Course Content
A. Place Value Foundations
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A.01. Identify the place value of digits in whole numbers up to millions.
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A.02. Convert numbers between standard and expanded form.
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A.03. Read and write word names for numbers up to millions.
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A.04. Compare and order whole numbers up to millions using place value understanding.
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A.05. Convert between different place values within a number.
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A.06. Apply rounding rules to estimate numbers to the nearest ten, hundred, thousand, etc.
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A.07. Explore the use of Roman numerals and their relationship to the decimal system.
B. Addition and Subtraction Fluency
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B.01. Add and subtract whole numbers up to millions with accuracy.
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B.02. Solve one-step and multi-step word problems involving addition and subtraction.
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B.03. Complete addition and subtraction sentences by finding missing addends or subtrahends.
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B.04. Apply properties of addition (commutative, associative, identity) to simplify calculations.
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B.05. Use inequalities to represent relationships between addition and subtraction problems.
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B.06. Estimate sums and differences of whole numbers and assess the reasonableness of answers.
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B.07. Determine missing digits in addition and subtraction problems.
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B.08. Explore real-world applications of addition and subtraction, such as budgeting and measurement.
C. Mastering Multiplication
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C.01. Multiply multi-digit numbers by one-digit numbers.
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C.02. Solve word problems involving multiplication with one-digit multipliers.
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C.03. Recognize and apply multiplication patterns over increasing place values (e.g., 10, 100, 1000).
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C.04. Multiply numbers ending in zeroes efficiently using mental math strategies.
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C.05. Apply properties of multiplication (commutative, associative, distributive, identity, zero) to solve problems.
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C.06. Estimate products and assess the reasonableness of the results.
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C.07. Use visual models (box multiplication, lattice multiplication) to represent multiplication.
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C.08. Multiply two-digit numbers by two-digit and three-digit numbers.
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C.09. Solve multi-step word problems involving multiplication with two-digit multipliers.
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C.10. Find missing steps in multi-digit multiplication problems.
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C.11. Multiply three or four numbers together.
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C.12. Apply inequalities to multiplicative relationships.
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C.13. Explore the concept of exponents as repeated multiplication.
D. Division Proficiency
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D.01. Recall division facts up to 12 x 12.
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D.02. Solve word problems involving basic division facts.
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D.03. Divide multi-digit numbers by one-digit numbers.
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D.04. Solve word problems involving division with one-digit divisors.
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D.05. Interpret remainders in division problems within the context of word problems.
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D.06. Divide numbers ending in zeroes efficiently.
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D.07. Recognize and apply division patterns over increasing place values.
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D.08. Divide multi-digit numbers by two-digit numbers.
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D.09. Estimate quotients and assess the reasonableness of answers.
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D.10. Solve multi-step word problems involving division with two-digit divisors.
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D.11. Use estimation to predict quotients in division problems.
E. Number Theory Basics
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E.01. Differentiate between prime and composite numbers.
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E.02. Determine the prime factorization of a number.
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E.03. Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10.
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E.04. Solve word problems involving divisibility rules.
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E.05. Find the highest common factor (HCF) of two or more numbers.
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E.06. Determine the lowest common multiple (LCM) of two or more numbers.
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E.07. Explore the relationship between prime factorization, HCF, and LCM.
F. Decimal Foundations
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F.01. Identify and represent decimal numbers using visual models.
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F.02. Relate decimals to fractions and vice versa.
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F.03. Read and write decimals using place value terminology (e.g., tenths, hundredths).
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F.04. Identify the place value of digits in decimal numbers.
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F.05. Convert decimals between standard and expanded form.
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F.06. Recognize and generate equivalent decimals.
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F.07. Round decimals to a specified place value.
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F.08. Represent decimals on a number line.
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F.09. Compare and order decimals using number lines and place value understanding.
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F.10. Compare and order decimals and fractions.
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F.11. Explore real-world applications of decimals, such as measurement and money.
G. Operations with Decimals
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G.01. Add and subtract decimal numbers.
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G.02. Solve word problems involving addition and subtraction of decimals.
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G.03. Complete addition and subtraction sentences with decimals.
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G.04. Use inequalities to represent relationships between decimal addition and subtraction problems.
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G.05. Estimate sums and differences of decimals and assess the reasonableness of answers.
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G.06. Explore the use of decimals in financial literacy, such as calculating sales tax and discounts.
H. Multiplying Decimals
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H.05. Multiply decimals by multi-digit whole numbers.
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H.06. Multiply three or four numbers, one of which is a decimal.
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H.07. Apply inequalities to decimal multiplication.
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H.08. Investigate the effect of multiplying by decimals less than one.
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H.01. Estimate products of decimals.
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H.02. Multiply decimals by powers of ten using mental math strategies.
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H.03. Multiply decimals and whole numbers.
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H.04. Solve word problems involving multiplication of decimals and whole numbers.
I. Dividing Decimals
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I.01. Divide decimals by powers of ten using mental math strategies.
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I.02. Recognize decimal division patterns over increasing place values.
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I.03. Perform division with decimal quotients.
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I.04. Round decimal quotients to a specified place value.
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I.05. Solve word problems involving division with decimal quotients.
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I.06. Explore real-world applications of dividing decimals, such as calculating unit prices.
J. Fraction Fundamentals
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J.01. Review basic fraction concepts (numerator, denominator, types of fractions).
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J.02. Represent fractions of a whole and fractions of a group using visual models.
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J.03. Generate equivalent fractions and write fractions in lowest terms.
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J.04. Convert between improper fractions and mixed numbers.
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J.05. Represent and compare fractions on a number line.
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J.06. Compare and order fractions and mixed numbers.
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J.07. Calculate fractions of a number.
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J.08. Solve word problems involving fractions of a number.
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J.09. Explore arithmetic and geometric sequences with fractions.
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J.10. Round mixed numbers to the nearest whole number.
K. Fraction Operations
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K.01. Decompose fractions into multiple sums of fractions with the same denominator.
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K.02. Add and subtract fractions with like denominators using number lines.
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K.03. Add and subtract fractions and mixed numbers with like denominators.
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K.04. Solve word problems involving addition and subtraction of fractions with like denominators.
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K.05. Add fractions with unlike denominators.
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K.06. Subtract fractions with unlike denominators.
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K.07. Add and subtract fractions with unlike denominators. word problems
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K.08. Add up to 4 fractions with denominators of 10 and 100
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K.09. Complete addition and subtraction sentences with fractions
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K.10. Add three or more fractions with unlike denominators
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K.11. Estimate sums and differences of mixed numbers
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K.12. Add mixed numbers with unlike denominators
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K.13. Subtract mixed numbers with unlike denominators
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K.14. Complete addition and subtraction sentences with mixed numbers
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K.15. Multiply unit fractions by whole numbers using number lines
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K.16. Determine multiples of fractions
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K.17. Multiply fractions by whole numbers
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K.18. Apply inequalities to addition and subtraction of fractions and mixed numbers.
L. Mixed Operations Mastery
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L.01. Perform addition, subtraction, multiplication, and division with whole numbers.
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L.02. Solve multi-step word problems involving mixed operations with whole numbers.
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L.03. Write and evaluate numerical expressions involving mixed operations using the order of operations (PEMDAS/BODMAS).
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L.04. Perform addition, subtraction, multiplication, and division with decimals.
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L.05. Solve multi-step word problems involving mixed operations with decimals.
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L.06. Create and solve real-world problems involving multiple operations with both whole numbers and decimals.
M. Problem-Solving Strategies
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M.01. Solve multi-step word problems using various strategies (e.g., drawing diagrams, making tables).
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M.02. Identify and use relevant information in word problems, including recognizing extra or missing information.
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M.03. Solve problems using the guess-and-check strategy.
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M.04. Determine the order of events in a problem and solve accordingly.
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M.05. Use Venn diagrams to solve problems involving sets and categories.
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M.06. Develop logical reasoning skills to solve non-routine problems.
N. Ratios and Rates
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N.01. Determine the ratio between two quantities.
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N.02. Write ratios to represent relationships in word problems.
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N.03. Identify equivalent ratios.
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N.04. Write an equivalent ratio given a ratio.
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N.05. Use ratio tables to solve problems.
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N.06. Determine unit rates and equivalent rates.
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N.07. Solve word problems involving scale drawings using ratios and proportions.
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N.08. Explore real-world applications of ratios and rates, such as comparing prices and calculating speeds.
O. Percents
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O.01. Identify and represent percentages using visual models.
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O.02. Convert between percents, fractions, and decimals.
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O.03. Calculate the percentage of a number.
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O.04. Solve word problems involving percentages.
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O.05. Compare percentages of different quantities.
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O.06. Apply percentages to real-world situations such as calculating discounts, tips, and taxes.
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O.07. Explore the relationship between percentages and proportions.
P. Financial Applications
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P.01. Add and subtract money amounts.
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P.02. Solve word problems involving addition and subtraction of money.
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P.03. Multiply money amounts in word problems.
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P.04. Divide money amounts in word problems.
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P.05. Solve word problems involving unit prices, discounts and sale prices
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P.06. Use price lists to determine the cost of purchasing multiple items.
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P.07. Calculate unit prices to compare the cost-effectiveness of different products.
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P.08. Calculate sale prices after discounts.
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P.09. Develop budgeting skills by creating and managing a simple budget.
Q. Numerical Sequences
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Q.01. Complete increasing number sequences.
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Q.02. Complete geometric number sequences.
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Q.03. Use a given rule to complete a number sequence.
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Q.04. Solve word problems involving number sequences.
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Q.05. Identify patterns in number sequences and express them as rules.
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Q.06. Extend number sequences to predict future terms.
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Q.07. Solve problems with mixed types of number sequences.
R. Introduction to Variables
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R.01. Write variable expressions to represent unknown quantities.
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R.02. Solve word problems by creating and using variable expressions.
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R.03. Evaluate variable expressions by substituting given values for the variables.
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R.04. Write variable equations to represent relationships in word problems.
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R.05. Solve simple equations with whole numbers using inverse operations.
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R.06. Find a value using two-variable equations.
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R.07. Complete a table for a two-variable relationship.
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R.08. Complete a table from a graph
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R.09. Graph a two-variable relationship
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R.10. Write a two-variable equation
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R.11. Understand the concept of a variable as a placeholder for an unknown value.
S. Data Analysis and Graphs
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S.01. Read and interpret data presented in tables, line graphs, bar graphs, double bar graphs, pictographs, histograms, line plots, frequency charts, stem-and-leaf plots, and pie charts.
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S.02. Create line graphs, bar graphs, double bar graphs, pictographs, histograms, and line plots to represent data.
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S.03. Choose the best type of graph to represent a given dataset.
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S.04. Formulate questions and collect data to create and analyze graphs.
T. Probability and Statistics Introduction
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T.01. Calculate the mean, median, and mode of a dataset.
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T.02. Determine a missing number given the mean, median, or mode.
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T.03. Interpret charts to find mean, median and mode
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T.04. Understand the basic concept of probability.
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T.05. Calculate the probability of a simple event.
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T.06. Make predictions based on probability.
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T.07. Calculate the number of possible combinations in a given scenario.
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T.08. Explore real-world applications of probability and statistics, such as weather forecasting and sports analysis.
U. Time Calculations
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U.01. Convert between different units of time (seconds, minutes, hours, days, weeks, months, years).
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U.02. Add and subtract mixed time units.
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U.03. Calculate elapsed time.
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U.04. Find start and end times given elapsed time in word problems.
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U.05. Convert between 12-hour and 24-hour time.
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U.06. Interpret and create schedules and timelines using 12-hour and 24-hour time formats.
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U.07. Identify and extend time patterns.
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U.08. Solve problems involving time zones and international travel.
V. Units of Measurement
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V.01. Choose the appropriate metric unit of measure for length, mass, and volume.
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V.02. Compare and convert metric units of length (mm, cm, m, km).
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V.03. Compare and convert metric units of mass (mg, g, kg).
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V.04. Compare and convert metric units of volume (mL, L).
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V.05. Choose the more reasonable temperature.
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V.06. Solve problems involving mixed metric units.
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V.07. Compare and convert between different customary units.
W. Two-Dimensional Geometry
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W.03. Differentiate between regular and irregular polygons.
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W.04. Identify parallel, perpendicular, and intersecting lines.
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W.05. Identify and classify types of angles (acute, right, obtuse, straight).
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W.06. Measure angles with a protractor.
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W.07. Classify triangles based on their angles and sides.
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W.08. Identify parallel sides in quadrilaterals.
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W.09. Identify and classify parallelograms, trapeziums, rectangles, and rhombuses.
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W.10. Find the unknown angle in triangles and quadrilaterals
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W.11. Identify parts of a circle (radius, diameter, chord, circumference).
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W.12. Explore tessellations and their relationship to polygons.
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W.01. Identify polygons and classify them based on their attributes.
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W.02. Count the number of sides in polygons.
X. Symmetry and Transformations
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X.01. Identify lines of symmetry in two-dimensional figures.
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X.02. Determine if a figure has rotational symmetry.
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X.03. Identify and perform reflections, rotations, and translations.
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X.04. Identify congruent and similar figures.
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X.05. Explore how transformations affect the properties of geometric figures.
Y. Three-Dimensional Geometry
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Y.01. Identify three-dimensional figures (cubes, prisms, pyramids, cones, cylinders, spheres).
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Y.02. Count vertices, edges, and faces on three-dimensional figures.
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Y.03. Identify nets of three-dimensional figures.
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Y.04. Visualize three-dimensional figures from different perspectives.
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Y.05. Explore the relationship between two-dimensional nets and three-dimensional shapes.
Z. Geometric Measurement Applications
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Z.01. Calculate the perimeter of polygons.
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Z.02. Calculate missing side lengths of a polygon given its perimeter.
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Z.03. Calculate the area of squares and rectangles.
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Z.04. Calculate the area of triangles.
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Z.05. Calculate the area of compound figures by decomposing them into simpler shapes.
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Z.06. Calculate the area between two rectangles.
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Z.07. Calculate area and perimeter of figures on grids.
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Z.08. Solve word problems involving area and perimeter.
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Z.09. Use area and perimeter to determine cost (e.g., fencing a yard, carpeting a room).
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Z.10. Calculate the volume of figures made of unit cubes.
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Z.11. Calculate the volume of cubes and rectangular prisms.
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Z.12. Explore the relationship between area, perimeter, and volume.
