BC Education - Introduction to Mathematics K to 7

Overview

This document contains four tables:
NUMBER
PATTERNS AND RELATIONS
SHAPE AND SPACE
STATISTICS AND PROBABILITY

NUMBER
Number Concepts Students: use numbers to describe quantities represent numbers in multiple ways	Number Operations Students: demonstrate an understanding of and proficiency with calculations decide which arithmetic operation or operations can be used to solve a problem and then solve the problem
KINDERGARTEN TO GRADE 1 Recognize, describe, and use numbers from 0 to 100 in a variety of familiar settings	KINDERGARTEN TO GRADE 1 Demonstrate and use a variety of methods to show the processes of addition and subtraction on one-digit whole numbers
GRADE 2 TO 3 Develop a number sense for whole numbers from 0 to 1000 and common fractions to tenths	GRADE 2 TO 3 Use a variety of strategies to apply a basic operation (+, -, x, ÷) on whole numbers and use these operations in solving problems. Choose, use, and defend the appropriate calculation strategy or technology to solve problems
GRADE 4 Demonstrate a number sense for whole numbers from 0 to 10 000 and for proper fractions	GRADE 4 Apply arithmetic operations on whole numbers and illustrate their use in solving problems. Demonstrate an understanding of the addition and subtraction of decimal fractions
GRADE 5 Demonstrate a number sense for whole numbers, from 0 to 100 000, and explore proper fractions and decimal fractions	GRADE 5 Apply arithmetic operations on whole numbers and decimal fractions and illustrate the use of decimal fractions in solving problems
GRADE 6 Develop a number sense for common fractions and explore number sense for whole numbers	GRADE 6 Apply arithmetic operations on whole numbers and decimal fractions in solving problems
GRADE 7 Demonstrate a number sense for decimal fractions and integers (including whole numbers)	GRADE 7 Apply arithmetic operations on decimal fractions and integers and illustrate their use in solving problems. Illustrate the use of ratios, rates, percentages, and decimal numbers in solving problems
GRADE 8 Demonstrate number sense about rational numbers, including common fractions, integers, and whole numbers	GRADE 8 Apply the four basic arithmetic operations to rational numbers to solve real-world problems. Apply the concepts of ratio, rate, percentage, and proportion to solve problems in practical contexts

PATTERNS AND RELATIONS
Patterns
Students:

use patterns to describe the world around them and to solve problems

Variables and Equations
Students:

represent algebraic expressions in multiple ways

Relations and Functions

Students:

use algebraic and graphical models to generalize patterns, make predictions, and solve problems

KINDERGARTEN TO GRADE 1
Identify, create, and compare patterns that arise from their daily experiences KINDERGARTEN TO GRADE 1
Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6 KINDERGARTEN TO GRADE 1
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 2 TO 3
Investigate, establish, and communicate rules for numerical and non-numerical patterns that arise from daily and mathematical experiences, and use these rules to make predictions GRADE 2 TO 3
Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6 GRADE 2 TO 3
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 4
Investigate, establish, and communicate rules for, and predictions from, numerical and non-numerical patterns GRADE 4
Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6 GRADE 4
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 5
Construct, extend, and summarize patterns, using rules, charts, mental mathematics, and calculators GRADE 5
Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6 GRADE 5
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 6
Use relationships to summarize, generalize, and extend patterns GRADE 6
Use informal and concrete representations of equality and operations on equality to solve problems GRADE 6
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 7
Express patterns in terms of variables and use expressions containing variables to make predictions GRADE 7
Use variables and equations to express, summarize, and apply relationships as problem-solving tools in a restricted range of contexts GRADE 7
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

GRADE 8
Create and use patterns, variables, expressions, equations, and graphs to solve problems. GRADE 8
Solve and verify one-step and two-step linear equations that have rational number solutions GRADE 8
Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

PATTERNS AND RELATIONS
Patterns Students: use patterns to describe the world around them and to solve problems	Variables and Equations Students: represent algebraic expressions in multiple ways	Relations and Functions Students: use algebraic and graphical models to generalize patterns, make predictions, and solve problems
KINDERGARTEN TO GRADE 1 Identify, create, and compare patterns that arise from their daily experiences	KINDERGARTEN TO GRADE 1 Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6	KINDERGARTEN TO GRADE 1 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 2 TO 3 Investigate, establish, and communicate rules for numerical and non-numerical patterns that arise from daily and mathematical experiences, and use these rules to make predictions	GRADE 2 TO 3 Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6	GRADE 2 TO 3 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 4 Investigate, establish, and communicate rules for, and predictions from, numerical and non-numerical patterns	GRADE 4 Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6	GRADE 4 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 5 Construct, extend, and summarize patterns, using rules, charts, mental mathematics, and calculators	GRADE 5 Learning outcomes for Patterns and Relations (Variables and Equations) commence in Grade 6	GRADE 5 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 6 Use relationships to summarize, generalize, and extend patterns	GRADE 6 Use informal and concrete representations of equality and operations on equality to solve problems	GRADE 6 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 7 Express patterns in terms of variables and use expressions containing variables to make predictions	GRADE 7 Use variables and equations to express, summarize, and apply relationships as problem-solving tools in a restricted range of contexts	GRADE 7 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10
GRADE 8 Create and use patterns, variables, expressions, equations, and graphs to solve problems.	GRADE 8 Solve and verify one-step and two-step linear equations that have rational number solutions	GRADE 8 Learning outcomes for Patterns and Relations (Relations and Functions) commence in Grade 10

SHAPE AND SPACE
Measurement

3-D Objects and 2-D Shapes

Transformations

Students:

describe and compare real-world phenomena using either direct or indirect measurement
Students:

describe the characteristics of 3-D objects and 2-D shapes and analyse the relationships among them
Students:

perform, analyse, and create transformations

KINDERGARTEN TO GRADE 1
Estimate, measure, and compare measures using whole numbers and non-standard units of measure KINDERGARTEN TO GRADE 1
Explore, sort, and classify real-world and three-dimensional objects according to their properties KINDERGARTEN TO GRADE 1
Describe verbally the relative position of both three-dimensional objects and two-dimensional shapes

GRADE 2 TO 3
Measure, estimate, and compare, using whole numbers and non-standard and standard units of measure GRADE 2 TO 3
Describe, classify, construct, and relate three-dimensional objects and two-dimensional shapes using common language to describe their properties GRADE 2 TO 3
Use positional language, numbers, and directional words to describe the relative positions of objects in one dimension and to communicate motion in real-world contexts

GRADE 4
Estimate, measure, and compare quantities, using decimal numbers and standard units of measure GRADE 4
Describe, classify, construct, and relate three-dimensional objects and two-dimensional shapes, using mathematical vocabulary to describe their properties GRADE 4
Use numbers and directional words to describe the relative positions of objects in two dimensions, using real-world contexts

GRADE 5
Use measurement concepts, appropriate tools, and the results of measurements to solve problems in real-life contexts GRADE 5
Use the visualization of two- dimensional shapes and three-dimensional objects to solve problems related to spatial relation GRADE 5
Describe motion in terms of a slide, a turn, or a flip

GRADE 6
Solve problems involving perimeter, area, surface area, volume, and angle measurement GRADE 6
Use visualization and symmetry to solve problems involving classification and sketching GRADE 6
Create patterns and designs that incorporate symmetry, translations, tessellations, and reflections

GRADE 7
Solve problems involving the properties of circles and their relationships to angles and time zones GRADE 7
Link angle measurements to the properties of parallel lines GRADE 7
Create and analyse patterns and designs using congruence, symmetry, translation, rotation, and reflection

GRADE 8
Apply the Pythagorean relationship to solve direct and indirect measurement problems. Discover patterns in measurement, and generalize procedures to solve problems involving area, perimeter, volume and surface area GRADE 8
Link angle measures and the properties of parallel lines to the classification and properties of quadrilaterals GRADE 8
Create and analyse design problems and architectual designs using the properties of scaling, proportion, and networks

SHAPE AND SPACE
Measurement	3-D Objects and 2-D Shapes	Transformations
Students: describe and compare real-world phenomena using either direct or indirect measurement	Students: describe the characteristics of 3-D objects and 2-D shapes and analyse the relationships among them	Students: perform, analyse, and create transformations
KINDERGARTEN TO GRADE 1 Estimate, measure, and compare measures using whole numbers and non-standard units of measure	KINDERGARTEN TO GRADE 1 Explore, sort, and classify real-world and three-dimensional objects according to their properties	KINDERGARTEN TO GRADE 1 Describe verbally the relative position of both three-dimensional objects and two-dimensional shapes
GRADE 2 TO 3 Measure, estimate, and compare, using whole numbers and non-standard and standard units of measure	GRADE 2 TO 3 Describe, classify, construct, and relate three-dimensional objects and two-dimensional shapes using common language to describe their properties	GRADE 2 TO 3 Use positional language, numbers, and directional words to describe the relative positions of objects in one dimension and to communicate motion in real-world contexts
GRADE 4 Estimate, measure, and compare quantities, using decimal numbers and standard units of measure	GRADE 4 Describe, classify, construct, and relate three-dimensional objects and two-dimensional shapes, using mathematical vocabulary to describe their properties	GRADE 4 Use numbers and directional words to describe the relative positions of objects in two dimensions, using real-world contexts
GRADE 5 Use measurement concepts, appropriate tools, and the results of measurements to solve problems in real-life contexts	GRADE 5 Use the visualization of two- dimensional shapes and three-dimensional objects to solve problems related to spatial relation	GRADE 5 Describe motion in terms of a slide, a turn, or a flip
GRADE 6 Solve problems involving perimeter, area, surface area, volume, and angle measurement	GRADE 6 Use visualization and symmetry to solve problems involving classification and sketching	GRADE 6 Create patterns and designs that incorporate symmetry, translations, tessellations, and reflections
GRADE 7 Solve problems involving the properties of circles and their relationships to angles and time zones	GRADE 7 Link angle measurements to the properties of parallel lines	GRADE 7 Create and analyse patterns and designs using congruence, symmetry, translation, rotation, and reflection
GRADE 8 Apply the Pythagorean relationship to solve direct and indirect measurement problems. Discover patterns in measurement, and generalize procedures to solve problems involving area, perimeter, volume and surface area	GRADE 8 Link angle measures and the properties of parallel lines to the classification and properties of quadrilaterals	GRADE 8 Create and analyse design problems and architectual designs using the properties of scaling, proportion, and networks

STATISTICS AND PROBABILITY
Data Analysis
Students:

collect, display, and analyse data to make predictions about a population

Chance and Uncertainty
Students:

use experimental or theoretical probability to represent and solve problems involving uncertainty

KINDERGARTEN TO GRADE 1
Collect, organize, and analyse (with assistance), data based on first-hand information KINDERGARTEN TO GRADE 1
Describe concepts of chance and chance events using ordinary vocabulary

GRADE 2 TO 3
Collect data based on first- and second-hand information, display results in more than one way, interpret data, and make predictions GRADE 2 TO 3
Use simple experiments designed by others to illustrate and explain probability and chance

GRADE 4
Collect first- and second-hand data, assess and validate the data collection process, and graph the data GRADE 4
Conduct simple probability experiments to explain outcomes

GRADE 5
Develop and implement a plan for the collection, display, and analysis of data gathered from appropriate samples GRADE 5
Predict outcomes, conduct experiments, and communicate the probability of single events

GRADE 6
Develop and implement a plan for the collection, display, and analysis of data gathered from appropriate samples GRADE 6
Use numbers to communicate the probability of single events from experiments and models

GRADE 7
Develop and implement a plan for the collection, display, and analysis of data using measures of variability and central tendency GRADE 7
Create and solve problems using probability

GRADE 8
Develop and implement a plan for the collection, display, and analysis of the data, using technology as required. Evaluate and use measures of central tendency and variability GRADE 8
Compare theoretical and experimental probability of independent events

STATISTICS AND PROBABILITY
Data Analysis Students: collect, display, and analyse data to make predictions about a population	Chance and Uncertainty Students: use experimental or theoretical probability to represent and solve problems involving uncertainty
KINDERGARTEN TO GRADE 1 Collect, organize, and analyse (with assistance), data based on first-hand information	KINDERGARTEN TO GRADE 1 Describe concepts of chance and chance events using ordinary vocabulary
GRADE 2 TO 3 Collect data based on first- and second-hand information, display results in more than one way, interpret data, and make predictions	GRADE 2 TO 3 Use simple experiments designed by others to illustrate and explain probability and chance
GRADE 4 Collect first- and second-hand data, assess and validate the data collection process, and graph the data	GRADE 4 Conduct simple probability experiments to explain outcomes
GRADE 5 Develop and implement a plan for the collection, display, and analysis of data gathered from appropriate samples	GRADE 5 Predict outcomes, conduct experiments, and communicate the probability of single events
GRADE 6 Develop and implement a plan for the collection, display, and analysis of data gathered from appropriate samples	GRADE 6 Use numbers to communicate the probability of single events from experiments and models
GRADE 7 Develop and implement a plan for the collection, display, and analysis of data using measures of variability and central tendency	GRADE 7 Create and solve problems using probability
GRADE 8 Develop and implement a plan for the collection, display, and analysis of the data, using technology as required. Evaluate and use measures of central tendency and variability	GRADE 8 Compare theoretical and experimental probability of independent events

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Revised: October 20, 1997

BC Ministry of Education

Number Concepts

Number Operations

Patterns

Variables and Equations

Relations and Functions

Measurement

3-D Objects and 2-D Shapes

Transformations

Data Analysis

Chance and Uncertainty