Course Content
A. Place Value and Number Recognition
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A.01. Identify the place value of digits in numbers up to millions
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A.02. Read and write whole numbers up to a million in standard and word form
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A.03. Convert numbers between different place values
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A.04. Compare and order numbers up to a million using place value understanding
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A.05. Recognize and write Roman numerals, and convert them to Arabic numerals
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A.06. Round whole numbers to the nearest ten, hundred, thousand, ten thousand, and million
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A.07. Determine if a number is even or odd based on arithmetic rules
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A.08. Apply place value understanding to solve real-world problems involving large numbers
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A.09. Explore the historical significance of different number systems
B. Addition and Subtraction of Whole Numbers
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B.01. Add and subtract whole numbers up to millions fluently
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B.02. Solve addition and subtraction word problems involving whole numbers up to millions
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B.03. Complete addition and subtraction sentences by finding missing addends or subtrahends
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B.04. Fill in missing digits in addition and subtraction problems
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B.05. Choose numbers that satisfy a particular sum or difference requirement
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B.06. Apply properties of addition (commutative, associative, identity) to simplify calculations
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B.07. Solve inequalities involving addition and subtraction
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B.08. Estimate sums and differences of whole numbers and apply estimation to solve word problems
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B.09. Justify the reasonableness of answers in addition and subtraction problems through estimation and rounding
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B.10. Investigate the relationship between addition and subtraction as inverse operations
C. Multiplication Facts and Properties
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C.01. Recall multiplication facts up to 10 x 10 fluently
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C.02. Find the missing factor in multiplication equations up to 10 x 10
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C.03. Multiply numbers by 10 or 100 mentally
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C.04. Recognize and extend multiplication patterns over increasing place values
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C.05. Multiply numbers ending in zeroes using mental math strategies
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C.06. Solve word problems involving multiplication of numbers ending in zeroes
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C.07. Recognize and calculate square numbers
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C.08. Choose numbers that satisfy a particular product requirement
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C.09. Apply multiplication facts to solve real-world problems efficiently
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C.10. Explore the connection between multiplication and area
D. Division Facts and Concepts
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D.01. Relate multiplication and division as inverse operations
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D.02. Recall division facts up to 144 ÷ 12 fluently
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D.03. Solve word problems involving division facts
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D.04. Divide whole numbers by one-digit numbers, including interpreting remainders
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D.05. Solve word problems involving division by one-digit numbers
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D.06. Interpret remainders in division problems within real-world contexts
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D.07. Estimate quotients in division problems
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D.08. Solve word problems involving estimation of quotients
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D.09. Recognize and extend division patterns over increasing place values
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D.10. Divide numbers ending in zeroes using mental math strategies
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D.11. Solve word problems involving division of numbers ending in zeroes
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D.12. Choose numbers that satisfy a particular quotient requirement
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D.13. Understand the relationship between division and fractions
E. Properties of Multiplication
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E.01. Identify and apply the commutative, associative, and identity properties of multiplication
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E.02. Multiply numbers using the distributive property
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E.03. Find the missing number in equations demonstrating the distributive property
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E.04. Use the distributive property to simplify mental calculations
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E.05. Understand how multiplication properties relate to real-world problem-solving
F. Multiplication by One-Digit Numbers
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F.01. Multiply multi-digit numbers by one-digit numbers using standard algorithm
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F.02. Solve word problems involving multiplication by one-digit numbers
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F.03. Apply estimation strategies to check the reasonableness of products
G. Exponents and Powers
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G.01. Understand the meaning of exponents as repeated multiplication
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G.02. Evaluate powers of whole numbers (e.g., 2^3, 5^2)
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G.03. Find the missing exponent or base in exponential expressions
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G.04. Express repeated multiplication in exponential form and vice versa
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G.05. Apply exponents to solve problems involving area and volume
H. Multiplication by Two-Digit Numbers
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H.01. Estimate products of multi-digit numbers
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H.02. Solve word problems involving estimation of products
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H.03. Multiply a two-digit number by a two-digit number using area models
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H.04. Multiply a two-digit number by a two-digit number using algorithms
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H.05. Multiply a two-digit number by a larger number using algorithms
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H.06. Multiply multi-digit numbers by two-digit numbers: complete the missing steps in the multiplication process
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H.07. Solve word problems involving multiplication by two-digit numbers
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H.08. Multiply three or more numbers up to two digits each
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H.09. Solve word problems involving multiplication of three or more numbers
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H.10. Solve inequalities involving multiplication
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H.11. Choose appropriate multiplication strategies based on the context of the problem
I. Number Theory
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I.01. Identify factors of a given number
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I.02. Find all the factor pairs of a number
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I.03. Distinguish between prime and composite numbers
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I.04. Determine the prime factorisation of a number
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I.05. Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10
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I.06. Solve word problems involving divisibility rules
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I.07. Find the highest common factor (HCF) of two or more numbers
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I.08. Find the least common multiple (LCM) of two or more numbers
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I.09. Use prime factorisation to find HCF and LCM
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I.10. Apply number theory concepts to solve real-world problems
J. Mixed Operations with Whole Numbers
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J.01. Add, subtract, multiply, and divide whole numbers in multi-step problems
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J.02. Solve word problems involving mixed operations with whole numbers
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J.03. Apply the order of operations (PEMDAS/BODMAS) to solve numerical expressions
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J.04. Create and solve real-world problems involving mixed operations
K. Numerical Expressions and Order of Operations
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K.01. Identify mistakes involving the order of operations in numerical expressions
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K.02. Evaluate numerical expressions with parentheses in different places
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K.03. Determine if mixed operation sentences are true or false
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K.04. Solve inequalities involving addition, subtraction, multiplication, and division
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K.05. Create numerical expressions to represent real-world situations
L. Fractions Review
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L.01. Identify parts of a fraction (numerator and denominator)
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L.02. Represent fractions using visual models (e.g., fraction bars, pie charts)
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L.03. Interpret fractions as parts of a whole
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L.04. Solve word problems involving fractions of a whole
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L.05. Solve word problems involving fractions of a group
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L.06. Recognize and generate equivalent fractions
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L.07. Identify patterns of equivalent fractions
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L.08. Write fractions in lowest terms (simplify fractions)
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L.09. Compare and order fractions with the same denominator
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L.10. Understand fractions as division
M. Mixed Numbers and Improper Fractions
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M.02. Represent mixed numbers using visual models
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M.03. Convert between improper fractions and mixed numbers
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M.04. Round mixed numbers to the nearest whole number or half
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M.05. Compare and order mixed numbers
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M.01. Define mixed numbers as a combination of a whole number and a fraction
N. Comparing Fractions
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N.01. Graph and compare fractions on number lines
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N.02. Compare fractions and mixed numbers using benchmarks (0, 1/2, 1)
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N.03. Compare fractions with different numerators and denominators
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N.04. Put fractions and mixed numbers in order from least to greatest
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N.05. Use cross-multiplication to compare fractions efficiently
O. Fractions of a Number
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O.01. Calculate fractions of a number (e.g., 1/4 of 20)
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O.02. Solve word problems involving fractions of a number
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O.03. Use models to visualize finding fractions of a number
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O.04. Relate finding a fraction of a number to multiplication
P. Adding and Subtracting Fractions
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P.01. Decompose fractions into sums of smaller fractions in multiple ways
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P.02. Add and subtract fractions with like denominators using number lines
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P.03. Add and subtract fractions with like denominators
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P.04. Solve word problems involving addition and subtraction of fractions with like denominators
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P.05. Add and subtract mixed numbers with like denominators
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P.06. Solve word problems involving addition and subtraction of mixed numbers with like denominators
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P.07. Add up to four fractions with denominators of 10 and 100
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P.08. Add three or more fractions with unlike denominators
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P.09. Solve word problems involving addition of three or more fractions
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P.10. Complete addition and subtraction sentences with fractions
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P.11. Solve inequalities with addition and subtraction of fractions
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P.12. Estimate sums and differences of mixed numbers
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P.13. Add and subtract fractions with related denominators (e.g., 1/2 + 1/4)
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P.14. Develop strategies for finding common denominators when adding and subtracting fractions
Q. Introduction to Decimals
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Q.01. What decimal number is illustrated?
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Q.02. Model decimals and fractions
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Q.03. Understanding decimals expressed in words
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Q.04. Identify the place value of digits in decimal numbers
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Q.05. Recognize the relationship between decimal place values (tenths, hundredths, thousandths)
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Q.06. Convert decimals between standard and expanded form
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Q.07. Convert decimals between standard and expanded form using fractions
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Q.08. Round decimals to the nearest tenth, hundredth, or whole number
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Q.09. Locate decimals on number lines
R. Comparing and Ordering Decimals
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R.01. Identify equivalent decimals
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R.02. Compare decimals on number lines
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R.03. Compare decimal numbers using place value understanding
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R.04. Put decimal numbers in order from least to greatest
S. Converting Between Fractions and Decimals
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S.01. Convert fractions to decimals using division
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S.02. Convert decimals to fractions in simplest form
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S.03. Recognize common fraction-decimal equivalents (e.g., 1/2 = 0.5)
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S.04. Understand the relationship between fractions, decimals and division
T. Comparing Fractions and Decimals
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T.01. Compare decimals and fractions on number lines
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T.02. Compare decimals and fractions using benchmark values
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T.03. Put assorted decimals, fractions, and mixed numbers in order
U. Adding and Subtracting Decimals
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U.01. Add and subtract decimal numbers using the standard algorithm
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U.02. Solve word problems involving addition and subtraction of decimals
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U.03. Choose decimals with a particular sum or difference
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U.04. Complete addition or subtraction sentences with decimals
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U.05. Solve inequalities with decimal addition and subtraction
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U.06. Estimate sums and differences of decimals
V. Multiplying and Dividing Decimals
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V.01. Estimate products of decimals
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V.02. Multiply a decimal by a power of ten (10, 100, 1000)
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V.03. Multiply decimals and whole numbers
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V.04. Solve word problems involving multiplication of decimals and whole numbers
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V.05. Solve inequalities with decimal multiplication
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V.06. Divide by powers of ten (10, 100, 1000)
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V.07. Divide by a power of ten with decimals: find the missing number
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V.08. Recognize decimal division patterns over increasing place values
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V.09. Apply decimal multiplication and division to solve real-world problems
W. Mixed Operations with Decimals
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W.01. Add, subtract, multiply, and divide decimals in multi-step problems
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W.02. Solve word problems involving addition, subtraction, and multiplication of decimals
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W.03. Apply the order of operations to solve expressions involving decimals
X. Percentages
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X.01. What percentage is illustrated?
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X.02. Compare percents to each other and to fractions
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X.03. Convert percents to fractions
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X.04. Calculate the percent of a number
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X.05. Solve word problems involving percents of numbers
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X.06. Convert between fractions, decimals, and percents fluently
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X.07. Estimate percentages of quantities
Y. Problem Solving Strategies
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Y.01. Solve multi-step word problems
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Y.02. Identify extra or missing information in word problems
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Y.03. Solve problems using the guess-and-check strategy
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Y.04. Find the order of events or items based on given clues
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Y.05. Use Venn diagrams to solve problems involving overlapping sets
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Y.06. Develop and apply different problem-solving heuristics
Z. Financial Applications
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Z.01. Add and subtract money amounts (dollars and cents)
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Z.02. Solve word problems involving addition and subtraction of money
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Z.03. Solve word problems involving multiplication of money amounts
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Z.04. Solve word problems involving multiplication of money amounts with decimals
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Z.05. Solve word problems involving division of money amounts with decimals
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Z.06. Calculate making change from a purchase
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Z.07. Interpret price lists to solve problems
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Z.08. Calculate unit prices to compare costs
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Z.09. Determine the best value for money
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Z.10. Create and interpret simple budgets
AA. Financial Literacy
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AA.01. Read and interpret financial records (e.g., bank statements)
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AA.02. Understand the importance of keeping financial records
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AA.03. Create and balance a simple budget
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AA.04. Adjust a budget based on changing income or expenses
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AA.05. Distinguish between needs and wants
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AA.06. Explore the concepts of saving, spending, and investing
BB. Number Sequences
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BB.01. Complete an increasing number sequence
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BB.02. Identify and extend arithmetic sequences with fractions
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BB.03. Complete a geometric number sequence
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BB.04. Identify and extend geometric sequences with fractions
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BB.05. Use a rule to complete a number sequence
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BB.06. Solve number sequences: word problems
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BB.07. Number sequences: mixed review
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BB.08. Create number sequences based on given rules or patterns
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BB.09. Determine whether a sequence is arithmetic or geometric
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BB.10. Find a missing term in a number sequence
CC. Basic Algebra
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CC.01. Solve one-step equations with addition
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CC.02. Solve one-step equations with subtraction
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CC.03. Solve one-step equations with multiplication
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CC.04. Solve one-step equations with division
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CC.05. Complete a table for a two-variable relationship
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CC.06. Complete a table from a graph
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CC.07. Graph a two-variable relationship on a coordinate plane
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CC.08. Find a value using two-variable equations
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CC.09. Write simple equations to represent real-world situations
DD. Data Representation and Interpretation
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DD.07. Create pictographs from given data
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DD.08. Interpret data presented in histograms
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DD.09. Create histograms from given data
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DD.10. Interpret data presented in line plots
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DD.11. Create line plots from given data
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DD.12. Organize data using frequency charts
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DD.13. Interpret data presented in stem-and-leaf plots
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DD.14. Create stem-and-leaf plots from given data
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DD.15. Interpret data presented in circle graphs (pie charts)
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DD.16. Choose the best type of graph to represent a given set of data
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DD.17. Calculate the range of a set of data
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DD.18. Analyze data to draw conclusions and make predictions
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DD.01. Read and interpret data presented in a table
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DD.02. Interpret data presented in line graphs
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DD.03. Create line graphs from given data
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DD.04. Interpret data presented in bar graphs
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DD.05. Create bar graphs from given data
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DD.06. Interpret data presented in pictographs
EE. Coordinate Plane
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EE.01. Identify the coordinates of objects on a coordinate plane
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EE.02. Interpret coordinate planes as maps
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EE.03. Follow directions to locate points on a coordinate plane
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EE.04. Plot points on a coordinate plane given their coordinates
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EE.05. Find the distance between two points on a coordinate plane
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EE.06. Use coordinate planes to represent real-world situations
FF. Probability and Statistics
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FF.01. Identify statistical questions
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FF.02. Calculate mean, median, and mode for a given data set
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FF.03. Mean, median, and mode: find the missing number given the other measures
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FF.04. Interpret charts to find mean, median, and mode
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FF.05. Understanding basic probability concepts (certain, likely, unlikely, impossible)
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FF.06. Identify sample spaces of simple events
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FF.07. Calculate the probability of a simple event
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FF.08. Determine experimental probability based on observed outcomes
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FF.09. Make predictions based on probability
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FF.10. Calculate the number of possible combinations in a given situation
GG. Time Measurement and Conversion
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GG.01. Convert between different units of time (seconds, minutes, hours, days, weeks, months, years)
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GG.02. Add and subtract mixed time units (e.g., 2 hours 30 minutes + 1 hour 45 minutes)
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GG.03. Calculate elapsed time between two given times
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GG.04. Find start and end times given elapsed time: word problems
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GG.05. Convert between 12-hour and 24-hour time formats
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GG.06. Interpret schedules and timelines using 12-hour time
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GG.07. Interpret schedules and timelines using 24-hour time
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GG.08. Recognize and extend time patterns
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GG.09. Solve real-world problems involving time calculations
HH. Units of Measurement (Metric System)
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HH.01. Choose the appropriate metric unit of measure for length, mass, and volume
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HH.02. Compare and convert metric units of length (mm, cm, m, km)
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HH.03. Convert metric units of length involving decimals
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HH.04. Compare and convert metric units of mass (mg, g, kg)
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HH.05. Convert metric units of mass involving decimals
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HH.06. Compare and convert metric units of volume (mL, L)
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HH.07. Convert metric units of volume involving decimals
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HH.08. Solve problems involving metric mixed units (e.g., 1 m 25 cm)
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HH.09. Convert between square metres and hectares
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HH.10. Convert between cubic centimetres and millilitres
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HH.11. Choose the more reasonable temperature (Celsius) for a given situation
II. Two-Dimensional Figures and Their Properties
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II.01. Determine if a given shape is a polygon
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II.02. Identify the number of sides in polygons
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II.03. Distinguish between regular and irregular polygons
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II.04. Identify parallel, perpendicular, and intersecting lines
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II.05. Identify different types of angles (acute, right, obtuse, straight, reflex)
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II.06. Measure angles using a protractor
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II.07. Find missing angles in triangles and quadrilaterals using angle properties
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II.08. Classify triangles based on their sides and angles (equilateral, isosceles, scalene, acute, right, obtuse)
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II.09. Identify parallel sides in quadrilaterals
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II.10. Identify parallelograms based on their properties
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II.11. Identify trapeziums (trapezoids) based on their properties
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II.12. Identify rectangles based on their properties
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II.13. Identify rhombuses based on their properties
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II.14. Classify quadrilaterals based on their properties
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II.15. Identify parts of a circle (centre, radius, diameter, circumference)
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II.16. Understand the relationships between different types of quadrilaterals
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II.17. Explore tessellations using different polygons
JJ. Transformations and Symmetry
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JJ.01. Identify lines of symmetry in two-dimensional figures
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JJ.02. Determine if a figure has rotational symmetry and identify its order
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JJ.03. Recognize and perform reflection, rotation, and translation transformations
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JJ.04. Recognize and perform dilations (enlargements and reductions)
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JJ.05. Identify congruent and similar figures
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JJ.06. Describe transformations using mathematical language
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JJ.07. Explore the properties preserved by different types of transformations
KK. Three-Dimensional Figures
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KK.01. Identify common three-dimensional figures (cubes, cuboids, spheres, cylinders, cones, pyramids, prisms)
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KK.02. Count vertices, edges, and faces of three-dimensional figures
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KK.03. Identify the bases of three-dimensional figures
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KK.04. Recognize and match nets of three-dimensional figures
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KK.05. Visualize three-dimensional figures viewed from different perspectives
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KK.06. Explore the relationship between two-dimensional nets and three-dimensional figures
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KK.07. Classify prisms and pyramids based on the shape of their base
LL. Geometric Measurement: Perimeter and Area
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LL.01. Calculate the perimeter of polygons with whole number side lengths
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LL.02. Calculate the perimeter of polygons with decimal side lengths
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LL.03. Calculate the area of squares and rectangles
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LL.04. Calculate the area of right triangles
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LL.05. Find the area and perimeter of figures on grids by counting unit squares and lengths
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LL.06. Use area and perimeter calculations to determine cost (e.g., fencing a garden, carpeting a room)
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LL.07. Apply the formulas for perimeter and area to solve real-world problems
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LL.08. Explore the relationship between perimeter and area
MM. Geometric Measurement: Volume
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MM.01. Calculate the volume of rectangular prisms made of unit cubes
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MM.02. Calculate the volume of irregular figures made of unit cubes
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MM.03. Calculate the volume of cubes and rectangular prisms using formulas
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MM.04. Relate volume to capacity (e.g., litres and cubic centimetres)
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MM.05. Solve real-world problems involving volume
