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Math Skill Builders
Skill Level Definitions
Worksheets to meet these objectives

Following is the scope and sequence of our curricula for whole number, decimal, and fraction arithmetic. Click the --> symbols to see sample problems.

Our services provide activities and resources to meet these objectives. Please see our products for details.

Whole Numbers

Whole Number Addition

  1. Add two numbers, the answer will be less than ten. -->
  2. Add zero to a number. -->
  3. Add two single digit numbers. Carry to the tens. -->
  4. Add tens without carrying. -->
  5. Add tens, carry to the tens. -->
  6. Add tens, carry to the tens. -->
  7. Add hundreds without carrying. -->
  8. Add hundreds, carry to the tens. -->
  9. Add hundreds, carry to the tens and hundreds. -->
  10. Add hundreds, carry to the tens and hundreds and thousands. -->
  11. Add thousands, carry when necessary. -->
  12. Add four two-digit numbers, carry when necessary. -->
  13. Add four three-digit numbers, carry when necessary. -->

Whole Number Subtraction

  1. Subtract ones from ones. -->
  2. Subtract tens without borrowing. -->
  3. Subtract tens. Borrow from the tens. -->
  4. Subtract tens. Borrow across a zero. -->
  5. Subtract hundreds without borrowing. -->
  6. Subtract hundreds. Borrow from the tens and hundreds. -->
  7. Subtract hundreds. Borrow across zeros to the hundreds. -->
  8. Subtract thousands without borrowing. -->
  9. Subtract thousands. Borrow from the tens. -->
  10. Subtract thousands. Borrow from the tens and hundreds. -->
  11. Subtract thousands. Borrow from tens, hundreds and thousands. -->
  12. Subtract thousands. Borrow across zeros to the thousands. -->
  13. Subtract thousands. Borrow when necessary. -->

Whole Number Multiplication

  1. Multiply ones. The answer will be less than ten. -->
  2. Multiply ones. The answer will be greater than ten. -->
  3. Multiply ones by zero -->
  4. Multiply tens by ones. Carry to the tens. -->
  5. Multiply ones by tens with a zero. -->
  6. Multiply tens by ones. Carry to the hundreds. -->
  7. Multiply hundreds by ones. Carry to the thousands. -->
  8. Multiply tens by tens. -->
  9. Multiply tens by tens with a zero. -->
  10. Multiply hundreds by tens. -->
  11. Multiply hundreds by tens with a zero. -->
  12. Multiply hundreds by hundreds. -->
  13. Multiply hundreds by hundreds with a zero. -->

Whole Number Division

  1. Divide ones by ones with no remainder. -->
  2. Divide zero by ones. -->
  3. Divide tens by ones with no remainder. -->
  4. Divide hundreds by ones with no remainder. -->
  5. Divide thousands by ones with no remainder. -->
  6. Divide tens by ones with a remainder.  -->
  7. Divide hundreds by ones with a remainder. -->
  8. Divide hundreds by tens with no remainder. -->
  9. Divide hundreds by tens with a remainder. -->
  10. Divide thousands by tens with a remainder. -->
  11. Divide thousands by hundreds with a remainder. -->
  12. Divide ten-thousands by hundreds with a remainder. -->
  13. Divide hundred-thousands by hundreds with a remainder. -->
Decimals

Decimal Addition

  1. Add tenths to a whole number. The answer will be less than 10. -->
  2. Add a whole number to tenths. The answer will be less than 10. -->
  3. Add tenths to tenths. The answer will be less than 10. -->
  4. Add hundredths to hundredths. The answer will be less than 100. -->
  5. Add thousandths to thousandths. The answer will be less than 1000. -->
  6. Add three numbers containing tenths. -->
  7. Add three numbers containing up to hundredths. -->
  8. Add three numbers containing up to thousandths. -->
  9. Add four numbers containing up to thousandths. -->
  10. Add four numbers containing up to ten-thousandths. -->

Decimal Subtraction

  1. Subtract a whole number from tenths. The answer will be less than 10. -->
  2. Subtract tenths from tenths without renaming. The answer will be less than 10. -->
  3. Subtract hundredths from hundredths without renaming. The answer will be less than 100. -->
  4. Subtract tenths from a whole number. The answer will be less than 10 -->
  5. Subtract tenths from tenths with renaming. The answer will be less than 100. -->
  6. Subtract hundredths from a whole number. The answer will be less than 100. -->
  7. Subtract hundredths, renaming as necessary. The answer will be less than 100. -->
  8. Subtract thousandths from a whole number. The answer will be less than 100. -->
  9. Subtract thousandths, renaming as necessary. The answer will be less than 100. -->
  10. Subtract ten-thousandths, renaming as necessary. The answer will be less than 100. -->

Decimal Multiplication

  1. Multiply tenths by ones. The answer will be less than ten. -->
  2. Multiply tenths by ones. The answer will be greater than ten. -->
  3. Multiply hundredths by ones. The answer will be less than one hundred. -->
  4. Multiply ones by tenths. The answer will be less than ten. -->
  5. Multiply ones by tenths. The answer will be greater than ten. -->
  6. Multiply tenths by tenths. The answer will be less than one hundred. -->
  7. Multiply hundredths by tenths. The answer will be less than one hundred. -->
  8. Multiply thousandths by tenths. The answer will be less than one hundred. -->
  9. Multiply hundredths by hundredths. The answer will be less than one hundred.  -->
  10. Multiply thousandths by hundredths. The answer will be less than one hundred. -->

Decimal Division

  1. Divide a whole number by a larger whole number. No rounding will be necessary. -->
  2. Divide tenths by a whole number. No rounding will be necessary. -->
  3. Divide tenths by a whole number. Round to the nearest tenth. -->
  4. Divide hundredths by a whole number. Round to the nearest hundredth. -->
  5. Divide a whole number by tenths. Round to the nearest tenth. -->
  6. Divide tenths by tenths. Round to the nearest tenth. -->
  7. Divide a whole number by hundredths. Round to the nearest hundredth. -->
  8. Divide hundredths by tenths. Round to the nearest hundredth. -->
  9. Divide thousandths by tenths. Round to the nearest thousandth. -->
  10. Divide thousandths by hundredths. Round to the nearest ten-thousandth. -->
Fractions

Fraction Addition

  1. Add two like fractions. The answer will be a proper fraction and will not require reducing to lowest terms. -->
  2. Add two like fractions. The answer will be a proper fraction and will require reducing to lowest terms. -->
  3. Add two like mixed numbers. The answer will contain a proper fraction. -->
  4. Add two like mixed numbers. The answer will contain an improper fraction and require regrouping. -->
  5. Add two unlike fractions. The answer will contain a proper fraction. -->
  6. Add two unlike mixed numbers. The answer will contain a proper fraction. -->
  7. Add two unlike mixed numbers. The answer will contain an improper fraction and require regrouping. -->

Fraction Subtraction

  1. Subtract two like fractions. The answer will not require reducing to lowest terms. -->
  2. Subtract two like fractions. The answer will require reducing to lowest terms. -->
  3. Subtract two like mixed numbers. Regrouping will not be required. -->
  4. Subtract two like mixed numbers. Regrouping will be required. -->
  5. Subtract two unlike fractions. -->
  6. Subtract two unlike mixed numbers. Regrouping will not be required. -->
  7. Subtract two unlike mixed numbers. Regrouping will be required. -->

Fraction Multiplication

  1. Multiply two fractions. Simplification will not be required. -->
  2. Multiply two fractions. Simplification will be required. -->
  3. Multiply a fraction by a whole number. -->
  4. Multiply a whole number by a fraction. -->
  5. Multiply a fraction by a mixed number. -->
  6. Multiply a mixed number by a fraction. -->
  7. Multiply two mixed numbers. -->

Fraction Division

  1. Divide two fractions. Simplification will not be required. -->
  2. Divide two fractions. Simplification will be required. -->
  3. Divide a fraction by a whole number.  -->
  4. Divide a whole number by a fraction. -->
  5. Divide a fraction by a mixed number. -->
  6. Divide a mixed number by a fraction -->
  7. Divide two mixed numbers. -->

Supplementary Skills

Whole Numbers

  • Basic facts tables, matrix and worksheets
  • Rounding whole numbers
  • Comparing whole numbers
  • Solving whole number equations with unknown variables

Decimals

  • Rounding decimals
  • Comparing decimals
  • Solving decimal equations with unknown variables

Fractions

  • Equivalent fractions
  • Greatest common factors
  • Reduce fractions to lowest terms
  • Least common multiples
  • Rounding fractions
  • Comparing fractions
  • Comparing fractions and decimals
  • Converting fractions to decimals
  • Converting decimals to fractions
  • Solving fraction equations with unknown variables
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