Cut-out a paper triangle. If using the fact family as a teaching tool, make sure it is large enough to be viewable to students in the back row of a classroom. Laminate the triangle for easy reuse. Select three numbers to make-up your fact family triangle. The largest of these numbers must be equal to the sum of the lesser numbers. Write one number in each corner of the triangle, positioning the sum in the top corner and marking it with an asterisk. Draw in the signs for the addition and subtraction operations in the center, separated by a comma.
Students are charged with the task of writing four number sentences based on the numerals and operations contained in the fact family. Teachers introducing the fact family triangle should start by completing the first card with their pupils. Show students how taking either of the numerals in the base corners of the triangle and adding it to the other base corner numeral is equal to the asterisked sum. Then show them how taking the asterisked number and subtracting either of the numerals in the base corners of the triangle will equal the other base corner numeral.
The most obvious benefit of a fact family triangle is that it allows students to learn multiple facts, rather than just one isolated number sentence. These interactive flash cards also demonstrate that addition is commutative, and that addition and subtraction are inverse operations. While students may not be able to articulate these particular properties, they nonetheless begin making the connection and understanding the relationship between the two operations.
Once students become familiar with the process of creating number sentences from the fact families presented to them, it's possible to challenge them further. Provide students with fact family triangles with only two numbers, and ask them to solve for the third. This exercise encourages students to be more active problem-solvers and to demonstrate a more advanced understanding of number concept. It's also possible to replace the addition and subtraction operations with multiplication and division operations.