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Elementary Math Learning Overview
Elementary Math Learning Overview
  • The Mathematical Processes
  • The Kindergarten Program
    • "Mathematics in the Kindergarten program builds on children’s desire to make sense of their world, and helps them develop and demonstrate their mathematical understanding. Young children use mathematics intuitively and develop their understanding of mathematics through their individual approaches to learning, as well as through their prior experience of their linguistic, family, cultural, and community backgrounds. It is therefore important for children’s existing conceptual understanding of mathematics to be valued and for children to be introduced to mathematical concepts in an appropriate manner and at an appropriate time in their development."

      The Kindergarten Program, 2016

      As children progress through the Kindergarten program, they:

      • demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships

      • measure, using non-standard units of the same size, and compare objects, materials, and spaces in terms of their length, mass, capacity, area, and temperature, and explore ways of measuring the passage of time, through inquiry and play-based learning

      • describe, sort, classify, build, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation

      • recognize, explore, describe, and compare patterns, and extend, translate, and create them, using the core of a pattern and predicting what comes next

      • collect, organize, display, and interpret data to solve problems and to communicate information, and explore the concept of probability in everyday contexts

      • apply the mathematical processes to support the development of mathematical thinking, to demonstrate understanding, and to communicate thinking and learning in mathematics, while engaged in play-based learning and in other contexts


      Taken and adapted from the The Kindergarten Program, 2016

  • Grade 1
    • *​For more on what your child is learning in Grade 1 mathematics, read "Key Learning for Grade 1" from mathies.ca.

      Number Sense and Numeration

      • repre​sent and order whole numbers to 50

      • e​stablish conservation1 of number

      • represent money amounts to 20¢

      • compose and decompose numbers to 20

      • count by 1’s, 2’s, 5’s, and 10’s

      • add and subtract numbers to 20


      Measurement​

      • measure using non-standard units2

      • tell time to the nearest half-hour

      • developing a sense of area

      • compare objects using measurable attribute3

      • compare objects using non-standard units

      • investigate relationships when measuring the length of an object


      Geometry and Spatial Sense

      • sort and classify4 two-dimensional shapes and three dimensional figures by attributes;

      • recognize symmetry

      • relate shapes to other shapes, to designs, and to figures

      • describe location using positional language (e.g., over, under, inside, outside, etc.)


      Patterning and Algebra

      • create and extend repeating patterns involving one attribute

      • introduce the concept of equality using only concrete materials5


      Data Management and Probability

      • organize objects into categories using one attribute

      • collect and organize categorical data6

      • read and display data using concrete graphs7 and pictographs

      • describe the likelihood that an event will occur


      1 Conservation. The property by which something remains the same, despite changes such as physical arrangement. For example, with conservation of number, whether three objects are close together or far apart, the quantity remains the same. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 122)


      2 Non-standard units. Common objects used as measurement units; for example, paper clips, cubes, and hand spans. Nonstandard units are used in the early development of measurement concepts. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)


      3 Attribute. A quantitative or qualitative characteristic of a shape, an object, or an occurrence; for example, colour, size, thickness, or number of sides. An attribute may or may not be a property. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 120)


      4 Classify. Make decisions about how to sort or categorize things. Classifying objects and numbers in different ways helps students recognize attributes and properties of objects and numbers, and develop flexible thinking. (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 165)


      5 Concrete materials. Objects that students handle and use in constructing or demonstrating their understanding of mathematical concepts and skills. Some examples of concrete materials are base ten blocks, connecting cubes, construction kits, number cubes, games, geoboards, geometric solids, measuring tapes, Miras, pattern blocks, spinners, and tiles. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 122)


      6 Categorical data. Data that can be sorted by type or quality, rather than by measured or counted values. Eye colour and favourite food are examples of categorical data.  (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 121)


      7 Concrete graph. A graph in which real objects are used to represent pieces of information; for example, coloured candy directly placed on a template of a bar graph. (A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 – Data Management and Probability, p. 142, 2007)

  • Grade 2
    • ​*For more on what your child is learning in Grade 2 mathematics, read "Key Learning for Grade 2​" from mathies.ca.

      Number Sense and Numeration

      • represent and order numbers to 100

      • represent money amounts to 100¢

      • compose and decompose two-digit numbers

      • investigate fractions of a whole

      • count by 1’s, 2’s, 5’s, 10’s, and 25’s

      • add and subtract two-digit numbers

      • relate equal-sized groups to multiplication

      • relate sharing equally to division ​


      Measurement

      • measure length using centimetres and metres

      • choose benchmarks (personal referents) for the centimetre and the metre

      • measure perimeter, area, mass, and capacity using non-standard units1

      • compare the mass and capacity of objects using non-standard units

      • tell time to the nearest quarter-hour

      • describe and establish temperature change

      • relate days to weeks and months to years


      Geometry and Spatial Sense

      • distinguish between attributes2 that are geometric properties3 and attributes that are not geometric properties

      • classify two-dimensional shapes by geometric properties (number of sides and vertices)

      • classify three-dimensional figures by geometric properties (number and shape of faces)

      • locate a line of symmetry4

      • compose and decompose shapes

      • describe relative locations of objects

      • represent objects on a map


      Patterning and Algebra

      • identify and describe repeating patterns

      • identify and describe growing and shrinking patterns

      • develop the concept of equality using the addition and subtraction of numbers to 18 and the equal sign

      • investigate the commutative property5 in addition

      • investigate the property of zero6 in addition and subtraction


      Data Management and Probability

      • organize objects into categories using two attributes

      • collect and organize categorical7 and discrete8 data

      • read and display data using line plots9 and simple bar graphs10

      • describe probability, in simple games and experiments, as the likelihood that an event will occur



      1 Non-standard units. Common objects used as measurement units; for example, paper clips, cubes, and hand spans. Nonstandard units are used in the early development of measurement concepts. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)


      2 Attribute. A quantitative or qualitative characteristic of a shape, an object, or an occurrence; for example, colour, size, thickness, or number of sides. An attribute may or may not be a property. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 120)


      3 Property (geometric). An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      4 Line of symmetry. A line that divides a shape into two parts that can be matched by folding the shape in half along this line. (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 125)


      5 Commutative property. A property of addition and multiplication that allows the numbers to be added or multiplied in any order, without affecting the sum or product of the operation. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 121)


      6 Properties of zero.  The properties of zero in addition and subtraction (i.e., when you add zero to a number, the number does not change; when you subtract zero from a number, the number does not change). (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.50)


      7 Categorical data. Data that can be sorted by type or quality, rather than by measured or counted values. Eye colour and favourite food are examples of categorical data.  (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 121)


      8 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      9 Line plot. A graph that shows a mark (usually an “X”) above a value on the number line for each entry in the data set. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)


      10 Bar graph. A graph consisting of horizontal or vertical bars that represent the frequency of an event or outcome. There are gaps between the bars to reflect the categorical or discrete nature of the data. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 125)​

  • Grade 3
    • ​*For more on what your child is learning in Grade 3 mathematics, read "Key Learning for Grade 3​" from mathies.ca.


      Number Sense and Numeration

      • represent and order numbers to 1000​

      • represent money amounts to $10

      • compose and decompose three-digit numbers

      • investigate fractions of a set

      • count by 1’s, 2’s, 5’s, 10’s, 25’s, and 100’s

      • add and subtract three-digit numbers in a variety of ways

      • relate one-digit multiplication to real-life situations

      • relate division, by one-digit divisors to real life situations


      Measurement:

      • measure distance using kilometres

      • tell time to the nearest 5 minutes

      • identify temperature benchmarks1

      • measure perimeter using standard units (e.g, cm, m, km)

      • measure mass in kilograms

      • measure capacity in litres

      • measure area using grid paper

      • compare the length, mass, and capacity of objects using standard units (e.g, cm, m, km, l, kg)

      • relate minutes to hours, hours to days, days to weeks, and weeks to years


      Geometry and Spatial Sense:

      • use a reference tool to identify right angles and to compare angles with a right angle

      • classify two-dimensional shapes by geometric properties2 (number of sides and angles)

      • classify three-dimensional figures by geometric properties (number of faces, edges, and vertices)

      • relate different types of quadrilaterals3

      • name prisms and pyramids

      • identify congruent4 shapes

      • describe movement on a grid map

      • recognize transformations5


      Patterning and Algebra:

      • create and extend growing and shrinking patterns

      • represent geometric patterns with a number sequence, a number line, and a bar graph

      • determine the missing numbers in equations involving addition and subtraction of one- and two-digit numbers

      • investigate the properties of zero6 and one in multiplication


      Data Management and Probability:

      • organize objects into categories using two or more attributes7

      • collect and organize categorical8 and discrete data9

      • read and display data using vertical and horizontal bar graphs10

      • understand mode11

      • predict the frequency of an outcome

      • relate fair games to equally likely events



      1 Benchmarks. A number or measurement that is internalized and used as a reference to help judge other numbers or measurements. For example, the width of the tip of the little finger is a common benchmark for one centimetre. Also called referent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 121)


      2 Geometric Properties. An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      3 Quadrilaterals. A polygon with four sides (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.131)


      4 Congruent. Having the same size and shape. For example, in two congruent triangles, the three corresponding pairs of sides and the three corresponding pairs of angles are equal.  (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 122)


      5 Transformations. A change in a figure that results in a different position, orientation, or size. The transformations include the translation (slide), reflection (flip), rotation (turn), and dilatation (reduction or enlargement).  (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 134)


      6 Properties of Zero. The properties of zero in addition and subtraction (i.e., when you add zero to a number, the number does not change; when you subtract zero from a number, the number does not change). (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.50)


      7 Attributes. A quantitative or qualitative characteristic of a shape, an object, or an occurrence; for example, colour, size, thickness, or number of sides. An attribute may or may not be a property. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 120)


      8 Categorical Data. Data that can be sorted by type or quality, rather than by measured or counted values. Eye colour and favourite food are examples of categorical data.  (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 121)


      9 Discrete Data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or​ the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      10 Bar Graph. A graph consisting of horizontal or vertical bars that represent the frequency of an event or outcome. There are gaps between the bars to reflect the categorical or discrete nature of the data. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 125)


      11 Mode. The value that occurs most often in a set of data. For example, in a set of data with the values 3, 5, 6, 5, 6, 5, 4, 5, the mode is 5.  (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 128)

  • Grade 4

    • Number Sense and Numeration:

      • ​​represent and order numbers to 10 000​
      • represent money amounts to $100

      • develop the concept of place value to tenths

      • represent and compare fractions using fractional notation (e.g ½ is bigger than ⅓)

      • add and subtract three-digit numbers in a variety of ways

      • multiply and divide two-digit whole numbers by one-digit whole numbers

      • relate halves, fifths, and tenths to decimals


      Measurement:

      • measure length using millimetres

      • measure time intervals to the nearest minute

      • determine elapsed time

      • measure mass in grams and capacity in millilitres

      • measure volume using concrete materials

      • determine area and perimeter relationships for rectangles

      • compare the mass and capacity of objects using standard units (e.g: g, kg, l, ml)

      • relating years to decades and decades to centuries


      Geometry and Spatial Sense:

      • identify geometric properties1 of parallelograms2

      • classify two-dimensional shapes by geometric properties (number of sides, angles, and symmetry)

      • identify a straight angle, a right angle, and half a right angle

      • classify prisms and pyramids by geometric properties

      • construct three-dimensional figures in a variety of ways

      • describe location using a grid system

      • perform and describe reflections3


      Patterning and Algebra:

      • relate the term and the term number in a numeric sequence

      • generate patterns that involve addition, subtraction, multiplication, and reflections

      • determine the missing numbers in equations involving multiplication of one- and two-digit numbers

      • use the commutative4 and distributive properties5 to facilitate computation


      Data Management and Probability:

      • collect and organize discrete data6

      • read and display data using stem-and-leaf plots7 and double bar graphs8

      • understand median9

      • compare two related sets of data

      • predict the frequency of an outcome

      • investigate how the number of repetitions of a probability experiment affects the conclusion drawn



      1 Geometric properties. An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      2 Parallelogram. A quadrilateral whose opposite sides are parallel. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 130)


      3 Reflection. A transformation that flips a shape over an axis to form a congruent shape. A reflection image is the mirror image that results from a reflection. Also called flip.(The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 132)


      4 Commutative property. A property of addition and multiplication that allows the numbers to be added or multiplied in any order, without affecting the sum or product of the operation. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 121)


      5 Distributive property. The property that allows a number in a multiplication expression to be decomposed into two or more numbers; for example, 51 x 12 = 51 x 10 + 51 x 2. More formally, the distributive property holds that, for three numbers, a, b, and c, a x (b + c) = (a x b) + (a x c) and a x (b – c) = (a x b) – (a x c); for example, 2 x (4 + 1) = 2 x 4 + 2 x 1 and 2 x (4 – 1) = 2 x 4 – 2 x 1. Multiplication is said to be distributed over addition and subtraction. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      6 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      7 Stem-and-leaf plot. An organization of data into categories based on place values. The plot allows easy identification of the greatest, least, and median values in a set of data. The following stem-and-leaf plot represents these test results: 72, 64, 68, 82, 75, 74, 68, 70, 92, 84, 77, 59, 77, 70, 85.(The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.126)

      8 Double bar graph. A graph that combines two bar graphs to compare two aspects of the data in related contexts; for example, comparing the populations of males and females in a school in different years. Also called comparative bar graph. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.125)


      9 Median. The middle value in a set of values arranged in order. For example, 14 is the median for the set of numbers 7, 9, 14, 21, 39. If there is an even number of numbers, the median is the average of the two middle numbers. For example, 11 is the median of 5, 10, 12, and 28. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)​​

  • Grade 5
    • Number Sense and Numeration:

      • represent and order numbers to 100 000
      • represent money amounts to $1000

      • develop the concept of place value to hundredths

      • compare and order fractional amounts with like denominators

      • add and subtract decimal amounts to hundredths

      • multiply two-digit whole numbers by two-digit whole numbers

      • divide three-digit whole numbers by one-digit whole numbers

      • relate simple fractions to decimals


      Measurement:

      • measure time intervals to the nearest second

      • determine elapsed time

      • measure temperature

      • convert from metres to centimetres and from kilometres to metres

      • relate the 12-hour clock to the 24-hour clock

      • develop and apply area and perimeter relationships for a rectangle

      • relate capacity and volume

      • develop and apply the volume relationship for a right rectangular prism


      Geometry and Spatial Sense:

      • distinguish among polygons1 and among prisms

      • identify acute, right, obtuse, and straight angles

      • measure angles to 90° with a protractor

      • construct triangles

      • construct nets of prisms and pyramids

      • locate objects using the cardinal directions

      • perform and describe translations2


      Patterning and Algebra:

      • represent a pattern using a table of values

      • predict terms in a pattern

      • determine the missing numbers in equations involving addition, subtraction, multiplication, or division and one- or two-digit numbers

      • investigate variables3 as unknown quantities

      • demonstrate equality using multiplication or division in equations with unknown quantities on both sides


      Data Management and Probability:

      • collect and organize discrete4 and continuous data5

      • display data using broken-line graphs6

      • sample data from a population

      • understand mean7

      • compare two related sets of data

      • represent probability using fractions



      1 Polygon. A closed shape formed by three or more line segments; for example, triangle, quadrilateral, pentagon, octagon. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.130)


      2 Translation. A transformation that moves every point on a shape the same distance, in the same direction, to form a congruent shape. A translation image is the result of a translation. Also called slide. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 134)


      3 Variable. A letter or symbol used to represent an unknown quantity, a changing value, or an unspecified number (e.g., a x b = b x a). (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 134)


      4 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      5 Continuous data. Data that can include any numerical value that is represented on a number line and that falls within the range of the data, including decimals and fractions. Continuous data usually represent measurements, such as time, height, and mass. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      6 Broken-line graph. A graph formed by line segments that join points representing the data. The horizontal axis represents discrete quantities such as months or years, whereas the vertical axis can represent continuous quantities. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 125)


      7 Mean. One measure of central tendency. The mean of a set of numbers is found by dividing the sum of the numbers by the number of numbers in the set. For example, the mean of 10, 20, and 60 is (10 + 20 + 60) ÷ 3 = 30. A change in the data produces a change in the mean, similar to the way in which changing the load on a lever affects the position of the fulcrum if balance is maintained. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.127)​

  • Grade 6
    • Number Sense and Numeration:

      • represent and order numbers to 1 000 000
      • develop the concept of place value to thousandths

      • compare and order fractional amounts with unlike denominators

      • estimate 10%, 25%, 50%, and 75% of a quantity

      • add and subtract decimal amounts to thousandths

      • multiply and divide four-digit whole numbers by two-digit whole number

      • multiply and divide decimals to tenths by whole numbers and two-digit by two-digit whole numbers

      • divide three-digit whole numbers by one-digit whole numbers

      • apply order of operations1 in expressions without brackets

      • relate simple fractions, decimals, and percents


      Measurement:

      • measure quantities using metric units

      • convert from larger to smaller metric units, including square metres to square centimetres

      • develop and apply area relationships for a parallelogram and a triangle

      • develop and apply the volume relationships for a triangular prism

      • determine and apply surface area relationships for rectangular and triangular prisms

      • relate square metres and square centimetres


      Geometry and Spatial Sense:

      • classify quadrilaterals2 by geometric properties3

      • sort polygons by lines of symmetry4 and by rotational symmetry5

      • measure angles to 180° with a protractor

      • construct polygons6

      • represent figures using views and isometric sketches

      • perform and describe rotations

      • plot points in the first quadrant


      Patterning and Algebra:

      • represent patterns using ordered pairs7 and graphs

      • describe pattern rules in words

      • calculate any term when given the term number

      • investigate variables as changing quantities

      • solve equations using concrete materials8 and guess and check


      Data Management and Probability:

      • collect and organize discrete9 and continuous data10

      • display data using continuous line graphs

      • select appropriate graphical representations

      • use continuous line graphs and mean to compare sets of data

      • find theoretical probabilities11

      • predict the frequency of an outcome based on the theoretical probability



      1 Order of operations. A convention or rule used to simplify expressions. The acronym BEDMAS is often used to describe the order: – brackets – exponents – division or multiplication, whichever comes first – addition or subtraction, whichever comes first (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 129)


      2 Quadrilateral. A polygon with four sides (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.131)


      3 Property (geometric). An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      4 Line of symmetry. A line that divides a shape into two parts that can be matched by folding the shape in half along this line. (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 125)


      5 Rotational symmetry. A geometric property of a shape whose position coincides with its original position after a rotation of less than 360º about its centre. (A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense, 2016, p. 132)


      6 Polygon. A closed shape formed by three or more line segments; for example, triangle, quadrilateral, pentagon, octagon. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.130)


      7 Ordered pair. Two numbers, in order, that are used to describe the location of a point on a plane, relative to a point of origin (0,0); for example, (2, 6). On a coordinate plane, the first number is the horizontal coordinate of a point, and the second is the vertical coordinate of the point. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 129)​

      8 Concrete materials. Objects that students handle and use in constructing or demonstrating their understanding of mathematical concepts and skills. Some examples of concrete materials are base ten blocks, connecting cubes, construction kits, number cubes, games, geoboards, geometric solids, measuring tapes, Miras, pattern blocks, spinners, and tiles. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 122)


      9 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      10 Continuous data. Data that can include any numerical value that is represented on a number line and that falls within the range of the data, including decimals and fractions. Continuous data usually represent measurements, such as time, height, and mass. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      11 Theoretical probability. A mathematical calculation of the chances that an event will happen in theory; if all outcomes are equally likely, it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 133)​

  • Grade 7
    • Number Sense and Numeration

      • represent and order decimals (to hundredths), fractions, and integers
      • represent squares and square roots

      • divide whole numbers by simple fractions and decimals

      • add and subtract simple fractions and integers

      • multiply and divide decimal numbers to thousandths by one-digit whole numbers

      • apply order of operations1 in expressions with brackets

      • relate fractions, decimals, and percents

      • solve problems involving whole-number percents and unit rates


      Measurement

      • convert between metric units, including converting between square centimetres and square metres

      • develop the area relationship for a trapezoid

      • develop and apply the formula for the volume of a prism

      • determine and apply surface-area relationships for prisms

      • relate millilitres and cubic centimetres


      Geometry and Spatial Sense

      • construct parallel, perpendicular, and intersecting lines

      • sort and classify triangles and quadrilaterals2 by geometric properties3

      • construct angle bisectors and perpendicular bisectors

      • investigate relationships among congruent4 shapes

      • relate enlarging and reducing to similar5 shapes

      • compare similar and congruent shapes

      • performing and describing dilatations

      • tile6 a plane

      • plot points in all four quadrants


      Patterning and Algebra

      • represent linear growing patterns

      • represent patterns algebraically

      • model real-life relationships involving constant rates graphically and algebraically

      • translate phrases, using algebraic expressions

      • find the term in a pattern algebraically when given any term number

      • solve linear equations7 using concrete materials8 or inspection and guess and check


      Data Management and Probability

      • collect and organizing categorical9, discrete10, and continuous11 data

      • display data in relative frequency12 tables and circle graphs

      • identify bias in data

      • relate changes in data to changes in central tendency13

      • make inferences based on data

      • investigate real-world applications of probability

      • determine the theoretical probability14 of two independent events



      1 Order of operations. A convention or rule used to simplify expressions. The acronym BEDMAS is often used to describe the order: – brackets – exponents – division or multiplication, whichever comes first – addition or subtraction, whichever comes first (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 129)


      2 Quadrilateral. A polygon with four sides (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.131)


      3 Property (geometric). An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      4 Congruent. Having the same size and shape. For example, in two congruent triangles, the three corresponding pairs of sides and the three corresponding pairs of angles are equal. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      5 Similar. Having the same shape but not always the same size. If one shape is similar to another shape, there exists a dilatation that will transform the first shape into the second shape. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.132)


      6 Tiling. The process of using repeated shapes, which may or may not be congruent, to cover a region completely. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.134)


      7 Linear equation. An algebraic representation of a linear relationship. The relationship involves one or more first-degree variable terms; for example, y = 2x – 1; 2x + 3y = 5; y = 3. The graph of a linear equation is a straight line. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.127)


      8 Concrete materials. Objects that students handle and use in constructing or demonstrating their understanding of mathematical concepts and skills. Some examples of concrete materials are base ten blocks, connecting cubes, construction kits, number cubes, games, geoboards, geometric solids, measuring tapes, Miras, pattern blocks, spinners, and tiles. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 122)


      9 Categorical data. Data that can be sorted by type or quality, rather than by measured or counted values. Eye colour and favourite food are examples of categorical data. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.121)


      10 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      11 Continuous data. Data that can include any numerical value that is represented on a number line and that falls within the range of the data, including decimals and fractions. Continuous data usually represent measurements, such as time, height, and mass. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      12 Relative frequency.The frequency of a particular outcome or event expressed as a percent of the total number of outcomes. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.132)


      13 Measure of central tendency. A value that summarizes a whole set of data; for example, the mean, the median, or the mode. A measure of central tendency represents the approximate centre of a set of data. Also called central measure. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)


      14 Theoretical probability. A mathematical calculation of the chances that an event will happen in theory; if all outcomes are equally likely, it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 133)​

  • Grade 8
    • Number Sense and Numeration

      • represent and order rational numbers1
      • represent numbers using exponential notation (e.g, 24)

      • solve multi-step problems2 involving whole numbers and decimals

      • multiply and divide fractions and integers (e.g., -10)

      • multiply and divide decimals by powers of ten (e.g., 230 000 ÷ 106)

      • apply order of operations3 in expressions with brackets and exponents

      • solving problems involving percents to one decimal place and percents greater than 100

      • solving problems involving rates and proportions


      Measurement

      • convert between cubic centimetres and cubic metres and between millilitres and cubic centimetres

      • develop circumference4 and area relationships for a circle

      • develop and apply the formula for the volume of a cylinder

      • determine and apply surface-area relationships for cylinders


      Geometry and Spatial Sense

      • sort quadrilaterals5 by geometric properties6 involving diagonals

      • construct circles

      • investigate relationships among similar7 shapes

      • determine and apply angle relationships for parallel and intersecting lines;

      • relating the numbers of faces, edges, and vertices of a polyhedron8

      • determine and apply the Pythagorean relationship9 geometrically

      • plotting the image of a point on the coordinate plane10 after applying a transformation


      Patterning and Algebra

      • represent the general term in a linear sequence, using one or more algebraic expressions

      • translate statements, using algebraic equations

      • find the term number in a pattern algebraically when given any term

      • solve linear equations11 involving one variable terms with integer solutions using a “balance” model


      Data Management and Probability

      • collect categorical12, discrete13, and continuous14 data

      • organize data into intervals

      • display data using histograms15 and scatter plots16

      • use measures of central tendency17 to compare sets of data

      • compare two attributes18 using data management tools; comparing experimental19 and theoretical probabilities20

      • calculate the probability of complementary events21



      1 Rational number. A number that can be expressed as a fraction in which the denominator is not 0. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 131)


      2 Multi-step problem. A problem that is solved by making at least two calculations The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 128)


      3 Order of operations. A convention or rule used to simplify expressions. The acronym BEDMAS is often used to describe the order: – brackets – exponents – division or multiplication, whichever comes first – addition or subtraction, whichever comes first (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 129)


      4 Perimeter. The length of the boundary of a shape, or the distance around a shape. For example, [...] the perimeter of a circle is its circumference. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.130)


      5 Quadrilateral. A polygon with four sides (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.131)


      6 Property (geometric). An attribute that remains the same for a class of objects or shapes. A property of any parallelogram, for example, is that its opposite sides are congruent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.168)


      7 Similar. Having the same shape but not always the same size. If one shape is similar to another shape, there exists a dilatation that will transform the first shape into the second shape. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.132)


      8 Polyhedron. A three-dimensional figure that has polygons as faces. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.130)


      9 Pythagorean relationship. The relationship that, for a right triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.131)


      10 Coordinate plane. A plane that contains an x-axis (horizontal) and a y-axis (vertical), which are used to describe the location of a point. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      11 Linear equation. An algebraic representation of a linear relationship. The relationship involves one or more first-degree variable terms; for example, y = 2x – 1; 2x + 3y = 5; y = 3. The graph of a linear equation is a straight line. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.127)


      12 Categorical data. Data that can be sorted by type or quality, rather than by measured or counted values. Eye colour and favourite food are examples of categorical data. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.121)


      13 Discrete data. Data that can include only certain numerical values (often whole numbers) within the range of the data. Discrete data usually represent things that can be counted; for example, the number of times a word is used or the number of students absent. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.123)


      14 Continuous data. Data that can include any numerical value that is represented on a number line and that falls within the range of the data, including decimals and fractions. Continuous data usually represent measurements, such as time, height, and mass. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.122)


      15 Histogram. A type of bar graph in which each bar represents a range of values, and the data are continuous. No spaces are left between the bars, to reflect the continuous nature of the data. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.125)


      16 Scatter plot. A graph designed to show a relationship between corresponding numbers from two sets of data measurements associated with a single object or event; for example, a graph of data about marks and the corresponding amount of study time. Drawing a scatter plot involves plotting ordered pairs on a coordinate grid. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.126)


      17 Measure of central tendency. A value that summarizes a whole set of data; for example, the mean, the median, or the mode. A measure of central tendency represents the approximate centre of a set of data. Also called central measure. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p.128)


      18 Attribute. A quantitative or qualitative characteristic of a shape, an object, or an occurrence; for example, colour, size, thickness, or number of sides. An attribute may or may not be a property. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 120)


      19 Experimental probability. The likelihood of an event occurring, determined from experimental results rather than from theoretical reasoning. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 124)


      20 Theoretical probability. A mathematical calculation of the chances that an event will happen in theory; if all outcomes are equally likely, it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 133)


      21 Complementary events. Two events that have no outcome(s) in common but that account for all possible outcomes of an experiment. For example, rolling an even number and rolling an odd number using a number cube are complementary events. The sum of the probabilities of complementary events is 1. (The Ontario Curriculum Grades 1-8, Mathematics, 2005, p. 121)​

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