Mathematics Delivery Plan
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, 2011
Number Sense & Numeration
Mathematics Delivery Plan – Grade 5
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.
Mathematics Delivery Plan – Grade 5
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.
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan
Measurement
Number Sense and Numeration
Term 1 Quantity Relationships whole numbers to 100 000 money to $1000
Operational Sense addition and subtraction ⋅ whole numbers multiplication ⋅ 2-digit by 2-digit whole numbers
Attributes, Units, and Measurement Sense temperature; change over time length; m, cm, dm, 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
Term 2 Quantity Relationships fractions and decimals ⋅ proper and improper; like denominators ⋅ equivalent ⋅ decimal numbers to hundredths Counting forward by hundredths Operational Sense division and multiplication ⋅ 3-digit by 1-digit whole numbers ⋅ decimal numbers by 10 and 100 (division) ⋅ decimal numbers by 10, 100, 1000, and 10 000 (multiplication) Proportional Relationships fractions whole-number rates Attributes, Units, and Measurement Sense time; elapsed 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
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan Term 1
Term 2 Geometric Properties
Patterning and Algebra
Geometry and Spatial Sense
2-D shapes ⋅ polygon and triangles ⋅ angles up to 90° 3-D figures ⋅ prisms and pyramids Geometric Relationships 3-D shapes ⋅ nets of prisms and pyramids Location and Movement cardinal directions translations ⋅ 2-D shapes
Patterns and Relationships growing and shrinking patterns ⋅ relationships ⋅ table of values ⋅ addition and subtraction
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
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan Data Management and Probability
Term 1 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
Term 2 Probability probability as fractions
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration
Overall Expectations for the Term 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)
(
Big Ideas Addressed and Related Specific Expectations Quantity Relationships - whole numbers to 100 000 - money to $1000 Specific Expectations 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 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
Operational Sense - addition and subtraction ⋅ whole numbers - multiplication ⋅ 2-digit by 2-digit Specific Expectations 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 multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms
) indicates skills and/or concepts to be addressed in alternate term
TERM: 1 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 6 Math Makes Sense ⋅ Unit 2 ⋅ Unit 4 ⋅ Unit 6 A Guide to Effective Instruction in Mathematics; (Grades 4 -6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 2 ⋅ Volume 3 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 2 ⋅ Chapter 3 ⋅ Chapter 4 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 2 ⋅ Chapter 5 Super Source
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration (continued)
Overall Expectations for the Term
Big Ideas Addressed and Related Specific Expectations
TERM: 1 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ base ten materials ⋅ drawings of base ten materials ⋅ number lines ⋅ currency manipulatives ⋅ 10 x 10 grids ⋅ concrete materials ⋅ calculator ⋅ drawings ⋅ arrays
(
) indicates skills and/or concepts to be addressed in alternate term
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Measurement
Overall Expectations for the Term estimate, measure, and record perimeter, area, temperature change, (and elapsed time,) using a variety of strategies
Term 1 Big Ideas Addressed and Related Specific Expectations
Attributes, Units and Measurement - temperature; change over time - length; m, cm, dm, km - perimeter and area; regular and irregular polygons Specific Expectations measure and record temperatures to determine and represent temperature changes over time estimate and measure the perimeter and area of regular and irregular polygons
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 Specific Expectations 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
Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 5 ⋅ Chapter 8 Math Makes Sense ⋅ Unit 6 ⋅ Unit 9 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 9 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8 Super Source Tools for Term and Strand ⋅ concrete materials ⋅ paper and pencil ⋅ grid paper ⋅ rulers (cm and mm) ⋅ dynamic geometry software ⋅ pattern blocks ⋅ Power Polygons ⋅ geoboard ⋅ connecting cubes
) indicates skills and/or concepts to be addressed in alternate term
M
Mathematics Delivery Plan – Grade 5
STRAND:
Patterning and Algebra
Overall Expectations for the Term 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 Specific Expectations Patterns and Relationships - growing and shrinking patterns ⋅ relationships ⋅ table of values ⋅ addition and subtraction Specific Expectations 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
TERM: 1 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 1 ⋅ Chapter 4 ⋅ Chapter 5 ⋅ Chapter 6 Math Makes Sense ⋅ Unit 1 ⋅ Unit 2 ⋅ Unit 10 A Guide to Effective Instruction in Mathematics (Grade 4-6) Patterning and Algebra Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 9 ⋅ Chapter 10 Super Source ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
Tools for Term and Strand concrete materials drawings calculators spreadsheets square tiles pattern blocks Cuisenaire rods dynamic geometry software dot paper
P&A
Mathematics Delivery Plan – Grade 5
STRAND:
Data Management and Probability
Overall Expectations for the Term collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including brokenline graphs
read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs
(
Big Ideas Addressed and Related Specific Expectations Collection and Organization of Data - discrete and continuous data - charts and graphs including broken-line graphs - surveys and experiments Specific Expectations 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 methods is appropriate
Data Relationships - mean - comparing related sets of data Specific Expectations 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
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 3-5 ⋅ Chapter 11 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 11 Super Source
Tools for Term and Strand ⋅ graph paper ⋅ simple spreadsheets ⋅ dynamic statistical software
) indicates skills and/or concepts to be addressed in alternate term
DM&P
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration
Overall Expectations for the Term 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 Specific Expectations Quantity Relationships - decimal numbers to hundredths - fractions ⋅ proper and improper; like denominators ⋅ equivalent Specific Expectations 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 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 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 materials
Counting - forward by hundredths Specific Expectations count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines
) indicates skills and/or concepts to be addressed in alternate term
TERM: 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 6 ⋅ Chapter 9 ⋅ Chapter 10 ⋅ Chapter 12 Math Makes Sense ⋅ Unit 4 ⋅ Unit 8 A Guide to Effective Instruction in Math; (Grade 4-6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 5 ⋅ Volume 6 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 5 ⋅ Chapter 6 ⋅ Chapter 7 Teaching Student-Centered Mathematics by J. Van de Walle Grade 5-8 ⋅ Chapter 3 ⋅ Chapter 4 ⋅ Chapter 6
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration (continued)
Overall Expectations for the Term 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 Specific Expectations Operational Sense - division ⋅ decimal numbers by 10 and 100 ⋅ 3-digit by 1-digit - multiplication ⋅ decimal numbers by 10, 100, 1000 and 10 000 - addition and subtraction ⋅ decimal numbers to hundredths Specific Expectations multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies 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 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
demonstrate an understanding of proportional reasoning by investigating whole-number rates
(
TERM: 2 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ base ten materials ⋅ drawings of base ten materials ⋅ number lines ⋅ currency manipulatives ⋅ 10 x 10 grids ⋅ calculator ⋅ fraction circles and strips ⋅ Cuisenaire rods ⋅ concrete materials ⋅ drawings
Proportional Relationships - fractions - whole-number rates Specific Expectations 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
) indicates skills and/or concepts to be addressed in alternate term
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Measurement
Overall Expectations for the Term 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
Term 2 Big Ideas Addressed and Related Specific Expectations
Attributes, Units and Measurement - time; elapsed time Specific Expectations estimate, measure, and represent time intervals to the nearest second estimate and determine elapsed time, with and without using a timeline, given the durations of events expressed in minutes, hours, days, weeks, months, or years
Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 11 Math Makes Sense ⋅ Unit 6
Measurement Relationships
Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 9
- volume ⋅ formula of a rectangular prism - relationship between volume and capacity - mass; mg, g, kg, tonne - time; 12-hour vs. 24-hour clock
Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8
Specific Expectations 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 solve problems involving the relationship between a 12-hour and 24-hour clock select and justify the most appropriate standard unit to measure mass
Super Source
Tools for Term and Strand ⋅ concrete materials - containers - bottles ⋅ connecting cubes ⋅ scale ⋅ dynamic geometry software ⋅ analogue clocks
M (
) indicates skills and/or concepts to be addressed in alternate term
Mathematics Delivery Plan – Grade 5
STRAND:
Geometry & Spatial Sense
Overall Expectations for the Term identify and classify twodimensional shapes by side and angle properties, and compare and sort three-dimensional figures
Big Ideas Addressed and Related Specific Expectations Geometric Properties - 2-D shapes ⋅ polygons and triangles ⋅ angles up to 90° - 3-D figures ⋅ prisms and pyramids Specific Expectations 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 90°, 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 distinguish among prisms, right prisms, pyramids, and other three-dimensional figures
identify and construct nets of prisms and pyramids
Geometric Relationships - 3-D figures ⋅ nets of prisms and pyramids
Term 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 7 ⋅ Chapter 11 ⋅ Chapter 14 Math Makes Sense ⋅ Unit 3 ⋅ Unit 7 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 8 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7 Super Source
Specific Expectations identify prisms and pyramids from their nets construct nets of prisms and pyramids, using a variety of tools
(
) indicates skills and/or concepts to be addressed in alternate term
G&SS
Mathematics Delivery Plan – Grade 5
STRAND:
Geometry & Spatial Sense (continued)
Overall Expectations for the Term identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes
Big Ideas Addressed and Related Specific Expectations Location and Movement - cardinal directions - translations ⋅ 2-D shapes Specific Expectations 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
(
Term 2 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ protractor ⋅ compass ⋅ dynamic geometry software ⋅ geoboard ⋅ Mira ⋅ drawings ⋅ grid paper ⋅ isometric dot paper ⋅ polydrons ⋅ computer applications
) indicates skills and/or concepts to be addressed in alternate term
G&SS
Mathematics Delivery Plan – Grade 5
STRAND:
Patterning and Algebra
Overall Expectations for the Term determine, through investigations using a table of values, relationships in growing and shrinking patterns and investigate repeating patterns involving translations
Big Ideas Addressed and Related Specific Expectations Patterns and Relationships - growing and shrinking patterns ⋅ table of values ⋅ multiplication and division - repeating patterns ⋅ translations Specific Expectations create, identify, and extend (numeric and) geometric patterns, using a variety of tools make a table of values for a pattern that is generated by (adding or subtracting a number to get the next term) 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 extend and create repeating patterns that result from translations, through investigation using a variety of tools
demonstrate, through investigation, an understanding of the use of variables in equations
Variables, Expressions and Equations - variables ⋅ as changing or unknown quantities - missing numbers in equations ⋅ addition, subtraction, multiplication and division Specific Expectations 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
(
TERM: 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 1 ⋅ Chapter 4 ⋅ Chapter 6 ⋅ Chapter 10 ⋅ Chapter 14 Math Makes Sense ⋅ Unit 1 ⋅ Unit 2 ⋅ Unit 7 ⋅ Unit 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7 ⋅ Chapter 9 ⋅ Chapter 10 Super Source Tools for Term and Strand ⋅ pattern blocks ⋅ dynamic geometry software ⋅ dot paper ⋅ calculator ⋅ concrete materials ⋅ drawings ⋅ spreadsheets ⋅ square tiles
) indicates skills and/or concepts to be addressed in alternate term
P&A
Mathematics Delivery Plan – Grade 5
STRAND:
Data Management & Probability
Overall Expectations for the Term represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models
Big Ideas Addressed and Related Specific Expectations Probability - probability as fractions Specific Expectations 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 results
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 3-5 ⋅ Chapter 12 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 12 Super Source
(
) indicates skills and/or concepts to be addressed in alternate term
DM&P
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, 2011
Number Sense & Numeration
Mathematics Delivery Plan – Grade 5
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.
Mathematics Delivery Plan – Grade 5
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.
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan
Measurement
Number Sense and Numeration
Term 1 Quantity Relationships whole numbers to 100 000 money to $1000
Operational Sense addition and subtraction ⋅ whole numbers multiplication ⋅ 2-digit by 2-digit whole numbers
Attributes, Units, and Measurement Sense temperature; change over time length; m, cm, dm, 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
Term 2 Quantity Relationships fractions and decimals ⋅ proper and improper; like denominators ⋅ equivalent ⋅ decimal numbers to hundredths Counting forward by hundredths Operational Sense division and multiplication ⋅ 3-digit by 1-digit whole numbers ⋅ decimal numbers by 10 and 100 (division) ⋅ decimal numbers by 10, 100, 1000, and 10 000 (multiplication) Proportional Relationships fractions whole-number rates Attributes, Units, and Measurement Sense time; elapsed 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
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan Term 1
Term 2 Geometric Properties
Patterning and Algebra
Geometry and Spatial Sense
2-D shapes ⋅ polygon and triangles ⋅ angles up to 90° 3-D figures ⋅ prisms and pyramids Geometric Relationships 3-D shapes ⋅ nets of prisms and pyramids Location and Movement cardinal directions translations ⋅ 2-D shapes
Patterns and Relationships growing and shrinking patterns ⋅ relationships ⋅ table of values ⋅ addition and subtraction
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
Mathematics Delivery Plan – Grade 5
Grade 5
Mathematics Delivery Plan Data Management and Probability
Term 1 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
Term 2 Probability probability as fractions
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration
Overall Expectations for the Term 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)
(
Big Ideas Addressed and Related Specific Expectations Quantity Relationships - whole numbers to 100 000 - money to $1000 Specific Expectations 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 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
Operational Sense - addition and subtraction ⋅ whole numbers - multiplication ⋅ 2-digit by 2-digit Specific Expectations 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 multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms
) indicates skills and/or concepts to be addressed in alternate term
TERM: 1 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 6 Math Makes Sense ⋅ Unit 2 ⋅ Unit 4 ⋅ Unit 6 A Guide to Effective Instruction in Mathematics; (Grades 4 -6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 2 ⋅ Volume 3 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 2 ⋅ Chapter 3 ⋅ Chapter 4 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 2 ⋅ Chapter 5 Super Source
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration (continued)
Overall Expectations for the Term
Big Ideas Addressed and Related Specific Expectations
TERM: 1 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ base ten materials ⋅ drawings of base ten materials ⋅ number lines ⋅ currency manipulatives ⋅ 10 x 10 grids ⋅ concrete materials ⋅ calculator ⋅ drawings ⋅ arrays
(
) indicates skills and/or concepts to be addressed in alternate term
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Measurement
Overall Expectations for the Term estimate, measure, and record perimeter, area, temperature change, (and elapsed time,) using a variety of strategies
Term 1 Big Ideas Addressed and Related Specific Expectations
Attributes, Units and Measurement - temperature; change over time - length; m, cm, dm, km - perimeter and area; regular and irregular polygons Specific Expectations measure and record temperatures to determine and represent temperature changes over time estimate and measure the perimeter and area of regular and irregular polygons
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 Specific Expectations 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
Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 5 ⋅ Chapter 8 Math Makes Sense ⋅ Unit 6 ⋅ Unit 9 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 9 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8 Super Source Tools for Term and Strand ⋅ concrete materials ⋅ paper and pencil ⋅ grid paper ⋅ rulers (cm and mm) ⋅ dynamic geometry software ⋅ pattern blocks ⋅ Power Polygons ⋅ geoboard ⋅ connecting cubes
) indicates skills and/or concepts to be addressed in alternate term
M
Mathematics Delivery Plan – Grade 5
STRAND:
Patterning and Algebra
Overall Expectations for the Term 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 Specific Expectations Patterns and Relationships - growing and shrinking patterns ⋅ relationships ⋅ table of values ⋅ addition and subtraction Specific Expectations 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
TERM: 1 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 1 ⋅ Chapter 4 ⋅ Chapter 5 ⋅ Chapter 6 Math Makes Sense ⋅ Unit 1 ⋅ Unit 2 ⋅ Unit 10 A Guide to Effective Instruction in Mathematics (Grade 4-6) Patterning and Algebra Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 9 ⋅ Chapter 10 Super Source ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
Tools for Term and Strand concrete materials drawings calculators spreadsheets square tiles pattern blocks Cuisenaire rods dynamic geometry software dot paper
P&A
Mathematics Delivery Plan – Grade 5
STRAND:
Data Management and Probability
Overall Expectations for the Term collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including brokenline graphs
read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs
(
Big Ideas Addressed and Related Specific Expectations Collection and Organization of Data - discrete and continuous data - charts and graphs including broken-line graphs - surveys and experiments Specific Expectations 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 methods is appropriate
Data Relationships - mean - comparing related sets of data Specific Expectations 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
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 3-5 ⋅ Chapter 11 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 11 Super Source
Tools for Term and Strand ⋅ graph paper ⋅ simple spreadsheets ⋅ dynamic statistical software
) indicates skills and/or concepts to be addressed in alternate term
DM&P
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration
Overall Expectations for the Term 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 Specific Expectations Quantity Relationships - decimal numbers to hundredths - fractions ⋅ proper and improper; like denominators ⋅ equivalent Specific Expectations 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 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 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 materials
Counting - forward by hundredths Specific Expectations count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines
) indicates skills and/or concepts to be addressed in alternate term
TERM: 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 2 ⋅ Chapter 4 ⋅ Chapter 6 ⋅ Chapter 9 ⋅ Chapter 10 ⋅ Chapter 12 Math Makes Sense ⋅ Unit 4 ⋅ Unit 8 A Guide to Effective Instruction in Math; (Grade 4-6) Number Sense and Numeration ⋅ Volume 1 ⋅ Volume 5 ⋅ Volume 6 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 5 ⋅ Chapter 6 ⋅ Chapter 7 Teaching Student-Centered Mathematics by J. Van de Walle Grade 5-8 ⋅ Chapter 3 ⋅ Chapter 4 ⋅ Chapter 6
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Number Sense and Numeration (continued)
Overall Expectations for the Term 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 Specific Expectations Operational Sense - division ⋅ decimal numbers by 10 and 100 ⋅ 3-digit by 1-digit - multiplication ⋅ decimal numbers by 10, 100, 1000 and 10 000 - addition and subtraction ⋅ decimal numbers to hundredths Specific Expectations multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies 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 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
demonstrate an understanding of proportional reasoning by investigating whole-number rates
(
TERM: 2 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ base ten materials ⋅ drawings of base ten materials ⋅ number lines ⋅ currency manipulatives ⋅ 10 x 10 grids ⋅ calculator ⋅ fraction circles and strips ⋅ Cuisenaire rods ⋅ concrete materials ⋅ drawings
Proportional Relationships - fractions - whole-number rates Specific Expectations 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
) indicates skills and/or concepts to be addressed in alternate term
NS&N
Mathematics Delivery Plan – Grade 5
STRAND:
Measurement
Overall Expectations for the Term 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
Term 2 Big Ideas Addressed and Related Specific Expectations
Attributes, Units and Measurement - time; elapsed time Specific Expectations estimate, measure, and represent time intervals to the nearest second estimate and determine elapsed time, with and without using a timeline, given the durations of events expressed in minutes, hours, days, weeks, months, or years
Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 11 Math Makes Sense ⋅ Unit 6
Measurement Relationships
Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 9
- volume ⋅ formula of a rectangular prism - relationship between volume and capacity - mass; mg, g, kg, tonne - time; 12-hour vs. 24-hour clock
Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 8
Specific Expectations 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 solve problems involving the relationship between a 12-hour and 24-hour clock select and justify the most appropriate standard unit to measure mass
Super Source
Tools for Term and Strand ⋅ concrete materials - containers - bottles ⋅ connecting cubes ⋅ scale ⋅ dynamic geometry software ⋅ analogue clocks
M (
) indicates skills and/or concepts to be addressed in alternate term
Mathematics Delivery Plan – Grade 5
STRAND:
Geometry & Spatial Sense
Overall Expectations for the Term identify and classify twodimensional shapes by side and angle properties, and compare and sort three-dimensional figures
Big Ideas Addressed and Related Specific Expectations Geometric Properties - 2-D shapes ⋅ polygons and triangles ⋅ angles up to 90° - 3-D figures ⋅ prisms and pyramids Specific Expectations 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 90°, 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 distinguish among prisms, right prisms, pyramids, and other three-dimensional figures
identify and construct nets of prisms and pyramids
Geometric Relationships - 3-D figures ⋅ nets of prisms and pyramids
Term 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 7 ⋅ Chapter 11 ⋅ Chapter 14 Math Makes Sense ⋅ Unit 3 ⋅ Unit 7 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 8 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7 Super Source
Specific Expectations identify prisms and pyramids from their nets construct nets of prisms and pyramids, using a variety of tools
(
) indicates skills and/or concepts to be addressed in alternate term
G&SS
Mathematics Delivery Plan – Grade 5
STRAND:
Geometry & Spatial Sense (continued)
Overall Expectations for the Term identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes
Big Ideas Addressed and Related Specific Expectations Location and Movement - cardinal directions - translations ⋅ 2-D shapes Specific Expectations 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
(
Term 2 Suggested Resources for Strand and Term Tools for Term and Strand ⋅ protractor ⋅ compass ⋅ dynamic geometry software ⋅ geoboard ⋅ Mira ⋅ drawings ⋅ grid paper ⋅ isometric dot paper ⋅ polydrons ⋅ computer applications
) indicates skills and/or concepts to be addressed in alternate term
G&SS
Mathematics Delivery Plan – Grade 5
STRAND:
Patterning and Algebra
Overall Expectations for the Term determine, through investigations using a table of values, relationships in growing and shrinking patterns and investigate repeating patterns involving translations
Big Ideas Addressed and Related Specific Expectations Patterns and Relationships - growing and shrinking patterns ⋅ table of values ⋅ multiplication and division - repeating patterns ⋅ translations Specific Expectations create, identify, and extend (numeric and) geometric patterns, using a variety of tools make a table of values for a pattern that is generated by (adding or subtracting a number to get the next term) 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 extend and create repeating patterns that result from translations, through investigation using a variety of tools
demonstrate, through investigation, an understanding of the use of variables in equations
Variables, Expressions and Equations - variables ⋅ as changing or unknown quantities - missing numbers in equations ⋅ addition, subtraction, multiplication and division Specific Expectations 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
(
TERM: 2 Suggested Resources for Strand and Term Nelson Mathematics ⋅ Chapter 1 ⋅ Chapter 4 ⋅ Chapter 6 ⋅ Chapter 10 ⋅ Chapter 14 Math Makes Sense ⋅ Unit 1 ⋅ Unit 2 ⋅ Unit 7 ⋅ Unit 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 3-5 ⋅ Chapter 10 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 7 ⋅ Chapter 9 ⋅ Chapter 10 Super Source Tools for Term and Strand ⋅ pattern blocks ⋅ dynamic geometry software ⋅ dot paper ⋅ calculator ⋅ concrete materials ⋅ drawings ⋅ spreadsheets ⋅ square tiles
) indicates skills and/or concepts to be addressed in alternate term
P&A
Mathematics Delivery Plan – Grade 5
STRAND:
Data Management & Probability
Overall Expectations for the Term represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models
Big Ideas Addressed and Related Specific Expectations Probability - probability as fractions Specific Expectations 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 results
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 3-5 ⋅ Chapter 12 Teaching Student-Centered Mathematics by J. Van de Walle Grades 5-8 ⋅ Chapter 12 Super Source
(
) indicates skills and/or concepts to be addressed in alternate term
DM&P
