Measurement Geometry & Spatial Sense Patterning & Algebra Mathematics Delivery Plan (term-by-term organizer) Data Management & Probability Grade 8 Number Sense & Numeration Based on: The Ontario Curriculum Grades 1-8: Mathematics REVISED, 2011
The Hamilton-Wentworth District School Board Mathematics Delivery Plan The following is HWDSB s mandated term-by-term organizer which was developed to assist you with planning your mathematics program. It is based on The Ontario Curriculum Grades 1-8 Mathematics REVISED document. Teachers are required to report on each strand once over the course of the year with a minimum of four strands being reported on each term. The order in which the big ideas/expectations are addressed within each term is up to the individual teacher. Also included are suggested resources that support the teaching and assessing of the big ideas being addressed each term. These resources are reference points for teachers to use to gain an understanding of the content, tools and strategies to support learners; identify lessons or investigations; and to gather assessment and/or evaluation ideas. It is important to note that Problem Solving is not a separate strand but rather an approach that should be woven throughout all of the strands. The mathematics Process Expectations are something that should be built into the teaching and assessing of all of the mathematics. Having students explore mathematical concepts, through Problem Solving, to gain a conceptual understanding prior to any direct instruction should be an integral part of every mathematics program.
The Mathematical Processes The mathematical processes are a set of seven expectations that describe how students acquire and apply their mathematical knowledge and skills (as found on pg. 11 of the curriculum). Students should be actively engaged in applying these processes throughout their math program. Students must problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of concepts, and the skills required in all the strands in every grade. Problem Solving apply developing problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding; Reasoning and Proving apply developing reasoning skills (e.g., pattern recognition, classification) to make and investigate conjectures (e.g., through discussion with others); Reflecting demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by explaining to others why they think their solution is correct); Selecting Tools and Computational Strategies select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems; Connecting make connections among simple mathematical concepts and procedures, and relate mathematical ideas to situations drawn from everyday contexts; Representing create basic representations of simple mathematical ideas (e.g., using concrete materials; physical actions, such as hopping or clapping; pictures; numbers; diagrams; invented symbols), make connections among them, and apply them to solve problems; Communicating communicate mathematical thinking orally, visually, and in writing, using everyday language, a developing mathematical vocabulary, and a variety of representations. The Mathematical Processes are embedded within the Achievement Chart Mathematics Grades 1-8, on pages 22-23 of the Revised Curriculum.
Grade 8 Number Sense and Numeration Quantity Relationships rational numbers exponential notation common factors and common multiplies Mathematics Delivery Plan Term 1 Term 2 Operational Sense addition, subtraction, multiplication and division whole numbers and decimal numbers multi-step problems percents to one decimal place integers square roots of whole numbers order of operation in expressions with brackets and exponents Operational Sense addition, subtraction, multiplication and division fractions Proportional Relationships percent, rate and proportion Measurement Measurement Relationships circle circumference, radius and diameter formula for circumference area formula of a circle Attributes, Units and Measurement Sense volume and capacity applications of Measurement Relationships conversion area, volume and capacity relationships circumference and area for a circle volume formula of a cylinder surface area cylinder
Grade 8 Mathematics Delivery Plan Term 1 Term 2 Geometric Properties quadrilaterals sort and classify by properties including diagonals circle Geometry and Spatial Sense Geometric Relationships measurement relationships similar shapes angle relationships parallel and intersecting lines Pythagorean relationship polyhedron faces, edges, vertices Location and Movement Cartesian coordinate plane plotting a point after a transformation transformations real-world movements
Grade 8 Patterning and Algebra Patterns and Relationships linear growing patterns whole numbers graphs, algebraic expressions and equations Variables, Expressions and Equations linear relationships model graphically and algebraically solve and verify algebraic equations balance model Mathematics Delivery Plan Term 1 Term 2 Data Management and Probability Collection and Organization of Data categorical, discrete and continuous data charts and graphs including relative frequency tables with intervals, histograms and scatter plots Data Relationships convincing arguments central tendency appropriate measure comparing two attributes using scatter plots Probability experimental vs theoretical probability two independent events complementary events
STRAND: Number Sense and Numeration TERM: 1 represent, compare, and order equivalent representations of numbers, including those involving positive exponents solve problems involving whole numbers, decimal numbers, (fractions) and integers using a variety of computational strategies Big Ideas Addressed and Related Quantity Relationships - rational numbers - exponential notation - common factors and common multiples express repeated multiplication using exponential notation represent whole numbers in expanded form using powers of ten represent, compare, and order rational numbers translate between equivalent forms of a number determine common factors and common multiples using the prime factorization of numbers Operational Sense - addition, subtraction, multiplication and division whole numbers and decimal numbers multi-step problems percents to one decimal place integers order of operation in expressions with brackets and exponents - square roots of whole numbers solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools and strategies solve problems involving percents expressed to one decimal place and wholenumber percents greater than 100 use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, (and fractions,) to help judge the reasonableness of a solution multiply and divide decimal numbers by various powers of ten estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not represent the multiplication and division of integers, using a variety of tools solve problems involving operations with integers, using a variety of tools evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations ( ) indicates skills and/or concepts to be addressed in alternate term Chapter 1 Chapter 2 Chapter 6 Unit 1 Unit 2 Unit 4 Unit 9 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 2 Chapter 4 Chapter 5 Chapter 6 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 1 Unit 5 Tools for Term and Strand fraction pieces grid paper two-coloured counters counters number lines virtual manipulatives NS&N
STRAND: Measurement Term 1 determine the relationships among units and measurable attributes, including the area of a circle (and the volume of a cylinder) Big Ideas Addressed and Related Measurement Relationships - circle circumference, radius and diameter formula for circumference - area formula of a circle measure the circumference, radius, and diameter of circular objects, using concrete materials determine, through investigation using a variety of tools and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas solve problems involving the estimation and calculation of the circumference and the area of a circle Chapter 5 Unit 6 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 8 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 3 Tools for Term and Strand concrete materials - cans and string dynamic geometry software ( ) indicates skills and/or concepts to be addressed in alternate term M
STRAND: Patterning and Algebra TERM: 1 represent linear growing patterns using graphs, algebraic expressions, and equations model linear relationships graphically and algebraically, and solve and verify algebraic equations, using a variety of strategies, including inspection, guess and check, and using a balance model Big Ideas Addressed and Related Patterns and Relationships - linear growing patterns whole numbers graphs, algebraic expressions and equations represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic expressions represent linear patterns graphically, using a variety of tools determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation Variables, Expressions and Equations - linear relationships model graphically and algebraically - solve and verify algebraic equations balance model describe different ways in which algebra can be used in real-life situations model linear relationships using tables of values, graphs, and equations, through investigation using a variety of tools translate statements describing mathematical relationships into algebraic expressions and equations evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables make connections between solving equations and determining the term number in a pattern, using the general term solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a balance model Chapter 4 Chapter 8 Unit 1 Unit 10 Teaching Student-Centred Mathematics by J. Van d Walle Chapter 9 Chapter 10 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 2 Unit 12 Tools for Term and Strand concrete materials calculators graph paper dynamic statistical software algebra tiles pattern blocks connecting cubes base ten materials ( ) indicates skills and/or concepts to be addressed in alternate term P&A
STRAND: Data Management and Probability TERM: 1 collect and organize categorical, discrete, or continuous primary data and secondary data and display the data using charts and graphs, including frequency tables with intervals, histograms, and scatter plots apply a variety of data management tools and strategies to make convincing arguments about data Big Ideas Addressed and Related Collection and Organization of Data - categorical, discrete and continuous data - charts and graphs: relative frequency tables with intervals, histograms, scatter plots collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements organize into intervals a set of data that is spread over a broad range collect and organize categorical, discrete, or continuous primary data and secondary data and display the data in charts, tables, and graphs (including histograms and scatter plots) that have appropriate titles, labels and scales that suit the range and distribution of the data, using a variety of tools select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph explain the relationship between a census, a representative sample, sample size, and a population Data Relationships - convincing arguments - central tendency: appropriate measure - comparing two attributes using scatter plots read, interpret and draw conclusions from primary data and from secondary data presented in charts, tables, and graphs determine, through investigation, the appropriate measure of central tendency (i.e., mean, median, or mode) needed to compare sets of data demonstrate an understanding of the appropriate uses of bar graphs and histograms by comparing their characteristics compare two attributes or characteristics, using a scatter plot, and determine whether or not the scatter plot suggests a relationship identify and describe trends, based on the rate of change of data from tables and graphs, using informal language make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs compare two attributes or characteristics, using a variety of data management tools and strategies ( ) indicates skills and/or concepts to be addressed in alternate term Chapter 3 Unit 5 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 11 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 11 Tools for Term and Strand graph paper spreadsheets dynamic statistical software DM&P
STRAND: Number Sense and Numeration TERM: 2 solve problems involving (whole numbers, decimal numbers,) fractions, (and integers), using a variety of computational strategies solve problems by using proportional reasoning in a variety of meaningful contexts Big Ideas Addressed and Related Operational Sense - addition, subtraction, multiplication and division fractions use estimation when solving problems involving operations with (whole numbers, decimals, percents, integers, and) fractions, to help judge the reasonableness of a solution represent the multiplication and division of fractions, using a variety of tools and strategies solve problems involving addition, subtraction, multiplication, and division with simple fractions Proportional Relationships - percent, ratio and proportion identify and describe real-life situations involving two quantities that are directly proportional solve problems involving proportions, using concrete materials, drawings, and variables solve problems involving percent that arise from real-life contexts solve problems involving rates Chapter 2 Chapter 9 Unit 2 Unit 4 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 3 Chapter 4 Chapter 6 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 5 Unit 8 Tools for Term and Strand - concrete materials - grid paper - geoboard - Cuisenaire rods - graphs - calculators - drawings ( ) indicates skills and/or concepts to be addressed in alternate term NS&N
STRAND: Measurement Term 2 research, describe, and report on applications of volume and capacity measurement determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder Big Ideas Addressed and Related Attributes, Units and Measurement Sense - volume and capacity applications of research, describe, and report on applications of volume and capacity measurement Measurement Relationships - conversions area, volume and capacity - relationships circumference and area for a circle - volume formula for a cylinder - surface area cylinder solve problems that require conversions involving metric units of area, volume, and capacity determine, through investigation using a variety of tools and strategies the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula determine, through investigation using concrete materials, the surface area of a cylinder solve problems involving the surface area and the volume of cylinders, using a variety of strategies Chapter 5 Chapter 11 Unit 3 Unit 6 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 8 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 3 Unit 7 Tools for Term and Strand concrete materials - cans and string - cylinders dynamic geometry software Polydrons ( ) indicates skills and/or concepts to be addressed in alternate term M
STRAND: Geometry & Spatial Sense Term 2 demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world develop geometric relationships involving lines, triangles, and polyhedra and solve problems involving lines and triangles Big Ideas Addressed and Related Geometric Properties - quadrilaterals sort and classify by properties including diagonals - circle sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation using a variety of tools construct a circle, given its centre and radius, or its centre and a point on the circle, or three points on the circle investigate and describe applications of geometric properties in the real world Geometric Relationships - measurement relationships similar shapes - angle relationships parallel and intersecting lines - Pythagorean relationship determine, through investigation using a variety of tools relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes determine, through investigation using a variety of tools and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle solve angle-relationship problems involving triangles, intersecting lines and parallel lines and transversals determine the Pythagorean relationship, through investigation using a variety of tools and strategies solve problems involving right triangles geometrically, using the Pythagorean relationship Chapter 7 Chapter 10 Unit 6 Unit 7 Unit 8 Unit 9 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 7 Targeted Implementation & Planning for Revised Math (TIPS4RM) Unit 3 Unit 4 Unit 9 Unit 10 Tools for Term and Strand concrete materials dynamic geometry software geoboard protractor ( ) indicates skills and/or concepts to be addressed in alternate term G&SS
STRAND: Geometry & Spatial Sense (continued) Term 2 represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world Big Ideas Addressed and Related Location and Movement - Cartesian coordinate plane plotting a point after a transformation - transformations real-world movements graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s) identify, through investigation, real-world movements that are translations, reflections, and rotations ( ) indicates skills and/or concepts to be addressed in alternate term G&SS
STRAND: Data Management & Probability TERM: 2 use probability models to make predictions about real-life events Big Ideas Addressed and Related Probability - experimental vs. theoretical probability two independent events - complementary events compare, through investigation, the theoretical probability on an event with experimental probability, and explain why they might differ determine, through investigation, the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases using class-generated data and technology-based simulation models identify the complementary event for a given event, and calculate the theoretical probability that a given event will occur Suggested Resources for Strand Chapter 12 Unit 11 Teaching Student-Centered Mathematics by J. Van de Walle Chapter 12 Targeted Implementation & Planning Support for Revised Math (TIPS4RM) Unit 6 Unit 11 ( ) indicates skills and/or concepts to be addressed in alternate term DM&P