Leading Math Success Notable Strategies: Closing the Gap Notable Strategies: Closing the Gap materials are designed to support educational leaders — teachers, principals, professional learning facilitators — in implementing effective mathematics programs in Grade 7, Grade 8, Grade 9 Applied, and combined Grades 7/8. The day-by-day lessons and student sheets align with outlines and lessons in TIPS (Targeted Implementation and Planning Supports: Grade 7, Grade 8, and Grade 9 Applied Mathematics). Strategies for assessing for learning and differentiating instruction are featured. Grade 7 Year Outline Lesson Time Number of Total Cluster of Curriculum Available - Term Reference Lessons Lesson Expectation “Instructional Planned Time Jazz” 1 Welcome and Problem Solving TIPS 1 - 4 4 4 Describing Patterns TIPS 5 - 9 5 2 7 Multiples and Factors TIPS 10 - 12 3 2 5 Parallelograms and Triangles TIPS 13 - 16 4 1 5 3-D Models TIPS 17 - 22 6 2 8 Rectangular Prisms TIPS 23 - 28 6 2 8 Exponents TIPS 29 - 31 3 1 4 Square Roots 1 3 4 Sub-totals 32 13 45 2 Data Management, Central 15 1 16 Tendency Solving Equations by Inspection 13 3 15 & Systematic Trial Adding and Subtracting LMS 29 - 38 11 4 16 Fractions Problem Solving with 2-D 13 3 16 Shapes and 3-D Figures Sub-totals 52 11 63 3 Investigating Trapezoids LMS 1-5 5 2 7 Analysis of Transformational 12 2 14 Geometry Integers LMS 18 – 29 13 3 16 Order of Operations 5 2 7 Sample Space 5 1 6 Interpreting Graphs and 5 1 6 Evaluating Arguments Application of Measurement 5 1 6 Tools Gazebo Investigation – GSP 3 2 5 Olympic Investigation – 3 2 5 Spreadsheets Sub-totals 56 16 72 140 days 40 days 180 days Targeted Implementation and Planning Supports (TIPS) Leading Math Success (LMS) The number of prepared lessons represents the lessons that could be planned ahead based on the range of student readiness, interests, and learning profiles that can be expected in a class. The extra time available for “instructional jazz” can be taken a few minutes at a time within a pre-planned lesson or taken a whole class at a time, as informed by teachers’ observations of student needs. (See software presentation, Differentiated Instruction… and all that jazz.) The reference numbers are intended to indicate which lessons are planned to precede and follow each other. Actual day numbers for particular lessons and separations between terms will need to be adjusted by teachers. Lesson Outline: Days 29 – 38 Grade 7 BIG PICTURE Students will: • explore fraction relationships; • develop an understanding of addition and subtraction of fractions (proper, improper, and mixed); • develop rules for addition and subtraction of fractions; • explore the relationship between fractions and decimals; • solve problems involving fractions and decimals. Day Lesson Title Description Expectations 29 Fraction Puzzles • Explore/review fractional parts of geometric shapes. 7m1, 7m6, 7m26 • Order fractions. CGE 3c, 5a, 5e 30 Combining • Investigate combinations of fractions using 7m2, 7m12, Fractions manipulatives. 7m17, 7m18, 7m26 CGE 3b, 3c, 5a 31 Adding Fractions • Add fractions by connecting concrete to symbolic. 7m17, 7m18, with Different • Recognize the need for equivalent fractions with 7m24 Denominators common denominators when adding fractions with different denominators. CGE 4b, 5e 32 Fractions Using • Explore fractions using relational rods. 7m2, 7m17 Relational Rods CGE 3c, 4a 33 Adding and • Practise adding and subtracting fractions using 7m2, 7m17, Subtracting relational rods in a game format. 7m18, 7m26 Fractions Using Relational Rods CGE 2c, 3b, 3c, 5e 34 Subtracting • Develop rules for subtracting fractions using 7m6, 7m18, Fractions Using equivalent fractions with common denominators. 7m24, 7m26 Equivalent • Practise adding and subtracting fractions. Fractions CGE 4e, 5g 35 Adding and • Demonstrate understanding and skills while 7m2, 7m6, 7m7, Subtracting performing operations with fractions. 7m17, 7m18, Fractions – 7m24 Performance Task CGE 2b, 3c 36 Exploring Fractions • Explore repeated addition of fractions and addition 7m6, 7m7, 7m18, Further and subtraction of mixed numbers. 7m19, 7m24 • Develop methods for multiplying a fraction by a whole number. CGE 3b, 4f, 5a 37 Fractions and • Explore the relationships between fractions and 7m8, 7m9, 7m23, Decimals decimals. 7m26, 7m27 CGE 2c, 3c 38 Summative • Demonstrate understanding of fractions and 7m6, 7m7, 7m8, Assessment operations with fractions on an open-ended, 7m16, 7m18, problem-solving task. 7m24, 7m26 CGE 2b, 3c, 4f Leading Math Success – Grade 7/Term 2 © Queen’s Printer for Ontario, 2004 Page 1 Day 29: Fraction Puzzles Grade 7 Description Materials • Explore/review fractional parts of geometric shapes. • pattern blocks • overhead pattern • Order fractions. blocks • BLM 29.1,29.2, 29.3 • 2 or 3 large Imperial socket wrench sets in cases Assessment Opportunities Minds On… Whole Class Æ Introducing a Problem Distribute pattern blocks. Present students with the following area fraction TIPS: Section 2 – Fractions, p.3 for puzzle: With your pattern blocks build two different triangles each with an teaching fraction area that is one-half green and one-half blue. concepts. Have students share their solutions using the overhead pattern blocks. Discuss Virtual pattern whether rearranging the blocks makes the solution “different.” blocks are available at http://arcytech.org/ja va/patterns/patterns Action! Pairs Æ Problem Solving _j.shtml Explain that all students are to complete questions 1 to 5 on BLM 29.3 then set it aside while they use pattern blocks and BLM 29.1 to solve area fraction puzzles with a partner. Students must show the graphic solution with each colour labelled with the appropriate fraction of the whole triangle, e.g., colouring on pattern block paper, (BLM 29.2). Briefly review the meaning of While students are working, provide selected pairs with an Imperial set of parallelogram (blue socket wrenches that are mixed up and ask them to complete number 6 on or beige block) and BLM 29.3. trapezoid (red block). Ask them to explain why they placed a certain socket between two others. Some methods Learning Skills & Curriculum Expectations/Observation/Anecdotal: students may use Circulate while students are working to assess prior knowledge of fractions. include physical size of each socket, Ask students to explain how they know their solution to the area puzzle is ordering of the correct. sockets could be accomplished using Consolidate Whole Class Æ Sharing/Discussion equivalent fractions, converting to Debrief Pairs of students share their solutions to an area puzzle using the overhead decimals or pattern blocks and explain how they know their solution satisfies the problem. measuring in Discuss possible answers to question 5 on the student worksheet. millimetres, among other methods. Several different pairs of students share their solutions, even if the solution is merely another arrangement of the same pattern blocks. This allows more students to be recognized and reinforces multiple solutions and explanations. Discuss the various methods students used to solve the socket set problem. Home Activity or Further Classroom Consolidation Concept Practice Choose one task: Refer students to 1. Complete the two area fraction puzzles provided and create one area the virtual pattern fraction puzzle of your own. block website listed above. 2. Create three area fraction puzzles of your own. Include the solutions, Students can work coloured and labelled with their fractional parts on pattern block paper. on pattern block paper, use cardboard cutouts or access the web to complete the assignment Leading Math Success – Grade 7/Term 2 © Queen’s Printer for Ontario, 2004 Page 2 29.1: Pattern Block Area Fraction Puzzles Name: Date: Use pattern blocks to solve each of the area fraction puzzles below. Draw each solution on pattern block paper. Label each colour with its fraction of the whole shape. 1. Build a parallelogram with an area that is one-third green, one-third blue, and one-third red. 2. Build a parallelogram with an area that is one-eighth green, one-half yellow, one-eighth red, and one-quarter blue. 3. Build a trapezoid with an area that is one-tenth green and nine-tenths red. 4. Rebuild each of the puzzles above in a different way. 5. Explain why it is not possible to build a parallelogram with an area that is one-half yellow, one-third green and one-quarter blue. 29.1: Pattern Block Area Fraction Puzzles Name: Date: Use pattern blocks to solve each of the area fraction puzzles below. Draw each solution on pattern block paper. Label each colour with its fraction of the whole shape. 1. Build a parallelogram with an area that is one-third green, one-third blue, and one-third red. 2. Build a parallelogram with an area that is one-eighth green, one-half yellow, one-eighth red, and one-quarter blue. 3. Build a trapezoid with an area that is one-tenth green and nine-tenths red. 4. Rebuild each of the puzzles above in a different way. 5. Explain why it is not possible to build a parallelogram with an area that is one-half yellow, one-third green and one-quarter blue. Leading Math Success – Grade 7/Term 2 © Queen’s Printer for Ontario, 2004 Page 3 29.2: Pattern Block Paper Leading Math Success – Grade 7/Term 2 © Queen’s Printer for Ontario, 2004 Page 4 29.3: Socket to you! Name: Date: 20 5 5 1. is an equivalent fraction for . Write two more equivalent fractions for . 32 8 8 3 2. Write two equivalent fractions for . 4 3 3 3. Circle which is larger: or . 8 16 7 9 4. Circle which is smaller: or . 16 16 7 9 5. Circle the fraction that fits between and . 16 16 13 1 3 1 5 3 19 32 4 8 2 8 4 32 6.