New Ontario Mathematics Curriculum (K 6) Correlation to the Patterns and Algebra Developmental Map

Transcription

1 Correlation to the Patterns and Algebra Developmental Map Pattern Rules, and Algebraic Concept 1 Patterns represent identified regularities based on rules describing the elements. K: recognize and use K: identify and reproduce simple K: create and extend simple using a variety of materials or actions Grade 1: identify, describe, extend, and create repeating Grade 1: identify, describe, and extend, through investigation, geometric repeating involving one attribute Grade 1: create a repeating pattern involving one attribute Grade 1: identify, describe, extend, and create repeating Grade 1: identify, describe, and extend, through investigation, geometric repeating involving one attribute Grade 1: identify and extend, through investigation, numeric repeating Grade 1: describe numeric repeating in a hundreds chart Grade 1: identify a rule for a repeating pattern Grade 1: create a repeating pattern involving one attribute Grade 2: identify, extend, and create repeating, growing, and shrinking Grade 2: identify and describe, through investigation, growing and shrinking generated by the repeated addition or subtraction of 1 s, 2 s, 5 s, 10 s on a number line and on a hundreds chart Grade 2: identify, describe, and create, through investigation, growing and shrinking involving addition and subtraction, with and without the use of calculators Grade 2: identify and describe, through investigation, growing and shrinking generated by the repeated addition or subtraction of 1 s and 25 s on a number line and on a hundreds chart Grade 2: identify, describe, and create, through investigation, growing pattern and shrinking involving addition and subtraction, with and without the use of calculators Grade 2: identify repeating, growing, and shrinking found in reallife contexts Grade 2: create growing or shrinking Grade 2: create a repeating pattern by combining two attributes Grade 3: describe, extend, and create a variety of numeric and geometric Grade 3: identify, extend, and create a repeating pattern involving two attributes, using a variety of tools Grade 3: identify and describe, through investigation, number involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart Grade 3: extend repeating, growing and shrinking number Grade 6: describe and represent shrinking (where the terms are whole numbers), and investigate repeating involving rotations Grade 6: identify geometric, through investigation, using concrete materials or drawings, and represent them numerically Grade 6: determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph Grade 6: describe pattern rules (in words) that generate by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term, then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number Grade 6: determine a term, given its term number, by extending growing and shrinking that are generated by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term Grade 6: extend and create repeating that result from rotations, through investigation using a variety of tools 1 of 14 November 2005

2 Pattern Rules, and Algebraic Concept 1 Patterns represent identified regularities based on rules describing the elements. Grade 2: identify repeating, growing, and shrinking found in reallife contexts Grade 2: create growing or shrinking Grade 2: demonstrate, through investigation, an understanding that a pattern results from repeating an operation or making a repeated change to an attribute Grade 3: describe, extend, and create a variety of numeric and geometric Grade 3: demonstrate, through investigation, an understanding that a pattern results from repeating an action or making some other repeated change to an attribute Grade 3: demonstrate, through investigation, an understanding that a pattern results from repeating an operation or making some other repeated change to an attribute Grade 4: describe, extend, and create a variety of numeric and geometric, make predictions, related to the and investigate repeating involving reflections Grade 4: extend, describe and create repeating, growing, and shrinking number Grade 4: connect each term in a growing or shrinking pattern with its term number, and record the in a table of values that shows the term number and the term Grade 4: create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words Grade 4: make predictions related to repeating geometric and numeric Grade 4: extend and create repeating that result from reflections, through investigation using a variety of tools Grade 5: determine, through investigation, using a table of values, shrinking, and investigate repeating involving translations 2 of 14 November 2005

3 Pattern Rules, and Algebraic Concept 1 Patterns represent identified regularities based on rules describing the elements. Grade 5: create, identify, and extend numeric and geometric, using a variety of tools Grade 5: make predictions related to growing and shrinking geometric and numeric Grade 5: extend and create repeating that result from translations, through investigation using a variety of tools Concept 2 Any pattern can be represented in a variety of ways. Grade 1: represent a given repeating pattern in a variety of ways Grade 2: represent a given growing or shrinking pattern in a variety of ways Grade 3: create a number pattern involving addition or subtraction, given a pattern represented on a number line or a pattern rule expressed in words Grade 3: represent simple geometric using a number sequence, a number line, or a bar graph Grade 5: build a model to represent a number pattern presented in a table of values that shows the term number and the term Grade 6: identify geometric, through investigation, using concrete materials or drawings, and represent them numerically and strategies, the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area length width; Perimeter = (2 length) (2 width)] investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume area of base height) Grade 6: describe and represent shrinking (where the terms are whole numbers), and investigate repeating involving rotations 3 of 14 November 2005

4 Pattern Rules, and Algebraic Concept 2 Any pattern can be represented in a variety of ways. Grade 6: make tables of values, for growing given pattern rules, in words, then list the ordered pairs (with the first coordinate representing the term number and the second coordinate representing the term) and plot the points in the first quadrant, using a variety of tools Grade 6: determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph Grade 6: describe pattern rules (in words) that generate by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term, then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number Grade 6: Meas. develop the formulas for the area of a parallelogram (i.e., Area of parallelogram base height) and the area of a triangle [i.e., Area of triangle (base height) 2], using the area relationships among rectangles, parallelograms, and triangles Grade 6: Meas. determine, through and strategies, the relationship between the height, the area of the base, and the volume of a triangular prism, and generalize to develop the formula (i.e., Volume area of base height) 4 of 14 November 2005

5 Concept 3 Patterns underlie mathematical concepts and can also be found in the real world. K: recognize and use Grade 1: identify, describe, extend, and create repeating Grade 1: identify, describe, and extend, through investigation, geometric repeating involving one attribute Grade 1: identify and extend, through investigation, numeric repeating Grade 1: NS&N. count by 1 s, 2 s Grade 1: demonstrate an understanding of the concept of equality, using concrete materials, and addition and subtraction to 10 Grade 1: demonstrate examples of equality, through investigation, using a balance model Grade 1: 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: NS&N. count by 1 s, 2 s, 5 s and 10 s to 100 using a variety of tools and strategies Grade 1: NS&N. count backwards from 20 by 2 s and 5 s, using a variety of tools Grade 2: demonstrate an understanding of the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 18. Grade 2: demonstrate, through investigation, an understanding that a pattern results from repeating an operation or making a repeated change to an attribute Grade 2: demonstrate an understanding of the concept of equality by partitioning whole numbers to 17 in a variety of ways, using concrete materials Grade 3: identify and describe, through investigation, number involving multiplication, represented on a number line, on a calendar, and on a hundreds chart Grade 3: 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 Grade 3: 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) Grade 4: describe, extend, and create a variety of numeric and geometric, make predictions related to the, and investigate repeating involving reflections Grade 4: demonstrate an understanding of equality between pairs of expressions, using multiplication Grade 4: make predictions related to repeating geometric, and numeric Grade 4: extend and create repeating that result from reflections, through investigation using a variety of tools Pattern Rules, and Algebraic Grade 5: determine, through investigation, using a table of values, shrinking Grade 5: build a model to represent a number pattern presented in a table of values that shows the term number and the term Grade 5: NS&N. multiply decimal numbers by 10, 100, 1000 and , and divide decimal numbers by 10 and 100, using mental strategies and strategies, the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area length width; Perimeter (2 length) (2 width)] investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume area of base height) Grade 6: extend and create repeating that result from rotations, through investigation using a variety of tools Grade 6: NS&N. multiply whole numbers by 0.1, 0.01, and using mental strategies 5 of 14 November 2005

6 Pattern Rules, and Algebraic Concept 3 Patterns underlie mathematical concepts and can also be found in the real world. Grade 2: represent, through investigation with concrete materials and pictures, two number expressions that are equal, using the equal sign Grade 2: determine the missing number in equations involving addition and subtraction to 18, using a variety of tools and strategies Grade 2: identify, through investigation, and use the commutative property of addition to facilitate computation with whole numbers Grade 2: identify, through investigation, 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.) Grade 2: NS&N. count forward by 5 s, 10 s, and 25 s to 200, using number lines and hundreds charts, starting from multiples of 5 and 10 Grade 2: NS&N. count backwards by 10 s from 100 and any number less than 100, using number lines and hundreds charts Grade 2: NS&N. represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups Grade 4: determine, through investigation, the inverse relationship between multiplication and division Grade 4: identify, through investigation, and use the commutative property of multiplication to facilitate computation with whole numbers Grade 4: identify, through investigation, and use the distributive property of multiplication over addition to facilitate computation with whole numbers Grade 4: NS&N. demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to , using a variety of tools and strategies Grade 4: NS&N. add and subtract decimal numbers to tenths, using concrete materials and studentgenerated algorithms Grade 4: NS&N. multiply whole numbers by 10, 100 and 1000, and divide whole numbers by 10 and 100, using mental strategies Grade 4: Meas. describe, through investigation, the relationship between various units of length Grade 5: determine, through investigation using a table of values, shrinking, and investigate repeating involving translations Grade 6: NS&N. multiply and divide decimal numbers by 10, 100, 1000 and using mental strategies Grade 6: Meas. determine, through and strategies, the relationship between the height, the area of the base, and the volume of a triangular prism, and generalize to develop the formula (i.e., Volume area of base height) 6 of 14 November 2005

7 Pattern Rules, and Algebraic Concept 3 Patterns underlie mathematical concepts and can also be found in the real world. Grade 3: demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers Grade 3: identify and describe, through investigation, number involving addition, subtraction, represented on a number line, on a calendar, and on a hundreds chart Grade 3: create a number pattern involving addition or subtraction, given a pattern represented on a number line or a pattern rule expressed in words Grade 3: demonstrate, through investigation, an understanding that a pattern results from repeating an operation Grade 3: determine, through investigation, the inverse relationship between addition and subtraction Grade 3: identify, through investigation, and use the associative property of addition to facilitate computation with whole numbers Grade 3: NS&N. count forward by 5 s, 10 s, and 100 s to 1000 from various starting points, and by 25s to 1000 starting from multiples of 25, using a variety of tools and strategies Grade 3: NS&N. count backwards by 2 s, 5 s and 10 s from 100 using multiples of 2, 5 and 10 as starting points, using a variety of tools and strategies Grade 5: create, identify, and extend numeric and geometric, using a variety of tools (e.g. concrete materials, paper and pencil, calculators, spreadsheets) Grade 5: make predictions related to growing and shrinking geometric and numeric Grade 5: extend and create repeating that result from translations, through investigation using a variety of tools Grade 5: NS&N. demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to , using a variety of tools and strategies Grade 5: Meas. solves problems requiring conversion from metres to centimetres and from kilometres to metres Grade 6: investigate repeating involving rotations Grade 6: NS&N. demonstrate an understanding of place value in whole numbers and decimal numbers from to , using a variety of tools and strategies 7 of 14 November 2005

8 Pattern Rules, and Algebraic Concept 4 Data can be arranged to highlight and relationships. Grade 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: NS&N. demonstrate, using concrete materials, the concept of conservation of number Grade 1: NS&N. relate numbers to the anchors of 5 and 10 Grade 1: describe numeric repeating in a hundreds chart Grade 2: identify and describe, through investigation, growing and shrinking generated by the repeated addition or subtraction of 1 s and 2 s on a number line and on a hundreds chart Grade 2: NS&N. count forward by 1 s and 2 s to 200, using number lines and hundreds charts Grade 2: identify and describe, through investigation, growing and shrinking generated by the repeated addition or subtraction of 1 s, 2 s, 5 s, 10 s and 25 s on a number line and on a hundreds chart Grade 3: identify and describe, through investigation, number involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart Grade 4: connect each term in a growing or shrinking pattern with its term number, and record the in a table of values that shows the term number and the term Grade 5: determine, through investigation, using a table of values, shrinking Grade 5: build a model to represent a number pattern presented in a table of values that shows the term number and the term Grade 5: 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 or the pattern rule in words Grade 5: determine, through investigation, using a table of values, shrinking Grade 5: build a model to represent a number pattern presented in a table of values that shows the term number and the term Grade 6: describe and represent shrinking (where the terms are whole numbers) Grade 6: make tables of values, for growing given pattern rules, in words, then list the ordered pairs (with the first coordinate representing the term number and the second coordinate representing the term) and plot the points in the first quadrant, using a variety of tools Grade 6: determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph 8 of 14 November 2005

9 Pattern Rules, and Algebraic Concept 5 between quantities can be described using rules involving variables. Grade 2: demonstrate an understanding of the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 18 Grade 2: determine the missing number in equations involving addition and subtraction to 18, using a variety of tools and strategies Grade 3: demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers Grade 3: determine the missing number in equations involving addition and subtraction of one-digit numbers, using a variety of tools and strategies Grade 3: demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers Grade 3: determine the missing number in equations involving addition and subtraction of two-digit numbers, using a variety of tools and strategies Grade 4: demonstrate an understanding of equality between pairs of expressions, using addition, subtraction, and multiplication Grade 4: determine the missing number in equations involving multiplication of one- and two-digit numbers, using a variety of tools and strategies Grade 4: Meas. determine the relationships among units and measureable attributes, including the area and perimeter of rectangles Grade 4: Meas. determine through investigation, the relationship between the side lengths of a rectangle and its perimeter and area Grade 5: demonstrate, through investigation, an understanding of variables as unknown quantities represented by a symbol Grade 5: demonstrate, through investigation, an understanding of the use of variables in equations Grade 5: demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates Grade 5: demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other symbol Grade 5: determine the missing number in equations involving addition, subtraction, multiplication, or division and one- or two-digit numbers, using a variety of tools and strategies Grade 5: Meas. determine the relationships among units and measureable attributes, including the area of a rectangle and the volume of a rectangular prism and strategies, the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area length width; Perimeter (2 length) (2 width) 9 of 14 November 2005

10 Pattern Rules, and Algebraic Concept 5 between quantities can be described using rules involving variables. Grade 5: determine the missing number in equations involving addition, subtraction, multiplication, or division and one- or two-digit numbers, using a variety of tools and strategies Grade 5: Meas. determine the relationships among units and measureable attributes, including the area of a rectangle and the volume of a rectangular prism and strategies, the relationships between the length and width of a rectangle and its area and perimeter investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume area of base height) Grade 6: describe and represent shrinking (where the terms are whole numbers) Grade 6: use variables in simple algebraic expressions and equations to describe relationships Grade 6: describe pattern rules (in words) that generate by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term, then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number Grade 6: demonstrate an understanding of different ways in which variables are used Grade 6: identify, through investigation, the quantities in an equation that vary and those that remain constant Grade 6: solve problems that use two or three symbols or letters as variables to represent different unknown quantities 10 of 14 November 2005

11 Pattern Rules, and Algebraic Concept 5 between quantities can be described using rules involving variables. Grade 6: determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies Grade 6: Meas. determine the relationships among units and measurable attributes, including the area of a parallelogram, the area of a triangle, and the volume of a triangular prism Grade 6: Meas. develop the formula for the area of a parallelogram (i.e., Area of parallelogram base height) and the area of a triangle [i.e., Area of triangle (base height) 2], using the area relationships among rectangles, parallelograms and triangles Grade 6: Meas. determine, through and strategies, the relationship between the height, the area of the base, and the volume of a triangular prism, and generalize to develop the formula (i.e. Volume area of base height) Skill 1 Sorts and classifies objects based on attributes. K: NS&N. sort and classify objects into sets according to specific characteristics, and describe those characteristics K: G&SS. sort three-dimensional objects K: G&SS. sort two-dimensional shapes Grade 1: G&SS. sort and classify twodimensional shapes and threedimensional figures by their geometric properties Grade 1: G&SS. sort and classify common two-dimensional shapes by their attributes, using concrete materials and pictorial representations Grade 3: G&SS. sort two-dimensional shapes and three-dimensional figures by their geometric properties Grade 3: G&SS. sort various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) by their geometric properties (i.e., number of sides, side lengths; number of interior angles; number of right angles) 11 of 14 November 2005

12 Pattern Rules, and Algebraic Skill 1 Sorts and classifies objects based on attributes. Grade 1: G&SS. sort and classify twodimensional shapes and threedimensional figures by their attributes Grade 1: G&SS. classify common two-dimensional shapes by their attributes, using concrete materials and pictorial representations Grade 1: G&SS. sort and classify common three-dimensional figures by their attributes, using concrete materials and pictorial representations Grade 1: DM&P. demonstrate an ability to organize objects into categories by sorting and classifying objects using one attribute, and by describing informal sorting experiences Grade 1: G&SS. sort and classify common three-dimensional figures by their attributes, using concrete materials and pictorial representations Grade 2: G&SS. sort and classify twodimensional shapes and threedimensional figures by their geometric properties Grade 2: G&SS. sort and classify various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) by their geometric properties (i.e., number of sides or number of vertices), using concrete materials and pictorial representations Grade 2: G&SS. sort and classify various three-dimensional figures (i.e., cubes, prisms, pyramids) by their geometric properties (i.e., number and shape of faces), using concrete materials Grade 2: DM&P. demonstrate an ability to organize objects into categories by sorting and classifying objects using two attributes simultaneously Grade 3: G&SS. sort prisms and pyramids by geometric properties (i.e., number and shape of faces, number of edges, number of vertices), using concrete materials Grade 3: DM&P. demonstrate an ability to organize objects into categories, by sorting and classifying objects using two or more attributes simultaneously Grade 3: DM&P. 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 4: G&SS. classify quadrilaterals and three-dimensional figures by their geometric properties Grade 4: G&SS. sort and classify different types of quadrilaterals (i.e., rectangle, square, trapezoid, parallelogram, rhombus) by their geometric properties (i.e., sides of equal length, parallel sides, symmetry, number of right angles) Grade 4: G&SS. classify prisms and pyramids by their geometric properties (i.e., shape of faces, number of edges, number of vertices), using concrete materials 12 of 14 November 2005

13 Pattern Rules, and Algebraic Skill 1 Sorts and classifies objects based on attributes. Grade 5: G&SS. classify twodimensional shapes by side and angle properties, and compare and sort three-dimensional figures Grade 5: G&SS. classify acute, right, obtuse, and straight angles Grade 5: G&SS. classify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral) according to angle and side properties Grade 6: G&SS. sort and classify quadrilaterals by geometric properties related to symmetry, angles, and sides, through and strategies Grade 6: G&SS. sort polygons according to the number of lines of symmetry and the order of rotational symmetry, through investigation using a variety of tools Skill 2 Applies a provided pattern rule or algebraic formula. Grade 2: create growing or shrinking Grade 3: extend repeating, growing and shrinking number Grade 3: extend repeating, growing and shrinking number Grade 3: NS&N. compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways, using concrete materials Grade 4: extend a variety of numeric and geometric Grade 4: extend repeating that result from reflections, through Grade 6: solve problems that use two or three symbols or letters as variables to represent different unknown quantities Grade 6: Meas. solve problems involving the estimation and calculation of the area of triangles and the are of parallelograms 13 of 14 November 2005

14 Pattern Rules, and Algebraic Skill 2 Applies a provided pattern rule or algebraic formula. Grade 5: identify, and extend numeric and geometric, using a variety of tools Grade 5: 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 or the pattern rule in words Grade 5: extend repeating that result from translations, through Grade 5: Meas. solve problems requiring conversion from metres to centimetres and from kilometres to metres Grade 6: extend repeating that result from translations, through Grade 6: Meas. solve problems requiring conversion from larger to smaller metric units Grade 6: Meas. apply the relationship between units used to measure area (i.e., square centimetres, square metres) to solve problems that involve conversions from square metres to square centimetres 14 of 14 November 2005