Math Delivery Plan Grade 6 HWDSB - WordPress.com

Measurement

Geometry & Spatial Sense Patterning & Algebra

Mathematics Delivery Plan (term-by-term organizer)

Data Management & Probability

Grade 6 Based on: The Ontario Curriculum Grades 1-8: Mathematics REVISED, 2011

Number Sense & Numeration

Mathematics Delivery Plan – Grade 6

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

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apply developing problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;

Reasoning and Proving

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apply developing reasoning skills (e.g., pattern recognition, classification) to make and investigate conjectures (e.g., through discussion with others);

Reflecting

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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 6

Mathematics Delivery Plan Number Sense and Numeration

Term 1 Quantity Relationships  whole numbers to 1 000 000  decimal numbers to thousandths  prime and composite numbers Operational Sense  addition and subtraction ⋅ whole numbers ⋅ decimal numbers to thousandths  multiplication ⋅ 4-digit by 2-digit whole numbers ⋅ decimal numbers by 10, 100, 1000 and 10,000 ⋅ decimal numbers to tenths

Measurement

Attributes, Units, and Measurement Sense  length, perimeter ⋅ metric system Measurement Relationships  area ⋅ formula of a parallelogram and triangle

Term 2 Quantity Relationships  fractions ⋅ proper and improper; unlike denominators ⋅ benchmarks of % Operational Sense  division ⋅ decimal numbers by 10, 100, 1000 and 10 000 ⋅ decimal numbers to tenths  division ⋅ 3-digit by 1-digit whole numbers Proportional Relationships  percent, ratio and unit rate Attributes Units and Measurement  volume ⋅ metric system  mass and capacity ⋅ metric system Measurement Relationships  volume ⋅ formula of a triangular prism  surface area ⋅ rectangular and triangular prism


Grade 6

Mathematics Delivery Plan Term 1

Term 2 Geometric Properties  2-D shapes ⋅ polygon and quadrilaterals ⋅ angles up to 180°

Patterning and Algebra

Geometry and Spatial Sense

Geometric Relationships  3-D shapes ⋅ models ⋅ isometric sketches Location and Movement  coordinate system ⋅ rotations, reflections and translations

Patterns and Relationships  growing and shrinking patterns ⋅ term and term numbers ⋅ relationships Variables, Expressions and Equations  variables ⋅ as an unknown quantity ⋅ as a changing quantity  2 or 3 symbols or letters as variables

Patterns and Relationships  repeating patterns ⋅ rotations


Grade 6

Mathematics Delivery Plan Data Management and Probability

Term 1 Collection and Organization of Data  discrete and continuous data  charts and graphs including continuous line graphs Data Relationships  mean  relationship between sets of data

Term 2 Probability  theoretical probability


STRAND:

Number Sense and Numeration

Overall Expectations for the Term  read, represent, compare, and order whole numbers to 1 000 000, decimal numbers to hundredths, (proper and improper fractions, and mixed numbers)

Big Ideas Addressed and Related Specific Expectations Quantity Relationships - whole numbers to 1 000 000 - decimal numbers to thousandths - prime and composite numbers Specific Expectations  represent, compare, and order whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools  demonstrate an understanding of place value in whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools and strategies  read and print in words whole numbers to one hundred thousand, using meaningful contexts  solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1 000 000  identify composite numbers and prime numbers and explain the relationship between them

TERM: 1 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 6 ⋅ Chapter 9  Math Makes Sense ⋅ Unit 2 ⋅ Unit 4  A Guide to Effective Instruction in Mathematics; (Grades 4 -6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 2 ⋅ Volume 3 ⋅ Volume 4 ⋅ Volume 6  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 5  Super Source

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) indicates skills and/or concepts to be addressed in alternate term

NS&N


STRAND:

Number Sense and Numeration (continued)

Overall Expectations for the Term  solve problems involving the multiplication (and division) of whole numbers, and the addition and subtraction of decimal numbers to thousandths, using a variety of strategies

Big Ideas Addressed and Related Specific Expectations Operational Sense - addition/ subtraction ⋅ whole numbers ⋅ decimal numbers to thousandths - multiplication ⋅ 4-digit by 2-digit whole numbers ⋅ decimal numbers by 10, 100, 1000 and 10, 000 ⋅ decimal numbers to tenths

TERM: 1 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ base ten materials for decimals ⋅ number lines ⋅ concrete materials ⋅ 10 x 10 grids ⋅ drawings ⋅ calculators ⋅ arrays

Specific Expectations  use a variety of mental strategies to solve addition, subtraction, multiplication, (and division) problems involving whole numbers  add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators  use estimation when solving problems involving the addition and subtraction of whole numbers and decimals, to help judge the reasonableness of a solution  solve problems involving the multiplication (and division) of whole numbers using a variety of tools  multiply whole numbers by 0.1, 0.01 and 0.001 using mental strategies  multiply (and divide) decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms and calculators  multiply (and divide) decimal numbers by 10, 100, 1000 and 10 000 using mental strategies  explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations

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NS&N


STRAND:

Measurement

Overall Expectations for the Term  estimate, measure, and record quantities, using the metric measurement system

Term 1 Big Ideas Addressed and Related Specific Expectations

Attributes, Units and Measurement - length and perimeter ⋅ metric system Specific Expectations  demonstrate an understanding of the relationship between estimated and precise measurements, and determine and justify when each kind is appropriate  estimate, measure, and record length, and area (mass, capacity and volume) using the metric measurement system

 determine the relationships among units and measurable attributes, including the area of a parallelogram, the areas of a triangle (and the volume of a triangular prism)

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Measurement Relationships - area ⋅ formula of a parallelogram and triangle Specific Expectations  select and justify the appropriate metric unit to measure length or distance in a given real-life situation  solve problems requiring conversion from larger to smaller metric units  construct a rectangle, a square, a triangle and a parallelogram, using a variety of tools given the area and/or perimeter  determine, through investigation using a variety of tools and strategies the relationship between the area of a rectangle and the areas of parallelograms and triangles by decomposing and composing  develop the formulas for the area of a parallelogram and the area of a triangle using the area relationships among rectangles, parallelograms and triangles  solve problems involving the estimation and calculation of the areas of triangles and the areas of parallelograms  determine, using concrete materials, the relationship between units used to measure area and apply the relationship to solve problems that involve conversions from square metres to square centimeters


Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 5 ⋅ Chapter 8  Math Makes Sense ⋅ Unit 9  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8  Super Source Tools for Term and Strand ⋅ rulers (cm and mm) ⋅ concrete materials ⋅ geoboard ⋅ dynamic geometry software ⋅ grid paper ⋅ pattern blocks ⋅ Power Polygons

M


STRAND:


Overall Expectations for the Term  describe and represent relationship in growing and shrinking patterns where the terms are whole numbers, (and investigate repeating patterns involving rotations)

 use variables in simple algebraic expressions and equations to describe relationships

Big Ideas Addressed and Related Specific Expectations Patterns and Relationships - growing and shrinking patterns ⋅ term and term numbers ⋅ relationships Specific Expectations  identify geometric patterns, through investigation using concrete materials or drawings, and represent them numerically  make tables of values, for growing patterns given pattern rules, in words, then list the ordered pairs and plot the points in the first quadrant, using a variety of tools  determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph  describe pattern rules in words that generate patterns by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term  determine a term, given its term number, by extending growing and shrinking patterns that are generated by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term

Variables, Expressions and Equations - variables ⋅ as an unknown quantity ⋅ as a changing quantity - 2 or 3 symbols or letters as variables

TERM: 1 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 1 ⋅ Chapter 14  Math Makes Sense ⋅ Unit 1 ⋅ Unit 10  Teaching Student-Centred Mathematics by J. Van d Walle Grades 5-8 ⋅ Chapter 9 ⋅ Chapter 10  Super Source Tools for Term and Strand ⋅ concrete materials ⋅ drawings ⋅ graph paper ⋅ calculators ⋅ dynamic statistical software

Specific Expectations  demonstrate an understanding of different ways in which variables are used  identify, through investigation, the quantities in an equation that vary and those that remain constant  solve problems that use two or three symbols or letters as variables to represent different unknown quantities  determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies

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P&A


STRAND:

Data Management and Probability

Overall Expectations for the Term  collect and organize discrete or continuous data and secondary data and display the data using charts and graphs, including continuous line graphs

 read, describe, and interpret data, and explain relationship between sets of data

Big Ideas Addressed and Related Specific Expectations Collection and Organization of Data ⋅ discrete and continuous data ⋅ graphs and charts; including continuous line graphs Specific Expectations  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 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  determine, through investigation, how well a set of data represents a population, on the basis of the method that was used to collect the data

Data Relationships

TERM: 1 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 3  Math Makes Sense ⋅ Unit 5  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 11  Super Source

Tools for Term and Strand ⋅ graph paper ⋅ spreadsheets ⋅ dynamic statistical software

- mean - relationship between sets of data Specific Expectations  read, interpret and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs  compare, through investigation, different graphical representations of the same data  explain how different scales used on graphs can influence conclusions drawn from the data  demonstrate an understanding of mean, and use mean to compare two sets of related data, with and without the use of technology  demonstrate, through investigation, an understanding of how data from charts, tables, and graphs can be used to make inferences and convincing arguments

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DM&P


STRAND:

Number Sense and Numeration

Overall Expectations for the Term

Big Ideas Addressed and Related Specific Expectations

 read, represent, compare, and order (whole numbers to 1 000 000, decimal numbers to hundredths,) proper and improper fractions, and mixed numbers

Quantity Relationships

 solve problems involving the (multiplication and) division of whole numbers, (and the addition and subtraction of decimal numbers to thousandths,) using a variety of strategies

Operational Sense

- fractions ⋅ proper and improper, unlike denominators ⋅ benchmarks of % Specific Expectations  represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation  estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100%

- division ⋅ 3-digt by 1-digit whole numbers ⋅ decimal numbers by 10, 100, 1000 and 10 000 ⋅ decimal numbers to tenths Specific Expectations  use a variety of mental strategies to solve (addition, subtraction, multiplication and) division problems involving whole numbers  solve problems involving the (multiplication and) division of whole numbers using a variety of tools  explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations  (multiply and) divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms and calculators  (multiply and) divide decimal numbers by 10, 100, 1000 and 10 000 using mental strategies

TERM: 2 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 6 ⋅ Chapter 9 ⋅ Chapter 10 ⋅ Chapter 12  Math Makes Sense ⋅ Unit 2 ⋅ Unit 4 ⋅ Unit 8  A Guide to Effective Instruction in Mathematics (Grades 4-6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 3 ⋅ Volume 4 ⋅ Volume 5 ⋅ Volume 6  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 2 ⋅ Chapter 3 ⋅ Chapter 4 ⋅ Chapter 5 ⋅ Chapter 6  Super Source

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NS&N


STRAND:

Number Sense and Numeration (continued)

Overall Expectations for the Term  demonstrate an understanding of relationships involving percent, ratio, and unit rate

(

Big Ideas Addressed and Related Specific Expectations Proportional Relationships

- percent, ratio and unit rate Specific Expectations  represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation  determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among decimal numbers and percents  represent relationships using unit rates

TERM: 2 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ fraction circles and strips ⋅ Cuisenaire rods ⋅ drawings ⋅ number lines ⋅ calculators ⋅ concrete materials ⋅ arrays


NS&N


STRAND:

Measurement

Overall Expectations for the Term  estimate measure, and record quantities, using the metric measurement system

Term 2 Big Ideas Addressed and Related Specific Expectations

Attributes, Units and Measurement - mass, capacity and volume ⋅ metric system Specific Expectations

 estimate, measure, and record (length, area,) mass, capacity and volume using the metric measurement system

 determine the relationships among units and measurable attributes, including (the area of a parallelogram, the areas of a triangle and) the volume of a triangular prism

(

Measurement Relationships - volume ⋅ formula of a triangular prism - surface area ⋅ rectangular and triangular prism Specific Expectations  determine, through investigation using a variety of tools and strategies, the relationship between the height, the area of the base, and the volume of a triangular prism, and generalize to develop the formula  determine, through investigation using a variety of tools and strategies, the surface area of rectangular and triangular prisms  solve problems involving the estimation and calculation of the surface area and volume of triangular and rectangular prisms


Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 11  Math Makes Sense ⋅ Unit 6 ⋅ Unit 9  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8  Super Source Tools for Term and Strand ⋅ concrete materials ⋅ drawings ⋅ nets ⋅ dynamic geometry software ⋅ Polydrons ⋅ scale

M


STRAND:

Geometry & Spatial Sense

Overall Expectations for the Term  classify and construct polygons and angles

 sketch three-dimensional figures, and construct three-dimensional figures from drawings

Big Ideas Addressed and Related Specific Expectations Geometric Properties - 2-D shapes ⋅ polygons and quadrilaterals ⋅ angles up to 180°

Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 7 ⋅ Chapter 11 ⋅ Chapter 14

Specific Expectations  sort and classify quadrilaterals by geometric properties related to symmetry, angles and sides, through investigations using a variety of tools  sort polygons according to the number of lines of symmetry and the order of rotational symmetry, through investigation using a variety of tools  measure and construct angles up to 180 degrees using a protractor, and classify them as acute, right, obtuse or straight angles  construct polygons using a variety of tools, given angle and side measurements

 Math Makes Sense ⋅ Unit 3 ⋅ Unit 7

Geometric Relationships

 Super Source

- 3-D figures ⋅ models ⋅ isometric sketches Specific Expectations  build three-dimensional models using connecting cubes, given isometric sketches or different views of the structure  sketch, using a variety of tools, isometric perspectives and different views of three-dimensional figures built with interlocking cubes

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Term 2


 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7

Tools for Term and Strand ⋅ geoboard ⋅ dynamic geometry software ⋅ Mira ⋅ protractor ⋅ grid paper ⋅ tissue paper ⋅ computer technology ⋅ drawings ⋅ square dot paper ⋅ isometric dot paper ⋅ Polydrons

G&SS


STRAND:

Geometry & Spatial Sense (continued)

Overall Expectations for the Term  describe location in the first quadrant of a coordinate system, and rotate twodimensional shapes

Big Ideas Addressed and Related Specific Expectations

Term 2 Suggested Resources for Strand and Term

Location and Movement - coordinate system - rotations, reflections and translations Specific Expectations  explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane  identify, perform, and describe, through investigation using a variety of, rotations of 180° and clockwise and counter clockwise rotations of 90°, with the centre of rotation inside or outside the shape  create and analyse designs made by reflecting, translating, and/or rotating a shape, or shapes, by 90° or 180°

G&SS (



STRAND:


Overall Expectations for the Term  describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations

Big Ideas Addressed and Related Specific Expectations Patterns and Relationships - repeating patterns ⋅ rotations Specific Expectations  extend and create repeating patterns that result from rotations, through investigation using a variety of tools

TERM: 2 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 14  Math Makes Sense ⋅ Unit 7  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7  Super Source Tools for Term and Strand ⋅ pattern blocks ⋅ dynamic geometry software ⋅ geoboards ⋅ dot paper ⋅ concrete materials

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P&A


STRAND:

Data Management & Probability

Overall Expectations for the Term  determine the theoretical probability of an outcome in a probability experiment, and use it to predict the frequency of the outcome

Big Ideas Addressed and Related Specific Expectations Probability - theoretical probability Specific Expectations  express theoretical probability as a ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely  represent the probability of an event, using a value from the range of 0 to 1  predict the frequency of an outcome of a simple probability experiment or game, by calculating and using the theoretical probability of that outcomes

TERM: 2 Suggested Resources for Strand and Term  Nelson Mathematics ⋅ Chapter 13  Math Makes Sense ⋅ Unit 11  Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 12  Super Source

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DM&P