#### Continually displaying student progress

The Ontario Curriculum “identifies the expectations for each grade and describes the knowledge and skills that students are expected to acquire, demonstrate, and apply in their class work and investigations, on tests, and in various other activities on which their achievement is assessed and evaluated.” To provide students with the foundation for deep, fundamental mathematical understanding, the DreamBox© curriculum reports are aligned to show student progress toward these Ontario Curriculum Overall Expectations: Quantity Relationships; Counting; Operational Sense; Patterns and Relationships; Expressions and Equality; Proportional Relationships; and Variables, Expressions, and Equations.

#### Standards Alignment

Region | Standard | Description | Level |
---|---|---|---|

Ontario | A.3.2.1 | Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant. | Algebra |

Ontario | A.3.3.1 | Construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations. | Algebra |

Ontario | A.3.3.2 | Construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources. | Algebra |

Ontario | A.3.3.3 | Identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear. | Algebra |

Ontario | A.3.3.4 | Compare the properties of direct variation and partial variation in applications, and identify the initial value. | Algebra |

Ontario | A.3.3.5 | Determine the equation of a line of best fit for a scatter plot, using an informal process. | Algebra |

Ontario | A.3.4.1 | Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation. | Algebra |

Ontario | A.3.4.3 | Determine other representations of a linear relation, given one representation. | Algebra |

Ontario | A.3.4.4 | Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied. | Algebra |

Ontario | A.4.2.1 | Determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations. | Algebra |

Ontario | A.4.2.2 | Identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b. | Algebra |

Ontario | A.4.3.1 | Determine, through investigation, various formulas for the slope of a line segment or a line and use the formulas to determine the slope of a line segment or a line. | Algebra |

Ontario | A.4.3.2 | Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b. | Algebra |

Ontario | A.4.3.3 | Determine, through investigation, connections among the representations of a constant rate of change of a linear relation. | Algebra |

Ontario | A.4.3.4 | Identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate. | Algebra |

Ontario | A.4.4.1 | Graph lines by hand, using a variety of techniques. | Algebra |

Ontario | A.4.4.2 | Determine the equation of a line from information about the line. | Algebra |

Ontario | 1.2.2.1 | Represent, compare, and order whole numbers to 50, using a variety of tools (e.g., connecting cubes, ten frames, base ten materials, number lines, hundreds charts) and contexts (e.g., real-life experiences, number stories) | Grade 1 |

Ontario | 1.2.2.8 | Compose and decompose numbers up to 20 in a variety of ways, using concrete materials (e.g., 7 can be decomposed using connecting cubes into 6 and 1, or 5 and 2, or 4 and 3) | Grade 1 |

Ontario | 1.2.2.9 | Divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names (e.g., halves; fourths or quarters). | Grade 1 |

Ontario | 1.2.3.1 | Demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when counting | Grade 1 |

Ontario | 1.2.3.2 | Count forward by 1's, 2's, 5's, and 10's to 100, using a variety of tools and strategies (e.g., move with steps; skip count on a number line; place counters on a hundreds chart; connect cubes to show equal groups; count groups of pennies, nickels, or dimes) | Grade 1 |

Ontario | 1.2.3.3 | Count backwards by 1's from 20 and any number less than 20 (e.g., count backwards from 18 to 11), with and without the use of concrete materials and number lines | Grade 1 |

Ontario | 1.2.4.1 | Solve a variety of problems involving the addition and subtraction of whole numbers to 20, using concrete materials and drawings (e.g., pictures, number lines) (Sample problem: Miguel has 12 cookies. Seven cookies are chocolate. Use counters to determine how many cookies are not chocolate.) | Grade 1 |

Ontario | 1.2.4.2 | Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., one more than, one less than, counting on, counting back, doubles) | Grade 1 |

Ontario | 1.3.2.7 | Read demonstration digital and analogue clocks, and use them to identify benchmark times (e.g., times for breakfast, lunch, dinner; the start and end of school; bedtime) and to tell and write time to the hour | Grade 1 |

Ontario | 1.4.2.1 | identify and describe common two dimensional shapes (e.g., circles, triangles, rectangles, squares) and sort and classify them by their attributes (e.g., colour; size; texture; number of sides), using concrete materials and pictorial representations | Grade 1 |

Ontario | 1.5.3.1 | Create a set in which the number of objects is greater than, less than, or equal to the number of objects in a given set | Grade 1 |

Ontario | 1.5.3.3 | Determine, through investigation using a balance model and whole numbers to 10, the number of identical objects that must be added or subtracted to establish equality | Grade 1 |

Ontario | 1.6.2.2 | Collect and organize primary data (e.g., data collected by the class) that is categorical (i.e., that can be organized into categories based on qualities such as colour or hobby), and display the data using one-to-one correspondence, prepared templates of concrete graphs and pictographs (with titles and labels), and a variety of recording methods (e.g., arranging objects, placing stickers, drawing pictures, making tally marks) | Grade 1 |

Ontario | 2.2.2.1 | Represent, compare, and order whole numbers to 100, including money amounts to 100¢, using a variety of tools (e.g., ten frames, base ten materials, coin manipulatives, number lines, hundreds charts and hundreds carpets) | Grade 2 |

Ontario | 2.2.2.3 | Compose and decompose two-digit numbers in a variety of ways, using concrete materials (e.g., place 42 counters on ten frames to show 4 tens and 2 ones; compose 37¢ using one quarter, one dime, and two pennies) (Sample problem: Use base ten blocks to show 60 in different ways.) | Grade 2 |

Ontario | 2.2.2.4 | Determine, using concrete materials, the ten that is nearest to a given two-digit number, and justify the answer (e.g., use counters on ten frames to determine that 47 is closer to 50 than to 40) | Grade 2 |

Ontario | 2.2.3.1 | Count forward by 1's, 2's, 5's, 10's, and 25's to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5's from 15; count by 25's from 125) | Grade 2 |

Ontario | 2.2.3.2 | Count backwards by 1's from 50 and any number less than 50, and count backwards by 10's from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.) | Grade 2 |

Ontario | 2.2.4.3 | Represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups (e.g., use counters to show that 3 groups of 2 is equal to 2 + 2 + 2 and to 3 x 2) | Grade 2 |

Ontario | 2.3.2.2 | Estimate and measure length, height, and distance, using standard units (i.e., centimetre, metre) and non-standard units | Grade 2 |

Ontario | 2.3.2.3 | Record and represent measurements of length, height, and distance in a variety of ways | Grade 2 |

Ontario | 2.3.2.8 | Tell and write time to the quarter-hour, using demonstration digital and analogue clocks (e.g. My clock shows the time recess will start [10:00], and my friendÍs clock shows the time recess will end [10:15].) | Grade 2 |

Ontario | 2.4.2.2 | identify and describe various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort and classify them by their geometric properties (i.e., number of sides or number of vertices), using concrete materials and pictorial representations | Grade 2 |

Ontario | 2.5.2.2 | Identify, describe, and create, through investigation, growing patterns and shrinking patterns involving addition and subtraction, with and without the use of calculators (e.g., 3 + 1 = 4, 3 + 2 = 5, 3 + 3 = 6) | Grade 2 |

Ontario | 2.5.3.2 | Represent, through investigation with concrete materials and pictures, two number expressions that are equal, using the equal sign (e.g., I can break a train of 10 cubes into 4 cubes and 6 cubes. I can also break 10 cubes into 7 cubes and 3 cubes. This means 4 + 6 = 7 + 3) | Grade 2 |

Ontario | 2.6.2.3 | Collect and organize primary data (e.g., data collected by the class) that is categorical or discrete (i.e., that can be counted, such as the number of students absent), and display the data using one-to-one correspondence in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers (e.g., tally charts, diagrams), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed | Grade 2 |

Ontario | 2.6.3.2 | Pose and answer questions about class generated data in concrete graphs, pictographs, line plots, simple bar graphs, and tally charts | Grade 2 |

Ontario | 3.2.2.1 | Represent, compare, and order whole numbers to 1000, using a variety of tools (e.g., base ten materials or drawings of them, number lines with increments of 100 or other appropriate amounts) | Grade 3 |

Ontario | 3.2.2.3 | Identify and represent the value of a digit in a number according to its position in the number (e.g., use base ten materials to show that the 3 in 324 represents 3 hundreds) | Grade 3 |

Ontario | 3.2.2.4 | Compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways, using concrete materials (e.g., use base ten materials to decompose 327 into 3 hundreds, 2 tens, and 7 ones, or into 2 hundreds, 12 tens, and 7 ones) | Grade 3 |

Ontario | 3.2.2.5 | Round two-digit numbers to the nearest ten, in problems arising from real-life situations | Grade 3 |

Ontario | 3.2.2.7 | Divide whole objects and sets of objects into equal parts, and identify the parts using fractional names (e.g., one half; three thirds; two fourths or two quarters), without using numbers in standard fractional notation | Grade 3 |

Ontario | 3.2.3.1 | 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 (e.g., skip count with and without the aid of a calculator; skip count by 10's using dimes) | Grade 3 |

Ontario | 3.2.3.2 | 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 (e.g., number lines, calculators, coins) and strategies. | Grade 3 |

Ontario | 3.2.4.1 | 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) | Grade 3 |

Ontario | 3.2.4.2 | Add and subtract three-digit numbers, using concrete materials, student-generated algorithms, and standard algorithms | Grade 3 |

Ontario | 3.2.4.6 | Multiply to 7 x 7 and divide to 81 Ö 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting) | Grade 3 |

Ontario | 3.3.2.2 | Draw items using a ruler, given specific lengths in centimetres | Grade 3 |

Ontario | 3.3.2.3 | Read time using analogue clocks, to the nearest five minutes, and using digital clocks (e.g., 1:23 means twenty-three minutes after one oÍclock), and represent time in 12-hour notation | Grade 3 |

Ontario | 3.4.2.1 | Use a reference tool to identify right angles and to describe angles as greater than, equal to, or less than a right angle | Grade 3 |

Ontario | 3.4.2.2 | Identify and compare various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort them by their geometric properties (i.e., number of sides; side lengths; number of interior angles; number of right angles) | Grade 3 |

Ontario | 3.4.3.2 | Explain the relationships between different types of quadrilaterals | Grade 3 |

Ontario | 3.5.3.2 | Determine, the missing number in equations involving addition and subtraction of one- and two-digit numbers, using a variety of tools and strategies (e.g., modeling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: What is the missing number in the equation 25 - 4 = 15 + ??) | Grade 3 |

Ontario | 3.6.2.3 | 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 | Grade 3 |

Ontario | 3.6.3.2 | Interpret and draw conclusions from data presented in charts, tables, and graphs | Grade 3 |

Ontario | 4.2.2.1 | Represent, compare, and order whole numbers to 10 000, using a variety of tools (e.g., drawings of base ten materials, number lines with increments of 100 or other appropriate amounts) | Grade 4 |

Ontario | 4.2.2.2 | Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to 10 000, using a variety of tools and strategies (e.g., use base ten materials to represent 9307 as 9000 + 300 + 0 + 7) (Sample problem: Use the digits 1, 9, 5, 4 to create the greatest number and the least number possible, and explain your thinking.) | Grade 4 |

Ontario | 4.2.2.5 | Represent, compare, and order decimal numbers to tenths, using a variety of tools (e.g., concrete materials such as paper strips divided into tenths and base ten materials, number lines, drawings) and using standard decimal notation (Sample problem: Draw a partial number line that extends from 4.2 to 6.7, and mark the location of 5.6.) | Grade 4 |

Ontario | 4.2.2.6 | Represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered | Grade 4 |

Ontario | 4.2.2.7 | Compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional 4/5 is greater than 3/5 because there are more parts in 4/5; 1/4 is greater than 1/5 because the size of the part is larger in 1/4) | Grade 4 |

Ontario | 4.2.2.9 | Demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawings (e.g., I can say that 3/6 of my cubes are white, or half of the cubes are white. This means that 3/6 and 1/2 are equal.) | Grade 4 |

Ontario | 4.2.4.1 | Add and subtract two-digit numbers, using a variety of mental strategies (e.g., one way to calculate 73 - 39 is to subtract 40 from 73 to get 33, and then add 1 back to get 34) | Grade 4 |

Ontario | 4.2.4.3 | Add and subtract decimal numbers to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms (e.g., When I added 6.5 and 5.6, I took five tenths in fraction circles and added six tenths in fraction circles to give me one whole and one tenth. Then I added 6 + 5 + 1.1, which equals 12.1) | Grade 4 |

Ontario | 4.2.4.5 | Multiply to 9 x 9 and divide to 81 Ö 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting) | Grade 4 |

Ontario | 4.2.4.6 | Solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8) | Grade 4 |

Ontario | 4.2.4.7 | Multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule) | Grade 4 |

Ontario | 4.2.4.8 | Multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithms | Grade 4 |

Ontario | 4.3.2.1 | Estimate, measure, and record length, height, and distance, using standard units | Grade 4 |

Ontario | 4.3.2.2 | Draw items using a ruler, given specific lengths in millimetres or centimetres | Grade 4 |

Ontario | 4.3.2.3 | Estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest minute | Grade 4 |

Ontario | 4.3.3.1 | Describe, through investigation, the relationship between various units of length (i.e., millimetre, centimetre, decimetre, metre, kilometre) | Grade 4 |

Ontario | 4.4.2.2 | Identify and compare different types of quadrilaterals (i.e., rectangle, square, trapezoid, parallelogram, rhombus) and sort and classify them by their geometric properties (e.g., sides of equal length; parallel sides; symmetry; number of right angles) | Grade 4 |

Ontario | 4.4.2.3 | Identify benchmark angles (i.e., straight angle, right angle, half a right angle), using a reference tool (e.g., paper and fasteners, pattern blocks, straws), and compare other angles to these benchmarks (e.g.,ññThe angle the door makes with the wall is smaller than a right angle but greater than half a right angle.îî) (Sample problem: Use paper folding to create benchmarks for a straight angle, a right angle, and half a right angle, and use these benchmarks to describe angles found in pattern blocks.) | Grade 4 |

Ontario | 4.4.2.4 | Relate the names of the benchmark angles to their measures in degrees (e.g., a right angle is 90 degrees) | Grade 4 |

Ontario | 4.4.4.1 | Identify and describe the general location of an object using a grid system (e.g.,"The library is located at A3 on the map."). | Grade 4 |

Ontario | 4.4.4.2 | Identify, perform, and describe reflections using a variety of tools (e.g., Mira, dot paper, technology). | Grade 4 |

Ontario | 4.4.4.3 | Create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools (e.g., pattern blocks, Mira, Geoboard, drawings), and identify the congruent shapes in the designs. | Grade 4 |

Ontario | 4.5.3.2 | Determine the missing number in equations involving multiplication of one-and two-digit numbers, using a variety of tools and strategies. | Grade 4 |

Ontario | 4.5.3.3 | Identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the commutative property of multiplication to facilitate computation with whole numbers (e.g., I know that 15 x 7 x 2 equals 15 x 2 x 7. This is easier to multiply in my head because I get 30 x 7 = 210.) | Grade 4 |

Ontario | 4.5.3.4 | Identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the distributive property of multiplication over addition to facilitate computation with whole numbers (e.g., I know that 9 x 52 equals 9 x 50 + 9 x 2. This is easier to calculate in my head because I get 450 + 18 = 468.) | Grade 4 |

Ontario | 5.2.2.1 | Represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals) | Grade 5 |

Ontario | 5.2.2.2 | 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 (e.g., use numbers to represent 23 011 as 20 000 + 3000 + 0 + 10 + 1; use base ten materials to represent the relationship between 1, 0.1, and 0.01) (Sample problem: How many thousands cubes would be needed to make a base ten block for 100 000?) | Grade 5 |

Ontario | 5.2.2.4 | Round decimal numbers to the nearest tenth, in problems arising from real-life situations | Grade 5 |

Ontario | 5.2.2.5 | Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation | Grade 5 |

Ontario | 5.2.2.6 | Demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3/4 is equal to 9/12) | Grade 5 |

Ontario | 5.2.4.1 | Solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180) | Grade 5 |

Ontario | 5.2.4.2 | Add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms (e.g., use 10 x 10 grids to add 2.45 and 3.25) | Grade 5 |

Ontario | 5.2.4.3 | Multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms | Grade 5 |

Ontario | 5.2.4.5 | Multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule) | Grade 5 |

Ontario | 5.3.3.3 | Solve problems involving the relationship between a 12-hour clock and a 24-hour clock (e.g., 15:00 is 3 hours after 12 noon, so 15:00 is the same as 3:00 p.m.) | Grade 5 |

Ontario | 5.4.2.1 | Distinguish among polygons, regular polygons, and other two-dimensional shapes | Grade 5 |

Ontario | 5.4.2.3 | Identify and classify acute, right, obtuse, and straight angles | Grade 5 |

Ontario | 5.4.2.4 | Measure and construct angles up to 90 degrees, using a protractor | Grade 5 |

Ontario | 5.4.2.5 | Identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral), and classify them according to angle and side properties | Grade 5 |

Ontario | 5.4.2.6 | Construct triangles, using a variety of tools (e.g., protractor, compass, dynamic geometry software), given acute or right angles and side measurements | Grade 5 |

Ontario | 5.4.3.3 | Identify, perform, and describe translations, using a variety of tools. | Grade 5 |

Ontario | 5.4.3.4 | Create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools. | Grade 5 |

Ontario | 5.5.2.3 | Make a table of values for a pattern that is generated by adding or subtracting a number(i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, ) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term). | Grade 5 |

Ontario | 6.2.2.1 | Represent, compare, and order whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals) | Grade 6 |

Ontario | 6.2.2.2 | Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools and strategies (e.g. use base ten materials to represent the relationship between 1, 0.1, 0.01, and 0.001) (Sample problem: How many thousands cubes would be needed to make a base ten block for 1 000 000?) | Grade 6 |

Ontario | 6.2.2.4 | Represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 1/2 is greater than 5/4.) | Grade 6 |

Ontario | 6.2.3.1 | Use a variety of mental strategies to solve addition, subtraction, multiplication, and division problems involving whole numbers (e.g., use the commutative property: 4 x 16 x 5 = 4 x 5 x 16, which gives 20 x 16 = 320; use the distributive property: (500 + 15) x 5 = 500 x 5 + 15 x 5, which gives 100 + 3 = 103) | Grade 6 |

Ontario | 6.2.3.2 | Solve problems involving the multiplication and division of whole numbers (four-digit by two-digit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms) | Grade 6 |

Ontario | 6.2.3.3 | Add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators | Grade 6 |

Ontario | 6.2.3.4 | Multiply and divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., calculate 4 x 1.4 using base ten materials; calculate 5.6 x 4 using base ten materials) | Grade 6 |

Ontario | 6.2.3.6 | Multiply and divide decimal numbers by 10, 100, 1000, and 10 000 using mental strategies (e.g., To convert 0.6 m to square centimetres, I calculated in my head 0.6 x 10 000 and got 6000 cm.) (Sample problem: Use a calculator to help you generalize a rule for multiplying numbers by 10 000.) | Grade 6 |

Ontario | 6.2.4.3 | Represent relationships using unit rates (Sample problem: If 5 batteries cost $4.75, what is the cost of 1 battery?). | Grade 6 |

Ontario | 6.3.3.3 | Construct a rectangle, a square, a triangle,nd a parallelogram, using a variety of tools. | Grade 6 |

Ontario | 6.4.2.1 | Sort and classify quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools (e.g., geoboard, dynamic geometry software) and strategies (e.g., using charts, using Venn diagrams). | Grade 6 |

Ontario | 6.4.2.3 | Measure and construct angles up to 180Áusing a protractor, and classify them as acute, right, obtuse, or straight angles. | Grade 6 |

Ontario | 6.4.2.4 | Construct polygons using a variety of tools, given angle and side measurements. | Grade 6 |

Ontario | 6.4.4.1 | Explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane. | Grade 6 |

Ontario | 6.4.4.2 | Identify, perform, and describe , through investigation using a variety of tools, rotations of 180 degreees and clockwise and countercolockwise rotations of 90 degrees, with the centre of rotation indisde or outside the shape. | Grade 6 |

Ontario | 6.4.4.3 | Create and analyse designs made by reflecting, translating and or rotating a shape or shapes by 90 degrees or 180 degrees that map congruent shapes, in a given design, onto eachother. | Grade 6 |

Ontario | 6.5.2.4 | Determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator). | Grade 6 |

Ontario | 7.2.1.4 | Represent and order integers, using a variety of tools (e.g., two colour counters, virtual manipulatives, number lines); | Grade 7 |

Ontario | 7.2.2.6 | Represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper). | Grade 7 |

Ontario | 7.2.3.5 | Use estimation when solving problems involving operations with whole numbers, decimals, and percents, to help judge the reasonableness of a solution (Sample problem: A book costs $18.49. The salesperson tells you that the total price,including taxes, is $22.37. How can you tell if the total price is reasonable without using a calculator?) | Grade 7 |

Ontario | 7.2.3.6 | Evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations. | Grade 7 |

Ontario | 7.2.3.7 | Add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms | Grade 7 |

Ontario | 7.2.3.9 | Add and subtract integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines). | Grade 7 |

Ontario | 7.2.4.1 | Determine, through investigation, the relationships among fractions, decimals, percents, and ratios | Grade 7 |

Ontario | 7.2.4.2 | Solve problems that involve determining whole number percents, using a variety of tools (e.g., base ten materials, paper and pencil, calculators) (Sample problem: If there are 5 blue marbles in a bag of 20 marbles, what percent of the marbles are not blue?) | Grade 7 |

Ontario | 7.4.3.3 | Demonstrate an understanding that enlarging or reducing two-dimensional shapes creates similar shapes. | Grade 7 |

Ontario | 7.4.4.1 | Plot points using all four quadrants of the Cartesian coordinate plane. | Grade 7 |

Ontario | 7.4.4.3 | Create and analyse designs involving translations, reflections, dilatations, and/or simple rotations of two-dimensional shapes, using a variety of tools (e.g., concrete materials, Mira, drawings, dynamic geometry software) and strategies(e.g., paper folding). | Grade 7 |

Ontario | 7.5.2.1 | Represent linear growing patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets) and strategies (e.g., make a table of values using the term number and the term; plot the coordinates on a graph; write a pattern rule using words). | Grade 7 |

Ontario | 7.5.2.3 | Develop and represent the general term of a linear growing pattern, using algebraic expressions involving one operation (e.g., the general term for the sequence 4, 5, 6, 7, can be written algebraically as n + 3, where n represents the term number; the general term for the sequence 5, 10, 15, 20, can be written algebraically as 5n, where n represents the term number). | Grade 7 |

Ontario | 7.5.2.4 | Evaluate algebraic expressions by substituting natural numbers for the variables. | Grade 7 |

Ontario | 7.5.3.6 | Solve linear equations of the form ax = c or c = ax and ax + b = c or variations such as b + ax = c and c = bx + a (where a, b, and c are natural numbers ) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator. | Grade 7 |

Ontario | 8.2.2.1 | Express repeated multiplication using exponential notation (e.g., 2x2x2x2 = 2^4). | Grade 8 |

Ontario | 8.2.2.7 | Solve problems involving operations with integers, using a variety of tools (e.g., two colour counters, virtual manipulatives, number lines); | Grade 8 |

Ontario | 8.2.3.4 | Represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent 1/4 multiplied by 1/3) | Grade 8 |

Ontario | 8.2.3.5 | Solve problems involving addition, subtraction, multiplication, and division with simple fractions | Grade 8 |

Ontario | 8.2.3.6 | Represent the multiplication and division of integers, using a variety of tools (e.g., if black counters represent positive amounts and red counters represent negative amounts, you can model 3 x (-2) as three groups of two red counts). | Grade 8 |

Ontario | 8.2.3.7 | Solve problems involving operations with integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines). | Grade 8 |

Ontario | 8.2.3.8 | Evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations. | Grade 8 |

Ontario | 8.2.3.9 | Multiply and divide decimal numbers by various powers of ten. | Grade 8 |

Ontario | 8.4.3.5 | Solve problems involving right triangles geometrically, using the Pythagorean relationship. | Grade 8 |

Ontario | 8.4.4.1 | Graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s) (i.e., translation; reflection in the x-axis, the y-axis, or the angle bisector of the axes that passes through the first and third quadrants; rotation of 90 degrees, 180 degrees, 270 degrees about the origin). | Grade 8 |

Ontario | 8.5.2.2 | Represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the coordinates on a graph), using a variety of tools (e.g., graph paper, calculators, dynamic statistical software). | Grade 8 |

Ontario | 8.5.2.3 | Determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation (Sample problem: Given the graph that represents the pattern 1, 3, 5, 7,, find the 10th term. Given the algebraic equation that represents the pattern, t = 2n _ 1, find the 100th term.). | Grade 8 |

Ontario | 8.5.3.2 | Model linear relationships using tables of values, graphs, and equations (e.g., the sequence 2, 3, 4, 5, 6, can be represented by the equation t = n + 1, where n represents the term number and t represents the term), through investigation using a variety of tools (e.g., algebra tiles, pattern blocks, connecting cubes, base ten materials)(Sample problem: Leah put $350 in a bank certificate that pays 4% simple interest each year. Make a table of values to show how much the bank certificate is worth after five years, using base ten materials to help you. Represent the relationship using an equation.). | Grade 8 |

Ontario | 8.5.3.5 | Make connections between solving equations and determining the term number in a pattern, using the general term (e.g., for the pattern with the general term 2 n + 1, solving the equation 2 n + 1 = 17 tells you the term number when the term is 17). | Grade 8 |

Ontario | 8.6.3.5 | Identify and describe trends, based on the rate of change of data from tables and graphs, using informal language (e.g., ñThe steep line going upward on this graph represents rapid growth. The steep line going downward on this other graph represents rapid decline.î). | Grade 8 |

Ontario | K.2.1.1 | Investigate the idea that quantity is greater when counting forwards and less when counting backwards (e.g., use manipulatives to create a quantity number line; move along a number line; move around on a hundreds carpet; play simple games on number-line game boards; build a structure using blocks, and describe what happens as blocks are added or removed) | Kindergarten |

Ontario | K.2.1.11 | Begin to make use of one-to-one correspondence in counting objects and matching groups of objects (e.g., one napkin for each of the people at the table) | Kindergarten |

Ontario | K.2.1.12 | Investigate addition and subtraction in everyday activities through the use of manipulatives (e.g., interlocking cubes), visual models (e.g., a number line, tally marks, a hundreds carpet), or oral exploration (e.g., dramatizing of songs) | Kindergarten |

Ontario | K.2.1.2 | Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects (e.g., find out which of two cups contains more or fewer beans, using counters; investigate the ideas of more, less, and the same, using five and ten frames; compare two sets of objects that have the same number of items, one set having the items spread out, and recognize that both sets have the same quantity [concept of conservation]; recognize that the last count represents the actual number of objects in the set [concept of cardinality]; compare five beans with five blocks, and recognize that the number 5 represents the same quantity regardless of the different materials [concept of abstraction]) | Kindergarten |

Ontario | K.2.1.3 | Recognize some quantities without having to count, using a variety of tools (e.g., dominoes, dot plates, dice, number of fingers) or strategies (e.g., composing and decomposing numbers, subitizing) | Kindergarten |

Ontario | K.2.1.5 | Use, read, and represent whole numbers to 10 in a variety of meaningful contexts (e.g., use a hundreds chart; use magnetic and sandpaper numerals; put the house number on a house built at the block centre; find and recognize numbers in the environment; use magnetic numerals to represent the number of objects in a set; write numerals on imaginary bills at the restaurant at the dramatic play centre) | Kindergarten |

Ontario | K.2.1.6 | Demonstrate awareness of addition and subtraction in everyday activities (e.g., in sharing crayons). | Kindergarten |

Ontario | K.2.1.7 | Demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation (e.g., initially: show smaller quantities using anchors of five and ten, such as their fingers or manipulatives; eventually: show quantities to 10, using such tools as five and ten frames and manipulatives) | Kindergarten |

Ontario | K.2.1.8 | Investigate and develop strategies for composing and decomposing quantities to 10 (e.g., use manipulatives or shake and spill activities; initially: to represent the quantity of 8, the child may first count from 1 through to 8 using his or her fingers; later, the child may put up one hand, count from 1 to 5 using each finger, pause, and then continue to count to 8 using three more fingers; eventually: the child may put up all five fingers of one hand at once and simply say Five, then count on, using three more fingers and saying 'Six, seven, eight. There are eight.') | Kindergarten |