IRELAND MATH YEAR 3 – EDmama Ireland

A. Classifying Numbers

A.01. Identify different sets of numbers (natural, whole, integers, rational, irrational, real).
A.02. Classify a given number into its appropriate number sets.
A.03. Explain the relationships between different sets of numbers using Venn diagrams.
A.04. Apply the closure property to determine if a set is closed under a given operation.

B. Properties of Operations

C. Number Lines and Ordering

D. Converting Between Number Forms

E. Ratios, Rates, and Proportions

F. Percents and Applications

G. Measurement and Error

H. Single-Variable Inequalities

H.01. Identify solutions to inequalities.
H.02. Graph inequalities on a number line.
H.03. Write inequalities from given graphs.
H.04. Solve one-step linear inequalities using addition, subtraction, multiplication, and division.
H.05. Graph solutions to one-step linear inequalities on a number line.
H.06. Solve two-step linear inequalities.
H.07. Graph solutions to two-step linear inequalities on a number line.
H.08. Solve advanced linear inequalities involving multiple steps and variable terms on both sides.
H.09. Graph solutions to advanced linear inequalities on a number line.
H.10. Formulate and solve linear inequalities to model and solve real-world constraints and optimization problems.

I. Data Representation and Interpretation

J. Properties of Equality

K. Square and Cube Roots

L. Variable Expressions and Equations

M. Solving Linear Equations

M.01. Solve one-step linear equations using inverse operations.
M.02. Solve two-step linear equations.
M.03. Solve advanced linear equations with variables on both sides.
M.04. Solve equations with complete solutions.
M.05. Find the number of solutions to a linear equation (none, one, or infinitely many).
M.06. Create equations with no solutions or infinitely many solutions.
M.07. Solve linear equations from word problems.
M.08. Solve linear equations using mixed review.

N. Geometric Foundations

O. Geometry: Transformations and Congruence

P. Geometry: Similarity and Scale

Q. The Pythagorean Theorem

R. Geometric Constructions

S. Trigonometric Ratios

S.01. Define trigonometric ratios (sin, cos, tan) in a right triangle.
S.02. Define reciprocal trigonometric ratios (csc, sec, cot) in a right triangle.
S.03. Find trigonometric functions of special angles (30°, 45°, 60°).
S.04. Find trigonometric functions using a calculator.
S.05. Use trigonometric ratios to find a side length in a right triangle.
S.06. Use trigonometric ratios to find an angle measure in a right triangle.
S.07. Solve a right triangle (find all side lengths and angle measures).
S.08. Apply trigonometric ratios to solve real-world problems involving angles of elevation and depression.

T. Coordinate Plane

U. Linear Functions

U.01. Identify linear functions from equations, graphs, and tables.
U.02. Find the slope of a line from a graph or two points.
U.03. Find a missing coordinate using the slope.
U.04. Identify the slope and y-intercept of a line in slope-intercept form.
U.05. Graph a line using slope-intercept form.
U.06. Write the equation of a line in slope-intercept form from a graph.
U.07. Write the equation of a line in slope-intercept form from two points or a table.
U.08. Write the equation of a line in point-slope form from a point and slope.
U.09. Write the equation of a line in standard form.
U.10. Graph a line in standard form by finding x- and y-intercepts.
U.11. Write equations of horizontal and vertical lines.
U.12. Determine if two lines are parallel or perpendicular based on their slopes.
U.13. Write the equation of a line parallel or perpendicular to a given line.
U.14. Complete a table and graph a linear function.
U.15. Compare linear functions represented in different ways (graphs, tables, equations).
U.16. Analyze transformations of linear functions (shifts, stretches, reflections).
U.17. Model real-world situations with linear functions and interpret their parameters.

V. Systems of Equations

W. Exponents and Exponential Functions

W.01. Evaluate powers with integer, decimal, and fractional bases.
W.02. Simplify expressions with negative exponents.
W.03. Apply the product, quotient, and power rules of exponents.
W.04. Evaluate expressions using properties of exponents.
W.05. Identify equivalent expressions involving exponents.
W.06. Evaluate exponential functions for given values of the independent variable.
W.07. Match exponential functions with their corresponding graphs.
W.08. Determine the domain and range of exponential functions.
W.09. Solve word problems involving exponential growth and decay.
W.10. Analyze the properties and behavior of exponential functions in various contexts.

X. Scientific Notation

Y. Polynomials and Monomials

Y.01. Identify monomials.
Y.02. Multiply monomials.
Y.03. Divide monomials.
Y.04. Simplify expressions involving powers of monomials.
Y.05. Define polynomial vocabulary (degree, leading coefficient, terms, etc.).
Y.06. Model polynomials with algebra tiles.
Y.07. Add and subtract polynomials using algebra tiles.
Y.08. Add and subtract polynomials algebraically.
Y.09. Multiply a polynomial by a monomial.
Y.10. Multiply two binomials.
Y.11. Multiply two polynomials using algebra tiles.
Y.12. Multiply two polynomials.
Y.13. Apply polynomial operations to solve geometric problems involving area and volume.

Z. Factoring Polynomials

Z.01. Find the greatest common factor (HCF) of monomials.
Z.02. Factor out a monomial from a polynomial.
Z.03. Factorize quadratics with a leading coefficient of 1.
Z.04. Factorize quadratics with other leading coefficients.
Z.05. Factorize special case quadratics (difference of squares, perfect square trinomials).
Z.06. Factorize quadratics using algebra tiles.
Z.07. Factorize polynomials by grouping.
Z.08. Factorize polynomials completely.
Z.09. Apply factoring techniques to solve polynomial equations and simplify rational expressions.

AA. Quadratic Equations and Functions

AA.01. Identify the characteristics of quadratic functions (vertex, axis of symmetry, intercepts).
AA.02. Complete a function table for quadratic functions.
AA.03. Solve a quadratic equation using square roots.
AA.04. Solve a quadratic equation using the zero product property.
AA.05. Solve a quadratic equation by factorizing.
AA.06. Solve a quadratic equation using the quadratic formula.
AA.07. Graph quadratic functions and analyze their properties.
AA.08. Apply quadratic equations to model real-world phenomena such as projectile motion and optimization problems.

BB. Functions: Linear, Quadratic, and Exponential

BB.01. Identify linear, quadratic, and exponential functions from graphs.
BB.02. Identify linear, quadratic, and exponential functions from tables.
BB.03. Write linear, quadratic, and exponential functions from given information.
BB.04. Analyze linear functions over unit intervals.
BB.05. Analyze exponential functions over unit intervals.
BB.06. Describe linear and exponential growth and decay.
BB.07. Compare and contrast the properties and behavior of linear, quadratic, and exponential functions.
BB.08. Model real-world situations with linear, quadratic, and exponential functions and interpret their parameters.

CC. Radical Expressions

DD. Rational Expressions and Functions

EE. Probability

EE.01. Calculate theoretical probability of an event.
EE.02. Calculate experimental probability of an event.
EE.03. Determine the number of outcomes in compound events.
EE.04. Identify independent and dependent events.
EE.05. Calculate the probability of independent and dependent events.
EE.06. Calculate factorials.
EE.07. Apply the counting principle to determine the number of possible outcomes.
EE.08. Apply probability concepts to solve real-world problems involving games, surveys, and decision-making.

FF. Descriptive Statistics

GG. Logic and Reasoning

HH. Number Sequences

HH.01. Identify arithmetic and geometric sequences.
HH.02. Determine the common difference in an arithmetic sequence.
HH.03. Determine the common ratio in a geometric sequence.
HH.04. Evaluate variable expressions for number sequences.
HH.05. Write variable expressions for arithmetic sequences (explicit and recursive formulas).
HH.06. Write variable expressions for geometric sequences (explicit and recursive formulas).
HH.07. Solve mixed review problems involving arithmetic and geometric sequences.
HH.08. Apply sequence concepts to model patterns and predict future terms in real-world scenarios.

II. Relations and Functions

II.01. Convert between tables, graphs, mappings, and lists of points to represent relations.
II.02. Determine the domain and range of relations.
II.03. Identify independent and dependent variables in a relation.
II.04. Identify functions using the definition of a function.
II.05. Identify functions using the vertical line test.
II.06. Find values using function graphs.
II.07. Evaluate a function for a given input value.
II.08. Evaluate a function by plugging in an expression for the input variable.
II.09. Complete a function table from a graph.
II.10. Complete a function table from an equation.
II.11. Interpret the graph of a function in word problems.
II.12. Analyze and interpret the properties and behavior of functions in various mathematical and real-world contexts.

Course Content

A. Classifying Numbers

A.01. Identify different sets of numbers (natural, whole, integers, rational, irrational, real).

A.02. Classify a given number into its appropriate number sets.

A.03. Explain the relationships between different sets of numbers using Venn diagrams.

A.04. Apply the closure property to determine if a set is closed under a given operation.

B. Properties of Operations

B.01. Identify and apply the commutative, associative, and distributive properties.

B.02. Apply the identity and inverse properties of addition and multiplication.

B.03. Simplify variable expressions using properties of operations.

B.04. Justify steps in simplifying expressions using the properties of real numbers.

B.05. Evaluate the validity of algebraic statements using properties of operations.

B.06. Compare and contrast the application of different properties in various algebraic contexts.

C. Number Lines and Ordering

C.01. Represent rational numbers on a number line.

C.02. Compare and order rational numbers using a number line.

C.03. Interpret the meaning of numbers and their order in real-world contexts using number lines.

C.04. Compare and order integers, fractions, decimals, and percentages on a number line.

C.05. Determine the absolute value of a number and its distance from zero on a number line.

D. Converting Between Number Forms

D.01. Convert between fractions, decimals, and percentages.

D.02. Convert numbers from standard notation to scientific notation and vice versa.

D.03. Express repeating decimals as fractions.

D.04. Apply conversions between number forms to solve real-world problems.

D.05. Use number form conversions to compare quantities with different units of measure.

E. Ratios, Rates, and Proportions

E.01. Identify and write equivalent ratios.

E.02. Calculate unit rates and unit prices.

E.03. Solve proportions using cross-multiplication.

E.04. Apply proportional reasoning to solve word problems involving scale drawings.

E.05. Determine the constant of proportionality from a table, graph, or equation.

E.06. Solve complex proportion problems involving multiple steps or conversions.

E.07. Analyze the relationship between ratios, rates, proportions, and their applications in everyday life.

F. Percents and Applications

F.01. Solve basic percent equations (e.g., finding a percentage of a number).

F.02. Solve percent word problems involving discounts, VAT, and markups.

F.03. Calculate the percent of change (increase or decrease).

F.04. Solve multi-step problems involving percents.

F.05. Calculate percent error in measurements.

F.06. Apply percentages to solve financial problems such as simple and compound interest.

F.07. Analyze the impact of different percentage changes in real-world scenarios.

G. Measurement and Error

G.01. Convert between different units of measurement (e.g., metric and imperial).

G.02. Calculate rates and measurements involving different units.

G.03. Determine the precision of a measurement.

G.04. Calculate the greatest possible error in a measurement.

G.05. Determine the minimum and maximum possible area and volume based on measurement error.

G.06. Calculate percent error in area and volume calculations.

G.07. Evaluate the impact of measurement errors on the accuracy of calculations and decisions.

H. Single-Variable Inequalities

H.01. Identify solutions to inequalities.

H.02. Graph inequalities on a number line.

H.03. Write inequalities from given graphs.

H.04. Solve one-step linear inequalities using addition, subtraction, multiplication, and division.

H.05. Graph solutions to one-step linear inequalities on a number line.

H.06. Solve two-step linear inequalities.

H.07. Graph solutions to two-step linear inequalities on a number line.

H.08. Solve advanced linear inequalities involving multiple steps and variable terms on both sides.

H.09. Graph solutions to advanced linear inequalities on a number line.

H.10. Formulate and solve linear inequalities to model and solve real-world constraints and optimization problems.

I. Data Representation and Interpretation

I.01. Interpret information presented in bar graphs, line graphs, and histograms.

I.02. Interpret information presented in pie charts and stem-and-leaf plots.

I.03. Interpret information presented in box-and-whisker plots and scatter plots.

I.04. Create bar graphs, line graphs, and histograms from data sets.

I.05. Analyze the correlation between variables shown in a scatter plot.

I.06. Critique the appropriateness of different data representations for a given data set.

J. Properties of Equality

J.01. Identify and apply the properties of equality (addition, subtraction, multiplication, division).

J.02. Use the properties of equality to justify steps in solving equations.

J.03. Solve equations using order of operations.

J.04. Apply the reflexive, symmetric, and transitive properties of equality.

J.05. Use properties of equality to manipulate and solve algebraic equations efficiently.

K. Square and Cube Roots

K.01. Calculate the square root of a perfect square.

K.02. Calculate the cube root of a perfect cube.

K.03. Estimate the square root of a non-perfect square.

K.04. Simplify expressions involving square and cube roots.

K.05. Apply square and cube roots to solve geometric problems involving area and volume.

K.06. Understand the relationship between squares, cubes, square roots, and cube roots.