Toronto Catholic District School Board Mathematics Continuum Kindergarten to Grade 8

Transcription

1 Toronto Catholic District School Board Mathematics Continuum Kindergarten to Grade 8

2 The Math Continuum Effective planning means beginning with the end in mind. It clarifies for teachers students, the target or objectives of learning. It illuminates the path to a clear final destination. It also helps teachers manage a sometimes overwhelming number of curricular goals. Planning with the end in mind means knowing where you are going in order to plan the steps needed to get there. The Math Continuum has been developed using the model for planning with the end in mind. Each unit plan identifies the big ideas for each of the five math strs. In every unit, the curriculum expectations are aligned with the big ideas. A culminating task (e.g., Nelson), the lessons that enable students to be successful on the culminating task, additional activities that could be used to support deeper concepts are part of each unit plan. The unit plans have been designed to provide teachers with a concise overview of the connections between the Ontario Mathematics Curriculum the Nelson Mathematics Resource. It is recognized that teachers will use assessment information to drive instruction. Therefore, teachers may need to make adjustments to the culminating task enabling lessons based on students strengths needs. If changes are made to the culminating task, a correlation must still be made with the big ideas curriculum expectations. The enabling lessons must also be adapted to ensure student success on the culminating task. Teachers can also access Nelson Skills Bank, Problem Bank, Mental Math, Math Games, Chapter Reviews, Chapter Tests Interviews. PURPOSE OF NUMERACY FRAMEWORK This document was produced as a guide to assist classroom teachers in the planning implementation of the Mathematics Ontario Curriculum, Grades 1 to 8 the Kindergarten Program. 3

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8 Teaching Plan for Mathematics Curriculum GRADES 1 TO 8 The following chart indicates the strs of math that will be taught, assessed evaluated each term. Please keep in mind these are guidelines. STRANDS TERM 1 TERM 2 TERM 3 Number Sense Numeration Measurement Geometry Spatial Sense Patterning Algebra Data Management Probability The Order of Instructional Strs GRADES 1 TO 8 The following chart outlines, by term, the general order of instruction by str. TERM 1 TERM 2 TERM 3 Patterning Measurement Number Sense Numeration Number Sense Numeration Number Sense Numeration Probability Data Management Geometry (2 D) Spatial Sense Geometry (3 D) Spatial Sense Patterning Algebra Measurement 5

9 The Strs by Grade KINDERGARTEN The following chart indicates the strs of math that will be taught, assessed evaluated each term. STRANDS TERM 1 TERM 2 (Sept to Jan) (Feb to June) Number Sense Numeration Measurement Geometry Spatial Sense Patterning Algebra Data Management Probability TERM 1 TERM 2 Number Sense Numeration (Section B) Number Sense Numeration (Section C) Data Management (Section A) Patterning (Section B) Patterning (Section A) Measurement (Section B) Measurement (Section A) Geometry Spatial Sense (Section A) Data Management Probability (Section B) Geometry Spatial Sense (Section B) Geometry Spatial Sense (Section C) Number Sense Numeration (Section C D) Measurement (Section C) SECTIONS A, B, C AND D REFER TO THE NELSON MATH RESOURCE 6

10 Focus on Strs by Term... Grades 1 to 3 TERM 1 TERM 2 TERM 3 PATTERNING ALGEBRA Grade 1: Patterns Grade 2: Patterns; Growing Shrinking Patterns Grade 3: Patterns; Growing Shrinking Patterns NUMBER SENSE AND NUMERATION Grade 1: Counting; Howmuchness; Representation Grade 2: Counting; Howmuchness; Place Value Grade 3: Counting; Howmuchness; Place Value DATA MANAGEMENT AND PROBABILITY Grade 1: Collection Organization of Data; Data Relationships Grade 2: Collection Organization of Data; Data Relationships Grade 3: Collection Organization of Data; Data Relationships MEASUREMENT Grade 1: Length; Area Grade 2: Length; Area; Perimeter Grade 3: Length; Area; Perimeter; Spatial Relationships NUMBER SENSE AND NUMERATION Grade 1: Addition; Subtraction; Money Grade 2: Addition; Subtraction; Money Grade 3: Addition; Subtraction; Money GEOMETRY AND SPATIAL SENSE Grade 1: Two-dimensional Shapes; Location; Symmetry Grade 2: Two-dimensional Shapes; Location; Symmetry Grade 3: Two-dimensional Shapes; Location Movement, Translations (slides), Reflections (flips) Rotations (turns); Symmetry PATTERNING AND ALGEBRA Grade 1: Expressions; Equality Grade 2: Expressions; Equality Grade 3: Expressions; Equality NUMBER SENSE AND NUMERATION Grade 1: Compose Decompose Numbers; Fractions Grade 2: Multiplication; Division; Fractions Grade 3: Multiplication; Division; Fractions DATA MANAGEMENT AND PROBABILITY Grade 1: Probability Grade 2: Probability Grade 3: Probability GEOMETRY AND SPATIAL SENSE Grade 1: Three-dimensional Figures Grade 2: Three-dimensional Figures Grade 3: Three-dimensional Figures MEASUREMENT Grade 1: Mass; Capacity; Time; Temperature Grade 2: Mass; Capacity; Time; Temperature Grade 3: Mass; Capacity; Time; Temperature 7

11 Focus on Strs by Term... Kindergarten TERM 1 March Report Number Sense Numeration: Counting; Howmuchness; Representation Data Management: Collection Organization Patterning: Patterns; Relationships Measurement: Non-stard; Comparing Ordering Geometry Spatial Sense: Location; Spatial Relationships; Movement Data Management Probability: Collection Organization; Probability Geometry Spatial Sense: 3-D shapes TERM 2 June Report Number Sense Numeration: Counting; Howmuchness; Anchors of 5 10; Representation Patterning: Relationships Within Between Patterns Measurement: Non-stard Stard; Measurable Attributes Geometry Spatial Sense: 2-D shapes Number Sense Numeration: Addition Subtraction; Money; Representation Measurement: Measurable Attributes; Sequence of Events It is generally understood that other grades from Grade 1 to Grade 8 will try to use the same focus on similar strs each term of the school year. At times, this may not be possible, but it is something that we try to intrinsically cultivate whenever possible. 8

12 THE BIG IDEAS IN MATHEMATICS The TCDSB Nelson Kindergarten to Grade 8, concentrates on the big ideas inherent in the Ontario Mathematics Curriculum expectations. In developing a mathematics program, it is vital to concentrate on important mathematical concepts, or big ideas, the knowledge skills that go with those concepts. Programs that are organized around big ideas focus on problem solving provide cohesive learning opportunities that allow students to explore concepts in depth. (A Guide to Effective Instruction in Mathematics, K to 3, 2007) Focusing on the big ideas helps teachers to cluster the expectations around a few major concepts skills. Seeing the curriculum expectations as a network of interrelated concepts allows teachers students to develop depth flexibility in their mathematical thinking. The big ideas also act as a lens for: Making instructional decisions. Identifying prior learning. Looking at students thinking understing in relation to the mathematical concepts addressed in the curriculum. Collecting observations making anecdotal records. Providing feedback to students. Determining next steps. Communicating concepts providing feedback on students achievement to parents. (A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, 2008) Big ideas, a pedagogy that supports student learning of big ideas, naturally provide opportunities for meeting the needs of students who are working at different levels of mathematical performance. The reason for this is that teaching around big ideas means teaching around ideas that incorporate a variety of levels of mathematical sophistication. (A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, 2008) Therefore, big ideas are not grade specific, but rather stards descriptions of what students should know be able to do by the end of grade six. When looking at grade specific unit plans, the culminating task curriculum expectations indicate which part of the big idea is developed in that grade. The spiraling nature of the Ontario Curriculum for Mathematics is based on the gradual development of big ideas through this process. 9

13 CONTINUUM OF LEARNING MEASUREMENT OVERALL EXPECTATIONS BIG IDEAS GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 estimate, estimate, measure measure estimate, estimate, estimate, describe record length, measure measure measure estimate, research, length, area, perimeter, record length, record length, record measure report on describe mass, area, mass, perimeter, perimeter, perimeter, record research into report on capacity, time capacity, time area, mass, area, mass, area, quantities, real-life applications of capacity, time capacity, temperature using the applications of volume temperature temperature volume change, metric area capacity using nonstard units stard units using stard using a variety using a variety system using non- temperature elapsed time elapsed time, measurement measurements measurement of the same stard units of strategies of strategies size units ATTRIBUTES, UNITS & MEASUREMENT SENSE MEASUREMENT RELATIONSHNIPS compare, describe order objects using attributes measured in non-stard units of the same size compare, describe order objects using attributes measured in non-stard units stard units compare, describe order objects using attributes measured in stard units determine the among units measurable attributes, including the area perimeter of rectangles determine the among units measurable attributes, including the area of a rectangle the volume of a rectangular prism determine the among units measurable attributes, including the area of a parallelogram, the area of a triangle, the volume of a triangular prism determine the among units measurable attributes, including the area of a trapezoid the volume of a right prism determine the among units measurable attributes, including the area of a circle volume of a cylinder 10

14 CONTINUUM OF LEARNING GEOMETRY AND SPATIAL SENSE overall EXPECTATIONS BIG IDEAS GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 identify demonstrate identify identify twodimensional compare two- quadrilaterals identify an common twodimensional shapes dimensional threedimensionadimensional construct of the classify two- understing shapes threedimensional three- shapes figures shapes by side classify related lines, geometric threedimensional figures dimensional classify them angle construct classify properties of by their properties, polygons triangles, quadrilaterals figures sort figures geometric compare angles quadrilaterals circles sort classify them sort them by properties, sort threedimensional of geometric prisms the application classify them by their their geometric compare by their geometric properties various angles figures properties in attributes properties to benchmarks the real world PROPERTIES OF TWO- DIMENSIONAL SHAPES AND THREE-DIMENSIONAL FIGURES GEOMETRIC RELATIONSHIPS LOCATION AND MOVEMENT compose decompose common twodimensional shapes threedimensional figures describe the relative location of objects using positional language compose decompose twodimensional shapes threedimensional figures describe represent the relative locations of objects, represent objects on a map describe between twodimensional shapes, between twodimensional shapes threedimensional figures identify describe the locations movements of shapes objects construct three dimensional figures using twodimensional shapes identify describe the location of an object, using a grid map, reflect twodimensional shapes 11 identify construct nets of prisms pyramids identify describe the location of an object, using the cardinal directions, translate twodimensional shapes sketch threedimensional figures, construct threedimensional figures from drawings describe location in the first quadrant of a coordinate system rotate twodimensional shapes develop an understing of similarity, distinguish similarity congruence describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, apply transformations to create analyse designs develop geometric involving lines, triangles, polyhedra, solve problems involving lines triangles represent transformations using the Cartesian coordinate plane, make connections between transformations the real world

15 CONTINUUM OF LEARNING PATTERNING AND ALGEBRA OVERALL EXPECTATIONS BIG IDEAS GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 describe, describe extend determine represent create, a through represent represent identify, variety of investigation linear growing in growing linear growing describe, describe, numeric using a table patterns shrinking patterns identify, extend, extend, geometric of values, (where the patterns (where the describe, create create a patterns, in terms are (where the terms are extend repeating variety of make growing whole terms are whole create patterns, numeric predictions shrinking numbers) whole numbers) repeating growing patterns related to the patterns, using concrete numbers) using graphs, patterns patterns, geometric patterns, investigate materials, investigate algebraic shrinking patterns investigate repeating graphs repeating expressions, patterns repeating patterns algebraic patterns equations patterns involving expressions involving involving translations rotations reflections PATTERNS AND RELATIONSHIPS EXPRESSIONS AND EQUALITY demonstrate an understing of the concept of equality, using concrete materials addition subtraction to 10 demonstrate an understing of the concept of equality between pairs of expressions using concrete materials, symbols addition subtraction to 18 demonstrate an understing of equality between pairs of expressions, using addition subtraction of one- twodigit numbers demonstrate an understing of equality between pairs of expressions, using addition, subtraction, multiplication PATTERNS AND RELATIONSHIPS VARIABLES, EXPRESSIONS AND EQUATIONS demonstrate, through investigation, an understing of the use of variables in equations use variables in simple algebraic expressions equations to describe model real-life linear graphically algebraically, solve simple algebraic equations using a variety of strategies, including inspection guess check model linear graphically algebraically, solve verify algebraic equations, using a variety of strategies, including inspection, guess check, using a balance model 12

16 CONTINUUM OF LEARNING NUMBER SENSE AND NUMERATION OVERALL EXPECTATIONS BIG IDEAS GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 QUANTITY RELATIONSHIPS OPERATIONAL RELATIONSHIPS COUNTING read, represent, compare, order whole numbers to 50, use concrete materials to investigate fractions money amounts solve problems involving the addition subtraction of single digit whole numbers, using a variety of strategies magnitude by counting forward to 100 backwards from 20 read, represent, compare, order whole numbers to 100, use concrete materials to represent fractions money amounts to 100 cents solve problems involving the addition subtraction of one two-digit numbers using a variety of strategies, investigate multiplication division magnitude by counting forward to 200 backwards from 50 using multiples of various numbers as starting points read, represent, compare, order whole numbers to 1000 use concrete materials to represent fractions money amounts to $10 solve problems involving the addition subtraction of single- multidigit whole numbers using a variety of strategies, multiplication division magnitude by counting forward backwards by various numbers from various starting points read, represent, compare, order whole numbers to , decimal numbers to tenths, simple fractions, represent money amount to $100 solve problems involving the addition, subtraction, multiplication, division of single multi- digit whole numbers, involving the addition subtraction of decimal numbers to tenths money amounts, using a variety of strategies magnitude by counting forward backwards by 0.1 by fractional amounts read, represent, compare, order whole numbers to , decimal numbers to hundredths, proper improper fractions, mixed numbers solve problems involving the multiplication division of multidigit whole numbers, involving the addition subtraction of decimal numbers to hundredths using a variety of strategies magnitude by counting forward backwards by 0.01 read, represent, compare, order whole numbers to , decimal numbers to thousths, proper improper fractions, mixed numbers solve problems involving the multiplication division of whole numbers, the addition subtraction of decimal numbers to thousths using a variety of strategies represent, compare, order numbers, including integers addition subtraction of fractions integers, apply a variety of computational strategies to solve problems involving whole numbers decimal numbers represent, compare, order equivalent representations of numbers including those involving positive exponents solve problems involving whole numbers, decimal numbers, fractions integers using a variety of computational strategies PROPORTIONAL REASONING proportional reasoning by investigating whole number unit rates proportional reasoning by investigating whole number rates involving percent, ratio, unit rate proportional using percent, ratio, rate solve problems by using proportional reasoning in a variety of meaningful contexts 13

17 CONTINUUM OF LEARNING BIG IDEAS DATA MANAGEMENT AND PROBABILITY OVERALL EXPECTATIONS GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 COLLECT AND ORGANIZE DATA UNDERSTANDING DATA PROBABILITY collect organize categorical primary data display the data using concrete graphs pictographs, without regard to the order of labels on the horizontal axis read describe primary data presented in concrete graphs pictographs describe the likelihood that everyday events will happen collect organize categorical or discrete primary data display the data, using tally charts, concrete graphs, pictographs, line plots, simple bar graphs other graphic organizers, with labels ordered appropriately along horizontal axes, as needed read describe primary data presented in tally charts, concrete graphs, pictographs, line plots, simple bar graphs, other graphic organizers describe probability in everyday situations simple games collect organize categorical or discrete primary data display the data, using charts graphs, including vertical horizontal bar graphs, with labels ordered appropriately along the horizontal axes, as needed read, describe, interpret primary data presented in charts graphs, including vertical horizontal bar graphs predict investigate the frequency of a specific outcome in a simple probability experiment collect organize discrete primary data display the data using charts graphs, including stem--leaf plots double bar graphs read, describe, interpret primary data secondary data presented in charts graphs, including stem--leaf plots double bar graphs predict the results of a simple probability experiment, then conduct the experiment compare the prediction to the results collect organize discrete or continuous primary data secondary data display the data using charts graphs, including brokenline graphs read, describe, interpret primary data secondary data presented in charts graphs, including broken-line graphs represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists area models collect organize discrete or continuous primary data secondary data display the data using charts graphs, including continuous line graphs read, describe, interpret data, explain between sets of data determine the theoretical probability of an outcome in a probability experiment, use it to predict the frequency of the outcome collect organize categorical, discrete or continuous primary data secondary data display the data using charts graphs, including relative frequency labels circle graphs make evaluate convincing arguments, based on the analysis of data compare experimental probabilities with the theoretical probability of an outcome involving two independent events collect organize categorical, discrete, or continuous primary data secondary data display the data using charts graphs, including frequency tables with intervals, histograms, scatter plots apply a variety of data management tools strategies to make convincing arguments about data use probability models to make predictions about real-life events 14

18 KEY RESOURCES IN THE SCHOOL: At TCDSB, our teachers use a variety mathematics programs - the most commonly used program is Nelson Math as the core numeracy resource. There is no reason why this continuum cannot be utilized as a companion resource to use with other mathematics programs. To support deeper the big ideas, teachers can also access other resources in order to meet the needs of students in their classrooms. The following is a list of Ministry key resources that are available to teachers in all schools: MINISTRY: Early Math Strategy: The Report of the Expert Panel on Early Math in Ontario for Teachers of Kindergarten to Grade 3, 2003 A Guide to Effective Instruction in Mathematics: Number Sense Numeration, 2003 Teaching Learning Mathematics: The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario, 2004 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, 2004 A Guide to Effective Instruction in Mathematics: Geometry Spatial Sense, Kindergarten to Grade 3, 2005 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Volumes 1 to 5, 2006 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Number Sense Numeration, Grades 4 to 6, Volumes 1 to 6, 2006 A Guide to Effective Instruction in Mathematics: Patterning Algebra, Kindergarten to Grade 3, 2007 A Guide to Effective Instruction in Mathematics: Measurement, Kindergarten to Grade 3, 2007 A Guide to Effective Instruction in Mathematics: Data Management Probability, Kindergarten to Grade 3, 2007 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Volumes 1 to 4, 2008 (Measurement, Grades 4 to 6; Geometry Spatial Sense, Grades 4 to 6; Patterning Algebra, Grades 4 to 6; Data Management Probability, Grades 4 to 6) 15

19 KEY RESOURCES IN EVERY SCHOOL: About Teaching Mathematics, 2 nd Edition, by Marilyn Burns Exploring With Power Polygons by Cindy Stevens Mary Kay Tonrose-Dyer Getting Your Math Message Out to Parents by Nancy Litton Hs-On Stards, Pre-Kindergarten to Kindergarten Lessons for Algebraic Thinking, Grades 3 to 5 by Marilyn Burns Math by All Means: Data Management Probability by Marilyn Burns (each school should have either the Grade 2/3 or 3/4 version) More Puddle Questions for Canadian Schools: Assessing Mathematical Thinking (3 volumes - Grades 4, 5 6) National Library of Virtual Manipulatives Puddle Questions Super Source, Kindergarten to Grade 2 (set of 7 books) Super Source, Grades 3 to 4 (set of 7 math manipulatives books which includes Base Ten Blocks, Colour Tiles, Cuisinenaire Rods, Geoboards, Pattern Blocks, Snap Cubes, Tangrams) Super Source, Grades 5 to 6 (set of 7 math manipulatives books) Teaching Student-Centered Mathematics, by John A. Van de Walle (Vol. 1 Kindergarten to Grade 3; Vol. 2 Grades 3 to 5; Vol. 3 Grades 5 to 8) The Problem Solving Binder: Activities for Learning Problem Solving Strategies Young Mathematicians at Work: Constructing Number Sense, Addition, Subtraction by Catherine Twomey Fosnot Maarten Dolk Young Mathematicians at Work: Constructing Fractions, Decimals, Percents by Catherine Twomey Fosnot Maarten Dolk Young Mathematicians at Work: Constructing Multiplication Division by Catherine Twomey Fosnot Maarten Dolk 25 Thinking Questions (3 volumes Grades 1, 2 3) ONTARIO CURRICULUM SUPPLEMENTS Currently, Nelson Mathematics 3, 4 5 are over 90% compliant to the new Ontario Curriculum, Grades 1 to 8: Mathematics, Revised To ensure 100% curriculum coverage, Nelson Education has developed Curriculum Supplements to help fill in the gaps. These supplements are detailed chapter-by-chapter, lesson-by-lesson guides that address changes in the revised 2005 curriculum with individual lessons all the necessary teacher notes. They are now available in the Online Teacher s Resource at for your convenience. In order to access the Nelson Online Teacher Resource (OTR) for grades 3 to 6, teachers will need to register with Nelson. Go online to the following site: When filling out the required information to get a username, use the access code, NM5OTR04. (The first O is a capital O the second is the numeral 0.) 16