ModuMath Arithmetic Lesson Listing

Following is a list of the lessons for basic arithmetic along with the educational objectives for each lesson.

1.1 Naming Whole Numbers

A. Read decimal numbers

B. Write in words decimal numbers for whole numbers

C. Write the decimal number for a whole number stated in words

D. Write decimal numbers in expanded notation

E. State the number represented by each digit in a decimal number

1.2 The Number Line

A. Construct a number Line

B. Graph whole numbers on a number line

C. Find the co-ordinate of a point on a number line

D. Decide which of two points represents the smaller (or larger) whole number.

E. Use the symbols < and > to compare whole numbers.

1.3 Adding Whole Numbers I

A. State from memory the 100 addition facts.

B. Interpret the addition of whole numbers on the number line.

C. Recognize and use the identity for addition.

D. Recognize and solve word problems involving addition of small whole numbers.

1.4 Adding Whole Numbers II

A. Find the sum of two or more whole numbers

1.5 Subtracting Whole Numbers

A. State from memory the 100 subtraction facts.

B. Subtract whole numbers, provided that the first is greater than or equal to the second.

C. Check a subtraction problem by addition.

D. Solve word problems involving subtraction.

1.6 Multiplying Whole Numbers I

A. Use multiplication as a shortcut for addition.

B. Interpret multiplication on the number line.

C. Show multiplication facts in arrays.

D. Use multiplication to find areas.

E. Use multiplication to figure out combinations.

F. Multiply by 0.

G. Recognize and use the identity for multiplication.

1.7 Multiplying Whole Numbers II

A. State from memory the 100 multiplication facts.

B. Solve word problems involving multiplication of small whole numbers.

1.8 Multiplying Whole Numbers III

A. Multiply any two whole numbers

B. solve word problems involving multiplication.

1.9 Exponents

A. Read expressions involving exponents.

B. Multiply two or more expressions with the same base by adding exponents.

C. Recognize and work with expressions having exponents equal to zero.

D. Write whole numbers in exponential notation.

1.10 Dividing Whole Numbers I

A. State from memory the 90 basic division facts.

B. Solve simple word problems involving division.

C. Use multiplication to check division.

1.11 Dividing Whole Numbers II

A. Divide any whole number by any other whole number. (excluding division by zero)

B. Solve word problems involving division of whole numbers.

C. Use multiplication to check division.

1.12 Word Problems

A. Express word problems as number sentences.

B. Solve word problems involving addition, subtraction, multiplication, and division of whole numbers.

1.13 Solving Equations

A. Solve simple equations.

B. Solve word problems involving simple equations.

1.14 Prime Numbers

A. Determine whether a given whole number greater than 1 is a prime or a composite number.

B. Use the Sieve of Eratosthenes.

C. Determine the prime factorization of a given whole number..

2.1 Introducing Fractions

A. Understand and use fractions in comparing two quantities.

B. Understand and use fractions in expressing parts of a whole.

C. Understand and use fractions in expressing division.

D. Understand and use fractions in measurement.

E. Locate fractions on the number line.

F. Recognize and use fractions with denominators of 1.

G. Divide whole numbers when the quotient is a fraction or a whole number plus a fraction.

2.2 Re-naming Fractions

A. Express fractions in higher and lower terms.

B. Reduce fractions to lowest terms.

C. Recognize and use fractions equal to 1

D. Recognize and use fractions equal to 0.

2.3 Adding Fractions with the Same Denominator

A. Add two or more fractions with the same denominator.

B. Change a mixed number to an improper fraction.

C. Change an improper fraction to a mixed number.

D. Add any combination of mixed numbers, fractions, and whole numbers.

2.4 Adding Fractions with Different Denominators

A. Find a common denominator of two or more fractions.

B. Find the least common denominator of two or more fractions.

C. Add two or more fractions with different denominators.

2.5 Subtracting Fractions

A. Indicate the larger (or smaller) of 2 fractions.

B. Subtract fractions.

C. Subtract mixed numbers.

D. Subtract a fraction or mixed number from a whole number.

E. Subtract a whole number from a mixed number.

F. Solve word problems involving subtraction of fractions.

2.6 Multiplying Fractions

A. Multiply a fraction or mixed number and a whole number.

B. Multiply any combination of fractions and mixed numbers.

C. Solve word problems involving multiplication of fractions.

2.7 Dividing Fractions

A. Divide a fraction by a mixed number, a whole number, or another fraction.

B. Divide a mixed number by a fraction, a whole number or another mixed number.

C. Divide a whole number by a fraction or a mixed number.

D. Solve word problems involving division of fractions.

2.8 Ratio and Proportion

A. Determine whether two ratios are equal.

B. Solve word problems involving proportions.

3.1 Understanding Decimal Fractions

A. Write decimal fractions in exponential notation.

B. Read decimal fractions.

C. Change decimals to fractions.

D. Change a fraction to a decimal, provided the denominator is a power of 10.

E. Recognize the meaning of zeros to the right of a decimal point.

3.2 Adding and Subtracting Decimal Fractions

A. Determine which is the larger (or smaller) of two decimal fractions.

B. Add two or more decimal fractions.

C. Subtract decimal fractions.

D. Solve word problems involving addition and subtraction of decimal fractions.

3.3 Rounding Numbers

A. Round a number to a given degree of precision.

3.4 Multiplying Decimals

A. Multiply decimal fractions.

B. Solve word problems involving multiplication of decimals.

3.5 Dividing Decimal Fractions

A. Divide a decimal by a whole number.

B. Divide a whole number by a decimal.

C. Divide a decimal by another decimal.

D. Divide two numbers accurately to a given number of decimal places.

E. Solve word problems involving division of decimals.

3.6 Changing Fractions to Decimals

A. Change a fraction or mixed number to a decimal.

B. Change a decimal to a fraction or mixed number.

3.7 Square Roots

A. Use a table to find square roots of whole numbers from 1 to 100

B. Recognize and use the fact that if a and b are any numbers, then .

4.1 Percent

A. Change fractions and decimals to percents.

B. Change percents to fractions and decimals.

4.2 Percent in Word Problems

A. Solve word problems involving percents by using proportions.

4.3 More Problems in Percent

A. Solve more complicated word problems involving percent.

5.1 Signed Numbers

A. Graph positive and negative numbers on the number line.

B. Decide which is larger (or smaller) of two given signed numbers.

C. Find the absolute value of any given number.

5.2 Adding Signed Numbers

A. Add two or more signed numbers.

B. Solve word problems involving addition of signed numbers.

5.3 Subtracting Signed Numbers

A. Subtract any two signed numbers.

5.4 Multiplying Signed Numbers

A. Multiply two or more signed numbers.

5.5 Dividing Signed Numbers

A. Divide a given signed number by another signed number.

5.6 Signed Fractions

A. Recognize that signed fractions such as are all equal.

B. Add signed fractions.

C. Subtract signed fractions.

D. Multiply signed fractions.

E. Divide signed fractions.

F. Solve equations involving signed fractions.

5.7 Negative Exponents

A. Recognize that an expression such as means .

B. Divide two expressions involving exponents when the bases are the same.

C. Write numbers in exponential notation using positive and negative exponents.

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Produced by David Schmidtke, Blackhawk Technical College, dschmidtke@blackhawk.edu 10/20022