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Math Big Ideas
Kindergarten
Numbers represent quantities that can be decomposed into smaller parts
.
One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.
Repeating elements in patterns can be identified.
Objects have attributes that can be described, measured, and compared.
Familiar events can be described as likely or unlikely and compared.
Grade 1
Numbers to 20 represent quantities that can be decomposed into 10s and 1s.
Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.
Repeating elements in patterns can be identified.
Objects and shapes have attributes that can be described, measured, and compared.
Concrete graphs help us to compare and interpret data and show one-to-one correspondence.
Grade 2
Numbers to 100 represent quantities that can be decomposed into 10s and 1s.
Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value.
The regular change in increasing patterns can be identified and used to make generalizations.
Objects and shapes have attributes that can be described, measured, and compared.
Concrete items can be represented, compared, and interpreted pictorially in graphs.
Grade 3
Fractions are a type of number that can represent quantities.
Development of computational fluency in addition, subtraction, multiplication, and division of whole numbers requires flexible decomposing and composing.
Regular increases and decreases in patterns can be identified and used to make generalizations.
Standard units are used to describe, measure, and compare attributes of objects’ shapes.
The likelihood of possible outcomes can be examined, compared, and interpreted.
Grade 4
Fractions and decimals are types of numbers that can represent quantities.
Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Regular changes in patterns can be identified and represented using tools and tables.
Polygons are closed shapes with similar attributes that can be described, measured, and compared.
Analyzing and interpreting experiments in data probability develops an understanding of chance.
Grade 5
Numbers describe quantities that can be represented by equivalent fractions.
Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.
Identified regularities in number patterns can be expressed in tables.
Closed shapes have area and perimeter that can be described, measured, and compared.
Data represented in graphs can be used to show many-to-one correspondence.
Grade 6
Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes.
Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.
Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form generalizations.
Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles.
Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.
Grade 7
Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers.
Computational fluency and flexibility with numbers extend to operations with integers and decimals.
Linear relations can be represented in many connected ways to identify regularities and make generalizations.
The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships.
Data from circle graphs can be used to illustrate proportion and to compare and interpret.
Grade 8
Number represents, describes, and compares the quantities of ratios, rates, and percents.
Computational fluency and flexibility extend to operations with fractions.
Discrete linear relationships can be represented in many connected ways and used to identify and
make generalizations.
The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships.
Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret.
Grade 9
The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.
Computational fluency and flexibility with numbers extend to operations with rational numbers.
Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.
Similar shapes have proportional relationships that can be described, measured, and compared.
Analyzing the validity, reliability, and representation of data enables us to compare and interpret.