IRELAND MATH CLASS 6 – EDmama Ireland

A. Whole Numbers and Place Value

A.01. Identify place values in whole numbers.
A.02. Write word names for whole numbers.
A.03. Read and interpret Roman numerals.
A.04. Compare and order whole numbers.
A.05. Round whole numbers to a specified place value.
A.06. Apply place value understanding to round numbers in real-world contexts.

B. Addition and Subtraction of Whole Numbers

C. Multiplication of Whole Numbers

C.01. Multiply whole numbers using standard algorithms.
C.02. Solve multiplication word problems involving whole numbers.
C.03. Multiply numbers ending in zeroes using mental math.
C.04. Solve word problems involving multiplication of numbers ending in zeroes.
C.05. Multiply three or more numbers.
C.06. Solve multi-step word problems involving multiplication of three or more numbers.
C.07. Estimate products of whole numbers.
C.08. Apply the distributive property to simplify multiplication problems.

D. Division of Whole Numbers

E. Exponents and Square Roots

E.01. Write multiplication expressions using exponents.
E.02. Evaluate powers (exponents).
E.03. Find the missing exponent or base in exponential expressions.
E.04. Evaluate powers with decimal bases.
E.05. Evaluate powers with fractional bases.
E.06. Find the square roots of perfect squares.
E.07. Estimate square roots of non-perfect squares.
E.08. Calculate cubes and cube roots of perfect cubes.
E.09. Compare and order numbers expressed in exponential form.

F. Number Theory

G. Decimals: Understanding and Ordering

H. Decimals: Rounding

I. Addition and Subtraction of Decimals

J. Multiplication and Division of Decimals

J.01. Multiply a decimal by a one-digit whole number.
J.02. Multiply a decimal by a multi-digit whole number.
J.03. Solve word problems involving multiplication of decimals and whole numbers.
J.04. Multiply two decimals using grids.
J.05. Multiply decimals using standard algorithms.
J.06. Estimate products of decimal numbers.
J.07. Use inequalities involving decimal multiplication.
J.08. Divide decimals by whole numbers.
J.09. Solve word problems involving division of decimals by whole numbers.
J.10. Multiply and divide decimals by powers of ten.
J.11. Perform division with decimal quotients.
J.12. Use inequalities involving decimal division.

K. Fractions and Mixed Numbers: Review and Conversion

K.01. Review basic concepts of fractions and mixed numbers.
K.02. Solve word problems involving understanding of fractions.
K.03. Identify and generate equivalent fractions.
K.04. Write fractions in lowest terms (simplify fractions).
K.05. Solve word problems involving fractions and real world context.
K.06. Find the lowest common denominator (LCD) of two or more fractions.
K.07. Convert between improper fractions and mixed numbers.
K.08. Convert between decimals and fractions or mixed numbers.
K.09. Put a mix of decimals, fractions, and mixed numbers in order.
K.10. Relate fractions to division.

L. Fractions: Comparing and Ordering

M. Addition and Subtraction of Fractions

M.01. Add and subtract fractions with like denominators.
M.02. Solve word problems involving addition and subtraction of fractions with like denominators.
M.03. Add and subtract fractions with unlike denominators.
M.04. Solve word problems involving addition and subtraction of fractions with unlike denominators.
M.05. Use inequalities involving addition and subtraction of like and unlike fractions.
M.06. Add and subtract mixed numbers.
M.07. Solve word problems involving addition and subtraction of mixed numbers.
M.08. Estimate sums and differences of mixed numbers.
M.09. Model fraction addition and subtraction using visual aids.

N. Multiplication and Division of Fractions

N.01. Find fractions of whole numbers (I and II).
N.02. Solve word problems involving fractions of a number.
N.03. Estimate products of fractions and whole numbers.
N.04. Multiply two fractions using models.
N.05. Multiply two fractions using standard algorithm.
N.06. Solve word problems involving multiplication of fractions.
N.07. Multiply three or more fractions and whole numbers.
N.08. Estimate products of fractions, whole numbers, and mixed numbers.
N.09. Multiply mixed numbers and whole numbers.
N.10. Divide whole numbers by unit fractions using models.
N.11. Identify reciprocals of numbers.
N.12. Divide whole numbers and unit fractions.
N.13. Divide whole numbers by fractions.
N.14. Solve word problems involving multiplication and division of fractions.

O. Integers: Understanding and Representation

P. Operations with Integers

P.01. Add integers using counters or other visual aids.
P.02. Add integers using rules for adding positive and negative numbers.
P.03. Subtract integers using counters or other visual aids.
P.04. Subtract integers using rules for subtracting positive and negative numbers.
P.05. Determine the sign of the result when adding and subtracting integers.
P.06. Complete input/output tables involving addition and subtraction of integers.
P.07. Add three or more integers.
P.08. Explain why subtracting a negative number is equivalent to adding a positive number.

Q. Mixed Operations: Whole Numbers, Decimals, and Fractions

Q.01. Add, subtract, multiply, or divide two whole numbers.
Q.02. Solve word problems involving mixed operations with whole numbers.
Q.03. Evaluate numerical expressions involving whole numbers using order of operations (PEMDAS/BODMAS).
Q.04. Add, subtract, multiply, or divide two decimals.
Q.05. Solve word problems involving mixed operations with decimals.
Q.06. Evaluate numerical expressions involving decimals using order of operations.
Q.07. Add, subtract, or multiply two fractions.
Q.08. Solve word problems involving mixed operations with fractions.
Q.09. Apply the order of operations to expressions containing fractions, decimals, and whole numbers.

R. Rational Numbers

S. Problem Solving and Estimation

T. Ratios and Rates

T.01. Write a ratio to compare two quantities.
T.02. Write a ratio to solve word problems.
T.03. Identify equivalent ratios.
T.04. Write an equivalent ratio.
T.05. Complete ratio tables.
T.06. Determine unit rates and equivalent rates.
T.07. Compare ratios to solve word problems.
T.08. Determine if ratios form a proportion.
T.09. Solve proportions.
T.10. Use scale drawings to solve word problems.
T.11. Use ratios and proportions to solve real-world problems involving measurement and comparison.

U. Percents: Understanding and Calculation

U.01. Identify the percentage illustrated by a visual model.
U.02. Convert between percents, fractions, and decimals.
U.03. Compare percents to each other and to fractions.
U.04. Solve word problems involving comparisons of percents and fractions.
U.05. Calculate percents of numbers and money amounts.
U.06. Solve word problems involving percents of numbers.
U.07. Find what percent one number is of another.
U.08. Solve word problems to find what percent one number is of another.
U.09. Apply percentages to calculate percentage increase and decrease.

V. Units of Measurement

V.01. Estimate metric measurements (e.g., length, mass, volume).
V.02. Convert and compare metric units.
V.03. Work with metric mixed units.
V.04. Convert square and cubic units of length.
V.05. Convert between square metres and hectares.
V.06. Convert between cubic metres and litres.
V.07. Compare temperatures above and below zero (Celsius).
V.08. Convert between different units of measurement within the same system (e.g., inches to feet, grams to kilograms).

W. Money: Operations and Applications

X. Consumer Maths

Y. Time: Calculation and Conversion

Z. Coordinate Plane

AA. Expressions and Properties

AA.08. Apply properties of addition (commutative, associative, identity).
AA.09. Apply properties of multiplication (commutative, associative, identity, distributive).
AA.10. Solve for a variable using properties of multiplication.
AA.11. Identify equivalent expressions.
AA.12. Simplify algebraic expressions by combining like terms.
AA.01. Write variable expressions to represent mathematical relationships.
AA.02. Write variable expressions to solve word problems.
AA.03. Evaluate variable expressions with whole numbers.
AA.04. Evaluate multi-variable expressions.
AA.05. Evaluate variable expressions with decimals.
AA.06. Identify terms and coefficients in algebraic expressions.
AA.07. Sort factors of expressions.

BB. One-Variable Equations

BB.01. Determine which value of x satisfies a given equation.
BB.02. Write an equation from a verbal description.
BB.03. Model and solve equations using algebra tiles.
BB.04. Write and solve equations that represent diagrams.
BB.05. Solve one-step equations with whole numbers.
BB.06. Solve one-step equations with decimals.
BB.07. Solve one-step equations in word problems.
BB.08. Solve two-step equations.
BB.09. Check the solution to an equation by substitution.

CC. Two-Variable Equations

CC.01. Determine if an ordered pair (x, y) satisfies a given equation.
CC.02. Identify independent and dependent variables in a relationship.
CC.03. Solve word problems involving two-variable equations.
CC.04. Complete a table for a two-variable relationship.
CC.05. Write a two-variable equation to represent a relationship.
CC.06. Identify the graph of a given equation.
CC.07. Interpret a graph of a two-variable relationship in word problems.
CC.08. Create a graph from a two-variable equation.

DD. Two-Dimensional Figures: Identification and Classification

DD.01. Identify and classify polygons based on their properties (number of sides, angles).
DD.02. Measure and classify angles (acute, obtuse, right, straight).
DD.03. Estimate angle measurements.
DD.04. Classify triangles based on their sides and angles (e.g., equilateral, isosceles, scalene, acute, right, obtuse).
DD.05. Identify trapeziums.
DD.06. Classify quadrilaterals (square, rectangle, parallelogram, rhombus).
DD.07. Graph triangles and quadrilaterals on a coordinate plane.
DD.08. Explore the properties of parallelograms (opposite sides parallel and equal, opposite angles equal).

EE. Two-Dimensional Figures: Angles and Properties

FF. Symmetry and Transformations

FF.01. Identify lines of symmetry in two-dimensional figures.
FF.02. Describe reflection, rotation, and translation transformations.
FF.03. Perform translations and graph the image of a figure.
FF.04. Perform reflections and graph the image of a figure.
FF.05. Perform rotations and graph the image of a figure.
FF.06. Determine if figures are similar or congruent.
FF.07. Find side lengths of similar figures using proportions.
FF.08. Identify the center of rotation and the angle of rotation.

GG. Three-Dimensional Figures

HH. Geometric Measurement: Perimeter and Area

HH.01. Calculate the perimeter of polygons.
HH.02. Calculate the area of figures made of unit squares.
HH.03. Calculate the area of squares and rectangles.
HH.04. Calculate the area of triangles.
HH.05. Calculate the area of compound figures by decomposing them into simpler shapes.
HH.06. Calculate area and perimeter of figures on grids.
HH.07. Solve word problems involving area and perimeter.
HH.08. Explore the relationship between perimeter and area of rectangles.
HH.09. Compare the area and perimeter of two figures.
HH.10. Calculate the area, circumference, radius, and diameter of circles.
HH.11. Solve word problems involving circles.
HH.12. Calculate the area, perimeter, radius, and diameter of semicircles.
HH.13. Calculate the area, perimeter, and radius of quarter circles.
HH.14. Calculate the area of compound figures with triangles, semicircles, and quarter circles.
HH.15. Calculate the area between two rectangles.
HH.16. Calculate the area between two triangles.
HH.17. Calculate the area between two circles.
HH.18. Relate area to real world problems (e.g., painting a wall).

II. Geometric Measurement: Volume and Surface Area

JJ. Data and Graphs: Representation

JJ.01. Interpret information presented in pictographs.
JJ.02. Create pictographs to represent data.
JJ.03. Interpret stem-and-leaf plots.
JJ.04. Create stem-and-leaf plots.
JJ.05. Interpret line plots.
JJ.06. Create line plots.
JJ.07. Create frequency tables to organize data.
JJ.08. Interpret bar graphs.
JJ.09. Create bar graphs.
JJ.10. Interpret double bar graphs.
JJ.11. Create double bar graphs.
JJ.12. Interpret histograms.
JJ.13. Create histograms.
JJ.14. Represent data in pie charts using fractions.
JJ.15. Organise real world data using the different graph types.

Course Content

A. Whole Numbers and Place Value

A.01. Identify place values in whole numbers.

A.02. Write word names for whole numbers.

A.03. Read and interpret Roman numerals.

A.04. Compare and order whole numbers.

A.05. Round whole numbers to a specified place value.

A.06. Apply place value understanding to round numbers in real-world contexts.

B. Addition and Subtraction of Whole Numbers

B.01. Add and subtract whole numbers using standard algorithms.

B.02. Solve addition and subtraction word problems involving whole numbers.

B.03. Estimate sums and differences of whole numbers to check for reasonableness.

B.04. Use addition and subtraction to solve multi-step word problems.

B.05. Explore the properties of addition (commutative, associative, identity).

B.06. Use mental math strategies to add and subtract whole numbers efficiently.

C. Multiplication of Whole Numbers

C.01. Multiply whole numbers using standard algorithms.

C.02. Solve multiplication word problems involving whole numbers.

C.03. Multiply numbers ending in zeroes using mental math.

C.04. Solve word problems involving multiplication of numbers ending in zeroes.

C.05. Multiply three or more numbers.

C.06. Solve multi-step word problems involving multiplication of three or more numbers.

C.07. Estimate products of whole numbers.

C.08. Apply the distributive property to simplify multiplication problems.

D. Division of Whole Numbers

D.01. State and apply divisibility rules for common numbers (e.g., 2, 3, 5, 10).

D.02. Recognize and apply division patterns with zeroes.

D.03. Solve word problems involving division of numbers ending in zeroes.

D.04. Estimate quotients of whole numbers.

D.05. Divide whole numbers by two-digit divisors using long division.

D.06. Interpret remainders in division problems.

D.07. Solve multi-step word problems involving division.

E. Exponents and Square Roots

E.01. Write multiplication expressions using exponents.

E.02. Evaluate powers (exponents).

E.03. Find the missing exponent or base in exponential expressions.

E.04. Evaluate powers with decimal bases.

E.05. Evaluate powers with fractional bases.

E.06. Find the square roots of perfect squares.

E.07. Estimate square roots of non-perfect squares.

E.08. Calculate cubes and cube roots of perfect cubes.

E.09. Compare and order numbers expressed in exponential form.

F. Number Theory

F.01. Classify numbers as prime or composite.

F.02. Identify factors of a given number.

F.03. Find the prime factorization of a number.

F.04. Write prime factorizations using exponents.

F.05. Find the highest common factor (HCF) of two or more numbers.

F.06. Find the lowest common multiple (LCM) of two or more numbers.

F.07. Solve word problems involving HCF and LCM.

F.08. Use prime factorization to simplify fractions.

G. Decimals: Understanding and Ordering

G.01. Identify decimal numbers represented by models.

G.02. Identify place values in decimal numbers.

G.03. Write word names for decimal numbers.

G.04. Convert decimals to mixed numbers and vice versa.

G.05. Put decimal numbers in order from least to greatest.

G.06. Use inequalities to compare decimals.

G.07. Place decimals on a number line.

G.08. Extend place value understanding to millionths and beyond.

H. Decimals: Rounding

H.01. Round decimals to a specified place value.

H.02. Round whole numbers and decimals to find a missing digit.

H.03. Apply rounding skills to estimate in real-world scenarios.

H.04. Explain the effect of rounding on precision and accuracy.

I. Addition and Subtraction of Decimals

I.01. Add and subtract decimal numbers using standard algorithms.

I.02. Solve addition and subtraction word problems involving decimals.

I.03. Estimate sums and differences of decimals.

I.04. Use maps with decimal distances to solve problems.

I.05. Apply decimal operations to solve problems involving measurement.

J. Multiplication and Division of Decimals

J.01. Multiply a decimal by a one-digit whole number.

J.02. Multiply a decimal by a multi-digit whole number.

J.03. Solve word problems involving multiplication of decimals and whole numbers.

J.04. Multiply two decimals using grids.

J.05. Multiply decimals using standard algorithms.

J.06. Estimate products of decimal numbers.

J.07. Use inequalities involving decimal multiplication.

J.08. Divide decimals by whole numbers.