Grade 9 - Mathematics K&E (2006)

Mathematics 

Number (Number Concepts and Number Operations) 

Patterns and Relations (Patterns and Relationships) 

Patterns and Relations (Variables and Equations)

Shape and Space (Measurement)

Shape and Space (3-D Objects and 2-D Shapes)

Shape and Space (Transformations) 

Statistics and Probability (Collecting and Analyzing Information)

Demonstrate a number sense for whole numbers, common fractions, mixed numbers, decimals, percents and ratios; explore integers; and apply arithmetic operations to solve problems in everyday contexts. 

Use relationships to summarize, generalize and extend patterns to understand the environment and solve everyday problems. 

Use informal and concrete representations of equality and operations to solve problems in everyday contexts.

Use measurement concepts, appropriate tools and results of measurement to solve problems in everyday contexts, including: perimeter, area, surface area, mass (weight), volume (capacity) and angle measurements. 

Use visualization and symmetry to extend their awareness of objects and shapes and solve problems that involve classification and sketching. 

Create and examine patterns and designs that incorporate symmetry, tessellations, translations and reflections. 

Develop and implement a plan for collecting, displaying and examining data and information used in everyday applications.

use estimation strategies to estimate quantities and read and write numerals in the millions 

round numbers to the nearest unit, tenth and hundredth 

recognize, model and describe, concretely, pictorially and symbolically:

write a whole number:

estimate and apply arithmetic operations to whole numbers and decimals, e.g., 2-digit whole number multipliers and divisors, in everyday contexts

estimate and apply arithmetic operations to proper fractions and mixed numbers with like denominators concretely, pictorially and symbolically

generate and verify equivalent fractions to solve problems that involve adding and subtracting fractions with unlike denominators

convert among fractions, decimals and percents concretely, pictorially and symbolically

assess the reasonableness of calculations and problem-solving strategies, using a variety of tools and/or strategies; e.g., estimation, mental mathematics, tables, graphs, calculators and/or computers

represent and explain the meaning of rates concretely, pictorially and symbolically

estimate and calculate mean (average) in relation to everyday contexts

estimate and calculate percents to solve everyday problems

use rates to estimate, calculate and compare prices

compare and order positive and negative numbers, using appropriate tools; e.g., a number line or a thermometer

identify, describe and summarize, in spoken and written form, patterns and relationships 

make predictions based on everyday patterns and use patterns to draw conclusions

create expressions and rules to describe, complete and extend patterns and relationships 

demonstrate and explain how to solve simple problems, using informal algebraic methods

read and graph relationships and draw conclusions in everyday contexts

use common metric (SI) units and instruments to take accurate measurements of: 

use conversion charts, calculators and/or other tools to compare and convert a variety of metric (SI) units

use common imperial units and instruments to take accurate measurements of: 

use conversion charts, calculators and/or other tools to compare and convert a variety of imperial units of measure

develop, verify and apply rules or expressions for the area of rectangles; e.g., mm2 , cm2 , m2 , km2  

estimate, measure and calculate areas of quadrilaterals and triangles to solve problems in everyday contexts

design and construct rectangles when given perimeter or area, or both, using a variety of tools; e.g., grids

estimate, measure and calculate the circumference, radius and diameter of circles to solve problems in everyday contexts

identify, discuss and classify examples of angles in the environment; e.g., right, acute, obtuse, straight or reflex 

estimate, measure and draw angles up to 180°, using a protractor or other tools

add and subtract hours and minutes in everyday applications 

classify and construct 3-D objects, using a variety of tools and strategies

sketch 3-D objects and skeletons with and without grids

sort quadrilaterals and regular polygons according to the number of lines and symmetry

relate reflections to lines and planes of symmetry

draw and classify triangles according to the measurements of their angles; e.g., acute, obtuse, scalene

use scale to reproduce a 2-D shape

create, examine and describe designs, using translations (slides), reflections (flips) and rotations (turns)

trace a path, given in oral or written instructions, and write or describe instructions for a given path 

draw designs and determine locations in the first and second quadrants of a coordinate grid, using ordered pairs 

read, interpret and communicate information represented in graphs, charts and other collection tools

collect, organize and display data and information, by hand and/or using technology, in a variety of ways; e.g., tables, charts, bar or line graphs, frequency diagrams, broken-line graphs

make conclusions and predictions based on data and information analysis

examine sets of data, draw conclusions and make comparisons

determine trends by identifying and examining extremes, gaps or clusters in a set of data

examine the distribution of a set of data, using smallest and largest value, frequency, value in the middle and patterns

use appropriate vocabulary, related to the home or workplace, to discuss and examine data; e.g., probable/improbable, equally likely/less likely/more likely, best/worst 

manipulate data in everyday applications, at home or in the workplace, by selecting appropriate tools such as spreadsheets

multiples; e.g., lowest common multiple for pairs of numbers less than 10 

factors; e.g., greatest common factor for pairs of numbers less than 25

composites

prime factorizations

as an expanded numeral, using powers of 10

in scientific notation

length 

mass (weight) 

volume (capacity) 

length

mass (weight) 

volume (capacity)