Number & Operations for Teachers 

Copyright David & Cynthia Thomas, 2009

1. Systems of Numeration

1.1. Counting

1.2. Numeration Systems

1.3. Making Sense of Numeration

1.4. Conclusion

2. Whole Numbers & Integers: Addition & Subtraction

2.1. Whole Numbers: Modeling the Meaning of Addition and Subtraction

2.2. Integers: Modeling the Meaning of Addition and Subtraction

2.3. Writing Sensible Word Problems

2.4. Modeling Addition and Subtraction with Regrouping

2.5. Operations in Other Bases

2.6. Properties of Whole Number & Integer Operations

3. Whole Numbers & Integers: Multiplication & Division

3.1. Whole Numbers: Modeling the Meaning of Multiplication and Division

3.2. Integers: Modeling the Meaning of Multiplication and Division

3.3. Properties and Fact Families

3.4. Writing Sensible Word Problems

3.5. Modeling Multiplication with Regrouping

4. Fractions: Addition & Subtraction

4.1. Modeling the Meaning of Addition and Subtraction

4.2. Properties of Fraction Operations

4.3. Representing Mixed and Improper Fractions

4.4. Writing Sensible Word Problems

4.5. Conclusion

5. Fractions: Multiplication & Division

5.1. Modeling the Meaning of Multiplication

5.2. Understanding the Standard Fraction Multiplication Algorithm

5.3. Modeling the Meaning of Division

5.4. Understanding the Standard Fraction Division Algorithm

5.5. Properties of Fraction Operations

5.6. Writing Sensible Word Problems

5.7. Conclusion

6. Decimals & Percents: Representations & Operations

6.1. Modeling the Meaning of Decimal Numbers

6.2. Arithmetic Operations with Decimals – Addition and Subtraction

6.3. Arithmetic Operations with Decimals – Multiplication and Division

6.4. Terminating and Repeating Decimals

6.5. The Meaning of 0.9999999 …

6.6. Irrational Numbers

6.7. Modeling the Meaning of Percent

6.8. The Meaning of “60% of 30%”

6.9. Writing Sensible Word Problems

6.10. Conclusion

7. Number Theory, Applications, & Problem-solving

7.1. Composite and Prime Numbers

7.2. Pythagorean Triples

7.3. Arithmetic and Geometric Sequences

7.4. Arithmetic and Geometric Series