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Introduction to Polynomials

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Break an expression into parts

Recognise the building blocks of algebraic expressions.

Topic: Algebraic Expressions Skill: Identify variables, constants and terms in expressions

Expression or equation?

Classify mathematical statements based on whether they contain an equality relation.

Topic: Algebraic Expressions Skill: Distinguish algebraic expressions from equations

Substitute and evaluate

Find the value of an expression after substituting numerical values.

Topic: Algebraic Expressions Skill: Evaluate algebraic expressions for given values

Understand polynomials

Recognise expressions that satisfy the definition of a polynomial.

Topic: Polynomial Basics Skill: Define a polynomial in one variable

Polynomial or not?

Use powers and variables to identify expressions that are not polynomials.

Topic: Polynomial Basics Skill: Distinguish polynomials from non-polynomials

Find terms and coefficients

Break a polynomial into terms and state their coefficients.

Topic: Polynomial Basics Skill: Identify terms and coefficients of a polynomial

Find polynomial degree

Identify the highest power with non-zero coefficient.

Topic: Polynomial Degree Skill: Determine the degree of a polynomial in one variable

Name by degree

Classify polynomials as constant, linear, quadratic, cubic or higher degree.

Topic: Polynomial Degree Skill: Classify polynomials by degree

Name by terms

Identify monomials, binomials and trinomials.

Topic: Polynomial Degree Skill: Classify polynomials by number of terms

Spot linear polynomials

Identify polynomials of degree one and their coefficients.

Topic: Linear Polynomials Skill: Recognise linear polynomials in one variable

Model growth with a line

Write a linear expression for situations with a constant increase.

Topic: Linear Polynomials Skill: Model linear growth using a polynomial

Model decrease with a line

Write a linear expression for situations with a constant decrease.

Topic: Linear Polynomials Skill: Model linear decay using a polynomial

Find a linear table pattern

Use constant differences to recognise a linear relationship.

Topic: Linear Relationships Skill: Identify linear patterns from tables

Write the pattern rule

Construct an algebraic rule from a linear sequence or table.

Topic: Linear Relationships Skill: Write a rule for a linear pattern

Plot a linear pattern

Represent ordered pairs from a table on the coordinate plane.

Topic: Graphs of Linear Relationships Skill: Plot points from a linear relationship

Understand slope

Explain slope as change in y for each unit change in x.

Topic: Graphs of Linear Relationships Skill: Interpret slope as rate of change

Find the y-intercept

Recognise where a line crosses the y-axis and connect it to y = ax + b.

Topic: Graphs of Linear Relationships Skill: Identify y-intercept from equation or graph

Match equation and graph

Use slope and intercept to connect equations with graphs.

Topic: Graphs of Linear Relationships Skill: Match linear equations with their graphs

Build a linear model

Translate simple real-world situations into linear polynomial expressions.

Topic: Applications of Linear Polynomials Skill: Create linear models from daily-life situations

Build expressions systematically

Describe an algorithm for converting a pattern into an algebraic expression.

Topic: Computational Thinking in Algebra Skill: Use step-by-step rules to construct linear expressions

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