# Thinking Mathematically : Integrating Arithmetic and Algebra in Elementary School

@inproceedings{Carpenter2003ThinkingM, title={Thinking Mathematically : Integrating Arithmetic and Algebra in Elementary School}, author={Thomas P. Carpenter and Megan L. Franke and Linda Levi}, year={2003} }

This unit provides opportunities for students to extend their ways of thinking about addition and subtraction to problems with larger numbers. Students use their prior knowledge of addition and skip counting to invent strategies for solving repeated addition and subtraction problems. Because multiplication and division are closely related, this unit presents both types of situations. As students solve problems based on familiar situations, they choose tools to support their extended use of…

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## References

SHOWING 1-3 OF 3 REFERENCES

### The Acquisition of Addition and Subtraction Concepts in Grades One through Three.

- Psychology
- 1984

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve…

### “ Developing Problem - Solving Abilities and Attitudes . ” In Mathematics for the Young Child

- 1990

### Developing Problem-Solving Abilities and Attitudes

- National Council of Teachers of Mathematics
- 1990