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Grade 3 Revised May 2011

Math Alignment Project

Revised 2011

Scope & Sequence

1. The Mathematics Alignment Project framework is outlined by term. Based on professional judgement and the needs of their students, teachers determine the specific sequence and duration spent addressing the expectations. The sequence presented in the Math Alignment Project is not linear – teachers must use their professional judgement to determine the order of mathematical instruction within a given term.

2. The intent of the calendar is to provide parents with an overview of the mathematics curriculum for a specific grade. It also provides samples of the concepts and skills that their children are learning throughout the term. They may or may not align with what is being taught in the classroom. The homework calendar is an optional piece of the Mathematics Alignment Project.

3. Reporting in mathematics should reflect learning in both the process expectations and the content expectations.

Based on: The Ontario Curriculum Grades 1-8: Mathematics Revised, 2005

Kindergarten Program Documents, Revised 2006

Grade 3

Please Note: The Overall Expectations have been identified by the first letter of the Strand, for example, the first overall expectation in Number Sense and Numeration is NV1 (Number sense and numeration oVerall expectation 1), the second overall expectation in Measurement in MV2, etc)


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Writing Team Ann Boyd - Teacher Consultant Annette Blake - Teacher Consultant / Administrator Heather Furtney - Instructional Coach Michelle Black - Teacher Consultant Nancy Norton - Elementary Program Coordinator William Valoppi - Principal Leader

With Thanks to: Cam MacDonald - Math Coach Chris Lambert- Program Secretary Rosanne Simpson - Program Secretary Sally Landon - System Research Leader Adrienne Patterson – Teacher Consultant Stacey Nicholls - Teacher Sue Young - Teacher Consultant Mark Kolenc – Teacher Consultant GEDSB Elementary Program HWDSB


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Purpose The Mathematics Alignment Project (MAP) has two main components:

1) Curriculum Framework Document 2) Home Support Communication Calendars

The Mathematics Alignment Project (MAP) curriculum framework document is intended to guide classroom teachers in the planning, implementation and reporting of their mathematics program. This MAP curriculum framework document is based on the Mathematics Ontario Curriculum Grades 1-8, 2005 and the Kindergarten Program, 2006 and meets minimum reporting requirements. Please refer to the GEDSB Progress Report and Report Card Directions document for additional reporting information. The MAP framework aligns the Overall Expectations addressed each term and allows for a consistent approach to the instruction of mathematics in Grand Erie. It highlights Tools and Manipulatives that will support each strand, as well as suggestions for learning opportunities and connections to resources. This MAP curriculum framework document is designed to have all curriculum expectations addressed by early June to align with reporting dates, however, the intent is that mathematics instruction in June will address the greatest needs of the students as indicated by student achievement throughout the year. In order to best support combined grades the same underlying concepts are addressed in the same term across several grade levels (where possible). Teachers must use their professional judgment to modify this framework since important factors such as developmental needs of their students, background knowledge, school based initiatives, and resources could not be considered in the development of the MAP curriculum framework document. The Home Support Communication Calendars provide suggestions of activities and conversations student can engage in at home that will support the delivery of the Mathematics Curriculum by term.

Please Note: The Overall Expectations have been identified by the first letter of the Strand, for example, the first overall expectation in Number Sense and Numeration is NV1 (Number sense and numeration oVerall expectation 1), the second overall expectation in Measurement in MV2, etc)


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When planning a program in mathematics, teachers must take into account a number of important areas, including those discussed below. The Ministry of Education has produced or supported the production of a variety of resource documents that teachers may find helpful as they plan programs based on the expectations outlined in this curriculum document. They include the following:

• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, 2005 (forthcoming; replaces the 2003 edition for Kindergarten to Grade 3), along with companion documents focusing on individual strands

• Early Math Strategy: The Report of the Expert Panel on Early Math in Ontario, 2003 • Teaching and Learning Mathematics: The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario, 2004 • Leading Math Success: Mathematical Literacy, Grades 7–12 – The Report of the Expert Panel on Student Success in Ontario,

2004 • Think Literacy: Cross-Curricular Approaches, Grades 7–12 – Mathematics: Subject-Specific Examples, Grades 7–9, 2004 • Targeted Implementation & Planning Supports (TIPS): Grades 7, 8, and 9 Applied Mathematics, 2003 • Growing Success, 2010 • EduGains

• GEDSB Math Profile Teaching Approaches Students in a mathematics class demonstrate diversity in the ways they learn best. It is important, therefore, that students have opportunities to learn in a variety of ways –collaboratively and independently through inquiry, consolidation, accountable talk and rich tasks. In addition, mathematics requires students to learn concepts and procedures, acquire skills, and learn and apply mathematical processes. These different areas of learning may involve different teaching and learning strategies. It is assumed, therefore, that the strategies teachers employ will vary according to both the objective of the learning and the needs of the students. In order to learn mathematics and to apply their knowledge effectively, students must develop a solid understanding of mathematical concepts. Research and successful classroom practice have shown that an investigative approach, with an emphasis on learning through problem solving and reasoning, best enables students to develop the conceptual foundation they need. When planning mathematics programs, teachers will provide activities and assignments that encourage students to search for patterns and relationships, engage in logical inquiry and communicate their reasoning to others. Teachers need to use rich problems and present situations that provide a variety of opportunities for students to develop mathematical understanding through problem solving.


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Some Considerations for Program

Planning in Mathematics All learning, especially new learning, should be embedded in well-chosen contexts for learning – that is, contexts allow students to investigate initial understandings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the underlying concepts, or key principles, of mathematics, such as pattern or relationship. This understanding of key principles will enable and encourage students to use mathematical reasoning throughout their lives. Effective instructional approaches and learning activities draw on students’ prior knowledge, capture their interest, and encourage meaningful practice both inside and outside the classroom. Students’ interest will be engaged when they are able to see the connections between the mathematical concepts they are learning and their application in the world around them and in real-life situations. Students will investigate mathematical concepts using a variety of tools and strategies, both manual and technological. Manipulatives are necessary tools for supporting the development and understanding of mathematical concepts by all students. These concrete learning tools invite students to explore and represent abstract mathematical ideas in varied, concrete, tactile, and visually rich ways. Moreover, using a variety of manipulatives helps deepen and extend students’ understanding of mathematical concepts. For example, students who have used only base ten materials to represent two-digit numbers may not have as strong a conceptual understanding of place value as students who have also bundled craft sticks into tens and hundreds and used an abacus. Manipulatives are also a valuable aid to teachers. By analysing students’ concrete representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into students’ thinking and provide supports to help enhance their thinking. Fostering students’ communication skills is an important part of the teacher’s role in the mathematics classroom. Through skillfully led classroom discussions, students build understanding and consolidate their learning. Discussions provide students with the opportunity to ask questions, make conjectures, share and clarify ideas, suggest and compare strategies, and explain their reasoning. As they discuss ideas with their peers, students learn to discriminate between effective and ineffective strategies for problem solving. Students’ understanding is revealed through both oral communication and writing, but it is not necessary for all mathematics learning to involve a written communication component. Young students need opportunities to focus on their oral communication without the additional responsibility of writing.


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Whether students are talking or writing about their mathematical learning, teachers can prompt them to explain their thinking and the mathematical reasoning behind a solution or the use of a particular strategy by asking the question “How do you know?” Since mathematical reasoning must be the primary focus of students’ communication, it is important for teachers to select instructional strategies that elicit mathematical reasoning from their students. Promoting Positive Attitudes Towards Mathematics Students’ attitudes have a significant effect on how they approach problem solving and how well they succeed in mathematics. Teachers can help students develop the confidence they need by demonstrating a positive disposition towards mathematics. Students need to understand that, for some mathematics problems, there may be several ways to arrive at the correct answer. They also need to believe that they are capable of finding solutions. It is common for people to think that if they cannot solve problems quickly and easily, they must be inadequate. Teachers can help students understand that problem solving of almost any kind often requires a considerable expenditure of time and energy and a good deal of perseverance. Once students have this understanding, teachers can encourage them to develop the willingness to persist, to investigate, to reason and explore alternative solutions, and to take the risks necessary to become successful problem solvers. Cross-Curricular and Integrated Learning The development of skills and knowledge in mathematics is often enhanced by learning in other subject areas. Teachers should ensure that all students have ample opportunities to explore a subject from multiple perspectives by emphasizing cross-curricular learning and integrated learning, as follows: a) In cross-curricular learning, students are provided with opportunities to learn and use related content and/or skills in two or more subjects. Students can use the concepts and skills of mathematics in their science or social studies lessons. Similarly, students can use what they have learned in science to illustrate or develop mathematical understanding. For example, in Grade 6, concepts associated with the fulcrum of a lever can be used to develop a better understanding of the impact that changing a set of data can have on the mean. b) In integrated learning, students are provided with opportunities to work towards meeting expectations from two or more subjects within a single unit, lesson, or activity. By linking expectations from different subject areas, teachers can provide students with multiple opportunities to reinforce and demonstrate their knowledge and skills in a range of settings. Also, the mathematical process expectation that focuses on connecting encourages students to make connections between mathematics and other subject areas. For example, students in Grade 2 could be given the opportunity to relate the study of location and movement in the Geometry and Spatial Sense strand of mathematics to the study of movement in the Structures and Mechanisms strand in science and technology. Similarly, the same students could link their study of the characteristics of symmetrical shapes in Visual Arts to the creation of symmetrical shapes in their work in Geometry and Spatial Sense.


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The Mathematical Process Expectations The mathematical processes are a set of seven interconnected expectations that describe the processes through which students acquire and apply mathematical knowledge and skills. Problem Solving Problem solving forms the basis of effective mathematics programs and should be the foundation of mathematical instruction.

�� Students learn to solve problems and learn through problem solving. �� Students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding. *See Problem-Solving Model

Reasoning and Proving The reasoning process supports a deeper understanding of mathematics by enabling students to make sense of the mathematics they

are learning. �� Students will learn by exploring phenomena, developing ideas, making mathematical conjectures, and justifying results. �� Students will reason from the evidence they find in their explorations and investigations or from what they already know to be true, �� Students will recognize the characteristics of an acceptable argument in the mathematics classroom.

Reflecting Reflecting on their own thinking and the thinking of others helps students make important connections and internalize a deeper

understanding of the mathematical concepts involved. �� Students will learn by regularly and consciously reflecting on and monitoring their own thought processes. �� Students will reflect on alternative ways to perform a task and on the reasonableness of an answer.

Selecting Tools and Computational Strategies

Students need to develop the ability to select the appropriate electronic tools, manipulatives, and computational strategies to perform particular mathematical tasks, to investigate mathematical ideas, and to solve problems.

Connecting Students need to have experiences that allow them to make connections between concepts and skills from one strand of mathematics to another to understand how the procedures, concepts and skills are related. �� Students will begin to see that mathematics is more than a series of isolated skills and concepts �� Students will understand they can use their learning in one area of mathematics to understand another. �� Students will make connections between the mathematics they learn at school and its applications in their everyday lives

Representing Students represent mathematical ideas and relationships and model situations using concrete materials, pictures, diagrams, graphs,

tables, numbers, words, and symbols. Learning the various forms of representation helps students to understand mathematical concepts and relationships; communicate their thinking, arguments, and understandings; recognize connections among related mathematical concepts; and use mathematics to model and interpret realistic problem situations. �� Students will recognize the connections between representations, and use the different representations appropriately and as needed to solve problems.

Communicating Communication is the process of expressing mathematical ideas and understanding orally, visually, and in writing, using numbers,

symbols, pictures, graphs, diagrams, and words. �� Students will provide effective explanations (e.g., apply correct mathematical notation in the development and presentation of mathematical ideas and solutions).


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A Problem-Solving Model The most commonly used problem-solving model is George Polya’s four-step model: understand the problem; make a plan; carry out the plan; and look back to check the results.1 (These four steps are now reflected in the Thinking category of the achievement chart first published in Polya’s How to Solve It, 1945. Below is a modified GEDSB version, which separates Step 1 into two distinct steps.

Please note: The five-step model is generally not taught directly before Grade 3, because young students tend to become too focused on the model and pay less attention to the mathematical concepts involved and to making sense of the problem.

Given: Understand the Information Given in the Problem reread and restate the problem

Required: Understand the Requirements of the Problem identify the information given and the information that needs to be determined to help solve the problem

Application: Make a Plan relate the problem to similar problems solved in the past consider possible strategies select a strategy or a combination of strategies revise or apply different strategies as necessary

Statement/Reflection Look Back at the Solution check the reasonableness of the answer review the method used: Did it make sense? Is there a better way to approach the problem? consider extensions or variations

Solution: Carry Out the Plan execute the chosen strategy do the necessary calculations monitor success revise or apply different strategies as necessary


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Math Alignment Project Grade 3 Overview

Term 1 Report Term 2 Report Number Sense and Numeration

Quantity Relationships �� Numbers to 1000 �� Money to $10

Counting �� Forwards by 1’s, 2’s, 5’s, 10’s and 100’s to 1000 �� Backwards by 2’s, 5’s, and 10’s from 100, and backwards by 100’s from 1000 and any number less than 1000

Operational Sense �� Addition and subtraction

ooo two-digit numbers ooo Mental math strategies

Operational Sense �� Addition and subtraction

o Three-digit numbers o Money to $10

�� Multiplication (to 7x7) �� (Introduction) Division (to 49 ÷ 7)

Quantity Relationships �� Fractions

o Whole objects o Sets of whole objects

Operational Sense �� Division (to 49 ÷ 7)

Measurement

Attributes, Units, and Measurement Sense �� length (cm, m, km) �� perimeter (standard units) �� area (cm)

Measurement Relationships �� compare cm, m and km �� compare area of 2-D shapes

Attributes, Units, and Measurement Sense �� mass (g, kg) �� capacity (ml, L) �� time

ooo analogue in 5 minute increments ooo 12 hour notation

�� temperature ooo nearest degree Celsius ooo benchmarks (freezing, melting)

Measurement Relationships �� mass (g, kg) �� capacity (ml, L) �� time (minutes in an hour, hours in a day, days in a week, weeks in a year)

Please note that expectations (or portions of expectations) in italics are addressed during another term


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Math Alignment Project Grade 3 Overview

Term 1 Report Term 2 Report Geometry and Spatial Sense

**Classroom instruction in Term 1 will support the expectations for Geometry and Spatial Sense, however, Geometry and Spatial Sense will carry forward through Term 2 and be reported on in Term 2.

**Geometric Properties �� 2-D Shapes

ooo polygons ooo comparing angles with right angles

Geometric Relationships �� 2-D Shapes (quadrilaterals) �� Congruent Shapes

Location and Movement �� Symmetry

ooo vertical, horizontal, diagonal �� Grid movement

Transformations (identify / name) Geometric Properties �� 3-D Figures

ooo prisms and pyramids

Geometric Relationships �� 3-D Figures

ooo prisms and pyramids Patterning and Algebra

Patterns and Relationships �� Growing, shrinking and repeating

ooo addition and subtraction Expressions and Equality �� Additional and subtraction

ooo Inverse relationship / missing numbers in equations

Patterns and Relationships �� Repeating (two attributes, including transformations) �� Growing and shrinking (multiplication)

Expressions and Equality �� Properties of zero and one in multiplication

Data Management and Probability

Collection and Organization of Data�� Primary Data �� Graphs, Tables, Charts

Data Relationships �� Graphs, Tables and Charts

Probability �� Outcomes


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Math Alignment Project STRAND: Number Sense and Numeration Fall Progress Report Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives base ten materials calculator coins and bills to $10 number lines (with increments of 100) partial number lines

Provide Students With Opportunities to: -Find numbers written in the daily environment (e.g., books, speed limit signs) -Use base ten materials to decompose numbers and show the relationship between 10s, 100s and 1000 -Use the $ symbol -Find different ways to use coins to determine a set amount of money - skip count with and without the aid of a calculator Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Number Sense and Numeration, Appendix D Math Makes Sense Components of: Unit 1 Unit 2 Unit 6

NV1: Quantity Relationships read, represent, compare, and order whole numbers to 1000, and use concrete materials to represent fractions and money amounts to $10

�� represent, compare, and order whole numbers to 1000, using a variety of tools

�� read and print in words whole numbers to one hundred, using meaningful contexts

�� identify and represent the value of a digit in a number according to its position in the number

�� compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways, using concrete materials

�� round two-digit numbers to the nearest ten, in problems arising from real-life situations

�� represent and explain, using concrete materials, the relationship among the numbers 1, 10, 100, and 1000

�� represent and describe the relationships between coins and bills up to $10

�� estimate, count, and represent the value of a collection of coins and bills with a maximum value of $10

�� solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1000

NV2: Counting demonstrate an understanding of magnitude by counting forward and backwards by various numbers and from various starting points

�� count forward by 1’s, 2’s, 5’s, 10’s, and 100’s to 1000 from various starting points, and by 25’s to 1000 starting from multiples of 25, using a variety of tools and strategies

�� count backwards by 2’s, 5’s, and 10’s from 100 using multiples of 2, 5, and 10 as starting points, and count backwards by 100’s from 1000 and any number less than 1000, using a variety of tools and strategies

NV3: Operational Sense solve problems involving the addition and subtraction of single- and multi-digit whole numbers, using a variety of strategies, and demonstrate an understanding of multiplication and division

�� solve problems involving the addition and subtraction of two-digit numbers, using a variety of mental strategies (e.g., to add 37 + 26, add the tens, add the ones, then combine the tens and ones, like this: 30 + 20 = 50, 7 + 6 = 13, 50 + 13 = 63)

�� use estimation when solving problems involving addition and subtraction, to help judge the reasonableness of a solution


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Math Alignment Project STRAND: Patterning and Algebra Fall Progress Report Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives calendar concrete materials hundreds chart number line

Provide Students With Opportunities to: -Write the next three terms in a number pattern and discuss the pattern rule, then create another pattern using the same rule -Find patterns on a hundreds chart -Use clapping, movement, etc, to show that a pattern results from repeating an action -Determine the missing number in an addition/subtraction equation -Use a ‘number house’ to show the inverse relationship between addition and subtraction and determine related number facts (e.g., since 4 + 5 = 9, then 9 - 5 = 4 Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Patterning and Algebra, Appendix D Math Makes Sense Components of: Unit 1 Unit 2 Unit 10

PV1: Patterns and Relationships describe, extend, and create a variety of numeric patterns and geometric patterns

�� identify and describe, through investigation, number patterns involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart

�� extend repeating, growing, and shrinking number patterns

�� create a number pattern involving addition or subtraction, given a pattern represented on a number line or a pattern rule expressed in words

�� demonstrate, through investigation, an understanding that a pattern results from repeating an action, repeating an operation, using a transformation, or making some other repeated change to an attribute

PV2: Expressions and Equality demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers

�� determine, through investigation, the inverse relationship between addition and subtraction

�� determine, the missing number in equations involving addition and subtraction of one- and two-digit numbers, using a variety of tools and strategies

�� identify, through investigation, and use the associative property of addition to facilitate computation with whole numbers


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Math Alignment Project STRAND: Data Management and Probability Fall Progress Report Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives concrete materials hundreds carpet

Provide Students With Opportunities to: - Display data using different types of charts, tables and graphs (including vertical and horizontal bar graphs) -Sort a collection of objects using two or more attributes (e.g, by size, colour, and number of holes) - Graph data related to the eye colour of students in the class, using a vertical bar graph. Why does the scale on the vertical axis include values that are not in the set of data -Find the mode in a set of data -Describe data in charts, tables and graphs using comparative language Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Data Management and Probability, Appendix D Math Makes Sense Components of: Unit 5

DV1: Collection and Organization of Data collect and organize categorical or discrete primary data and display the data using charts and graphs, including vertical and horizontal bar graphs, with labels ordered appropriately along horizontal axes, as needed

�� demonstrate an ability to organize objects into categories, by sorting and classifying objects using two or more attributes simultaneously

�� collect data by conducting a simple survey about themselves, their environment, issues in their school or community, or content from another subject

�� collect and organize categorical or discrete primary data and display the data in charts, tables, and graphs (including vertical and horizontal bar graphs), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed, using many-to-one correspondence

DV2: Data Relationships read, describe, and interpret primary data presented in charts and graphs, including vertical and horizontal bar graphs

�� read primary data presented in charts, tables, and graphs (including vertical and horizontal bar graphs), then describe the data using comparative language, and describe the shape of the data

�� interpret and draw conclusions from data presented in charts, tables, and graphs

�� demonstrate an understanding of mode, and identify the mode in a set of data

Please note that expectations (or portions of expectations) in italics are addressed during another term


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Math Alignment Project STRAND: Number Sense and Numeration Term 1 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives arrays base ten materials coins and bills concrete materials connecting cubes number lines place value mat square tiles

Provide Students With Opportunities to: -place objects in equal groups -use arrays - write repeated addition / subtraction sentences with 3-digit numbers -Select a handful of coins and determine what other coins are needed to reach an amount up to $10 -relate skip counting, doubling, and other number patterns to multiplication -solve multiplication problems (to 7x7) Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Number Sense and Numeration, Appendix D Math Makes Sense Components of: Unit 2 Unit 4 Unit 6


�� add and subtract three-digit numbers, using concrete materials, student-generated algorithms, and standard algorithms

�� add and subtract money amounts, using a variety of tools to make simulated purchases and change for amounts up to $10

�� relate multiplication of one-digit numbers and division by one-digit divisors to real-life situations, using a variety of tools and strategies

�� multiply to 7 x 7 and divide to 49 divided by 7, using a variety of mental strategies


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Math Alignment Project STRAND: Measurement Term 1 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives arrays cm and two-cm grid paper colour tiles connecting cubes measuring tape pattern blocks power polygons ruler (cm) and metre stick

Provide Students With Opportunities to: -Walking with your class, stop when you think you have travelled different distances (one metre, 10 metres, one kilometer) -Use a ruler to draw specific lengths -Use a ruler / metre stick to find the perimeter of common 2-D objects -Determine the difference between the numbers of squares needed to cover the front of a book using centimetre grid paper and using two-centimetre grid paper Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Measurement, Appendix D Math Makes Sense Components of: Unit 6

MV1: Attributes, Units, and Measurement Sense estimate, measure, and record length, perimeter, area, mass, capacity, time, and temperature, using standard units

�� estimate, measure, and record length, height, and distance, using standard units

�� draw items using a ruler, given specific lengths in centimetres

�� estimate, measure, and record the perimeter of two-dimensional shapes, through investigation using standard units

�� estimate, measure, and record area

MV2: Measurement Relationships compare, describe, and order objects, using attributes measured in standard units

�� compare standard units of length and select and justify the most appropriate standard unit to measure length

�� compare and order objects on the basis of linear measurements in centimetres and/or metres in problem-solving contexts

�� compare and order various shapes by area, using congruent shapes and grid paper for measuring

�� describe, through investigation using grid paper, the relationship between the size of a unit of area and the number of units needed to cover a surface


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Math Alignment Project STRAND: Patterning and Algebra Term 1 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives attribute blocks calendar concrete materials hundreds charts / carpets number lines pattern blocks

Provide Students With Opportunities to: -Use tiles to create arrays that represent multiplication facts (e.g., 3 x 3, 3 x 2, 3 x 1, and 3 x 0) -Explain what will happen when you multiply any number by 1, and when you multiply any number by 0 -Create a repeating pattern using two or more attributes (e.g., by size, colour, and number of holes) -explore the relationship between multiplication and growing patterns Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Patterning and Algebra, Appendix D Math Makes Sense Components of: Unit 4 Unit 10

PV1: Patterns and Relationships describe, extend, and create a variety of numeric patterns and geometric patterns

�� identify, extend, and create a repeating pattern involving two attributes using a variety of tools

�� identify and describe, through investigation, number patterns involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart

�� represent simple geometric patterns using a number sequence, a number line, or a bar graph

�� demonstrate, through investigation, an understanding that a pattern results from repeating an action, repeating an operation, using a transformation or making some other repeated change to an attribute

PV2: Expressions and Equality demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers

�� identify, through investigation, the properties of zero and one in multiplication (i.e., any number multiplied by zero equals zero; any number multiplied by 1 equals the original number)


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Math Alignment Project STRAND: Geometry and Spatial Sense Term 1 / 2 **Classroom instruction in Term 1 will support the expectations for Geometry and Spatial Sense, however, Geometry and Spatial Sense will carry forward through Term 2 and be reported on in Term 2. Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives carpenter's square concrete materials Miras paper corners pattern blocks Polygons / power polygons tangrams

Provide Students With Opportunities to: -Opportunities to determine and prove which objects have angles bigger than a right angle using paper corner, pattern block or carpenter’s square -Identify and sort polygons based on the geometric properties (i.e., side lengths # of sides/ interior angle / right angles) -Use geometric properties to determine is a square is a rectangle, or if a rhombus is a parallelogram -Build structures from blocks, toothpicks, or other concrete materials, and describe it using geometric terms, so that your partner will be able to build your structure without seeing it -Draw the missing portion of a symmetrical object on grid paper Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Geometry and Spatial Sense, Appendix D Math Makes Sense Components of: Unit 3 Unit 7

GV1: Geometric Properties compare two-dimensional shapes and three-dimensional figures and sort them by their geometric properties

�� use a reference tool to identify right angles and to describe angles as greater than, equal to, or less than a right angle

�� identify and compare various polygons and sort them by their geometric properties

�� compare various angles, using concrete materials and pictorial representations, and describe angles as bigger than, smaller than, or about the same as other angles

GV2: Geometric Relationships describe relationships between two-dimensional shapes, and between two-dimensional shapes and three-dimensional figures

�� solve problems requiring the greatest or least number of two-dimensional shapes needed to compose a larger shape in a variety of ways

�� explain the relationships between different types of quadrilaterals

�� identify and describe the two-dimensional shapes that can be found in a three-dimensional figure


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Math Alignment Project STRAND: Number Sense and Numeration Term 2 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives arrays colour tiles connecting cubes counters grid paper

Provide Students With Opportunities to: -Divide sets of objects equally and use fractional names to describe the equal parts (e.g., one half; three thirds; two fourths or two quarters) -Discuss the relationship between related facts (e.g., 2 groups of 3 and 3 groups of 2 have the same total, but they are different) Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Number Sense and Numeration, Appendix D Math Makes Sense Components of: Unit 4 Unit 8

NV1: Quantity Relationships read, represent, compare, and order whole numbers to 1000, and use concrete materials to represent fractions and money amounts to $10

�� divide whole objects and sets of objects into equal parts, and identify the parts using fractional names, without using numbers in standard fractional notation


�� relate multiplication of one-digit numbers and division by one-digit divisors to real-life situations, using a variety of tools and strategies

�� multiply to 7 x 7 and divide to 49 divided by 7, using a variety of mental strategies


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Math Alignment Project STRAND: Measurement Term 2 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives analogue and digital clock balance scale concrete materials non-standard materials number line thermometers

Provide Students With Opportunities to: -Measure the temperature outside each day to th nearest degree Celsius using a thermometer (and appropriate notation), and compare their measurements with those reported in the daily news and with benchmarks (e.g., freezing, hot) -Use different tools to compare time (e.g., hours, weeks, years) using clocks, calendars, calculators, etc. Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Measurement, Appendix D Math Makes Sense Components of: Unit 6

MV1: Attributes, Units, and Measurement Sense estimate, measure, and record length, perimeter, area, mass, capacity, time, and temperature, using standard units

�� read time using analogue clocks, to the nearest five minutes, and using digital clocks, and represent time in 12-hour notation

�� estimate, read, and record positive temperatures to the nearest degree Celsius

�� identify benchmarks for freezing, cold, cool, warm, hot, and boiling temperatures as they relate to water and for cold, cool, warm, and hot temperatures as they relate to air

�� choose benchmarks for a kilogram and a litre to help them perform measurement tasks

�� estimate, measure, and record the mass of objects, using the standard unit of the kilogram or parts of a kilogram

�� estimate, measure, and record the capacity of containers, using the standard unit of the litre or parts of a litre

MV2: Measurement Relationships compare, describe, and order objects, using attributes measured in standard units

�� compare and order a collection of objects, using standard units of mass and/or capacity

�� solve problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools


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Math Alignment Project STRAND: Geometry and Spatial Sense Term 2 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives concrete materials nets polydrons prisms pyramids

Provide Students With Opportunities to: -Compare the properties various 3-D figures (prisms and pyramids) -Use nets and polydrons to create a rectangular prism -sort prisms and pyramids based on the shape of the faces and number of faces, edges and vertices and -Use proper mathematical vocabulary to describe prisms and pyramids -Play games using language to describe movement from one location to the other Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Geometry and Spatial Sense, Appendix D Math Makes Sense Components of: Unit 3

GV1: Geometric Properties compare two-dimensional shapes and three-dimensional figures and sort them by their geometric properties

�� compare and sort prisms and pyramids by geometric properties, using concrete materials

�� construct rectangular prisms, and describe geometric properties of the prisms

GV2: Geometric Relationships describe relationships between two-dimensional shapes, and between two-dimensional shapes and three-dimensional figures

�� identify and describe the two-dimensional shapes that can be found in a three-dimensional figure

�� describe and name prisms and pyramids by the shape of their base

GV3: Location and Movement identify and describe the locations and movements of shapes and objects

�� describe movement from one location to another using a grid map

�� identify flips, slides, and turns, through investigation using concrete materials and physical motion, and name flips, slides, and turns as reflections, translations, and rotations

�� complete and describe designs and pictures of images that have a vertical, horizontal, or diagonal line of symmetry


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Math Alignment Project STRAND: Data Management and Probability Term 2 Overall Expectation & Big Idea

Specific Expectations Tools and Manipulatives coins dice spinners

Provide Students With Opportunities to: -predict the likelihood of outcomes when rolling a die or spinning a spinner -compare different spinners or die to determine which has the most likely change of a given outcome. Suggested Resources: Guide to Effective Instruction in Mathematics (K-3): Data Management and Probability, Appendix D Math Makes Sense Components of: Unit 11

DV3: Probability predict and investigate the frequency of a specific outcome in a simple probability experiment

�� predict the frequency of an outcome in a simple probability experiment or game, then perform the experiment, and compare the results with the predictions, using mathematical language

�� demonstrate, through investigation, an understanding of fairness in a game and relate this to the occurrence of equally likely outcomes

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