represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life

Source

describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts

Source

estimate and calculate square roots, in various contexts

Source

use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems

Source

use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations

Source

understand and recall commonly used square numbers and their square roots

Source

use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used

Source

add and subtract integers, using appropriate strategies, in various contexts

Source

add and subtract fractions, using appropriate strategies, in various contexts

Source

multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts

Source

multiply and divide integers, using appropriate strategies, in various contexts

Source

compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts

Source

identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values

Source

create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns

Source

determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing and shrinking patterns

Source

create and describe patterns to illustrate relationships among rational numbers

Source

add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools

Source

evaluate algebraic expressions that involve rational numbers

Source

solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions

Source

solve inequalities that involve integers, and verify and graph the solutions

Source

solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions

Source

read and alter existing code involving the analysis of data in order to inform and communicate decisions, and describe how changes to the code affect the outcomes and the efficiency of the code

Source

identify situations involving one-variable data and situations involving two-variable data, and explain when each type of data is needed

Source

collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values

Source

select from among a variety of graphs, including scatter plots, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs

Source

use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers

Source

analyse different sets of data presented in various ways, including in scatter plots and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions

Source

create an infographic about a data set, representing the data in appropriate ways, including in tables and scatter plots, and incorporating any other relevant information that helps to tell a story about the data

Source

solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams

Source

determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening

Source

identify geometric properties of tessellating shapes and identify the transformations that occur in the tessellations

Source

make objects and models using appropriate scales, given their top, front, and side views or their perspective views

Source

use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios

Source

describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations

Source

represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation

Source

solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons

Source

solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas

Source

describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle

Source

describe some advantages and disadvantages of various methods of payment that can be used when dealing with multiple currencies and exchange rates

Source

create a financial plan to reach a long-term financial goal, accounting for income, expenses, and tax implications

Source

identify different ways to maintain a balanced budget, and use appropriate tools to track all income and spending, for several different scenarios

Source

determine the growth of simple and compound interest at various rates using digital tools, and explain the impact interest has on long-term financial planning

Source

compare various ways for consumers to get more value for their money when spending, including taking advantage of sales and customer loyalty and incentive programs, and determine the best choice for different scenarios

Source

compare interest rates, annual fees, and rewards and other incentives offered by various credit card companies and consumer contracts to determine the best value and the best choice for different scenarios

Source