Integers are a common tripping point with students who are moving into advanced mathematics. They often understand the concepts we are teaching but make errors with signed numbers that prevent them from being successful. This handout is a collection of 30 years of the best practices I have found for teaching integer calculations. You’ll find five strategies that appeal to all types of learners: mathematical, linguistic, and visual and kinesthetic.
to see state-specific standards (only available in the US).
Solve real-world and mathematical problems involving the four operations with rational numbers.
Apply properties of operations as strategies to multiply and divide rational numbers.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If 𝘱 and 𝘲 are integers, then –(𝘱/𝘲) = (–𝘱)/𝘲 = 𝘱/(–𝘲). Interpret quotients of rational numbers by describing real-world contexts.
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
Apply properties of operations as strategies to add and subtract rational numbers.