Measurement Geometry & Spatial Sense Patterning & Algebra Mathematics Delivery Plan (term-by-term organizer) Data Management & Probability Grade 5 Based on: The Ontario Curriculum Grades 1-8: Mathematics REVISED, 2005 Number Sense & Numeration
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 twice over the course of the year with a minimum of two strands being reported on each term. The following organizer meets those requirements. It is important to note that these are the minimum requirements set by the Ministry of Education. The organization of strands within this document ensures a balanced math program within each term; resulting in Number Sense being addressed every term and related concepts from other strands being covered within the same term. See Core Connections between s page for details. There are valid arguments for many of the expectations to be addressed in each term. Please note, there are many factors that this type of organizer cannot take into account: e.g., the nature of your students, the background knowledge of a particular class of students, the integration amongst subject areas, school initiatives, the length of the school terms from year to year, etc. The order in which the big ideas/expectations are addressed within each term is up to the individual teacher. Where possible (and in most cases) the same big ideas are addressed in the same term across several grade levels. This makes it easier for teachers of combined grades to plan and deliver the big ideas (e.g., three-dimensional figures are addressed in term 3 in grades 1 to 8 so a split- grade teacher could address this big idea in the same term). This was not possible in all cases (e.g., addition and subtraction is addressed in term 1 for grades 2 to 6, but in term 2 and 3 for grade 1). 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. Many of the chapters or units are listed more than once throughout this document. In many cases the repetition is within the same term, this is due to how strands and big ideas have been embedded within each other. There are some expectations that appear in more than one term because they combine several ideas at once. In most cases, these expectations require repeated opportunities for students to completely consolidate the learning. 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 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. 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 develop, select, and apply problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding; Reasoning and Proving develop and apply reasoning skills (e.g., classification, recognition of relationships, us of counter-examples) to make and investigate conjectures and construct and defend arguments; 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 comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal); 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 mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports); Representing create a variety of representations of mathematical ideas (e.g., by using physical models, pictures, numbers, variables, diagrams, graphs, onscreen dynamic representations), make connections among them, and apply them to solve problems; Communicating communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
Core Connections Between s Term 1 Term 2 Term 3 Addition and Subtraction Number Concepts Growing and Shrinking Patterns Numbers to 100 000 Area 2-D Shapes Repeating Patterns Translations Volume 3-D Figures Properties Prisms and Pyramids Money Perimeter Polygons and Triangles Capacity Mass Growing and Shrinking Patterns Equations As Decimals Multiplication and Division Fractions Counting Variables Multiplicative Relationships
Grade 5 Number Sense and Numeration Quantity Relationships whole numbers to 100 000 decimal numbers to hundredths money to $1000 Counting forward by hundredths Mathematics Delivery Plan Term 1 Term 2 Term 3 Operational Sense addition and subtraction whole numbers decimal numbers to hundredths Operational Sense multiplication 2-digit by 2-digit whole numbers decimal numbers by 10, 100, 1000 and 10,000 division 3-digit by 1-digit whole numbers Quantity Relationships fractions proper and improper; like denominators equivalent Operational Sense division decimal numbers by 10 and 100 Proportional Relationships fractions whole-number rates Measurement Attributes, Units and Measurement Sense length; m, cm, dm, m, km perimeter and area regular and irregular polygons Measurement Relationships length conversions: m to cm, km to m perimeter and area formula of a rectangle Attributes, Units and Measurement Sense time; elapsed time temperature; change over time Measurement Relationships volume formula of a rectangular prism relationship between volume and capacity mass; mg, g, kg, tonne time 12-hour vs 24-hour clock
Geometry and Spatial Sense Geometric Properties 2-D shapes polygons and triangles angles up to 90 Location and Movement cardinal directions translations 2-D shapes Geometric Properties 3-D figures prisms and pyramids Geometric Relationships 3-D figures nets of prisms and pyramids Patterning and Algebra Data Management and Probability Patterns and Relationships growing and shrinking patterns relationships table of values addition and subtraction Collection and Organization of Data discrete and continuous data charts and graphs including broken-line graphs surveys and experiments Data Relationships mean comparing related sets of data Patterns and Relationships growing and shrinking patterns table of values multiplication and division repeating patterns translations Variables, Expressions and Equations variables as changing or unknown quantities missing numbers in equations addition, subtraction, multiplication and division Probability probability as fractions
STRAND: Number Sense and Numeration TERM: 1 read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, (proper and improper fractions, and mixed numbers) demonstrate an understanding of magnitude by counting forward and backwards by 0.01 Big Ideas Addressed and Related Quantity Relationships - whole numbers to 100 000 - decimal numbers to hundredths - money to $1000 represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools and strategies read and print in words whole numbers to ten thousand, using meaningful contexts round decimal numbers to the nearest tenth, in problems arising from real-life situations demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings read and write money amounts to $1000 solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 100 000 Counting - forward by hundredths count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines Chapter 2 Chapter 4 Unit 2 Unit 4 Unit 6 Unit 8 Chapter 2 Chapter 3 Chapter 4 Chapter 7 Chapter 2 Chapter 4 Chapter 5 A Guide to Effective Instruction in Math, Grades 4 to 6: Number Sense and Numeration Volume 1 Volume 2 cont d NS&N
STRAND: Number Sense and Numeration - continued TERM: 1 solve problems (involving the multiplication and division of multi-digit whole numbers and) involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies Big Ideas Addressed and Related Operational Sense - addition and subtraction whole numbers decimal numbers to hundredths solve problems involving the addition, subtraction (and multiplication) of whole numbers, using a variety of mental strategies add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms use estimation when solving problems involving the addition, subtraction (multiplication and division) of whole numbers, to help judge the reasonableness of a solution base ten materials drawings of base ten materials number lines currency manipulatives 10 X 10 grids NS&N
STRAND: Patterning and Algebra TERM: 1 determine, through investigation using a table of values, relationships in growing and shrinking patterns (and investigate repeating patterns involving translations) Big Ideas Addressed and Related Patterns and Relationships growing and shrinking patterns relationships table of values addition and subtraction create, identify, and extend numeric and geometric patterns, using a variety of tools build a model to represent a number pattern presented in a table of values that shows the term number and the term make a table of values for a pattern that is generated by adding or subtracting a number to get the next term, (or by multiplying or dividing by a constant to get the next term,) given either the sequence or the pattern rule in words make predictions related to growing and shrinking geometric and numeric patterns Chapter 1 Unit 1 Unit 10 Chapter 10 Chapter 9 concrete materials drawings calculators spreadsheets square tiles P&A
STRAND: Data Management and Probability TERM: 1 collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs Big Ideas Addressed and Related Collection and Organization of Data - discrete and continuous data - charts and graphs including broken-line graphs - surveys and experiments distinguish between discrete data and continuous data 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 collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs (including broken-line graphs) that have appropriate titles, labels, and scales that suit the range and distribution of the data, using a variety of tools demonstrate an understanding that sets of data can be samples of larger populations describe, through investigation, how a set of data is collected and explain whether the collection method is appropriate Data Relationships - mean - comparing related sets of data read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs compare similarities and differences between two related sets of data, using a variety of strategies Chapter 3 Unit 5 Chapter 11 Chapter 11 graph paper simple spreadsheets dynamic statistical software DM&P
STRAND: Number Sense and Numeration TERM: 2 solve problems involving the multiplication and division of multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies Big Ideas Addressed and Related Operational Sense - multiplication 2-digit by 2-digit decimal numbers by 10, 100, 1000 and 10,000 - division 3-digit by 1-digit solve problems involving the (addition, subtraction, and) multiplication of whole numbers, using a variety of mental strategies multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms divide three-digit whole numbers by one-digit whole numbers, using concrete materials, estimation, student-generated algorithms, and standard algorithms multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies use estimation when solving problems involving the addition, subtraction, multiplication, and division of whole numbers, to help judge the reasonableness of a solution Chapter 6 Chapter 9 Unit 2 Unit 4 Chapter 3, 4 and 7 Chapter 2 and 4 A Guide to Effective Instruction in Math, Grades 4 to 6: Number Sense and Numeration Volume 3, 4 and 6 concrete materials calculator drawings arrays base ten materials NS&N
STRAND: Measurement TERM: 2 estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies Big Ideas Addressed and Related Attributes, Units, and Measurement Sense - length; m, cm, dm, m, km - perimeter and area; regular and irregular polygons estimate and measure the perimeter and area of regular and irregular polygons Chapter 5 Chapter 8 Unit 6 Unit 9 determine the relationships among units and measurable attributes, including the area of a rectangle (and the volume of a rectangular prism.) Measurement Relationships - length; conversions: m to cm, km to m - perimeter and area; formula of a rectangle select and justify the most appropriate standard unit to measure length, height, width, and distance, and to measure the perimeter of various polygons solve problems requiring conversion from metres to centimetres and from kilometres to metres create, through investigation using a variety of tools and strategies, twodimensional shapes with the same perimeter or the same area determine, through investigation using a variety of tools and strategies, the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas solve problems requiring the estimation and calculation of perimeters and areas of rectangles Chapter 9 Chapter 8 concrete materials paper and pencil grid paper rulers (cm and mm) dynamic geometry software pattern blocks Power Polygons geoboard M
STRAND: Geometry and Spatial Sense TERM: 2 identify and classify twodimensional shapes by side and angle properties, and compare and sort three-dimensional figures Big Ideas Addressed and Related Geometric Properties - 2-D shapes polygons and triangles angles up to 90º distinguish among polygons, regular polygons, and other two-dimensional shapes identify and classify acute, right, obtuse, and straight angles measure and construct angles up to 90º, using a protractor identify triangles and classify them according to angle and side properties construct triangles, using a variety of tools, given acute or right angles and side measurements Chapter 7 Chapter 14 Unit 3 Unit 7 Chapter 8 identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes Location and Movement - cardinal directions - translations 2-D shapes locate an object using the cardinal directions and a coordinate system compare grid systems commonly used on maps identify, perform, and describe translations, using a variety of tools create and analyze designs by translating and/or reflecting a shape, or shapes, using a variety of tools Chapter 7 protractor compass dynamic geometry software geoboard dot paper computer programs grid paper Mira drawings G&SS
STRAND: Patterning and Algebra TERM: 2 determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations demonstrate, through investigation, an understanding of the use of variables in equations Big Ideas Addressed and Related Patterns and Relationships - growing and shrinking patterns table of values multiplication and division - repeating patterns translations make a table of values for a pattern that is generated by (adding or subtracting a number to get the next term, or by) multiplying or dividing by a constant to get the next term, given either the sequence or the pattern rule in words extend and create repeating patterns that result from translations, through investigation using a variety of tools Variables, Expressions and Equations - variables as changing or unknown quantities - missing numbers in equations addition, subtraction, multiplication and division demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other determine the missing number in equations involving addition, subtraction, multiplication, or division and one-or two-digit numbers, using a variety of tools and strategies Chapter 1 Chapter 4 Chapter 6 Chapter 14 Unit 1 Unit 2 Unit 7 Unit 10 Chapter 10 Chapter 7, 9 and 10 pattern blocks dynamic geometry software dot paper concrete materials calculator P&A
STRAND: Number Sense and Numeration TERM: 3 read, represent, compare, and order( whole numbers to 100 000, decimal numbers to hundredths,) proper and improper fractions, and mixed numbers solve problems involving the (multiplication and) division of multi-digit whole numbers, (and involving the addition and subtraction of decimal numbers to hundredths,) using a variety of strategies demonstrate an understanding of proportional reasoning by investigating wholenumber rates Big Ideas Addressed and Related Quantity Relationships - fractions proper and improper; like denominators equivalent represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation; demonstrate and explain the concept of equivalent fractions, using concrete Operational Sense - division decimal numbers by 10 and 100 (multiply decimal numbers by 10, 100, 1000, and 10 000, and) divide decimal numbers by 10 and 100, using mental strategies Proportional Relationships - fractions - whole-number rates describe multiplicative relationships between quantities by using simple fractions and decimals determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings Chapter 10 and 12 Unit 4 and 8 Chapter 5, 6 and 7 Chapter 3, 4 and 6 A Guide to Effective Instruction in Math, Grades 4 to 6: Number Sense and Numeration Volume 1, 4, 5 and 6 calculator fraction circles and strips Cuisenaire rods number lines concrete materials drawings base ten NS&N
STRAND: Measurement TERM: 3 estimate, measure, and record (perimeter, area) temperature change, and elapsed time, using a variety of strategies determine the relationships among units and measurable attributes, including (the area of a rectangle and) the volume of a rectangular prism Big Ideas Addressed and Related Attributes, Units, and Measurement Sense - time; elapsed time - temperature; change over time estimate, measure, and represent time intervals to the nearest second estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in minutes, hours, days, weeks, months, or years measure and record temperatures to determine and represent temperature changes over time Measurement Relationships - volume formula of a rectangular prism - relationship between volume and capacity - mass; mg, g, kg, tonne - time; 12-hour vs 24-hour clock Chapter 5 Chapter 11 Unit 6 Chapter 9 Chapter 8 solve problems involving the relationship between a 12-hour clock and a 24-hour clock determine, through investigation, the relationship between capacity and volume, by comparing the volume of an object with the amount of liquid it can contain or displace determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula analogue clock concrete materials o containers o bottles connecting cubes scale M
STRAND: Geometry and Spatial Sense TERM: 3 identify and classify twodimensional shapes by side and angle properties and compare and sort three-dimensional figures identify and construct nets of prisms and pyramids Big Ideas Addressed and Related Geometric Properties - 3-D figures prisms and pyramids distinguish among prisms, right prisms, pyramids, and other three-dimensional figures Geometric Relationships - 3-D figures nets of prisms and pyramids identify prisms and pyramids from their nets construct nets of prisms and pyramids, using a variety of tools Chapter 11 Math Makes Sense Unit 3 Chapter 8 Chapter 7 grid paper isometric dot paper Polydrons computer applications G&SS
STRAND: Data Management and Probability TERM: 3 represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models Probability Big Ideas Addressed and Related - probability as fractions determine and represent all the possible outcomes in a simple probability experiment, using systematic lists and area models represent, using a common fraction, the probability that an event will occur in simple games and probability pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the Chapter 13 Unit 11 Chapter 12 Chapter 12 DM&P