Course Content
A. Numbers and Counting
-
A.01. Read and write whole numbers using place value.
-
A.02. Identify the place value of digits in whole numbers.
-
A.03. Express numbers using word names.
-
A.04. Understand and use Roman numerals.
-
A.05. Apply divisibility rules to determine factors of numbers.
-
A.06. Identify prime and composite numbers.
-
A.07. Determine the prime factorization of a number.
-
A.08. Calculate the highest common factor (HCF) and least common multiple (LCM) of two or more numbers.
-
A.09. Solve word problems involving HCF and LCM.
-
A.10. Understand the concept of multiplicative inverses.
-
A.11. Explore the properties of special numbers like perfect, abundant, deficient, and amicable numbers.
B. Add and Subtract Whole Numbers
-
B.01. Add and subtract whole numbers up to millions.
-
B.02. Solve word problems involving addition and subtraction of whole numbers.
-
B.03. Identify and apply the properties of addition (commutative, associative, identity).
-
B.04. Estimate sums and differences of whole numbers.
-
B.05. Solve estimation word problems involving sums and differences.
-
B.06. Use mental math strategies to add and subtract whole numbers efficiently.
-
B.07. Investigate the impact of changing addends or minuends on the sum or difference.
C. Multiply Whole Numbers
-
C.01. Recall multiplication facts up to 10×10.
-
C.02. Determine the missing factor in multiplication equations.
-
C.03. Multiply multi-digit whole numbers.
-
C.04. Solve word problems involving multiplication of whole numbers.
-
C.05. Multiply numbers ending in zeroes.
-
C.06. Solve word problems involving multiplication of numbers ending in zeroes.
-
C.07. Multiply three or more numbers.
-
C.08. Solve word problems involving multiplication of three or more numbers.
-
C.09. Estimate products of whole numbers.
-
C.10. Identify and apply the properties of multiplication (commutative, associative, distributive, identity, zero).
-
C.11. Use arrays and area models to visually represent multiplication.
D. Divide Whole Numbers
-
D.01. Apply divisibility rules to simplify division.
-
D.02. Divide whole numbers by one-digit numbers.
-
D.03. Solve word problems involving division by one-digit numbers.
-
D.04. Divide whole numbers by two-digit numbers.
-
D.05. Solve word problems involving division by two-digit numbers.
-
D.06. Identify and extend division patterns with zeroes.
-
D.07. Solve word problems involving division of numbers ending in zeroes.
-
D.08. Estimate quotients of whole numbers.
-
D.09. Use long division to divide larger numbers accurately.
-
D.10. Relate division to multiplication through inverse operations.
E. Fractions and Mixed Numbers
-
E.01. Review the concepts of fractions and mixed numbers.
-
E.02. Solve word problems involving understanding fractions.
-
E.03. Identify and generate equivalent fractions.
-
E.04. Write fractions in their lowest terms (simplest form).
-
E.05. Solve word problems involving fractions in various contexts.
-
E.06. Determine the least common denominator (LCD) of two or more fractions.
-
E.07. Compare fractions with like and unlike denominators.
-
E.08. Solve word problems involving comparison of fractions.
-
E.09. Convert between improper fractions and mixed numbers.
-
E.10. Convert between decimals and fractions or mixed numbers.
-
E.11. Order a mix of decimals, fractions, and mixed numbers on a number line.
-
E.12. Investigate the historical development of fraction notation and usage across cultures.
F. Decimals
-
F.01. Identify the decimal number represented by a visual model.
-
F.02. Understand and identify decimal place values.
-
F.03. Express decimal numbers using word names.
-
F.04. Convert decimals to mixed numbers.
-
F.05. Order decimal numbers from least to greatest.
-
F.06. Use inequalities to compare decimal numbers.
-
F.07. Round decimals to a specified place value.
-
F.08. Round whole numbers and decimals by identifying the missing digit.
-
F.09. Locate and represent decimals on a number line.
-
F.10. Relate decimals to fractions with denominators that are powers of 10.
G. Add and Subtract Decimals
-
G.01. Add and subtract decimal numbers.
-
G.02. Solve word problems involving addition and subtraction of decimals.
-
G.03. Estimate sums and differences of decimals.
-
G.04. Interpret maps with decimal distances to solve problems.
-
G.05. Perform mental calculations with decimals in simple contexts.
-
G.06. Analyze error patterns in decimal addition and subtraction.
H. Multiply and Divide Decimals
-
H.01. Multiply a decimal by a one-digit whole number.
-
H.02. Multiply a decimal by a multi-digit whole number.
-
H.03. Solve word problems involving multiplication of decimals and whole numbers.
-
H.04. Estimate products of decimal numbers.
-
H.05. Use inequalities involving multiplication of decimals.
-
H.06. Divide decimals by whole numbers.
-
H.07. Solve word problems involving division of decimals by whole numbers.
-
H.08. Multiply and divide decimals by powers of ten.
-
H.09. Explore the connection between decimal multiplication/division and scaling.
-
H.10. Apply the concept of significant figures when multiplying and dividing decimals.
I. Add and Subtract Fractions
-
I.01. Add and subtract fractions with like denominators.
-
I.02. Solve word problems involving addition and subtraction of fractions with like denominators.
-
I.03. Use inequalities with addition and subtraction of like fractions.
-
I.04. Add fractions with unlike denominators.
-
I.05. Subtract fractions with unlike denominators.
-
I.06. Solve word problems involving addition and subtraction of fractions with unlike denominators.
-
I.07. Add and subtract mixed numbers with like denominators.
-
I.08. Solve word problems involving addition and subtraction of mixed numbers with like denominators.
-
I.09. Estimate sums and differences of mixed numbers.
-
I.10. Visualize fraction addition and subtraction using area models and number lines.
-
I.11. Simplify fractions after adding or subtracting, if possible.
J. Multiply Fractions
-
J.01. Multiply unit fractions by whole numbers using number lines.
-
J.02. Multiply fractions by whole numbers using number lines.
-
J.03. Calculate fractions of whole numbers (I).
-
J.04. Calculate fractions of whole numbers (II).
-
J.05. Solve word problems involving fractions of a number.
-
J.06. Estimate products of fractions and whole numbers.
-
J.07. Complete input/output tables for multiplying fractions by whole numbers.
-
J.08. Multiply mixed numbers and whole numbers.
-
J.09. Use area models to understand fraction multiplication visually.
-
J.10. Relate fraction multiplication to real-world scaling and proportions.
K. Exponents and Square Roots
-
K.01. Understand powers of ten.
-
K.02. Evaluate powers of ten.
-
K.03. Write multiplication expressions using exponents.
-
K.04. Evaluate powers.
-
K.05. Find the missing exponent or base in exponential expressions.
-
K.06. Determine the square roots of perfect squares.
-
K.07. Estimate square roots of non-perfect squares.
-
K.08. Explore patterns in the powers of different numbers.
-
K.09. Apply exponents to represent large numbers in scientific notation.
L. Integers
-
L.01. Understand the concept of integers and their use in representing real-world situations.
-
L.02. Represent integers on a number line.
-
L.03. Identify opposite integers.
-
L.04. Graph integers on horizontal and vertical number lines.
-
L.05. Compare integers using inequality symbols.
-
L.06. Order a set of integers from least to greatest.
-
L.07. Use integers to represent quantities like temperature, elevation, and debt.
-
L.08. Explain the importance of zero as a reference point on the number line.
M. Add and Subtract Integers
-
M.01. Determine the sign of the result when adding and subtracting integers.
-
M.02. Add integers using counters or visual aids.
-
M.03. Add integers using rules and number lines.
-
M.04. Subtract integers using counters or visual aids.
-
M.05. Subtract integers using rules and number lines.
-
M.06. Relate integer addition and subtraction to real-world scenarios involving gains and losses.
-
M.07. Explore the concept of absolute value and its relationship to integer operations.
N. Rational Numbers
-
N.01. Compare rational numbers using inequality symbols.
-
N.02. Order a set of rational numbers from least to greatest.
-
N.03. Determine the sign of a rational number.
-
N.04. Convert between different forms of rational numbers (fractions, decimals, percentages).
-
N.05. Represent rational numbers on a number line.
-
N.06. Identify real-world applications of rational numbers.
-
N.07. Explain why all integers are rational numbers but not all rational numbers are integers.
O. Ratios and Rates
-
O.01. Write a ratio to compare two quantities.
-
O.02. Solve word problems involving writing ratios.
-
O.03. Identify equivalent ratios.
-
O.04. Write an equivalent ratio.
-
O.05. Use ratio tables to find equivalent ratios and solve problems.
-
O.06. Determine unit rates and equivalent rates.
-
O.07. Solve word problems involving comparing ratios.
-
O.08. Determine if two ratios form a proportion.
-
O.09. Solve proportions for a missing value.
-
O.10. Solve scale drawing problems using proportions.
-
O.11. Calculate speed using ratios and rates in word problems.
-
O.12. Connect ratios and rates to real-world situations like recipes, maps, and conversions.
P. Percents
-
P.01. Identify the percentage represented by a visual model.
-
P.02. Convert between percents, fractions, and decimals.
-
P.03. Compare percents to each other and to fractions.
-
P.04. Solve word problems comparing percents and fractions.
-
P.05. Calculate the percentage of a number or money amount.
-
P.06. Solve word problems involving finding percentages of numbers.
-
P.07. Find what percent one number is of another.
-
P.08. Solve word problems finding what percent one number is of another.
-
P.09. Find the total when given a part and a percent.
-
P.10. Investigate applications of percentages in finance, statistics, and everyday life.
Q. Units of Measurement
-
Q.01. Estimate metric measurements of length, mass, and capacity.
-
Q.02. Choose the appropriate metric unit of measure for a given situation.
-
Q.03. Convert and compare metric units.
-
Q.04. Work with metric mixed units.
-
Q.05. Convert between square meters and hectares.
-
Q.06. Convert square and cubic units of length.
-
Q.07. Convert between cubic meters and liters.
-
Q.08. Compare temperatures above and below zero.
-
Q.09. Understand the relationship between different units of time.
-
Q.10. Apply unit conversions to solve real-world problems involving measurement.
R. Money
-
R.01. Determine the number of each type of coin needed to make a specific amount.
-
R.02. Add and subtract money amounts.
-
R.03. Solve word problems involving addition and subtraction of money amounts.
-
R.04. Multiply money amounts by whole numbers.
-
R.05. Solve word problems involving multiplication of money.
-
R.06. Divide money amounts.
-
R.07. Solve word problems involving division of money amounts.
-
R.08. Calculate total cost including tax and discounts.
-
R.09. Develop budgeting and financial literacy skills through practical exercises.
S. Time
-
S.01. Calculate elapsed time between two events.
-
S.02. Understand and convert between different units of time.
-
S.03. Determine start and end times given elapsed time.
-
S.04. Convert between 12-hour and 24-hour time formats.
-
S.05. Interpret schedules and timelines using 12-hour time.
-
S.06. Interpret schedules using 24-hour time.
-
S.07. Solve problems involving time zones and international travel.
-
S.08. Apply time management strategies to plan and prioritize tasks.
T. Geometric Measurement
-
T.01. Calculate the perimeter of various shapes.
-
T.02. Calculate the area of squares and rectangles.
-
T.03. Calculate the area of parallelograms.
-
T.04. Calculate the area of triangles.
-
T.05. Calculate the area of compound figures.
-
T.06. Calculate the area between two rectangles.
-
T.07. Determine area and perimeter of figures on grids.
-
T.08. Solve word problems involving area and perimeter.
-
T.09. Analyze the relationship between perimeter and area of rectangles.
-
T.10. Compare the area and perimeter of two figures.
-
T.11. Calculate the volume of cubes and rectangular prisms.
-
T.12. Apply geometric measurement formulas to solve real-world problems.
U. Two-Dimensional Figures
-
U.01. Identify and classify polygons based on their properties.
-
U.02. Measure and classify angles using protractors.
-
U.03. Estimate angle measurements.
-
U.04. Classify triangles based on their angles and sides.
-
U.05. Identify trapeziums.
-
U.06. Classify quadrilaterals based on their properties.
-
U.07. Graph triangles and quadrilaterals on a coordinate plane.
-
U.08. Identify the parts of a circle (radius, diameter, circumference).
-
U.09. Find missing angles in triangles and quadrilaterals using angle properties.
-
U.10. Calculate the sums of angles in polygons.
-
U.11. Name angles using proper notation.
-
U.12. Identify and calculate complementary and supplementary angles.
-
U.13. Analyze transversals of parallel lines and their resulting angles.
-
U.14. Explore tessellations and how different polygons can fit together without gaps or overlaps.
V. Three-Dimensional Figures
-
V.01. Identify polyhedra based on their properties.
-
V.02. Match a description to the corresponding three-dimensional figure.
-
V.03. Draw and identify nets of three-dimensional figures.
-
V.04. Draw and interpret front, side, and top views of 3D objects.
-
V.05. Interpret base plans (architectural drawings).
-
V.06. Calculate the surface area of basic three-dimensional figures.
-
V.07. Investigate real-world applications of different three-dimensional shapes.
W. Coordinate Plane
-
W.01. Identify objects on a coordinate plane in the first quadrant.
-
W.02. Identify objects on a coordinate plane in all four quadrants.
-
W.03. Graph points on a coordinate plane given their coordinates.
-
W.04. Identify the quadrants of the coordinate plane.
-
W.05. Use coordinate planes as maps to locate objects and determine distances.
-
W.06. Follow directions on a coordinate plane to reach a specific location.
-
W.07. Determine the distance between two points on a coordinate plane with the same x or y coordinate.
X. Symmetry and Transformations
-
X.01. Identify lines of symmetry in two-dimensional figures.
-
X.02. Recognize and describe reflection, rotation, and translation transformations.
-
X.03. Perform translations and graph the resulting image on a coordinate plane.
-
X.04. Perform reflections and graph the resulting image on a coordinate plane.
-
X.05. Perform rotations and graph the resulting image on a coordinate plane.
-
X.06. Distinguish between similar and congruent figures.
-
X.07. Find missing side lengths of similar figures using proportions.
-
X.08. Explore how transformations can be used to create patterns and designs.
Y. Data and Graphs
-
Y.01. Create pictographs to represent data.
-
Y.02. Interpret information presented in pictographs.
-
Y.03. Create line plots to display data.
-
Y.04. Interpret information displayed in line plots.
-
Y.05. Create stem-and-leaf plots to organize and display data.
-
Y.06. Interpret information presented in stem-and-leaf plots.
-
Y.07. Create bar graphs to represent categorical data.
-
Y.08. Interpret information presented in bar graphs.
-
Y.09. Create double bar graphs to compare two sets of data.
-
Y.10. Interpret information presented in double bar graphs.
-
Y.11. Create histograms to display the distribution of numerical data.
-
Y.12. Interpret information presented in histograms.
-
Y.13. Create frequency tables to organize data.
-
Y.14. Interpret circle graphs with fractions to represent proportions.
-
Y.15. Create line graphs to show trends over time.
-
Y.16. Interpret information presented in line graphs.
-
Y.17. Create double line graphs to compare trends over time for two sets of data.
-
Y.18. Interpret information presented in double line graphs.
-
Y.19. Choose the best type of graph to represent a given data set.
-
Y.20. Interpret information presented in box-and-whisker plots.
-
Y.21. Analyze the advantages and disadvantages of different graph types.
Z. Statistics
-
Z.01. Calculate the mean, median, mode, and range of a data set.
-
Z.02. Interpret charts to find the mean, median, mode, and range.
-
Z.03. Determine the missing number in a data set given its mean, median, mode, or range.
-
Z.04. Distinguish between populations and samples in statistical studies.
-
Z.05. Make inferences and predictions based on data from multiple samples.
-
Z.06. Discuss the impact of outliers on measures of central tendency.
-
Z.07. Design and conduct simple statistical surveys to collect and analyze data.
AA. Probability
-
AA.01. Determine the number of possible combinations in a given situation.
-
AA.02. Calculate the probability of a single event occurring.
-
AA.03. Make predictions based on probability.
-
AA.04. Calculate the probability of opposite, mutually exclusive, and overlapping events.
-
AA.05. Determine experimental probability through data collection.
-
AA.06. Calculate the number of outcomes for compound events by counting.
-
AA.07. Use collected data to find probabilities and make predictions about future events.
-
AA.08. Design and conduct probability experiments to test theoretical predictions.
BB. Problem Solving and Estimation
-
BB.01. Estimate to solve word problems.
-
BB.02. Solve multi-step word problems.
-
BB.03. Solve word problems with extra or missing information.
-
BB.04. Use a guess-and-check strategy to solve word problems.
-
BB.05. Determine distance and direction to a starting point after a series of movements.
-
BB.06. Use logical reasoning to determine the order of events.
-
BB.07. Apply different problem-solving strategies (e.g., draw a diagram, work backwards) to solve complex problems.
CC. Mixed Operations
-
CC.05. Solve word problems involving addition, subtraction, multiplication, or division of two decimals.
-
CC.06. Add, subtract, or multiply two fractions.
-
CC.07. Solve word problems involving addition, subtraction, or multiplication of two fractions.
-
CC.08. Apply order of operations to expressions involving fractions and decimals.
-
CC.01. Add, subtract, multiply, or divide two whole numbers.
-
CC.02. Solve word problems involving addition, subtraction, multiplication, or division of two whole numbers.
-
CC.03. Evaluate numerical expressions using the order of operations (PEMDAS/BODMAS).
-
CC.04. Add, subtract, multiply, or divide two decimals.
DD. Expressions and Properties
-
DD.01. Write variable expressions to represent mathematical relationships.
-
DD.02. Write variable expressions to represent real-world scenarios.
-
DD.03. Evaluate variable expressions with whole numbers.
-
DD.04. Evaluate multi-variable expressions.
-
DD.05. Evaluate variable expressions with decimals.
-
DD.06. Identify terms and coefficients in algebraic expressions.
-
DD.07. Sort factors of expressions.
-
DD.08. Identify equivalent expressions using algebraic properties.
-
DD.09. Solve for a variable using properties of multiplication.
-
DD.10. Simplify algebraic expressions by combining like terms and using the distributive property.
EE. One-Variable Equations
-
EE.01. Determine which value of x satisfies a given equation.
-
EE.02. Write an equation from a given word problem.
-
EE.03. Model and solve equations using algebra tiles.
-
EE.04. Write and solve equations that represent diagrams.
-
EE.05. Solve one-step equations with whole numbers using inverse operations.
-
EE.06. Solve one-step equations with decimals using inverse operations.
-
EE.07. Solve one-step equations and apply it to word problems.
-
EE.08. Solve two-step equations involving whole numbers and decimals.
FF. Two-Variable Equations
-
FF.01. Determine whether a given (x, y) pair satisfies a given equation.
-
FF.02. Identify the independent and dependent variables in a relationship.
-
FF.03. Solve word problems involving two-variable equations.
-
FF.04. Complete a table of values for a two-variable relationship.
-
FF.05. Write a two-variable equation to represent a relationship.
-
FF.06. Identify the graph of a given two-variable equation.
-
FF.07. Create a graph of a two-variable equation by plotting points from a table of values.
-
FF.08. Analyze the relationship between the slope and y-intercept of a linear equation and its graph.
GG. Consumer Maths
-
GG.01. Calculate sale prices after discounts.
-
GG.02. Determine which coupon offers the better deal.
-
GG.03. Calculate unit prices to compare the cost of different items.
-
GG.04. Calculate unit prices with fractions and decimals.
-
GG.05. Calculate tip, mark-up, and other percentages related to consumer transactions.
-
GG.06. Calculate Goods and Services Tax (GST) or other sales taxes.
-
GG.07. Calculate simple interest earned on savings or paid on loans.
-
GG.08. Compare different loan options based on interest rates and repayment schedules.
HH. Number Sequences
-
HH.01. Complete an increasing number sequence.
-
HH.02. Complete a geometric number sequence.
-
HH.03. Use a given rule to complete a number sequence.
-
HH.04. Solve word problems involving number sequences.
-
HH.05. Complete number sequences with mixed arithmetic and geometric patterns.
-
HH.06. Identify and describe the pattern in a given number sequence.
-
HH.07. Create number sequences based on a given rule or pattern.
