NEW ZEALAND MATH YEAR 8 – EDmama New Zealand

A. Numbers and Counting

A.01. Classify numbers as prime or composite.
A.02. Identify multiples and factors of a given number.
A.03. Apply divisibility rules to determine if a number is divisible by another number.
A.04. Determine the prime factorization of a number.
A.05. Find the highest common factor (HCF) of two or more numbers.
A.06. Find the least common multiple (LCM) of two or more numbers.
A.07. Solve word problems involving HCF and LCM.
A.08. Explore the historical significance and applications of prime numbers.

B. Understanding Integers

B.01. Define and represent integers on a number line.
B.02. Graph integers on horizontal and vertical number lines.
B.03. Find the absolute value of an integer.
B.04. Identify opposite integers.
B.05. Compare and order integers.
B.06. Interpret and solve integer inequalities, including those with absolute values.
B.07. Apply integers to real-world contexts such as temperature and altitude.
B.08. Explore the historical development and use of negative numbers.

C. Operations with Integers

C.01. State and apply the rules for adding and subtracting integers.
C.02. Add and subtract integers using visual aids like counters and number lines.
C.03. Add and subtract integers efficiently.
C.04. Complete addition and subtraction sentences involving integers.
C.05. Translate and 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.
C.08. Complete multiplication and division sentences involving integers.
C.09. Evaluate numerical expressions involving integers using the order of operations.
C.10. Model real-world situations using integer operations and interpret the results.

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

F. Fractions and Mixed Numbers

F.01. Define fractions and their components (numerator, denominator).
F.02. Interpret fractions using word problems.
F.03. Identify and generate equivalent fractions.
F.04. Write fractions in lowest terms (simplify).
F.05. Interpret fractions using graphs and tables to solve word problems.
F.06. Identify the least common denominator (LCD) of two or more fractions.
F.07. Compare and order fractions.
F.08. Solve word problems comparing fractions.
F.09. Convert between mixed numbers and improper fractions.
F.10. Compare mixed numbers and improper fractions.
F.11. Round mixed numbers to the nearest whole number.

G. Operations with Fractions

G.01. Add and subtract fractions with like denominators.
G.02. Solve word problems involving addition and subtraction of fractions with like denominators.
G.03. Add fractions with unlike denominators.
G.04. Subtract fractions with unlike denominators.
G.05. Add and subtract fractions with unlike denominators: word problems
G.06. Add and subtract mixed numbers.
G.07. Solve word problems involving addition and subtraction of mixed numbers.
G.08. Multiply fractions and whole numbers.
G.09. Solve word problems involving multiplication of fractions and whole numbers.
G.10. Multiply two fractions using models.
G.11. Multiply fractions.
G.12. Multiply fractions: word problems
G.13. Multiply three or more fractions and whole numbers
G.14. Divide whole numbers by unit fractions using models
G.15. Define reciprocals.
G.16. Divide whole numbers and unit fractions
G.17. Divide fractions
G.18. Divide fractions: word problems
G.19. Estimate products and quotients of fractions and mixed numbers
G.20. Solve word problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers.
G.21. Evaluate numerical expressions involving fractions

H. Rational Numbers

H.03. Compare rational numbers.
H.04. Order a set of rational numbers.
H.05. Convert between decimals and fractions or mixed 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.
H.01. Identify rational numbers and their properties.
H.02. Find the absolute value of rational numbers.

I. Exponents and Square Roots

I.01. Understand the concept of exponents and their notation.
I.02. Evaluate powers (exponents).
I.03. Solve simple equations with variable exponents.
I.04. Evaluate powers with negative bases.
I.05. Evaluate powers with decimal and fractional bases.
I.06. Evaluate numerical expressions involving exponents.
I.07. Write numbers in standard form (scientific notation).
I.08. Compare numbers written in standard form.
I.09. Find square roots of perfect squares.
I.10. Find positive square roots and cube roots.
I.11. Estimate square roots.

J. Ratios, Rates, and Proportions

J.01. Understand the concept of a ratio.
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. Compare ratios in word problems.
J.06. Apply ratios to scale drawings.
J.07. Determine if two ratios form a proportion.
J.08. Determine if two ratios form a proportion in word problems.
J.09. Solve proportions.
J.10. Solve proportions in word problems.
J.11. Understand and calculate unit rates.
J.12. Determine the rate of change.
J.13. Identify a constant rate of change.
J.14. Calculate speed, distance, or time in word problems.
J.15. Estimate population size using proportions.

K. Proportional Relationships

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

L. Percents

L.01. Illustrate a given percentage using visual aids.
L.02. Convert fractions to percents using grid models.
L.03. Represent percents with grid models, decimals, and fractions.
L.04. Convert between percents, fractions, and decimals.
L.05. Compare percents to fractions and decimals.
L.06. Estimate percents of numbers.
L.07. Calculate percents of numbers and money amounts.
L.08. Solve word problems involving percents of numbers.
L.09. Determine what percent one number is of another.
L.10. Find the whole given a part and a percent.
L.11. Solve percent equations.
L.12. Solve percent equations in word problems.

M. Consumer Maths

M.01. Solve word problems involving addition, subtraction, multiplication, and division of money amounts.
M.02. Interpret and use price lists.
M.03. Calculate and compare unit prices.
M.04. Use unit prices to find the total price.
M.05. Calculate percent of a number, including GST, discount, and mark-up.
M.06. Determine which coupon offers a better deal.
M.07. Calculate the percent discount and mark-up.
M.08. Determine the original price given the sale price.
M.09. Solve multi-step problems with percents.
M.10. Calculate simple interest.
M.11. Calculate compound interest.
M.12. Balance a budget.
M.13. Adjust a budget based on changing circumstances.

N. Problem Solving and Estimation

N.01. Use estimation to solve word problems.
N.02. Solve multi-step word problems.
N.03. Solve word problems using the guess-and-check strategy.
N.04. Use Venn diagrams to solve problems.
N.05. Determine the number of each type of coin in a given situation.
N.06. Interpret and use schedules and timelines (12-hour time).
N.07. Interpret and use schedules (24-hour time).
N.08. Solve elapsed time word problems.
N.09. Interpret transportation schedules.

O. Units of Measurement

P. Coordinate Plane

Q. Number Sequences

R. Expressions and Properties

R.01. Write variable expressions from verbal descriptions.
R.02. Translate word problems into variable expressions.
R.03. Evaluate linear expressions.
R.04. Evaluate multi-variable expressions.
R.05. Evaluate absolute value expressions.
R.06. Evaluate nonlinear expressions.
R.07. Identify terms and coefficients in an expression.
R.08. Sort factors of expressions.
R.09. State and apply the properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
R.10. Multiply using the distributive property.
R.11. Solve equations using properties.
R.12. Write equivalent expressions using properties.
R.13. Add and subtract like terms.
R.14. Add, subtract and multiply linear expressions.
R.15. Factor linear expressions.
R.16. Identify equivalent linear expressions.

S. One-Variable Equations

T. Two-Variable Equations

T.05. Write a two-variable equation from a table or verbal description.
T.06. Identify the graph of a given two-variable equation.
T.07. Graph a two-variable equation.
T.08. Interpret a graph in the context of a word problem.
T.09. Write an equation from a graph using a table of values.
T.01. Determine if an ordered pair (x, y) satisfies a given equation.
T.02. Identify independent and dependent variables in a two-variable equation.
T.03. Solve word problems involving two-variable equations.
T.04. Complete a table for a two-variable relationship.

U. Two-Dimensional Figures

U.01. Define and classify polygons based on their properties.
U.02. Name, measure, and classify angles (acute, obtuse, right, straight, reflex).
U.03. Classify triangles by their sides and angles.
U.04. Identify trapeziums (trapezoids).
U.05. Classify quadrilaterals based on their properties (parallelogram, rectangle, square, rhombus).
U.06. Graph triangles and quadrilaterals on the coordinate plane.
U.07. Identify and describe the parts of a circle (radius, diameter, circumference, chord, arc).
U.08. Find missing angles in triangles and quadrilaterals using angle properties.
U.09. Calculate interior angles of polygons using formulas.
U.10. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
U.11. Find measures of complementary, supplementary, vertical, and adjacent angles given angle relationships.
U.12. Find lengths and measures of bisected line segments and angles using algebraic methods.

V. Lines

W. Transformations, Congruence, and Similarity

W.01. Understand and identify symmetry in geometric figures.
W.02. Identify reflections, rotations, and translations as types of transformations.
W.03. Perform translations and graph the image of a figure.
W.04. Determine the coordinates of an image after a translation.
W.05. Perform reflections and graph the image of a figure.
W.06. Determine the coordinates of an image after a reflection.
W.07. Perform rotations and graph the image of a figure.
W.08. Determine the coordinates of an image after a rotation.
W.09. Define and differentiate between similar and congruent figures.
W.10. Write congruence statements and identify corresponding parts of congruent figures.
W.11. Determine side lengths and angle measures of congruent figures.
W.12. Determine side lengths and angle measures of similar figures using ratios.
W.13. Use similar figures and proportions to solve indirect measurement problems.

X. Three-Dimensional Figures

Y. Geometric Measurement

Y.01. Calculate the perimeter of polygons.
Y.02. Calculate the area of rectangles and parallelograms.
Y.03. Calculate the area of triangles.
Y.04. Calculate the area between two shapes.
Y.05. Solve word problems involving area and perimeter.
Y.06. Calculate the volume of cubes and rectangular prisms.
Y.07. Calculate the volume of prisms and cylinders.
Y.08. Calculate the volume of compound figures I
Y.09. Calculate the volume of compound figures II

Z. Data and Graphs

Z.01. Interpret data presented in tables.
Z.02. Create line plots to display data.
Z.03. Interpret information from line plots.
Z.04. Create stem-and-leaf plots to organize data.
Z.05. Interpret information from stem-and-leaf plots.
Z.06. Create bar graphs to represent categorical data.
Z.07. Interpret information from bar graphs.
Z.08. Create histograms to represent continuous data.
Z.09. Interpret information from histograms.
Z.10. Create frequency charts to summarize data.
Z.11. Interpret information from circle graphs (pie charts).
Z.12. Calculate central angles for circle graphs.
Z.13. Create line graphs to show trends over time.
Z.14. Interpret information from line graphs.
Z.15. Interpret information from box-and-whisker plots.
Z.16. Create and interpret scatter plots to analyze relationships between variables.
Z.17. Choose the best type of graph to represent a given dataset.

Course Content

A. Numbers and Counting

A.01. Classify numbers as prime or composite.

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

A.03. Apply divisibility rules to determine if a number is divisible by another number.

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

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

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

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

A.08. Explore the historical significance and applications of prime numbers.

B. Understanding Integers

B.01. Define and represent integers on a number line.

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

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

B.04. Identify opposite integers.

B.05. Compare and order integers.

B.06. Interpret and solve integer inequalities, including those with absolute values.

B.07. Apply integers to real-world contexts such as temperature and altitude.

B.08. Explore the historical development and use of negative numbers.

C. Operations with Integers

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

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

C.03. Add and subtract integers efficiently.

C.04. Complete addition and subtraction sentences involving integers.

C.05. Translate and 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.

C.08. Complete multiplication and division sentences involving integers.

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

C.10. Model real-world situations using integer operations and interpret the results.

D. Decimals

D.01. Review decimal place values and representations.

D.02. Plot decimals on a number line.

D.03. Compare and order decimals.

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

D.05. Relate decimals to fractions and percentages.

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

E.05. Divide decimals.

E.06. Solve word problems involving division of decimals by whole numbers.

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

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

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

E.10. Solve multi-step inequalities with decimals.

E.11. Interpret and use maps with decimal distances.

F. Fractions and Mixed Numbers

F.01. Define fractions and their components (numerator, denominator).

F.02. Interpret fractions using word problems.

F.03. Identify and generate equivalent fractions.

F.04. Write fractions in lowest terms (simplify).

F.05. Interpret fractions using graphs and tables to solve word problems.

F.06. Identify the least common denominator (LCD) of two or more fractions.

F.07. Compare and order fractions.

F.08. Solve word problems comparing fractions.

F.09. Convert between mixed numbers and improper fractions.

F.10. Compare mixed numbers and improper fractions.

F.11. Round mixed numbers to the nearest whole number.

G. Operations with Fractions

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

G.02. Solve word problems involving addition and subtraction of fractions with like denominators.

G.03. Add fractions with unlike denominators.

G.04. Subtract fractions with unlike denominators.

G.05. Add and subtract fractions with unlike denominators: word problems

G.06. Add and subtract mixed numbers.

G.07. Solve word problems involving addition and subtraction of mixed numbers.

G.08. Multiply fractions and whole numbers.

G.09. Solve word problems involving multiplication of fractions and whole numbers.

G.10. Multiply two fractions using models.

G.11. Multiply fractions.

G.12. Multiply fractions: word problems

G.13. Multiply three or more fractions and whole numbers

G.14. Divide whole numbers by unit fractions using models

G.15. Define reciprocals.

G.16. Divide whole numbers and unit fractions

G.17. Divide fractions

G.18. Divide fractions: word problems

G.19. Estimate products and quotients of fractions and mixed numbers