blacklines needed to make any overheads, game materials, and/or student sheets are included after each activity. Many of the supplement sets in this collection include independent worksheets, designed to be completed by students in class or assigned as homework after related activities. See page 5 for a complete list of materials required to teach the activities in each Supplement set. Note Fifth grade standards not listed on pages 2 3 are adequately addressed in Bridges and/or Number Corner sessions. For a full correlation of Bridges Grade Five to the Oregon Content Standards in Mathematics, see pages i vi. Bridges in Mathematics Grade 5 Supplement

4 Oregon Supplement Sets Activities & Oregon Mathematic Content Standards (Listed in Order of Appearance in the Supplement) SET A3 NUMBER & OPERATIONS: ESTIMATING TO MULTIPLY & DIVIDE Page Name Oregon Content Standards A3. Independent Worksheet Using Compatible Numbers Select and use appropriate estimation strategies for division A3.3 Independent Worksheet 2 More Compatible Numbers (e.g., use benchmarks, overestimate, underestimate, round) to calculate A3.5 Independent Worksheet 3 Reasonable Estimates mentally based on the problem situation when computing with whole numbers. SET A4 NUMBER & OPERATIONS: LONG DIVISION Page Name Oregon Content Standards A4. Activity Introducing the Standard Algorithm Select and use appropriate estimation strategies for division A4. Activity 2 Extending the Standard Algorithm (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers Develop and use accurate, efficient, and generalizable methods to find quotients for multi-digit division problems Develop fluency with efficient procedures for dividing whole numbers and justify why the procedures work on the basis of place value and number properties. SET A5 NUMBER & OPERATIONS: ADDING & SUBTRACTING FRACTIONS Page Name Oregon Content Standards A5. A5.5 Independent Worksheet Fractions through the School Day Independent Worksheet 2 Fractions on the Trail 5..4 Develop fluency with efficient procedures for adding and subtracting fractions and decimals and justify why the procedures work Solve problems involving the addition and subtraction of fractions A5.9 Independent Worksheet 3 Adding & Subtracting Fractions and decimals. SET A6 NUMBER & OPERATIONS: FRACTION CONCEPTS Page Name Oregon Content Standards A6. Activity Simplify & Compare 5..3 Select and use appropriate strategies to estimate fraction and A6.9 Activity 2 Same-Sized Pieces decimal sums and differences Develop fluency with efficient procedures for adding and subtracting fractions and decimals and justify why the procedures work. A6.9 Independent Worksheet Using the Greatest Common Factor to Simplify Fractions 5..5 Solve problems involving the addition and subtraction of fractions and decimals. A6.2 Independent Worksheet 2 Finding the Least Common Denominator A6.23 Independent Worksheet 3 LCM and GCF 2 Bridges in Mathematics Grade 5 Supplement

5 Oregon Supplement Sets Activities & Oregon Matheatics Content Standards (cont.) SET C GEOMETRY: TRIANGLES & QUADRILATERALS Page Name Oregon Content Standards C. Activity Classifying Triangles 5.3. Identify and classify triangles by their angles (acute, right, obtuse) C.3 Activity 2 Sorting & Classifying Quadrilaterals and sides (scalene, isosceles, equilateral) Find and justify relationships among the formulas for the areas of C.25 Activity 3 Finding the Perimeter and Area of a triangles and parallelograms. Parallelogram Identify and measure necessary attributes of shapes to use area, C.35 Activity 4 Three Mathematical Ideas surface area, and volume formulas to solve problems (e.g., to find which C.43 Independent Worksheet More Geoboard Triangles of two gift boxes needs the most wrapping paper or has the greater C.45 Independent Worksheet 2 Color & Construct Triangles volume?). C.47 Independent Worksheet 3 Classifying Quadrilaterals C.5 Independent Worksheet 4 Quad Construction C.53 Independent Worksheet 5 Perimeter & Area Puzzles C.55 Independent Worksheet 6 Ebony s Quilt SET C3 GEOMETRY: 3-DIMENSIONAL SHAPES Page Name Oregon Content Standards C3. Activity Three-D Shape Posters Describe three-dimensional shapes (triangular and- rectangular C3. Activity 2 Faces, Edges & Vertices prisms, cube, triangular- and square-based pyramids, cylinder, cone, C3.5 Independent Worksheet Nets & 3-D Shapes and sphere) by the number of edges, faces, and/or vertices as well as types of faces. SET D2 MEASUREMENT: VOLUME Page Name Oregon Content Standards D2. Activity Introducing Volume Describe three-dimensional shapes (triangular and- rectangular D2.7 Activity 2 More Paper Boxes prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as D2. Independent Worksheet Volume Review types of faces. D2.5 Independent Worksheet 2 The Camping Trip Recognize volume as an attribute of three-dimensional space Determine volume by finding the total number of same-sized units of volume that fill a three-dimensional shape without gaps or overlaps Recognize a cube that is one unit on an edge as the standard unit for measuring volume Determine the appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms Identify and measure necessary attributes of shapes to use area, surface area, and volume formulas to solve problems (e.g., to find which of two gift boxes needs the most wrapping paper or has the greater volume?). SET E DATA ANALYSIS: PROBABILITY & TECHNOLOGY Page Name Oregon Content Standards E. Activity Introducing Virtual Spinners 5..7 Construct and analyze double bar, line, and circle graphs to solve E.7 Activity 2 The Spinner problems involving fractions and decimals. E.3 Independent Worksheet Make & Test Your Own Spinner Bridges in Mathematics Grade 5 Supplement 3

6 Oregon Supplement Sets Activities & Recommended Timings (Listed in Recommended Teaching Order) REPLACE SELECTED SESSIONS IN BRIDGES, UNIT 3 Page Set, Strand & Topic Name Recommended Timing C. Set C Geometry: Triangles & Quadrilaterals Activity Classifying Triangles Replaces Unit 3, Session 8 C.3 Set C Geometry: Triangles & Quadrilaterals Activity 2 Sorting & Classifying Replaces Unit 3, Session 9 Quadrilaterals C.25 Set C Geometry: Triangles & Quadrilaterals Activity 3 Finding the Perimeter and Replaces Unit 3, Session 0 Area of a Parallelogram C.35 Set C Geometry: Triangles & Quadrilaterals Activity 4 Three Mathematical Ideas Replaces Unit 3, Session C.43 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet More Geoboard Any time after Set C, Activity Triangles C.45 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet 2 Color & Construct Any time after Set C, Activity Triangles C.47 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet 3 Classifying Any time after Set C, Activity 2 Quadrilaterals C.5 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet 4 Quad Construction Any time after Set C, Activity 2 C.53 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet 5 Perimeter & Any time after Set C, Activity 4 Area Puzzles C.55 Set C Geometry: Triangles & Quadrilaterals Independent Worksheet 6 Ebony s Quilt Any time after Set C, Activity 4 C3. Set C3 Geometry: 3-Dimensional Shapes Activity Three-D Shape Posters Replaces Unit 3, Session 2 C3. Set C3 Geometry: 3-Dimensional Shapes Activity 2 Faces, Edges & Vertices Replaces Unit 3, Session 5 C3.5 Set C3 Geometry: 3-Dimensional Shapes Independent Worksheet Nets & 3-D Shapes Any time after Set C3, Activity 2 USE ANY TIME AFTER BRIDGES, UNIT 4, SESSION 0 Page Set, Strand & Topic Name Recommended Timing A3. Set A3 Number & Operations: Estimating Independent Worksheet Using Compatible Any time after Bridges, Unit 4, Session 0 to Multiply & Divide Numbers A3.3 Set A3 Number & Operations: Estimating Independent Worksheet 2 More Compatible Any time after Bridges, Unit 4, Session 0 to Multiply & Divide Numbers A3.5 Set A3 Number & Operations: Estimating to Multiply & Divide Independent Worksheet 3 Reasonable Estimates Any time after Bridges, Unit 4, Session 0 USE ANY TIME AFTER BRIDGES, UNIT 4, SESSION 23 Page Set, Strand & Topic Name Recommended Timing A5. Set A5 Number & Operations: Adding & Independent Worksheet Fractions Any time after Bridges, Unit 4, Session 23 Subtracting Fractions through the School Day A5.5 Set A5 Number & Operations: Adding & Independent Worksheet 2 Fractions on Any time after Bridges, Unit 4, Session 23 Subtracting Fractions the Trail A5.9 Set A5 Number & Operations: Adding & Subtracting Fractions Independent Worksheet 3 Adding & Subtracting Fractions Any time after Bridges, Unit 4, Session 23 4 Bridges in Mathematics Grade 5 Supplement

7 Oregon Supplement Sets Activities and Recommended Timings (cont.) REPLACE SELECTED SESSIONS IN BRIDGES, UNIT 5 Page Set, Strand & Topic Name Recommended Timing A4. Set A4 Number & Operations: Long Activity Introducing the Standard Replaces Unit 5, Session 7 Division Algorithm A4. Set A4 Number & Operations: Long Activity 2 Extending the Standard Replaces Unit 5, Session 8 Division Algorithm E. Set E Data Analysis: Probability & Activity Introducing Virtual Spinners Replaces Unit 5, Session 9 Technology E.7 Set E Data Analysis: Probability & Activity 2 The Spinner Replaces Unit 5, Session 0 Technology E.3 Set E Data Analysis: Probability & Technology Independent Worksheet Make & Test Replaces Unit 5, Session Your Own Spinner D2. Set D2 Measurement: Volume Activity Introducing Volume Replaces Unit 5, Session 6 D2.7 Set D2 Measurement: Volume Activity 2 More Paper Boxes Replaces Unit 5, Session 7 D2. Set D2 Measurement: Volume Independent Worksheet Volume Replaces Unit 5, Session 8 Review D2.5 Set D2 Measurement: Volume Independent Worksheet 2 The Camping Trip Replaces Unit 5, Session 8 REPLACE SELECTED SESSIONS IN BRIDGES, UNIT 6 Page Set, Strand & Topic Name Recommended Timing A6. Set A6 Number & Operations: Fraction Activity Simplify & Compare Replaces Unit 6, Session 3 Concepts A6.9 Set A6 Number & Operations: Fraction Activity 2 Same-Sized Pieces Replaces Unit 6, Session 4 Concepts A6.9 Set A6 Number & Operations: Fraction Independent Worksheet Using the GCF Any time after Set A6, Activity Concepts to Simplify Fractions A6.2 Set A6 Number & Operations: Fraction Independent Worksheet 2 Finding the Any time after Set A6, Activity 2 Concepts Least Common Denominator A6.23 Set A6 Number & Operations: Fraction Concepts Independent Worksheet 3 LCM and GCF Any time after Set A6, Activity 2 Bridges in Mathematics Grade 5 Supplement 5

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9 Oregon Supplement Sets Unit Three Planner (Bridges & OR Grade 5 Supplement Sets C, C3) SESSION SESSION 2 SESSION 3 SESSION 4 SESSION 5 Problems & Investigations Which Is Bigger? Problems & Investigations Dividing a Rectangle Problems & Investigations Area of a Rectangle Problems & Investigations Areas of Triangles & Parallelograms Assessment Unit Three Pre- Assessment Work Sample Home Connection 22 Work Sample Work Sample Shape Puzzles Home Connection 23 Areas of Geoboard Figures SESSION 6 SESSION 7 SUPPLEMENT SUPPLEMENT SUPPLEMENT Problems & Problems & Supplement Set C Supplement Set C Supplement Set C Investigations Investigations Geometry: Triangles & Geometry: Triangles & Geometry: Triangles & Pattern Block Angles Angle Measures Triangles Quadrilaterals Activity : Quadrilaterals Quadrilaterals & Quadrilaterals Classifying Triangles Activity 2: Sorting & Classifying Activity 3: Finding the Home Connection 24 Quadrilaterals Perimeter and Area of a Thinking about Home Connection Parallelogram Quadrilaterals Supp Set C Ind. Home Connection Worksheet : More Supp Set C Ind. Home Connection Geoboard Triangles Worksheet 3: Classifying Supp Set C Ind. Quadrilaterals Worksheet. Worksheet 4: Quad Construction SUPPLEMENT SESSION 3 SESSION 4 SUPPLEMENT Supplement Supplement Set C Problems & Problems & Supplement Set C3 Supplement Set C3 Geometry: Triangles & Investigations Investigations Geometry: Geometry: Quadrilaterals Guess My Polygon Writing Polygon Riddles 3-Dimensional Shapes 3-Dimensional Shapes Activity 4: Three Mathematical Activity : Three-D Shape Activity 2: Faces, Edges & Ideas Home Connection 28 Posters Vertices Home Connection Area Bingo Practice Supp Set C Ind. Home Connection Worksheet 2: Color & Supp Set C Ind. Construct Triangles Worksheet 5: Perimeter & Area Puzzles SESSION 6 SESSION 7 SESSION 8 SESSION 9 SESSION 20 Work Places Problems & Problems & Problems & Problems & 3A Area Bingo Investigations Investigations Building Investigations Investigations 3B Polygon Riddles Similarity 3-Dimensional Similar Solids Volume Figure Work Sample Home Connection 29 Work Sample Work Sample Home Connection Supp Drawing Similar Figures Home Connection Supp Set C Ind. Worksheet 6: Set C3 Ind. Worksheet : Ebony s Quilt Nets & 3-D Shapes SESSION 2 SESSION 22 Problems & Assessment Unit Three Investigations Post-Assessment Surface Area Work Sample Home Connection 3 Volume & Surface Area Bridges in Mathematics Grade 5 Supplement 7

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11 Oregon Supplement Sets Unit Four Planner (Bridges & OR Grade 5 Supplement Set A3) SESSION SESSION 2 SESSION 3 SESSION 4 SESSION 5 Assessment Unit Four Pre-Assessment Problems & Investigations Estimate & Check Problems & Investigations Multiplication Menus Problems & Investigations Using Menus to Solve Long Division Problems Problems & Investigations Making Menus & Solving Problems Home Connection 32 Estimation Interviews Home Connection 33 Multiplication Menus SESSION 6 SESSION 7 SESSION 8 SESSION 9 SESSION 0 Problems & Investigations Water Conservation Division Problems & Investigations Lowest Remainder Wins Home Connection 34 Multiplication & Division Practice Work Places 4A Estimate & Check 4B Lowest Remainder Wins Work Places 4C Measure & Convert 4D Go for Zero Home Connection 35 The Tangerine Problem Problems & Investigations Same Dividend, Double the Divisor Home Connection Supp Set A3 Ind. Worksheet : Using Compatible Numbers SESSION SESSION 2 SESSION 3 SESSION 4 SESSION 5 Problems & Investigations Making Fraction Kits Problems & Investigations Race to Two & Back Problems & Investigations The Licorice & Trail Mix Problems Problems & Investigations Quilt Block Fractions Problems & Investigations Fractions on the Geoboard Home Connection Supp Set A3 Ind. Worksheet 2: More Compatible Numbers Home Connection 36 Lady Liberty Home Connection Supp Set A3 Ind. Worksheet 3: Reasonable Estimates Home Connection 37 Fractions & Division Story Problems Work Sample SESSION 6 SESSION 7 SESSION 8 SESSION 9 SESSION 20 Problems & Investigations Designing Quilt Blocks Problems & Investigations Egg Carton Fractions Problems & Investigations Name That Fraction Problems & Investigations Combining Egg Carton Fractions Problems & Investigations Fraction Story Problems Work Sample Home Connection 38 The Mini-Quilt Project Home Connection 39 Egg Carton Fractions & More Work Sample Home Connection 40 More Fraction Story Problems SESSION 2 SESSION 22 SESSION 23 Work Places 4E Dozens of Eggs 4F Measuring to Fractions Work Places Unit Four Work Places 4G Target Practice Assessment Unit Four Post- Assessment of an Inch Home Connection Supp Set A5 Ind. Worksheet : Fractions through the School Day Home Connection 4 Unit Four Review Bridges in Mathematics Grade 5 Supplement 9

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13 Oregon Supplement Sets Unit Five Planner (Bridges & OR Grade 5 Supplement Sets A4, A5, D2, E) SESSION SESSION 2 SESSION 3 SESSION 4 SESSION 5 Problems & Investigations Graphing Shirt Colors Assessment Unit Five Pre-Assessment Problems & Investigations Pet Survey Problems & Investigations Creating Double Bar Problems & Investigations More about Names & Graphs Double Bar Graphs Home Connection Home Connection 42 Supp Set A5 Ind. Worksheet 2: Fractions Bar & Circle Graphs Home Connection 43 Presidents Names on the Trail SUPPLEMENT SUPPLEMENT SESSION 6 SUPPLEMENT SUPPLEMENT Supplement Set A4 Number & Operations: Long Division Activity Introducing the Supplement Set A4 Number & Operations: Long Division Activity 2 Extending the Problems & Investigations What Is Probability? Supplement Set E Data Analysis: Probability & Technology Activity : Introducing Supplement Set E Data Analysis: Probability & Technology Activity 2: The Spinner Standard Algorithm Standard Algorithm Virtual Spinners Home Connection 45 Another Spinner Experiment SUPPLEMENT SESSION 2 SESSION 3 SESSION 4 SESSION 5 Supplement Set E Ind. Worksheet : Make & Test Your Own Spinner Problems & Investigations The Dragon s Lair, Part of 2 Problems & Investigations The Dragon s Lair, Part 2 of 2 Problems & Investigations Secret Sacks, Part of 2 Problems & Investigations Secret Sacks, Part 2 of 2 Work Sample Home Connection 46 Spinner & Dice Probabilities SUPPLEMENT SUPPLEMENT SUPPLEMENT SESSION 9 Supplement Set D2 Supplement Set D2 Supplement Set D2 Assessment Unit Five Measurement: Volume Measurement: Volume Measurement: Volume Post-Assessment Activity : Introducing Activity 2: More Paper Ind. Worksheets & 2: Volume Boxes Volume Review and The Camping Trip Home Connection Supp Set A5 Ind. Worksheet 3: Adding & Subtracting Fractions Bridges in Mathematics Grade 5 Supplement

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15 Oregon Supplement Sets Unit Six Planner (Bridges & OR Grade 5 Supplement Set A6) SESSION SESSION 2 SUPPLEMENT SUPPLEMENT SESSION 5 Assessment Unit Six Pre-Assessment Problems & Investigations Fractions Are Quotients Supplement Set A6 Number & Operations: Fraction Concepts Activity Simplify & Supplement Set A6 Number & Operations: Fraction Concepts Activity 2 Same-Sized Problems & Investigations Adding & Subtracting Fractions, Part of 2 Work Sample Home Connection 49 Interpreting Remainders Compare Home Connection Supp Set A6 Ind. Worksheet : Using the Greatest Common Factor Pieces Home Connection 50 Equivalent Fractions on a Clock Home Connection Supp Set A6 Ind. Worksheet 2: Finding the Least Common Denominator to Simplify Fractions SESSION 6 SESSION 7 SESSION 8 SESSION 9 SESSION 0 Problems & Investigations Adding & Subtracting Fractions, Part 2 of 2 Work Sample Home Connection 5 The Smaller the Better Work Places 6A Spin, Add & Compare Fractions Home Connection Supp Set A6 Ind. Worksheet 3: LCM and GCF Problems & Investigations Shifting into Decimals: The Great Wall of BaseTen Home Connection 52 Cafeteria Problems Problems & Investigations Modeling, Reading & Comparing Decimals Problems & Investigations Fractions, Money, Decimals & Division Home Connection 53 Modeling, Reading & Comparing Decimals Fraction Game SESSION SESSION 2 SESSION 3 SESSION 4 SESSION 5 Problems & Investigations Thousandths and Ten Thousandths Home Connection 54 Problems & Investigations Decimal & Fraction Equivalencies Problems & Investigations Decimals on a NumberLine Home Connection 55 Decimal Sense & Nonsense Problems & Investigations Adding & Subtracting Decimals Work Sample Problems & Investigations Modeling Percent Home Connection 56 Working with Decimals More Decimal Work SESSION 6 SESSION 7 SESSION 8 SESSION 9 Problems & Investigations The Number Line Game Work Places 6B Number Line Game 6C Roll & Compare Decimals 6D Sporting Percentages (Challenge) Work Places Unit Six Work Places Home Connection 58 Unit Six Review Assessment Unit Six Post-Assessment Home Connection 57 Finding Percents Bridges in Mathematics Grade 5 Supplement 3

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17 Oregon Supplement Sets Grade 5 Oregon Supplement Materials List Manipulatives Item # A3 A4 A5 A6 C C3 D2 E Color Tile ( set of 400)* T400T Clear geoboards & bands (class set GBC plus )* Geoblocks (class set) GEOS2 Opt. Centimeter cubes (2 sets of,000)* CW-CM More/Less cubes (5)* Not yet assigned Overhead double spinner overlay* SPOH-TEMP Rulers that show inches & centimeters (class set)* RLC Protractors (class set)* PRO80 Word Resource Cards* BWRC Student Math Journals* All manipulatives available from Math Learning Center. Those items marked with an asterisk are included in the Grade 5 Bridges Grade Level Package. General Materials (provided by the teacher) A3 A4 A5 A6 C C3 D2 E Computers/Internet Access Opt. Computer projection equipment Overhead or document camera Blank overhead transparencies if you are using an overhead projector rather than a doc camera 8.5 x white copy paper, sheets per student x lined or grid paper, sheets per student 2 9 x 2 and 2 x 8 construction paper 8 /2 x cardstock (sheets) 6 8 x 24 chart paper 3 x 5 index cards (3 per student) Overhead pens (black, blue, red) Scissors, class set Glue sticks, class set Marking pens for student use Scotch tape (several rolls) empty cereal box or other similar shaped box Children s Books (provided by the teacher) A3 A4 A5 A6 C C3 D2 E Counting on Frank, by Rod Clement Opt. Bridges in Mathematics Grade 5 Supplement 5

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19 Grade 5 supplement Set A3 Number & Operations: Estimating to Multiply & Divide Includes Independent Worksheet : Using Compatible Numbers to Multiply & Divide A3. Independent Worksheet 2: More Multiplication & Division with Compatible Numbers A3.3 Independent Worksheet 3: Reasonable Estimates in Multiplication & Division A3.5 Skills & Concepts H develop and use strategies to estimate the results of multi-digit multiplication and division and judge the reasonableness of such results P08

20 Bridges in Mathematics Grade 5 Supplement Set A3 Numbers & Operations: Estimating to Multiply & Divide The Math Learning Center, PO Box 2929, Salem, Oregon Tel by The Math Learning Center All rights reserved. Prepared for publication on Macintosh Desktop Publishing system. Printed in the United States of America. P08 The Math Learning Center grants permission to classroom teachers to reproduce blackline masters in appropriate quantities for their classroom use. Bridges in Mathematics is a standards-based K 5 curriculum that provides a unique blend of 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 mathematical confidence 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

21 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. name date Set A3 H Independent Worksheet Independent Worksheet Using Compatible Numbers to Multiply & Divide Mathematicians sometimes estimate answers to multiplication and division problems by using compatible numbers. Compatible numbers are numbers that work well together. example A page in my chapter book has 2 words in each line and 32 lines on the page. About how many words on the whole page? Change 2 and 32 to nearby numbers that are easier to multiply in your head. 2 is close to 0 32 is close to 30 0 x 30 = 300, so the page has about 300 words. example 2 Mr. Gomez had 396 crayons left over at the end of the year. He s putting them in bags to send home with the kids. He has 20 students in his class. About how many crayons will each student get? Change 396 to a nearby number that is easier to divide by is close to is already a friendly number. You don t always have to change both numbers = 20, so each student will get about 20 crayons. Choose a chapter book from your classroom. Turn to a page in the middle of the book. About how many words do you think there are on the page? To find out, count the number of words in one line. Next, count the number of lines on the page. Record the information: Words in one line Lines on the page 2 Use compatible numbers to estimate the number of words on the page. Show your work. (Continued on back.) Bridges in Mathematics Grade 5 Supplement A3.

22 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. Independent Worksheet Using Compatible Numbers to Multiply & Divide (cont.) 3 All the fourth and fifth graders at King School are going on a field trip with their teachers and some parent helpers. In all, there will be 97 people. The bus company plans to use 4 buses. Estimate how many people will ride in each bus. Use compatible numbers to help you. Show your work. 4 Use compatible numbers to estimate the answer to each problem below. To use this estimation strategy, change the actual numbers to nearby numbers that are compatible. The first two are done for you. multiplication example is close to is close to =, 400 so the answer is about. 400 division example is close to is close to =, 0 so the answer is about. 0 a is close to. 29 is close to. =, so the answer is about. b is close to. 9 is close to. =, so the answer is about. c is close to. 9 is close to. =, so the answer is about. d is close to. 9 is close to. =, so the answer is about. A3.2 Bridges in Mathematics Grade 5 Supplement

23 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. name date Set A3 H Independent Worksheet 2 Independent Worksheet More Multiplication & Division with Compatible Numbers Which 2 numbers in the box could you multiply to come closest to 600? Circle them. Show your thinking Estimate the answers to the following multiplication problems. Use compatible numbers to help. Show your work. The first one is done for you. example is close to. 30 a is close to =, 900 so the answer is about. 900 b 84 c 48 8 (Continued on back.) Bridges in Mathematics Grade 5 Supplement A3.3

24 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. Independent Worksheet 2 More Multiplication & Division with Compatible Numbers (cont.) 3 Estimate the answers to the following division problems. Use compatible numbers to help you. Show your work. a About how much does each can of sugar-free soda cost if a case of 24 costs $5.99? b 9 scouts want to split a bag of 262 peanuts equally. About how many peanuts will each of the scouts get? c The scouts in Lincoln City collected 594 cans of food Now they re going to put the cans into bags to take to the Food Bank. If they put 2 cans in each bag, about how many bags of food can they make? A3.4 Bridges in Mathematics Grade 5 Supplement

25 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. name date Set A3 H Independent Worksheet 3 Independent Worksheet Reasonable Estimates in Multiplication & Division Fill in the bubble in front of the answer that gives a reasonable estimate for each problem. (Hint: Try using compatible numbers to help.) To the right of the problem, use words, numbers and/or pictures to explain why you think it is a reasonable estimate. The first one is done for you. example 9 22 a is close to is close to x 20 =400, so 400 is the best estimate b d = c = e = (Continued on back.) Bridges in Mathematics Grade 5 Supplement A3.5

26 Set A3 Number & Operations: Estimating to Multiply & Divide Blackline Run a class set. Independent Worksheet 3 Reasonable Estimates in Multiplication & Division (cont.) 2 Brianna has $9.00. Baseball trading cards cost $0.49 each. She estimates that she will be able to buy about 27 cards with her money. Is this a reasonable estimate? Use words, numbers and/or pictures to explain your answer. A3.6 Bridges in Mathematics Grade 5 Supplement

27 Grade 5 supplement Set A4 Numbers & Operations: Long Divison Includes Activity : Introducing the Standard Algorithm A4. Activity 2: Extending the Standard Algorithm A4. Skills & Concepts H fluently and accurately divide up to a 4-digit number by - and 2-digit divisors accurately using the standard long division algorithm H estimate quotients to approximate solutions and determine reasonableness of answers in problems involving up to 2-digit divisors H determine and interpret the mean of a small data set of whole numbers P0509

28 Bridges in Mathematics Grade 5 Supplement Set A4 Numbers & Operations: Long Division The Math Learning Center, PO Box 2929, Salem, Oregon Tel by The Math Learning Center All rights reserved. Prepared for publication on Macintosh Desktop Publishing system. Printed in the United States of America. P0509 The Math Learning Center grants permission to classroom teachers to reproduce blackline masters in appropriate quantities for their classroom use. Bridges in Mathematics is a standards-based K 5 curriculum that provides a unique blend of 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 mathematical confidence 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

29 Set A4 Numbers & Operations: Long Division Set A4 H Activity activity Introducing the Standard Algorithm Overview Chances are, many of your students are using the strategies taught in Unit Four with pretty good success by now. There are times, however, when the multiplication menu is not the most efficient or effective method to divide one number by another. This activity introduces the standard algorithm for long division as another method. Skills & Concepts H fluently and accurately divide up to a 4-digit number by - and 2-digit divisors accurately using the standard long division algorithm H estimate quotients to approximate solutions and determine reasonableness of answers in problems involving up to 2-digit divisors You ll need H Schools in Two Towns (pages A4.5 and A4.6, run one copy of each sheet on a transparency) H More Long Division Problems (page A4.7, run one copy on a transparency) H Using the Standard Algorithm for Long Division (pages A4.8 and A4.9, run a class set) H a piece of paper to mask parts of the transparency H overhead pens H Student Math Journals or piece of lined or grid paper per student H determine and interpret the mean of a small data set of whole numbers Instructions for Introducing the Standard Algorithm. Let students know that you are going to introduce a strategy for long division that may be new to some of them, and familiar to others. Place the top portion of the first overhead on display as students get out their journals and pencils. Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. Schools in Two Towns page of 2 There are 3 elementary schools in Jewel. The chart below shows how many students there are in each school. School Number of Students Lincoln Elementary 296 Washington Elementary 322 King Elementary 245 a What is the average (mean) number of students in the Jewel elementary schools? 2. Read the information on the overhead with the class. Review the definition of the term mean, and ask students to record an estimate in their journals, along with a brief explanation of their thinking. After a minute or two, ask them to pair-share their estimates. Then call on volunteers to share their estimates with the class and explain their thinking. Bridges in Mathematics Grade 5 Supplement A4.

30 Set A4 Numbers & Operations: Long Division Activity Introducing the Standard Algorithm (cont.) Marcus I said the average is going to be around 280. The first school is almost 300. The second one is more than 300, but the third school is a little less than 250. I think the third school is going to bring the average down to around 280. Elisha I pretty much agree with Marcus, but I think the average is going to be around Now show the bottom portion of the overhead. Review with students how to find the mean by adding and then dividing. Ask them to add the three numbers in their journals, but go no further for now. Have them raise their hands when they have the total. When most hands are raised, call on a few students to share their answers. When there is general consensus that the total is 863, work with student input to record the division problem on the grid that has been provided. b Estimate the average. c Find the average Think with students about how using the multiplication menu would play out for this problem. What if you started with 0 3, then 20 3, then 5 3, as you have so many times in solving long division problems this year. Would this information be useful and helpful? Does it seem as if the multiplication menu would be an effective and efficient strategy for solving this problem? Let students pair-share for a minute about these questions. 5. Then explain that there is another strategy that might be easier in this situation. It is called the standard algorithm for long division because it is a common paper-and-pencil method for finding a quotient. When people use this strategy, they work with the numbers in the divisor separately. Tell students you are going to demonstrate the strategy. Ask them to watch closely to see if they can understand what you are doing. Challenge them to watch for some of the differences and likenesses between the standard algorithm and the multiplication menu strategy. Teacher First I look at the 8 in 863 and think, 8 divided by 3 is more than 2, just not more than 3, because 2 3 is 6, and 3 3 is too much. So I write a 2 in the hundreds place. Then I write 6 under the 8 and subtract. That s 2, so I bring down the 6. Now I divide 26 by 3. I get 8 with 2 left over since 8 3 is 24. So I write an 8 in the tens place and subtract 24 from 26. Does it look like the average is going to be close to your estimate? Students I ve seen this way to divide from my sister. It looks like it s going to come out to two eighty-something. I think maybe 275 is a little too low. 6. Continue until the problem is complete. Then discuss the remainder with the students. What does a remainder of 2 mean in this context? Would it make best sense to express the remainder as a whole number, a decimal, or a fraction? Why? A4.2 Bridges in Mathematics Grade 5 Supplement

31 Set A4 Numbers & Operations: Long Division Activity Introducing the Standard Algorithm (cont.) Students You can t cut up the 2. These are kids, not cookies! If you put exactly the same number of kids in each school, there would be 287 in one school and 288 in the other two. c Find the average r The average number of students is 287. The is a remainder of 2. It s kids, so we ll leave the number whole 7. Ask students to compare the answer with their estimates. Is 287 with a remainder of 2 a reasonable answer? Why or why not? Invite them to comment on the long division algorithm as well. How does it compare with the multiplication menu? Do they think this strategy would be equally useful in all contexts? Why or why not? 8. After students have had a chance to share their thinking, display the second overhead. Repeat the steps described above, but this time, ask students to work the problem with you in their journals. Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. Schools in Two Towns page 2 of 2 2 There are 4 elementary schools in Emerald. The chart below shows how many students there are in each school. School Number of Students Sarah Goode Elementary 397 Hayes Elementary 423 Carver Elementary 229 Grover Elementary 486 a Do you think that the average number of students in the Emerald schools is greater or less than the average number of students in the Jewel Schools? Why? b Estimate the average. c Find the average r Bridges in Mathematics Grade 5 Supplement A4.3

32 Set A4 Numbers & Operations: Long Division Activity Introducing the Standard Algorithm (cont.) 9. Now display the problems on the More Long Division Problems overhead one at a time. Each time, ask students to generate a word problem to match, and record an estimate in their journals, along with a brief explanation of their thinking. You can also ask them apply what they know about divisibility to predict whether or not there will be a remainder. Have them record each problem in their journals, using the grid lines to help align the numbers correctly, and work it as you do so at the overhead. If some of your students are already very familiar with the algorithm, you might let them take turns leading the class at the overhead. Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. More Long Division Problems Set A4 Numbers & Operations: Long Division Blackline Run a class set. NAME DATE Using the Standard Algorithm for Long Division Page of 2 2 The standard algorithm is not the only strategy for long division. However, many people find it especially useful when they are dividing a very large number, like 8,746 by a very small number, like For each of the long division problems on this page and the next: write a story problem to match. estimate the answer and write a sentence to explain your estimate. predict whether there will be a remainder or not, and explain your thinking. example Story Problem r Estimate: Reamainder or Not? Story Problem Estimate Reamainder or Not? 0. Finally, give students each a copy of Using the Standard Algorithm for Long Division. Review the instructions on the first sheet with the class. When students understand what to do, let them go to work. Depending on the strengths and needs of your students, you might give them the choice of working on the sheet independently or working as a smaller group with you. A4.4 Bridges in Mathematics Grade 5 Supplement

33 Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. Schools in Two Towns page of 2 There are 3 elementary schools in Jewel. The chart below shows how many students there are in each school. School Number of Students Lincoln Elementary 296 Washington Elementary 322 King Elementary 245 a What is the average (mean) number of students in the Jewel elementary schools? b Estimate the average. c Find the average. Bridges in Mathematics Grade 5 Supplement A4.5

34 Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. Schools in Two Towns page 2 of 2 2 There are 4 elementary schools in Emerald. The chart below shows how many students there are in each school. School Number of Students Sarah Goode Elementary 397 Hayes Elementary 423 Carver Elementary 229 Grover Elementary 486 a Do you think that the average number of students in the Emerald schools is greater or less than the average number of students in the Jewel Schools? Why? b Estimate the average. c Find the average. A4.6 Bridges in Mathematics Grade 5 Supplement

35 Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. More Long Division Problems Bridges in Mathematics Grade 5 Supplement A4.7

36 Set A4 Numbers & Operations: Long Division Blackline Run a class set. name date Using the Standard Algorithm for Long Division Page of 2 The standard algorithm is not the only strategy for long division. However, many people find it especially useful when they are dividing a very large number, like 8,746 by a very small number, like 5. For each of the long division problems on this page and the next: write a story problem to match. estimate the answer and write a sentence to explain your estimate. predict whether there will be a remainder or not, and explain your thinking. example Story Problem r Estimate: Remainder or Not? Story Problem Estimate Remainder or Not? A4.8 Bridges in Mathematics Grade 5 Supplement

37 Set A4 Numbers & Operations: Long Division Blackline Run a class set. name date Using the Standard Algorithm for Long Division Page 2 of 2 2 Story Problem Estimate: Remainder or Not? 3 Story Problem Estimate Remainder or Not? Bridges in Mathematics Grade 5 Supplement A4.9

38 A4.0 Bridges in Mathematics Grade 5 Supplement

39 Set A4 Numbers & Operations: Long Division Set A4 H Activity 2 activity Extending the Standard Algorithm Overview Students use the standard algorithm to divide 3- and 4-digit numbers by 2-digit numbers. In the process, they explore the idea of using a mini multiplication menu if and when needed. Skills & Concepts H fluently and accurately divide up to a 4-digit number by - and 2-digit divisors accurately using the standard long division algorithm H estimate quotients to approximate solutions and determine reasonableness of answers in problems involving up to 2-digit divisors H read and interpret a line plot H determine and interpret the mean of a small data set of whole numbers You ll need H Family Math Night (page A4.5, run one copy on a transparency) H Family Math Night Worksheet (pages A4.6 and A4.7, run a class set) H a piece of paper to mask parts of the overhead H overhead pens H Student Math Journals or piece of lined or grid paper per student Instructions for Extending the Standard Algorithm. Open the activity by explaining that the class is going to think some more about strategies for handling long division problems today. Then place the top portion of the Family Math Night overhead on display. Read the text with the class, and give students a minute or two to examine the line plot quietly. Ask them to think of at least two observations they can share with a partner in a minute. Set A4 Numbers & Operations: Long Division Blackline Run one copy on a transparency. Family Math Night Every year, King School holds a big math night in the spring. They invite all the families to come from 6:30 to 8:00 pm for refreshments, math games, and prizes. They also award a big prize to the classroom that brings in the most families. King School has 28 classrooms. The line plot on your sheet shows how many families came to Math Night this year. Family Math Night at King School Number of Classrooms X = classroom X X X X X X X X X X X X X X X X X X X X X X X X X X X X Number of Families Bridges in Mathematics Grade 5 Supplement A4.

40 Set A4 Numbers & Operations: Long Division Activity 2 Extending the Standard Algorithm (cont.) 2. Have students pair-share their observations about the line plot. Then pose the following questions about the line plot. What information does the line plot provide? Who might be interested in this information? What does each x stand for? (a classroom) How many classrooms brought 4 families to Math Night? (8 classrooms) How many families was that in all? (2 families) About how many families in all came to Math Night? Can you find the exact total by counting up the x s? Why not? What do you need to do to find the total number of families that came to Math Night? Be sure students understand that they can t find the total number of families by simply counting the x s on the line plot, because each x stands for a classroom. There are 6 x s above the 5, which means that 6 classrooms brought in 5 families each. 6 5 is 90, and that s only part of the total. 3. Now give students each a copy of the Family Math Night Worksheets, and display the prompt toward the bottom of the Family Math Night overhead that instructs students to use the information on theline plot to answer the questions on their sheets. Be sure students undertand they need to stop after question 4b on the second sheet. Set A4 Numbers & Operations: Long Division Blackline Run a class set. Set A4 Numbers & Operations: Long Division Blackline Run a class set. NAME DATE NAME DATE Family Math Night Worksheet page of 2 Family Math Night Worksheets page 2 of 2 Every year, King School holds a big math night in the spring. They invite all the families to come from 6:30 to 8:00 pm for refreshments, math games, and prizes. They also award a big prize to the classroom that brings in the most families. King School has 28 classrooms. The line plot below shows how many families came to Math Night this year. Family Math Night at King School 4a Sara thinks the average number of families that came to Math Night from each classroom is 4. Do you agree with Sara? (Circle your answer.) Yes b If you think the average is 4 families per classroom, explain why. If you think the average is not 4 families, tell what you think it is and explain why. No Number of Classrooms X = classroom X X X X X X X X X X X X X X X X X X X X X X X X X X X X c Use the standard algorithm for long division to find the average number of families per classroom that came to Math Night at King School Number of Families How many families did the winning classroom bring to Math Night? 2 How many families did most of the classrooms bring in? 3 Use the information from the line plot to complete the chart below. Classrooms Families Total Number of Families a = families b = 24 families c = families d 4 4 = families e 6 6 = families f 7 = families g h 8 = families Grand Total: How many families in all attended Math Night? families 5 Copy each of the problems below into your Math Journal. Use the standard algorithm for long division to solve each. Make mini-menus when you need them. a d g The average number of families per classroom was b e h c f i Read the information on the overhead to the class, and review the worksheets with them. When they understand what to do, let them go to work. Encourage them to share and compare their answers to problems 3, 4a, and 4b, and use scratch paper to make or check their calculations. If their solutions don t match, challenge them to work together until they can come to consensus. A4.2 Bridges in Mathematics Grade 5 Supplement