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• You must use all the rods to make the shape.• The rods may not overlap.Use the rods to create a shape, following the rules. Ask students how they could find the perimeter of theshape. Elicit a variety of responses.Working on ItInstructional Grouping: Pairs, individualsChallenge the students, in pairs, to make a variety of shapes with a perimeter of 18 cm. Explain that studentsmust use only the allotted Cuisenaire rods, and that they must follow the rules explained in “Getting Started”.Have students trace the shapes on grid paper and cut them out.Observe students’ strategies for making shapes that have a perimeter of 18 cm. Some students may need asmall-group guided lesson on perimeter, since a common student misconception in this type of activity is thatthe square units should be counted – students find the area of the shapes rather than the perimeter.Note: Some students may rely on the use of the Cuisenaire rods to form their shapes for the entirety of themathematics lesson. Other students may realize that each rod represents a certain number of units on thegrid paper and may not feel the need to use the rods for tracing. They may go directly to recording theshapes on the centimetre grid paper without the assistance of the manipulatives.Independent Work: Students work independently to make a variety of shapes, using the rules above; they tracethe shapes on centimetre grid paper; and they record the perimeters. Challenge the students to arrange therods to get the shortest perimeter and the longest perimeter. Ask the students, “Can you form more than oneshape with the shortest perimeter and more than one shape with the longest perimeter?” Give the studentssufficient time to work through the problem of finding and recording all the possible shapes with the longestand shortest perimeters.Reflecting and ConnectingInstructional Grouping: Whole classAsk students to explain their methods for finding the perimeter of the different shapes they created. Have studentscompare and discuss different possibilities for making different shapes with the same perimeter.Discuss students’ results in finding the shapes with the longest and the shortest perimeters. Have students usetheir Cuisenaire rods to make the different shapes with the longest and shortest perimeters on the overheadprojector.Draw up a chart that shows all of the shapes with the longest and shortest perimeters. Ask students, “Havewe found all of the possible shapes with the longest and shortest perimeters? How do you know?” Give studentstime to discuss these two questions in pairs or small groups. Have the students share their responseswith the large group.76 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One
Professional ResourcesNumerous professional resources are available through publishers, on the Internet,and in bookstores. Not all of these resources are aligned with the research-basedpedagogical approach that is described in this guide. The following is a list of booksthat do support such an approach. Although this list is selective, and not exhaustive,it includes a broad range of resources that teachers can use to acquire knowledge ofeffective instructional and assessment strategies, to broaden their skills, and to deepentheir knowledge of pedagogy in mathematics.Overall Instruction GuidesBaroody, A.J. (1998). Fostering children’s mathematical power. Mahwah, NJ: Erlbaum.Burns, M. (2000). About teaching mathematics: A K–8 resource (2nd ed.). Sausalito, CA:Math Solutions Publications.Chapin, S.H., & Johnson, A. (2000). Math matters: Understanding the math you teach,Grades K–6. Sausalito, CA: Math Solutions Publications.Clements, D.H., Sarama, J., & DiBiase, A.-M. (Eds.). (2004). Engaging young childrenin mathematics: Standards for early childhood mathematics education. Mahwah, NJ:Erlbaum.Expert Panel on Early Math in Ontario. (2003). Early math strategy: The report of theExpert Panel on Early Math in Ontario. Toronto: Ontario Ministry of Education.Expert Panel on Mathematics in Grades 4 to 6 in Ontario. (2004). Teaching andlearning mathematics: The report of the Expert Panel on Mathematics in Grades 4 to 6in Ontario. Toronto: Ontario Ministry of Education.Haylock, D., & McDougall, D. (1999). Mathematics every elementary teacher shouldknow, Grades K–8. Toronto: Trifolium Books.Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K.C., Wearne, D., Murray, H.,Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematicswith understanding. Portsmouth, NH: Heinemann.Jensen, E. (1998). Teaching with the brain in mind. Alexandria, VA: Association forSupervision and Curriculum Development.77
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Belief 4: The teacher is the key to
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Chapter 10 is devoted to the subjec
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1.Achievingand SustainingImprovemen
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Educators striving to achieve the c
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In schools that successfully bring
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• Intervention and special assist
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Boards and schools have improvement
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• assisting with team and individ
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• incorporating current knowledge
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• ascertaining the needs of staff
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and reflect on their observations o
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• hosting a family math event, em
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Principles Underlying EffectiveMath
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Page 115 and 116: ReferencesAdams, L., Waters, J., Ch
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Page 119 and 120: Payne, J.N. (Ed.). (1990). Mathemat
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