IRELAND MATH YEAR 2 – EDmama Ireland

A. Factors and Multiples

A.01. Define factors and multiples of a given number.
A.02. Identify factors of a given number.
A.03. Identify multiples of a given number.
A.04. Determine if a number is prime or composite.
A.05. Find the prime factorization of a number.
A.06. Determine the highest common factor (HCF) of two or more numbers.
A.07. Determine the lowest common multiple (LCM) of two or more numbers.
A.08. Solve word problems involving HCF and LCM.
A.09. Classify numbers based on their properties (e.g., perfect, abundant, deficient).

B. Integers and the Number Line

C. Operations with Integers

C.01. State and apply the rules for adding and subtracting integers.
C.02. Add integers using visual aids such as counters or number lines.
C.03. Subtract integers using visual aids such as counters or number lines.
C.04. Add and subtract integers fluently without visual aids.
C.05. Add and subtract three or more integers.
C.06. Translate and solve word problems involving addition and subtraction of integers.
C.07. State and apply the rules for multiplying and dividing integers.
C.08. Multiply and divide integers fluently.
C.09. Evaluate numerical expressions involving integers using the order of operations.
C.10. Apply integer operations to solve multi-step problems.

D. Rational Numbers: Identification and Conversion

D.01. Define rational and irrational numbers and provide examples of each.
D.02. Identify rational and irrational numbers.
D.03. Express fractions in their lowest terms (simplify fractions).
D.04. Determine the lowest common denominator (LCD) for a set of fractions.
D.05. Round decimals and mixed numbers to a specified place value.
D.06. Find the absolute value of rational numbers.
D.07. Convert between decimals, fractions, and mixed numbers accurately.
D.08. Compare rational numbers using inequality symbols.
D.09. Order a set of rational numbers from least to greatest or greatest to least.
D.10. Explain the difference between terminating and repeating decimals.

E. Operations with Rational Numbers

E.01. Define reciprocals and multiplicative inverses.
E.02. Find the reciprocal of a rational number.
E.03. Add and subtract rational numbers, including fractions and decimals.
E.04. Translate and solve word problems involving addition and subtraction of rational numbers.
E.05. Apply the rules of addition and subtraction to simplify expressions with rational numbers.
E.06. Multiply and divide rational numbers, including fractions and decimals.
E.07. Translate and solve word problems involving multiplication and division of rational numbers.
E.08. Apply the rules of multiplication and division to simplify expressions with rational numbers.
E.09. Apply addition, subtraction, multiplication, and division rules to evaluate numerical expressions involving rational numbers.
E.10. Solve complex problems involving multiple operations with rational numbers.

F. Exponents and Roots

F.16. Estimate positive and negative square roots of non-perfect squares.
F.17. Describe the relationship between squares and square roots.
F.18. Solve equations involving squares and square roots.
F.19. Determine the cube roots of perfect cubes.
F.20. Estimate cube roots of non-perfect cubes.
F.21. Simplify expressions containing square roots and cube roots.
F.01. Understand the meaning of exponents and exponential notation.
F.02. Evaluate powers, including those with positive, negative, and zero exponents.
F.03. Solve simple equations with variable exponents.
F.04. Evaluate powers with negative bases.
F.05. Evaluate powers with decimal and fractional bases.
F.06. Understand and apply the concept of negative exponents.
F.07. Evaluate powers with negative exponents.
F.08. Apply the product of powers property to simplify expressions.
F.09. Apply the quotient of powers property to simplify expressions.
F.10. Simplify expressions using both the product and quotient of powers properties.
F.11. Apply the power of a power property to simplify expressions.
F.12. Evaluate expressions using all properties of exponents.
F.13. Identify equivalent expressions involving exponents.
F.14. Determine the square roots of perfect squares.
F.15. Identify positive and negative square roots.

G. Scientific Notation

H. Ratios, Rates and Proportions

H.01. Understand the concept of a ratio.
H.02. Identify equivalent ratios.
H.03. Write an equivalent ratio.
H.04. Solve word problems involving equivalent ratios.
H.05. Define and calculate unit rates.
H.06. Compare ratios in word problems.
H.07. Determine if two ratios form a proportion.
H.08. Solve word problems to determine if the ratios form a proportion
H.09. Solve proportions using cross-multiplication.
H.10. Solve proportions in word problems.
H.11. Estimate population size using proportions.
H.12. Solve problems involving scale drawings using proportions.
H.13. Apply ratios and proportions to solve problems involving percentages.

I. Proportional Relationships

I.01. Identify the constant of proportionality from a table.
I.02. Write equations for proportional relationships based on data in tables.
I.03. Identify proportional relationships by analyzing graphs.
I.04. Find the constant of proportionality from a graph.
I.05. Write equations for proportional relationships based on graphs.
I.06. Distinguish between proportional and non-proportional relationships.
I.07. Graph proportional relationships on the coordinate plane.
I.08. Interpret graphs of proportional relationships in real-world contexts.
I.09. Write and solve equations for proportional relationships.
I.10. Analyze real-world scenarios to determine if a proportional relationship exists.

J. Percents

J.01. Convert between percents, fractions, and decimals.
J.02. Compare percents to fractions and decimals.
J.03. Calculate what percent one number is of another.
J.04. Solve word problems to find what percent one number is of another.
J.05. Estimate percents of numbers.
J.06. Calculate percents of numbers and money amounts.
J.07. Solve word problems involving percents of numbers.
J.08. Compare percents of numbers.
J.09. Solve percent equations.
J.10. Define and calculate percent of change.
J.11. Solve word problems involving percent of change.
J.12. Apply percent concepts to solve problems involving discounts, taxes, and interest.

K. Consumer Maths

K.01. Interpret and use price lists.
K.02. Calculate unit prices to compare costs.
K.03. Calculate the total price using unit prices.
K.04. Calculate the percent of a number in the context of VAT (Value Added Tax), discounts, and more.
K.05. Find the percent related to discounts and mark-ups.
K.06. Determine the original price given the sale price and discount percentage.
K.07. Solve multi-step problems involving percents in real-world financial scenarios.
K.08. Estimate tips.
K.09. Calculate simple interest.
K.10. Calculate compound interest.
K.11. Understand and compare different types of investments.

L. Units of Measurement

M. Problem Solving Strategies

N. Coordinate Plane

O. Two-Dimensional Figures

O.01. Identify and classify polygons based on their properties.
O.02. Classify triangles based on their sides and angles.
O.03. Identify trapeziums.
O.04. Classify quadrilaterals based on their properties.
O.05. Graph triangles and quadrilaterals on the coordinate plane.
O.06. Find missing angles in triangles and quadrilaterals using angle properties.
O.07. Calculate the sum of interior angles of polygons.
O.08. Distinguish between lines, line segments, and half lines (rays).
O.09. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
O.10. Find measures of complementary, supplementary, vertical, and adjacent angles.
O.11. Understand the properties of transversals of parallel lines.
O.12. Find lengths and measures of bisected line segments and angles.
O.13. Identify and describe the parts of a circle (radius, diameter, chord, circumference, arc, sector, tangent).

P. Transformations and Congruence

P.01. Define and identify symmetry (line and rotational).
P.02. Identify reflections, rotations, and translations.
P.03. Perform translations and graph the image.
P.04. Determine the coordinates of an image after a translation.
P.05. Perform reflections and graph the image.
P.06. Determine the coordinates of an image after a reflection.
P.07. Perform rotations and graph the image.
P.08. Determine the coordinates of an image after a rotation.
P.09. Determine the side lengths and angle measures of congruent figures.
P.10. Write congruence statements and identify corresponding parts of congruent figures.
P.11. Prove triangle congruence using SSS, SAS, and ASA postulates.
P.12. Apply congruence transformations to create geometric patterns.

Q. Transformations and Similarity

R. Geometric Constructions

R.01. Construct the midpoint or perpendicular bisector of a line segment using a compass and straightedge.
R.02. Construct an angle bisector using a compass and straightedge.
R.03. Construct a congruent angle using a compass and straightedge.
R.04. Construct a perpendicular line from a point to a given line using a compass and straightedge.
R.05. Construct parallel lines using a compass and straightedge.
R.06. Construct an equilateral triangle or regular hexagon using a compass and straightedge.
R.07. Construct a square using a compass and straightedge.
R.08. Apply geometric constructions to solve design and engineering problems.

S. Pythagoras’ Theorem

T. Three-Dimensional Figures

U. Geometric Measurement

U.01. Calculate the perimeter of polygons.
U.02. Calculate the area of polygons.
U.03. Calculate the area between two shapes.
U.04. Solve word problems involving area and perimeter.
U.05. Calculate the area and circumference of circles, semicircles, and quarter circles.
U.06. Solve word problems involving circles.
U.07. Calculate the volume of prisms and cylinders.
U.08. Calculate the surface area of prisms and cylinders.
U.09. Calculate the volume of cones.
U.10. Calculate the surface area of cones.
U.11. Calculate the volume and surface area of spheres.
U.12. Calculate the volume and surface area of similar solids.
U.13. Analyze how perimeter, area, and volume change with changes in scale.
U.14. Apply geometric measurement concepts to solve real-world problems.

V. Number Sequences

V.01. Identify arithmetic and geometric sequences.
V.02. Find the common difference in arithmetic sequences.
V.03. Generate terms of an arithmetic sequence.
V.04. Find the common ratio in geometric sequences.
V.05. Generate terms of a geometric sequence.
V.06. Identify and work with different types of number sequences (mixed review).
V.07. Solve word problems involving number sequences.
V.08. Evaluate variable expressions for number sequences.
V.09. Write variable expressions for arithmetic sequences.
V.10. Determine the nth term of an arithmetic or geometric sequence.
V.11. Apply sequence concepts to model real-world situations such as compound interest and population growth.

W. Expressions and Properties

W.01. Translate verbal phrases into variable expressions.
W.02. Write variable expressions from diagrams.
W.03. Translate word problems into variable expressions.
W.04. Evaluate one-variable expressions by substitution.
W.05. Evaluate multi-variable expressions by substitution.
W.06. Evaluate absolute value expressions.
W.07. Evaluate radical expressions.
W.08. Evaluate rational expressions.
W.09. Identify terms and coefficients in algebraic expressions.
W.10. Sort factors of expressions.
W.11. State and apply the properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
W.12. Multiply expressions using the distributive property.
W.13. Simplify variable expressions using properties of operations.
W.14. Add and subtract like terms.
W.15. Add, subtract, and multiply linear expressions.
W.16. Factor linear expressions.
W.17. Identify equivalent linear expressions.
W.18. Use algebraic properties to justify steps in simplifying expressions.

X. One-Variable Equations

X.01. Determine which value of x satisfies an equation.
X.02. Translate word problems into algebraic equations.
X.03. Model and solve equations using algebra tiles.
X.04. Write and solve equations that represent diagrams.
X.05. State and apply the properties of equality (addition, subtraction, multiplication, division).
X.06. Solve one-step equations using inverse operations.
X.07. Solve two-step equations using inverse operations.
X.08. Solve multi-step equations using inverse operations.
X.09. Solve equations involving like terms by combining them.
X.10. Complete the solution to a given equation by providing missing steps.
X.11. Solve equations by translating and solving word problems.
X.12. Verify solutions to equations by substitution.

Y. One-Variable Inequalities

Z. Linear Equations

Z.01. Determine the slope of a line from its graph.
Z.02. Calculate the slope of a line given two points on the line.
Z.03. Find a missing coordinate given the slope and one point on the line.
Z.04. Determine the slope of a line from its equation.
Z.05. Graph a line using its slope and y-intercept.
Z.06. Graph a line from its equation using various methods (slope-intercept, point-slope, two points).
Z.07. Write a linear equation in slope-intercept form given the slope and y-intercept.
Z.08. Write a linear equation from a graph.
Z.09. Write a linear equation given the slope and a point on the line.
Z.10. Write a linear equation given two points on the line.
Z.11. Determine if lines are parallel or perpendicular based on their slopes.
Z.12. Use linear equations to model and solve real-world problems.

AA. Functions

AA.01. Define and identify functions.
AA.02. Determine if an ordered pair (x, y) satisfies a given linear function.
AA.03. Identify independent and dependent variables in a function.
AA.04. Calculate the rate of change of a linear function.
AA.05. Recognize and work with constant rates of change.
AA.06. Evaluate a linear function for a given value of x.
AA.07. Complete a table of values for a linear function.
AA.08. Complete a table and graph a linear function.
AA.09. Interpret the graph of a linear function in the context of word problems.
AA.10. Write a linear function from a table of values.
AA.11. Compare linear functions presented as graphs, tables, and equations.
AA.12. Write linear functions to model and solve word problems.
AA.13. Interpret linear functions in real-world scenarios.
AA.14. Differentiate between linear and nonlinear functions.
AA.15. Determine if an ordered pair (x, y) satisfies a given nonlinear function.
AA.16. Evaluate a nonlinear function for a given value of x.
AA.17. Find values using function graphs.
AA.18. Complete a table for a function graph.
AA.19. Analyze the domain and range of a function from its graph or equation.

BB. Monomials and Polynomials

BB.01. Identify monomials.
BB.02. Model polynomials with algebra tiles.
BB.03. Add and subtract polynomials using algebra tiles.
BB.04. Add and subtract polynomials algebraically.
BB.05. Add polynomials to find the perimeter of geometric figures.
BB.06. Multiply monomials.
BB.07. Divide monomials.
BB.08. Simplify expressions by multiplying and dividing monomials.
BB.09. Raise monomials to a power.
BB.10. Find square and cube roots of monomials.
BB.11. Multiply polynomials using algebra tiles.
BB.12. Multiply polynomials algebraically.
BB.13. Multiply polynomials to find the area of geometric figures.
BB.14. Factor simple polynomials.

CC. Data and Graphs

CC.12. Create frequency charts.
CC.13. Interpret data presented in box-and-whisker plots.
CC.14. Interpret scatter plots to identify trends and relationships.
CC.15. Interpret data presented in pie charts.
CC.16. Relate pie charts to central angles and proportions.
CC.17. Choose the best type of graph to represent a given set of data.
CC.18. Analyze and compare different types of graphs.
CC.01. Interpret data presented in tables.
CC.02. Interpret data presented in bar graphs.
CC.03. Create bar graphs from given data.
CC.04. Interpret data presented in line graphs.
CC.05. Create line graphs from given data.
CC.06. Interpret data presented in line plots.
CC.07. Create line plots from given data.
CC.08. Interpret data presented in stem-and-leaf plots.
CC.09. Create stem-and-leaf plots from given data.
CC.10. Interpret data presented in histograms.
CC.11. Create histograms from given data.

Course Content

A. Factors and Multiples

A.01. Define factors and multiples of a given number.

A.02. Identify factors of a given number.

A.03. Identify multiples of a given number.

A.04. Determine if a number is prime or composite.

A.05. Find the prime factorization of a number.

A.06. Determine the highest common factor (HCF) of two or more numbers.

A.07. Determine the lowest common multiple (LCM) of two or more numbers.

A.08. Solve word problems involving HCF and LCM.

A.09. Classify numbers based on their properties (e.g., perfect, abundant, deficient).

B. Integers and the Number Line

B.01. Represent integers on a number line.

B.02. Graph integers on horizontal and vertical number lines.

B.03. Define absolute value and find the opposite of an integer.

B.04. Compare and order integers using number lines.

B.05. Interpret and solve integer inequalities, including those with absolute values.

B.06. Apply understanding of integers to real-world contexts, such as temperature and finance.

B.07. Understand the relationship between integers and rational numbers.

C. Operations with Integers

C.01. State and apply the rules for adding and subtracting integers.

C.02. Add integers using visual aids such as counters or number lines.

C.03. Subtract integers using visual aids such as counters or number lines.

C.04. Add and subtract integers fluently without visual aids.

C.05. Add and subtract three or more integers.

C.06. Translate and solve word problems involving addition and subtraction of integers.

C.07. State and apply the rules for multiplying and dividing integers.

C.08. Multiply and divide integers fluently.

C.09. Evaluate numerical expressions involving integers using the order of operations.

C.10. Apply integer operations to solve multi-step problems.

D. Rational Numbers: Identification and Conversion

D.01. Define rational and irrational numbers and provide examples of each.

D.02. Identify rational and irrational numbers.

D.03. Express fractions in their lowest terms (simplify fractions).

D.04. Determine the lowest common denominator (LCD) for a set of fractions.

D.05. Round decimals and mixed numbers to a specified place value.

D.06. Find the absolute value of rational numbers.

D.07. Convert between decimals, fractions, and mixed numbers accurately.

D.08. Compare rational numbers using inequality symbols.

D.09. Order a set of rational numbers from least to greatest or greatest to least.

D.10. Explain the difference between terminating and repeating decimals.

E. Operations with Rational Numbers

E.01. Define reciprocals and multiplicative inverses.

E.02. Find the reciprocal of a rational number.

E.03. Add and subtract rational numbers, including fractions and decimals.

E.04. Translate and solve word problems involving addition and subtraction of rational numbers.

E.05. Apply the rules of addition and subtraction to simplify expressions with rational numbers.

E.06. Multiply and divide rational numbers, including fractions and decimals.

E.07. Translate and solve word problems involving multiplication and division of rational numbers.

E.08. Apply the rules of multiplication and division to simplify expressions with rational numbers.

E.09. Apply addition, subtraction, multiplication, and division rules to evaluate numerical expressions involving rational numbers.

E.10. Solve complex problems involving multiple operations with rational numbers.

F. Exponents and Roots

F.16. Estimate positive and negative square roots of non-perfect squares.

F.17. Describe the relationship between squares and square roots.

F.18. Solve equations involving squares and square roots.

F.19. Determine the cube roots of perfect cubes.

F.20. Estimate cube roots of non-perfect cubes.

F.21. Simplify expressions containing square roots and cube roots.

F.01. Understand the meaning of exponents and exponential notation.

F.02. Evaluate powers, including those with positive, negative, and zero exponents.

F.03. Solve simple equations with variable exponents.

F.04. Evaluate powers with negative bases.

F.05. Evaluate powers with decimal and fractional bases.

F.06. Understand and apply the concept of negative exponents.

F.07. Evaluate powers with negative exponents.

F.08. Apply the product of powers property to simplify expressions.

F.09. Apply the quotient of powers property to simplify expressions.

F.10. Simplify expressions using both the product and quotient of powers properties.

F.11. Apply the power of a power property to simplify expressions.

F.12. Evaluate expressions using all properties of exponents.

F.13. Identify equivalent expressions involving exponents.

F.14. Determine the square roots of perfect squares.

F.15. Identify positive and negative square roots.

G. Scientific Notation

G.01. Convert numbers from standard notation to scientific notation.

G.02. Convert numbers from scientific notation to standard notation.

G.03. Compare numbers written in scientific notation.

G.04. Multiply numbers written in scientific notation.

G.05. Divide numbers written in scientific notation.