NEW ZEALAND MATH YEAR 9 – EDmama New Zealand

A. Numbers and Counting

A.01. Classify whole numbers as prime or composite
A.02. Identify factors of a given number.
A.03. Apply divisibility rules for common numbers (2, 3, 5, 10).
A.04. Determine the prime factorization of a number.
A.05. Calculate the highest common factor (HCF) of two or more numbers.
A.06. Calculate the least common multiple (LCM) of two or more numbers.
A.07. Solve word problems involving HCF and LCM.
A.08. Classify different types of numbers (natural, integer, rational, irrational).
A.09. Explore the historical significance and applications of different number systems.

B. Integers

C. Operations with Integers

C.01. State and apply the rules for adding and subtracting integers.
C.02. Model addition and subtraction of integers using counters or number lines.
C.03. Add and subtract integers accurately.
C.04. Add and subtract three or more integers.
C.05. Solve word problems involving addition and subtraction of integers.
C.06. State and apply the rules for multiplying and dividing integers.
C.07. Multiply and divide integers accurately.
C.08. Evaluate numerical expressions involving integers, following the order of operations.

D. Rational Numbers

D.01. Define and identify rational and irrational numbers.
D.02. Write fractions in their lowest terms (simplest form).
D.03. Determine the least common denominator (LCD) for a set of fractions.
D.04. Round decimals and mixed numbers to a specified number of decimal places.
D.05. Determine the absolute value of a rational number.
D.06. Convert fluently between decimals, fractions, and mixed numbers.
D.07. Compare rational numbers using inequality symbols.
D.08. Arrange a set of rational numbers in ascending or descending order.
D.09. Explain why some rational numbers have terminating decimal representations and others have repeating decimal representations.

E. Operations with Rational Numbers

E.01. Define reciprocals and multiplicative inverses.
E.02. Add and subtract rational numbers (fractions and decimals).
E.03. Solve word problems involving addition and subtraction of rational numbers.
E.04. Apply the correct order of operations to expressions involving addition and subtraction of rational numbers.
E.05. Multiply and divide rational numbers (fractions and decimals).
E.06. Solve word problems involving multiplication and division of rational numbers.
E.07. Apply the correct order of operations to expressions involving multiplication and division of rational numbers.
E.08. Apply all four operations (addition, subtraction, multiplication, and division) to solve problems with rational numbers.
E.09. Evaluate complex numerical expressions involving rational numbers, using the correct order of operations.
E.10. Solve multi-step problems involving all four operations with rational numbers.

F. Ratios, Rates, and Proportions

F.02. Identify equivalent ratios.
F.03. Write an equivalent ratio for a given ratio.
F.04. Solve word problems involving equivalent ratios.
F.05. Define and calculate unit rates.
F.06. Compare ratios in word problems using unit rates.
F.07. Solve proportions using cross-multiplication.
F.08. Determine if two ratios form a proportion.
F.09. Solve word problems to determine if ratios form a proportion.
F.10. Apply proportions to estimate population size.
F.11. Solve word problems involving scale drawings.
F.12. Apply ratio and proportion concepts to solve real-world problems.
F.01. Understand the concept of a ratio and its different representations.

G. Percents

G.01. Convert between percents, fractions, and decimals.
G.02. Compare percents to fractions and decimals.
G.03. Calculate what percent one number is of another.
G.04. Solve word problems to find what percent one number is of another.
G.05. Estimate percents of numbers.
G.06. Calculate percents of numbers and money amounts.
G.07. Solve word problems involving percents of numbers.
G.08. Compare percents of numbers.
G.09. Solve percent equations.
G.10. Calculate percent of change (increase or decrease).
G.11. Solve word problems involving percent of change.
G.12. Apply percentages to solve real-world problems.

H. Proportional Relationships

H.01. Find the constant of proportionality from a table of values.
H.02. Write equations for proportional relationships based on data in tables.
H.03. Identify proportional relationships by examining graphs.
H.04. Determine the constant of proportionality from a graph.
H.05. Write equations for proportional relationships based on graphs.
H.06. Determine if a relationship is proportional.
H.07. Graph proportional relationships on the coordinate plane.
H.08. Interpret the meaning of points and slopes on graphs of proportional relationships.
H.09. Write and solve equations for proportional relationships.
H.10. Create tables and graphs to represent proportional relationships in real-world contexts.

I. Consumer Maths

I.01. Interpret and use price lists to determine costs.
I.02. Calculate unit prices of items.
I.03. Use unit prices to calculate the total price of multiple items.
I.04. Calculate percentage-based amounts like GST, discounts, and markups.
I.05. Calculate the percentage of discount or markup applied to an item.
I.06. Determine the original price of an item after a sale or discount.
I.07. Solve multi-step problems involving percentages in consumer contexts.
I.08. Calculate simple interest earned on an investment or paid on a loan.
I.09. Calculate compound interest earned on an investment or paid on a loan.
I.10. Compare different loan options based on interest rates and repayment schedules.

J. Units of Measurement

K. Exponents and Roots

K.01. Understand the meaning of exponents and their notation.
K.02. Evaluate powers (e.g., 2³, 5²).
K.03. Solve equations with variable exponents (simple cases).
K.04. Evaluate powers with negative bases.
K.05. Evaluate powers with decimal and fractional bases.
K.06. Understand the meaning of negative exponents.
K.07. Evaluate powers with negative exponents.
K.08. Apply the product of powers property (multiplication with exponents).
K.09. Apply the quotient of powers property (division with exponents).
K.10. Simplify expressions using multiplication and division with exponents.
K.11. Apply the power of a power rule.
K.12. Evaluate expressions using multiple properties of exponents.
K.13. Identify equivalent expressions involving exponents.
K.14. Determine the square roots of perfect squares.
K.15. Distinguish between positive and negative square roots.
K.16. Estimate square roots of non-perfect squares.
K.17. Understand the relationship between squaring and taking square roots.
K.18. Solve equations involving squares and square roots.
K.19. Determine the cube roots of perfect cubes.
K.20. Estimate cube roots of non-perfect cubes.
K.21. Solve equations involving cubes and cube roots.
K.22. Apply exponential growth and decay to real-world scenarios.

L. Standard Form (Scientific Notation)

M. Problem Solving

N. Two-Dimensional Figures

N.01. Identify and classify polygons by their number of sides.
N.02. Classify triangles based on their sides and angles.
N.03. Identify trapeziums (trapezoids).
N.04. Classify quadrilaterals (square, rectangle, parallelogram, rhombus).
N.05. Graph triangles and quadrilaterals on the coordinate plane.
N.06. Find missing angles in triangles and quadrilaterals using angle properties.
N.07. Calculate the sum of interior angles of polygons.
N.08. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
N.09. Find measures of complementary, supplementary, vertical, and adjacent angles.
N.10. Understand the angle relationships formed when a transversal intersects parallel lines.
N.11. Find lengths and measures of bisected line segments and angles.
N.12. Identify and define the parts of a circle (radius, diameter, circumference, chord, arc).
N.13. Apply geometric properties to solve problems involving two-dimensional figures.

O. Three-Dimensional Figures

P. Geometric Measurement

P.01. Calculate the perimeter of various two-dimensional shapes.
P.02. Calculate the area of various two-dimensional shapes.
P.03. Calculate the area between two shapes.
P.04. Solve word problems involving area and perimeter.
P.05. Calculate the circumference and area of circles, semicircles, and quarter circles.
P.06. Solve word problems involving circles.
P.07. Calculate the volume of prisms and cylinders.
P.08. Calculate the surface area of prisms.
P.09. Calculate the surface area of cylinders.
P.10. Calculate the volume of pyramids and cones.
P.11. Calculate the surface area of pyramids.
P.12. Calculate the surface area of cones.
P.13. Calculate the volume and surface area of spheres.
P.14. Determine the relationships between volume and surface area of similar solids.
P.15. Analyze how changes in scale affect perimeter, area, and volume.
P.16. Apply measurement concepts to solve practical problems.

Q. Coordinate Plane

R. Transformations and Congruence

R.01. Identify and describe symmetry in geometric figures.
R.02. Identify reflections, rotations, and translations.
R.03. Perform translations on the coordinate plane and graph the image.
R.04. Determine the coordinates of an image after a translation.
R.05. Perform reflections on the coordinate plane and graph the image.
R.06. Determine the coordinates of an image after a reflection.
R.07. Perform rotations on the coordinate plane and graph the image.
R.08. Determine the coordinates of an image after a rotation.
R.09. Identify corresponding side lengths and angle measures of congruent figures.
R.10. Write congruence statements and identify corresponding parts of congruent figures.
R.11. Apply transformations to demonstrate congruence of geometric shapes.

S. Transformations and Similarity

T. Pythagoras’ Theorem

U. Expressions and Properties

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

V. Number Sequences

V.01. Identify arithmetic and geometric sequences.
V.02. Determine the common difference in an arithmetic sequence.
V.03. Determine the common ratio in a geometric sequence.
V.04. Solve mixed review problems involving both arithmetic and geometric sequences.
V.05. Solve word problems involving number sequences.
V.06. Evaluate variable expressions to find terms in a number sequence.
V.07. Write variable expressions (formulas) for arithmetic sequences.
V.08. Find the nth term of an arithmetic or geometric sequence.
V.09. Explore patterns in different types of number sequences.

W. One-Variable Equations

W.01. Determine which value of x satisfies a given equation.
W.02. Translate word problems into algebraic equations.
W.03. Model and solve equations using algebra tiles.
W.04. Write and solve equations that represent given diagrams.
W.05. Apply the properties of equality (addition, subtraction, multiplication, division).
W.06. Solve one-step equations using inverse operations.
W.07. Solve two-step equations using inverse operations.
W.08. Solve multi-step equations involving the distributive property and combining like terms.
W.09. Solve equations involving like terms on one or both sides.
W.10. Complete the steps to solve equations given a partial solution.
W.11. Solve word problems by setting up and solving one-variable equations.
W.12. Check solutions to equations to ensure accuracy.

X. One-Variable Inequalities

Y. Linear Functions

Y.01. Define and identify functions.
Y.02. Determine if an ordered pair (x, y) satisfies a given linear function.
Y.03. Identify independent and dependent variables in a linear function.
Y.04. Calculate the rate of change (slope) of a linear function.
Y.05. Recognize and interpret constant rate of change in a linear function.
Y.06. Evaluate a linear function for a given input value.
Y.07. Complete a table of values for a linear function.
Y.08. Complete a table of values and graph a linear function.
Y.09. Interpret the graph of a linear function in the context of a word problem.
Y.10. Find the gradient (slope) of a line from a graph.
Y.11. Find the gradient (slope) of a line given two points.
Y.12. Find a missing coordinate on a line given the gradient (slope) and another point.
Y.13. Find the gradient (slope) from the equation of a line.
Y.14. Graph a line using its gradient (slope) and y-intercept.
Y.15. Graph a line from its equation (slope-intercept form, standard form).
Y.16. Write a linear function from a table of values.
Y.17. Write linear functions to represent word problems.
Y.18. Compare linear functions represented as graphs, tables, and equations.
Y.19. Apply linear functions to model and solve real-world problems.

Z. Nonlinear Functions

AA. Monomials and Polynomials

AA.01. Identify monomials.
AA.02. Model polynomials using algebra tiles.
AA.03. Add and subtract polynomials using algebra tiles.
AA.04. Add and subtract polynomials algebraically.
AA.05. Add polynomials to find the perimeter of geometric figures.
AA.06. Multiply monomials.
AA.07. Divide monomials.
AA.08. Simplify expressions by multiplying and dividing monomials.
AA.09. Raise monomials to a power.
AA.10. Determine the square and cube roots of monomials.
AA.11. Multiply polynomials using algebra tiles.
AA.12. Multiply polynomials algebraically.
AA.13. Multiply polynomials to find the area of geometric figures.
AA.14. Apply polynomial operations to solve algebraic problems.

BB. Data and Graphs

BB.15. Interpret information presented in circle graphs (pie charts).
BB.16. Relate central angles in a circle graph to the corresponding data values.
BB.17. Choose the best type of graph to represent a given set of data.
BB.18. Analyze and compare different data representations.
BB.19. Communicate data insights effectively using visual displays.
BB.01. Interpret data presented in tables.
BB.02. Interpret information presented in bar graphs.
BB.03. Create bar graphs from given data.
BB.04. Interpret information presented in line graphs.
BB.05. Create line graphs from given data.
BB.06. Interpret information presented in line plots.
BB.07. Create line plots from given data.
BB.08. Interpret information presented in stem-and-leaf plots.
BB.09. Create stem-and-leaf plots from given data.
BB.10. Interpret information presented in histograms.
BB.11. Create histograms from given data.
BB.12. Create frequency charts from given data.
BB.13. Interpret information presented in box-and-whisker plots.
BB.14. Interpret scatter plots and identify trends.

CC. Statistics

DD. Probability

DD.01. Calculate the probability of simple events.
DD.02. Calculate the probability of opposite, mutually exclusive, and overlapping events.
DD.03. Determine experimental probability from observed data.
DD.04. Make predictions based on experimental probability.
DD.05. Calculate the number of possible outcomes for compound events.
DD.06. Identify independent and dependent events.
DD.07. Calculate the probability of independent and dependent events.
DD.08. Apply the counting principle to determine the total number of outcomes in a situation.
DD.09. Use probability to make informed decisions in real-world situations.

Course Content

A. Numbers and Counting

A.01. Classify whole numbers as prime or composite

A.02. Identify factors of a given number.

A.03. Apply divisibility rules for common numbers (2, 3, 5, 10).

A.04. Determine the prime factorization of a number.

A.05. Calculate the highest common factor (HCF) of two or more numbers.

A.06. Calculate the least common multiple (LCM) of two or more numbers.

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

A.08. Classify different types of numbers (natural, integer, rational, irrational).

A.09. Explore the historical significance and applications of different number systems.

B. Integers

B.01. Represent integers on a number line.

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

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

B.04. Identify the opposite of an integer.

B.05. Compare and order integers using inequality symbols.

B.06. Interpret integer inequalities involving absolute values.

B.07. Apply integers to represent real-world situations (e.g., temperature, altitude).

C. Operations with Integers

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

C.02. Model addition and subtraction of integers using counters or number lines.

C.03. Add and subtract integers accurately.

C.04. Add and subtract three or more integers.

C.05. Solve word problems involving addition and subtraction of integers.

C.06. State and apply the rules for multiplying and dividing integers.

C.07. Multiply and divide integers accurately.

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

D. Rational Numbers

D.01. Define and identify rational and irrational numbers.

D.02. Write fractions in their lowest terms (simplest form).

D.03. Determine the least common denominator (LCD) for a set of fractions.

D.04. Round decimals and mixed numbers to a specified number of decimal places.

D.05. Determine the absolute value of a rational number.

D.06. Convert fluently between decimals, fractions, and mixed numbers.

D.07. Compare rational numbers using inequality symbols.

D.08. Arrange a set of rational numbers in ascending or descending order.

D.09. Explain why some rational numbers have terminating decimal representations and others have repeating decimal representations.

E. Operations with Rational Numbers

E.01. Define reciprocals and multiplicative inverses.

E.02. Add and subtract rational numbers (fractions and decimals).

E.03. Solve word problems involving addition and subtraction of rational numbers.

E.04. Apply the correct order of operations to expressions involving addition and subtraction of rational numbers.

E.05. Multiply and divide rational numbers (fractions and decimals).

E.06. Solve word problems involving multiplication and division of rational numbers.

E.07. Apply the correct order of operations to expressions involving multiplication and division of rational numbers.

E.08. Apply all four operations (addition, subtraction, multiplication, and division) to solve problems with rational numbers.

E.09. Evaluate complex numerical expressions involving rational numbers, using the correct order of operations.

E.10. Solve multi-step problems involving all four operations with rational numbers.

F. Ratios, Rates, and Proportions

F.02. Identify equivalent ratios.

F.03. Write an equivalent ratio for a given ratio.

F.04. Solve word problems involving equivalent ratios.

F.05. Define and calculate unit rates.

F.06. Compare ratios in word problems using unit rates.

F.07. Solve proportions using cross-multiplication.

F.08. Determine if two ratios form a proportion.

F.09. Solve word problems to determine if ratios form a proportion.

F.10. Apply proportions to estimate population size.

F.11. Solve word problems involving scale drawings.

F.12. Apply ratio and proportion concepts to solve real-world problems.

F.01. Understand the concept of a ratio and its different representations.

G. Percents

G.01. Convert between percents, fractions, and decimals.

G.02. Compare percents to fractions and decimals.

G.03. Calculate what percent one number is of another.

G.04. Solve word problems to find what percent one number is of another.

G.05. Estimate percents of numbers.

G.06. Calculate percents of numbers and money amounts.

G.07. Solve word problems involving percents of numbers.

G.08. Compare percents of numbers.

G.09. Solve percent equations.

G.10. Calculate percent of change (increase or decrease).

G.11. Solve word problems involving percent of change.

G.12. Apply percentages to solve real-world problems.

H. Proportional Relationships

H.01. Find the constant of proportionality from a table of values.

H.02. Write equations for proportional relationships based on data in tables.

H.03. Identify proportional relationships by examining graphs.

H.04. Determine the constant of proportionality from a graph.