IRELAND MATH YEAR 1 – EDmama Ireland

A. Understanding Integers

A.01. Define integers and their representation on the number line.
A.02. Graph integers on horizontal and vertical number lines.
A.03. Determine the absolute value of an integer.
A.04. Identify the opposite of an integer.
A.05. Compare and order integers using number lines and inequalities.
A.06. Evaluate integer inequalities, including those involving absolute values.
A.07. Apply integers to represent real-world situations, such as temperature, elevation, and debt.

B. Number and Counting

B.01. Distinguish between prime and composite numbers.
B.02. Identify factors and multiples of a given number.
B.03. Find the prime factorisation of a number.
B.04. Determine the greatest common factor (HCF) of two or more numbers.
B.05. Determine the least common multiple (LCM) of two or more numbers.
B.06. Solve word problems involving HCF and LCM.
B.07. Define multiplicative inverses and identify them for given numbers.
B.08. Classify numbers as natural, whole, integer, rational, or irrational.
B.09. Convert numbers into scientific notation.
B.10. Compare numbers written in scientific notation.
B.11. Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10.
B.12. Understand the properties of number systems and their relevance in real-world contexts.

C. Operations with Integers

C.01. Apply the rules for adding and subtracting integers.
C.02. Add and subtract integers using visual aids like counters and number lines.
C.03. Complete addition and subtraction sentences with integers.
C.04. Solve word problems involving addition and subtraction of integers.
C.05. Apply the rules for multiplying and dividing integers.
C.06. Multiply and divide integers.
C.07. Complete multiplication and division sentences with integers.
C.08. Evaluate numerical expressions involving integers using the order of operations.
C.09. Translate real-world scenarios into mathematical expressions using integers.

D. Decimals

E. Operations with Decimals

E.01. Add and subtract decimals.
E.02. Solve word problems involving addition and subtraction of decimals.
E.03. Multiply decimals.
E.04. Multiply decimals and whole numbers in word problems.
E.05. Divide decimals.
E.06. Divide decimals by whole numbers in word problems.
E.07. Estimate sums, differences, and products of decimals.
E.08. Solve multi-step word problems involving addition, subtraction, multiplication, and division of decimals.
E.09. Evaluate numerical expressions involving decimals using the order of operations.
E.10. Interpret maps involving decimal distances.
E.11. Formulate and solve multi-step inequalities with decimals.

F. Fractions and Mixed Numbers

F.01. Understand fractions through word problems and visual models.
F.02. Identify and generate equivalent fractions.
F.03. Write fractions in lowest terms (simplest form).
F.04. Determine the lowest common denominator (LCD) for a set of fractions.
F.05. Compare and order fractions.
F.06. Solve word problems involving comparison of fractions.
F.07. Convert between mixed numbers and improper fractions.
F.08. Compare mixed numbers and improper fractions.
F.09. Round mixed numbers to the nearest whole number or specified fraction.
F.10. Apply fractions to solve real-world problems using graphs and tables.
F.11. Visualise and interpret fractions on a number line

G. Operations with Fractions

G.01. Add and subtract fractions with like denominators.
G.02. Add and subtract fractions with unlike denominators.
G.03. Add and subtract fractions in word problems.
G.04. Add and subtract mixed numbers.
G.05. Add and subtract mixed numbers in word problems.
G.06. Estimate sums and differences of mixed numbers.
G.07. Multiply fractions and whole numbers.
G.08. Multiply two fractions using models.
G.09. Multiply fractions.
G.10. Multiply mixed numbers.
G.11. Multiply fractions and mixed numbers in word problems.
G.12. Divide whole numbers and unit fractions.
G.13. Divide fractions.
G.14. Divide mixed numbers.
G.15. Divide fractions and mixed numbers in word problems.
G.16. Estimate products and quotients of fractions and mixed numbers.
G.17. Evaluate numerical expressions involving fractions, including order of operations.
G.18. Solve inequalities involving addition and subtraction of fractions and mixed numbers.
G.19. Solve complex word problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers.

H. Rational Numbers

H.01. Identify rational numbers.
H.02. Determine the absolute value of rational numbers.
H.03. Convert between decimals and fractions or mixed numbers.
H.04. Compare rational numbers.
H.05. Order rational numbers.
H.06. Add and subtract rational numbers.
H.07. Apply addition and subtraction rules to rational numbers.
H.08. Multiply and divide rational numbers.
H.09. Apply multiplication and division rules to rational numbers.

I. Exponents and Square Roots

I.01. Understand the concept of exponents and their notation.
I.02. Evaluate powers (exponents).
I.03. Evaluate powers with negative bases.
I.04. Evaluate powers with decimal and fractional bases.
I.05. Evaluate numerical expressions involving exponents using order of operations.
I.06. Find the square roots of perfect squares.
I.07. Estimate square roots of non-perfect squares.
I.08. Solve simple equations with variable exponents using trial and error.
I.09. Simplify expressions involving radicals.

J. Ratios, Rates and Proportions

J.01. Understand the concept of ratios and their different representations.
J.02. Identify equivalent ratios.
J.03. Write an equivalent ratio for a given ratio.
J.04. Solve word problems involving equivalent ratios.
J.05. Determine unit rates.
J.06. Compare ratios in word problems.
J.07. Determine if ratios form a proportion.
J.08. Solve proportions.
J.09. Solve proportion word problems.
J.10. Use proportions to estimate population sizes.
J.11. Calculate rate of change.
J.12. Determine if a rate of change is constant.
J.13. Apply ratios to solve scale drawing word problems.
J.14. Apply ratio and proportion concepts to real-world scenarios.

K. Percents

K.01. Visually determine what percentage is illustrated.
K.02. Convert between percents, fractions and decimals.
K.03. Compare percents to fractions and decimals.
K.04. Estimate percents of numbers.
K.05. Calculate percentages of numbers and money amounts.
K.06. Solve percent word problems.
K.07. Solve percent equations.
K.08. Solve percent equations in word problems.
K.09. Use percentages to calculate percentage increase and decrease.

L. Proportional Relationships

L.01. Identify proportional relationships from tables.
L.02. Find the constant of proportionality from a table.
L.03. Write equations for proportional relationships from tables.
L.04. Identify proportional relationships by graphing.
L.05. Find the constant of proportionality from a graph.
L.06. Write equations for proportional relationships from graphs.
L.07. Interpret graphs of proportional relationships.
L.08. Write and solve equations for proportional relationships.
L.09. Differentiate between proportional and non-proportional relationships.

M. Units of Measurement

M.01. Estimate metric measurements (length, mass, volume).
M.02. Compare and convert metric units (e.g., mm to cm, g to kg, mL to L).
M.03. Perform calculations with metric mixed units.
M.04. Convert between square metres and hectares.
M.05. Convert square and cubic units of length (e.g., cm² to m², m³ to km³).
M.06. Convert between cubic metres and litres.
M.07. Understand and apply the concept of precision in measurement.
M.08. Convert between different units of time.
M.09. Apply unit conversions to solve real-world problems involving measurements.

N. Consumer Maths

N.10. Calculate simple interest on loans and investments.
N.11. Calculate compound interest on loans and investments.
N.12. Understand the impact of interest rates and compounding periods on financial outcomes.
N.01. Add, subtract, multiply and divide money amounts in word problems.
N.02. Interpret price lists to determine the cost of items.
N.03. Calculate unit prices to compare the cost of different items.
N.04. Use unit prices to find the total price of multiple items.
N.05. Apply percentages to calculate VAT, discount and more.
N.06. Find the percentage of discount and mark-up.
N.07. Calculate the original price after a sale.
N.08. Solve multi-step problems with percentages related to consumer maths.
N.09. Estimate tips for services.

O. Problem Solving and Estimation

P. Expressions and Properties

P.01. Write variable expressions from verbal statements.
P.02. Translate real-world scenarios into variable expressions.
P.03. Evaluate linear expressions by substituting given values for variables.
P.04. Evaluate multi-variable expressions by substituting given values for variables.
P.05. Evaluate absolute value expressions.
P.06. Evaluate nonlinear expressions.
P.07. Identify terms and coefficients in algebraic expressions.
P.08. Sort factors of expressions.
P.09. Apply properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
P.10. Multiply using the distributive property.
P.11. Solve equations using properties of equality.
P.12. Write equivalent expressions using properties.
P.13. Add and subtract like terms in algebraic expressions.
P.14. Add, subtract and multiply linear expressions.
P.15. Identify factors of linear expressions.
P.16. Identify equivalent linear expressions.
P.17. Simplify algebraic expressions by combining like terms and applying the distributive property.

Q. One-Variable Equations

Q.01. Determine which value of x satisfies a given equation.
Q.02. Write an equation from a verbal description.
Q.03. Model and solve equations using algebra tiles.
Q.04. Write and solve equations that represent diagrams.
Q.05. Solve one-step equations using inverse operations.
Q.06. Solve two-step equations using inverse operations.
Q.07. Solve equations: word problems.
Q.08. Solve equations involving like terms by combining them first.
Q.09. Solve equations by completing the solution steps.
Q.10. Verify the solution to an equation by substitution.
Q.11. Apply the order of operations correctly while solving equations.

R. One-Variable Inequalities

S. Two-Variable Equations

S.01. Determine if an ordered pair (x, y) satisfies a given equation.
S.02. Identify independent and dependent variables in a two-variable equation.
S.03. Find a missing value using two-variable equations.
S.04. Solve word problems involving two-variable equations.
S.05. Complete a table of values for a two-variable relationship.
S.06. Write a two-variable equation to represent a given relationship.
S.07. Identify the graph of a two-variable equation.
S.08. Graph a two-variable equation on the coordinate plane.
S.09. Interpret a graph of a two-variable relationship in word problems.
S.10. Write an equation from a graph using a table of values.
S.11. Translate real-world scenarios into two-variable equations and graphs.

T. Linear Functions

T.01. Find the slope of a line from its graph.
T.02. Find the slope of a line given two points on the line.
T.03. Find a missing coordinate of a point on a line, given the slope and another point.
T.04. Find the slope of a line from its equation.
T.05. Graph a line using its slope and y-intercept.
T.06. Write a linear function in slope-intercept form (y = mx + b).
T.07. Identify linear and nonlinear functions from equations, graphs, and tables.
T.08. Determine the x and y intercepts of a linear function.
T.09. Use slope-intercept form to analyze and compare different linear functions.

U. Coordinate Plane

V. Number Sequences

V.01. Identify arithmetic and geometric sequences.
V.02. Determine the common difference in an arithmetic sequence.
V.03. Write an expression for the nth term of an arithmetic sequence.
V.04. Solve word problems involving arithmetic sequences.
V.05. Determine the common ratio in a geometric sequence.
V.06. Write an expression for the nth term of a geometric sequence.
V.07. Solve word problems involving geometric sequences.
V.08. Evaluate variable expressions for number sequences.
V.09. Identify and continue mixed number sequences.
V.10. Create and analyse different types of number sequences (Fibonacci, etc.).

W. Two-Dimensional Figures

W.01. Identify and classify polygons based on their properties (number of sides, angles, etc.).
W.02. Name, measure and classify angles (acute, obtuse, right, straight, reflex).
W.03. Classify triangles by their sides (equilateral, isosceles, scalene) and angles (acute, obtuse, right).
W.04. Identify trapeziums based on their properties.
W.05. Classify quadrilaterals (square, rectangle, parallelogram, rhombus, kite).
W.06. Graph triangles and quadrilaterals on the coordinate plane.
W.07. Find missing angles in triangles and quadrilaterals using angle sum properties.
W.08. Determine the interior angles of polygons using formulas.
W.09. Define lines, line segments and half lines.
W.10. Identify parallel, perpendicular and intersecting lines.
W.11. Identify complementary, supplementary, vertical, adjacent and congruent angles.
W.12. Find measures of complementary, supplementary, vertical and adjacent angles.
W.13. Analyse angles formed by a transversal intersecting parallel lines.
W.14. Find lengths and measures of bisected line segments and angles.
W.15. Identify and describe parts of a circle (centre, radius, diameter, chord, arc, sector, segment).
W.16. Construct different two-dimensional figures using geometric tools.

X. Transformations and Congruence

X.01. Understand the concept of symmetry (line and rotational).
X.02. Identify reflections, rotations and translations.
X.03. Perform translations: graph the image of a figure after a translation.
X.04. Perform translations: find the coordinates of the image after a translation.
X.05. Perform reflections: graph the image of a figure after a reflection.
X.06. Perform reflections: find the coordinates of the image after a reflection.
X.07. Perform rotations: graph the image of a figure after a rotation.
X.08. Perform rotations: find the coordinates of the image after a rotation.
X.09. Distinguish between similar and congruent figures.
X.10. Identify corresponding side lengths and angle measures of congruent figures.
X.11. Write congruence statements and identify corresponding parts of congruent figures.
X.12. Identify corresponding side lengths and angle measures of similar figures.
X.13. Use similar figures and indirect measurement to find unknown lengths.
X.14. Apply transformations to analyse symmetry and patterns in geometric figures.

Y. Constructions

Y.01. Construct the midpoint or perpendicular bisector of a segment using geometric tools.
Y.02. Construct an angle bisector using geometric tools.
Y.03. Construct a congruent angle using geometric tools.
Y.04. Construct a perpendicular line using geometric tools.
Y.05. Construct parallel lines using geometric tools.
Y.06. Construct an equilateral triangle or regular hexagon using geometric tools.
Y.07. Construct a square using geometric tools.
Y.08. Apply geometric constructions to solve real-world problems.

Z. Pythagoras’ Theorem

AA. Three-Dimensional Figures

BB. Geometric Measurement

BB.01. Calculate the perimeter of polygons.
BB.02. Calculate the area of rectangles and parallelograms.
BB.03. Calculate the area of triangles and trapeziums.
BB.04. Solve word problems involving area and perimeter.
BB.05. Calculate area, circumference, radius and diameter of circles.
BB.06. Solve word problems involving circles.
BB.07. Calculate area, perimeter, radius and diameter of semicircles.
BB.08. Calculate area, perimeter and radius of quarter circles.
BB.09. Calculate the area of compound figures with triangles, semicircles and quarter circles.
BB.10. Calculate the area between two shapes.
BB.11. Calculate the volume of prisms, cylinders, pyramids and cones.
BB.12. Calculate the surface area of prisms, cylinders, pyramids and cones.
BB.13. Describe how perimeter, area and volume change with changes in scale.
BB.14. Apply geometric measurement principles to solve real-world problems.

CC. Data and Graphs

CC.01. Interpret data presented in tables.
CC.02. Interpret data presented in line plots.
CC.03. Create line plots from given data.
CC.04. Interpret data presented in stem-and-leaf plots.
CC.05. Create stem-and-leaf plots from given data.
CC.06. Interpret data presented in bar graphs.
CC.07. Create bar graphs from given data.
CC.08. Interpret data presented in histograms.
CC.09. Create histograms from given data.
CC.10. Create frequency charts from given data.
CC.11. Interpret data presented in pie charts.
CC.12. Relate pie charts to central angles and proportions.
CC.13. Interpret data presented in line graphs.
CC.14. Create line graphs from given data.
CC.15. Interpret data presented in box-and-whisker plots.
CC.16. Interpret scatter plots to identify relationships between variables.
CC.17. Choose the best type of graph to represent a given dataset.
CC.18. Identify potential sources of bias in data collection and representation.

DD. Statistics

EE. Probability

EE.01. Calculate the probability of simple events.
EE.02. Determine the probability of opposite events.
EE.03. Determine the probability of mutually exclusive and overlapping events.
EE.04. Calculate experimental probability from observed data.
EE.05. Make predictions based on probability calculations.
EE.06. Determine the number of possible outcomes for compound events.
EE.07. Apply the counting principle to determine the total number of outcomes in a compound event.
EE.08. Differentiate between independent and dependent events and calculate their probabilities.

Course Content

A. Understanding Integers

A.01. Define integers and their representation on the number line.

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

A.03. Determine the absolute value of an integer.

A.04. Identify the opposite of an integer.

A.05. Compare and order integers using number lines and inequalities.

A.06. Evaluate integer inequalities, including those involving absolute values.

A.07. Apply integers to represent real-world situations, such as temperature, elevation, and debt.

B. Number and Counting

B.01. Distinguish between prime and composite numbers.

B.02. Identify factors and multiples of a given number.

B.03. Find the prime factorisation of a number.

B.04. Determine the greatest common factor (HCF) of two or more numbers.

B.05. Determine the least common multiple (LCM) of two or more numbers.

B.06. Solve word problems involving HCF and LCM.

B.07. Define multiplicative inverses and identify them for given numbers.

B.08. Classify numbers as natural, whole, integer, rational, or irrational.

B.09. Convert numbers into scientific notation.

B.10. Compare numbers written in scientific notation.

B.11. Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10.

B.12. Understand the properties of number systems and their relevance in real-world contexts.

C. Operations with Integers

C.01. Apply the rules for adding and subtracting integers.

C.02. Add and subtract integers using visual aids like counters and number lines.

C.03. Complete addition and subtraction sentences with integers.

C.04. Solve word problems involving addition and subtraction of integers.

C.05. Apply the rules for multiplying and dividing integers.

C.06. Multiply and divide integers.

C.07. Complete multiplication and division sentences with integers.

C.08. Evaluate numerical expressions involving integers using the order of operations.

C.09. Translate real-world scenarios into mathematical expressions using integers.

D. Decimals

D.01. Review the concept of decimal numbers and place value.

D.02. Represent decimals on a number line.

D.03. Compare and order decimals.

D.04. Round decimals to a specified place value.

D.05. Convert decimals to fractions and vice versa.

E. Operations with Decimals

E.01. Add and subtract decimals.

E.02. Solve word problems involving addition and subtraction of decimals.

E.03. Multiply decimals.

E.04. Multiply decimals and whole numbers in word problems.

E.05. Divide decimals.

E.06. Divide decimals by whole numbers in word problems.

E.07. Estimate sums, differences, and products of decimals.

E.08. Solve multi-step word problems involving addition, subtraction, multiplication, and division of decimals.

E.09. Evaluate numerical expressions involving decimals using the order of operations.

E.10. Interpret maps involving decimal distances.

E.11. Formulate and solve multi-step inequalities with decimals.

F. Fractions and Mixed Numbers

F.01. Understand fractions through word problems and visual models.

F.02. Identify and generate equivalent fractions.

F.03. Write fractions in lowest terms (simplest form).

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

F.05. Compare and order fractions.

F.06. Solve word problems involving comparison of fractions.

F.07. Convert between mixed numbers and improper fractions.

F.08. Compare mixed numbers and improper fractions.

F.09. Round mixed numbers to the nearest whole number or specified fraction.

F.10. Apply fractions to solve real-world problems using graphs and tables.

F.11. Visualise and interpret fractions on a number line

G. Operations with Fractions

G.01. Add and subtract fractions with like denominators.

G.02. Add and subtract fractions with unlike denominators.

G.03. Add and subtract fractions in word problems.

G.04. Add and subtract mixed numbers.

G.05. Add and subtract mixed numbers in word problems.

G.06. Estimate sums and differences of mixed numbers.

G.07. Multiply fractions and whole numbers.

G.08. Multiply two fractions using models.

G.09. Multiply fractions.

G.10. Multiply mixed numbers.

G.11. Multiply fractions and mixed numbers in word problems.

G.12. Divide whole numbers and unit fractions.

G.13. Divide fractions.

G.14. Divide mixed numbers.

G.15. Divide fractions and mixed numbers in word problems.

G.16. Estimate products and quotients of fractions and mixed numbers.

G.17. Evaluate numerical expressions involving fractions, including order of operations.