# Alberta Mathematics Kindergarten to Grade 12 Scope and Sequence 2017

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1 Alberta Mathematics Kindergarten to Grade 12 Scope and Sequence 2017

2 Alberta Mathematics Kindergarten to Grade 12 Scope and Sequence ISBN Questions or concerns regarding this document can be addressed to the Director, Mathematics, Arts and Communication Branch, Alberta Education. Telephone To be connected toll-free inside Alberta, dial first. The primary intended audience for this document is: Administrators Counsellors General Audience Parents Students Teachers Copyright 2017, Alberta Education. The Crown in Right of Alberta, as represented by the Minister of Education. Every effort has been made to provide proper acknowledgement of original sources. If cases are identified where this has not been done, please notify Alberta Education so appropriate corrective action can be taken. This document is issued under the Open Government Licence Alberta ( Please note that the terms of this licence do not apply to any third-party materials included in this document. The document is available through the Open Government Portal at

3 Table of Contents Introduction... 1 K 9 Scope and Sequence Number... 2 K 9 Scope and Sequence Patterns and Relations... 4 K 9 Scope and Sequence Shape and Space... 5 K 9 Scope and Sequence Statistics and Probability C, 20-1 and 30-1 Scope and Sequence C, 20-2 and 30-2 Scope and Sequence , 20-3 and 30-3 Scope and Sequence... 12

4 Introduction The Mathematics Kindergarten to Grade 12 Scope and Sequence has been derived from the Alberta Program of Studies for Mathematics K 9 (2007, Updated 2016) and the Alberta Program of Studies for Mathematics (2008). The scope and sequence outlines the progression of concepts in the programs of study. Specifically, the grades K 9 scope and sequence is divided into the four strands that are in the program of studies: Number, Patterns and Relations, Shape and Space, and Statistics and Probability. The last column in each of these tables indicates some of the grades high school (HS) concepts that are related to each row of concepts. The grades scope and sequence is divided into three separate tables, one for each of the course sequences (-1, -2 and -3). The column titled Prerequisite Knowledge indicates the last grade in which students would have studied a particular concept. Background The scope and sequence, recommended in the Mathematics Review Report to Premier and Minister, highlights the connections between strands, topics and grades. This scope and sequence is a support resource and does not replace the programs of study. It identifies concepts, rather than general and specific outcomes, and does not include the mathematical processes, ICT outcomes or 2016 clarification notes identified in the programs of study. To gain a more complete understanding of the student experience in Kindergarten to Grade 12 Mathematics, and to view the general and specific outcomes in their entirety, the programs of study documents should be examined. The sequences identified in this document are not intended to be exhaustive or prescriptive. Strands/Topics K 9 Strands Number (N) Patterns and Relations (PR) Shape and Space (SS) Statistics and Probability (SP) Topics Algebra (A) Algebra and Number (AN) Geometry (G) Logical Reasoning (LR) Mathematics Research Project (RP) Measurement (M) Number (N) Number and Logic (NL) Permutations, Combinations and Binomial Theorem (PCBT) Probability (P) Relations and Functions (RF) Statistics (S) Trigonometry (T) Alberta Mathematics K 9 Scope and Sequence Introduction 1

5 Alberta Mathematics K 9 Scope and Sequence Number K HS Counting Forward and backward by 1s (1 10) (N1) Forward by 1s, 5s and 10s (0 100); forward by 2s (0 20); and backward by 1s (20 0) (N1) Forward and backward by 2s, 5s and 10s (0 100) (N1) Forward and backward by 3s, 4s, 5s, 10s, 25s and 100s (0 1000) (N1) Ordinal numbers to tenths (N3) Subitizing 1 5 (N2) Subitizing 1 10 (N2) Understanding counting (N3) Conservation of number (N7) Estimate to 20 using referents (N6) Estimate to 100 using referents (N6) Estimate to 1000 using referents (N4) Number Concepts Natural numbers to 10 (N3, N4, N5) Whole numbers to 20 (N4, N5) Whole numbers to 100 (N4, N5) Even and odd numbers (N2) Place value to 100 (N7) Whole numbers to 1000 (N2, N3) Place value to 1000 (N5) Whole numbers to (N1, N2) and decimals to hundredths (N9) Whole numbers to (N1) and decimals to thousandths (N8, N10) Integers (N7) Percent (N6) Ratio (N5) Place value: greater than 1 million and less than thousandths (N1) Solve problems 1 100% (N3) Perfect squares and square roots (N1) Approximate square root (N2) Percent 0 and > 100 (N3) Square roots of rational numbers (N5, N6) Powers with whole-number exponents (N1) and operations on powers (N2) Factors, multiples and roots (10C AN1) Powers (10C AN3) Irrational numbers (10C AN2) Fractions, like denominators and parts of a whole (N13) Fractions and parts of a whole or a set (N8) Decimals to fractions and fractions to decimals (N10) Fractions, like and unlike denominators and equivalent fractions (N7) Decimals to fractions and fractions to decimals (N9) Improper fractions and mixed numbers (N4) Fractions and terminating and repeating decimals (N4) Fractions, decimals and whole numbers (N7) Rate and ratio (N4, N5) Rational numbers (N3) Rational expressions (20-1 AN4, 30-2 RF1) Proportional reasoning (10C M2, 10-3 N1) Alberta Mathematics K 9 Scope and Sequence Number 2

6 K HS Number Facts Addition and subtraction strategies to recall to a sum of 5 (N10) Addition and subtraction strategies to recall to (N10) Addition and subtraction understand, recall and apply to (N10) Multiplication and division understand and recall to 5 x 5 (N11, N12) Multiplication and division strategies to 9 x 9 recall to 7 x 7 (N5) Multiplication and division understand, recall and apply to 9 x 9 (N3) All outcomes where operations are used Addition and Subtraction Whole numbers to 20 (N9) Identify 1 or 2 more/less than a number, up to 20 (N8) Whole numbers to 100 (N9) Effect of zero (N8) Whole numbers to 1000 (N9) Mental math strategies (N6, N7) Whole numbers to (N3) and decimals to hundredths (N11) Decimals to thousandths (N11) Problems using whole numbers and decimals (N2) Order of operations (whole numbers, no exponents) (N9) Decimals (N2) Fractions (N5) Integers (N6) Rational numbers, including order of operations (N3, N4) Rational expressions (20-1 AN5, 30-2 RF2) Radical expressions (20-1 AN2) Estimation strategies (N8) Estimation strategies in context (N2) Multiplication and Division Multiplication, including estimation (2- or 3-digit by 1-digit) (N6) Division, including estimation (1-digit divisor, up to 2-digit dividend) (N7) Multiply by 0 and 1 and divide by 1 (N4) Multiplication (two 2-digit) (N5) Division (3-digit by 1-digit) and remainders (N6) Estimation strategies in context (N2) Decimals (1-digit multiplier and divisor) (N8) Problems using whole numbers and decimals (N2) Order of operations (whole numbers, no exponents) (N9) Decimals (N2) Divisibility rules (including 0) (N1) Fractions (N6) Integers (N7) Rational numbers, including order of operations (N3, N4) Rational expressions (20-1 AN5, 30-2 RF2) Radical expressions (20-1 AN2) Mental math strategies for multiplication (N4) Factors and multiples, prime and composite (N3) Factors (10C AN1) Polynomial expressions (10C AN4, AN5) Alberta Mathematics K 9 Scope and Sequence Number 3

7 Alberta Mathematics K 9 Scope and Sequence Patterns and Relations K HS Patterns and Relations Repeating patterns, 2 or 3 elements (PR1) Repeating patterns, 2 to 4 elements (PR1) Translate from one representation to another (PR2) Repeating patterns, 3 to 5 elements (PR1) Increasing patterns, numerical (to 100) and non-numerical (PR2) Increasing and decreasing patterns, numerical (to 1000) and non-numerical (PR1, PR2) Patterns and relationships in tables, charts or diagrams (PR1, PR3, PR4) Translate representations (table, chart, concrete materials) (PR2) Pattern rule for predictions (PR1) Graphs and tables (PR1, PR2) Oral patterns, written patterns and linear relations (PR1) Table of values, graph, analyze and problem solve with linear relations (PR2) Graph and analyze twovariable linear relations (PR1) Problem-solving using linear equations (PR1) Graph, analyze and interpolate and extrapolate linear relations (PR2) Linear relations (10C RF3-7) Relationships among data and graphs (10C RF1) Arithmetic and geometric sequences and series (20-1 RF9, RF10) Sort and Sorting Rule Single attribute (set of objects) (PR2) Single attribute (set of objects) (PR3) Two attributes (set of objects) (PR3) One or more attributes (set of objects or numbers) (PR3) Equations, Inequalities and Expressions Balance and imbalance (PR4) Equal symbol (PR5) Equality and inequality using symbols (PR4, PR5) One-step equation, addition and subtraction (symbol for unknown number) (PR4) Express problem as one-step equation (symbol for unknown number) and solve (PR5, PR6) Express problem as one-step equation (letter variable for unknown number) and solve (PR2, PR3) Express problem as equation, letter variable for unknown number and solve (PR3, PR4) Preservation of equality (PR5) One-step and two-step linear equations (single variable) (PR6, PR7) Difference between expression and equation (PR4) Evaluate using given value (PR5) Preservation of equality (PR3) Two-step linear equations (single variable) (PR2) Multi-step linear equations (single variable) (PR3) Linear inequalities (single variable) (PR4) Polynomials (degree less than or equal to 2) (PR5) Manipulate formulas (10-3 A1) Systems of linear equations (10C RF9) Linear and quadratic inequalities (20-1 RF7, RF8) Multiplying and factoring polynomials (10C AN4, AN5) Polynomial operations (PR6, PR7) Alberta Mathematics K 9 Scope and Sequence Patterns and Relations 4

8 Alberta Mathematics K 9 Scope and Sequence Shape and Space K HS Measurement Direct comparison (length, mass and volume) (SS1) Measurement as comparing (SS1) Nonstandard units (length, height, distance around and mass) (SS2, SS3, SS4) Days to a week and months to a year (SS1) Length and perimeter (cm, m); mass (g, kg) (SS3, SS4, SS5) Nonstandard and standard units of time (SS1, SS2) Area of regular and irregular shapes (cm 2, m 2 ) (SS3) Time (digital and analog clocks, 24-hour clocks) (SS1) Length (mm), volume (cm 3, m 3 ) and capacity (ml, L) (SS3, SS4, SS5) Rectangles, given perimeter or area (SS2) Perimeter (polygons), area (rectangles) and volume (rectangular prisms) (SS3) Area (triangles, parallelograms and circles) (SS2) Surface area and nets (rectangular and triangular prisms, cylinders) (SS2, SS3) Volume (rectangular and triangular prisms, cylinders) (SS4) Surface area of composite 3-D objects (SS2) Surface area, volume (10C M3) Area (10-3 M4) SI and imperial units (10C M1; 10-3 M3) Calendar dates (SS2) Identify 90 angles (SS1) Angles (SS1) Sum of interior angles (triangle and quadrilateral) (SS2) Circles (radius, diameter and circumference) (SS1) Circle properties (SS1) Angles (10-3 G6, 30-1 T1) Line and angle problems (10-3 G5, G6) Properties of angles and triangles (20-2 G1, G2) Pythagorean theorem (SS1) Pythagorean theorem (10-3 G2) Primary trigonometric ratios (10C M4, 10-3 G4) Alberta Mathematics K 9 Scope and Sequence Shape and Space 5

9 K HS Geometric Characteristics and Relationships Sort 3-D objects, single attribute (SS2) Build 3-D objects (SS3) Sort (one attribute), replicate and compare 3-D objects and 2-D shapes (SS2, SS3) Compare 2-D shapes to parts of 3-D objects (SS4) Sort (two attributes), describe, compare and construct 3-D objects and 2-D shapes (SS6, SS7, SS8) Identify 2-D shapes as parts of 3-D objects (SS9) Sort regular and irregular polygons (triangles, quadrilaterals, pentagons, hexagons and octagons) (SS7) 3-D objects (faces, edges and vertices) (SS6) Describe and construct rectangular and triangular prisms (SS4) Quadrilaterals (rectangles, squares, trapezoids, parallelograms and rhombuses) (SS7) Parallel, intersecting, perpendicular, vertical and horizontal (edges, faces and sides) (SS6) Triangles (scalene, isosceles, equilateral, right, obtuse and acute) (SS4) Regular and irregular polygons (SS5) Geometric constructions (SS3) Top, front and side views (3-D objects) (SS5) Similarity, polygons (SS3) Similarity, polygons (10-3 G3) Line and angle problems (10-3 G5, G6) 3-D objects and their views (20-3 G3, G4) Position and Transformations Orientation and measurement (SS5) Congruency (SS5) Line symmetry (SS6) Single transformation concretely (SS8, SS9) Plot points (1st quadrant of Cartesian plane) (SS8) Single transformation (SS6, SS9) Combination of transformations of 2-D shapes (SS7) Plot points (all quadrants) (SS4) Single transformation (all quadrants) (SS5) Congruency, polygons (SS6) Scale diagrams (SS4) Line and rotation symmetry (SS5) Scale (20-2 M2, M3; 20-3 G2, G4) Transformations (30-3 G3) Quadratic functions (20-1 RF3, 20-2 RF1) Alberta Mathematics K 9 Scope and Sequence Shape and Space 6

10 Alberta Mathematics K 9 Scope and Sequence Statistics and Probability K HS Data Collection Gather and record data (SP1) Collect and organize firsthand data (SP1) First-hand and second-hand data (SP1) Methods of collecting data (SP2) Data project (SP3) Factors that affect data collection (SP1) Research project (20-2 RP1) Population vs. sample (SP2) Data and Graphs Concrete graphs and pictographs (one-to-one correspondence) (SP2) Bar graphs (one-to-one correspondence) (SP2) Bar graphs and pictographs (many-to-one correspondence) (SP1, SP2) Double bar graphs (SP2) Line graphs (SP1) Graph collected data and analyze graph (SP3) Circle graphs (SP3) Critique representation of data in graphs (SP1) Data project (SP3) Graphs (20-3 S1) Statistical data (20-2 S2) Normal distribution (20-2 S1) Central tendency, range and outliers (SP1, SP2) Central tendency (30-3 S1) Probability Likelihood of one or two outcomes (using words) (SP3, SP4) Experimental vs. theoretical probability (SP4) Experimental vs. theoretical probability (two events, sample space) (SP5, SP6) Probability as ratio, fraction and percent (SP4) Independent events (SP2) Role of probability in society (SP4) Probability problems (30-2 P1 3, 30-3 P1) Fundamental counting principle (30-1 PCBT1, 30-2 P4) Alberta Mathematics K 9 Scope and Sequence Statistics and Probability 7

16 Prerequisite Knowledge Relations and Functions Problem solving using linear equations (Grade 9 PR1) Slope (A2) Linear relations (A1) Reasoning All Number and Shape and Space outcomes Puzzles and games that involve spatial reasoning (G1) Puzzles and games that involve numerical reasoning (N1) Puzzles and games that involve logical reasoning (N1) Data and Graphs Central tendency (Grade 7 SP1, SP2) Problem solving (S1) Central tendency (S1) Data project (Grade 9 SP3) Percentiles (S2) Probability Independent events (Grade 8 SP2) Probability (P1) Alberta Mathematics 10-3, 20-3 and 30-3 Scope & Sequence 13

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