Fact Family Triangles

 

Since I teach high school, I am not always aware of the latest developments in the younger grades.  A friend turned me on to fact family triangles.  I actually like them better for showing the relationships between numbers since the standard addition or multiplication charts do not.

If you have not seen them yet, they are triangles with the sum or product at the top leg of the isosceles triangle with the two numbers that combine to make them on the other two legs.  I am more familiar with the multiplication ones since those are the ones my students use.  

The triangles make it easy for students to multiply or divide and they can easily see the relationship between the product and it's factors.  In addition, students who have difficulty distinguishing rows and columns in a regular chart, have only the three numbers to deal with and there is less confusion.  Furthermore, fact family triangles make it easier for students to write mathematical sentences with only three given numbers.  Students can also develop their critical thinking skills and ability to analyze while learning about and expanding their knowledge about inverse operations.  The triangles allow them to see that subtraction is the inverse of addition and vice versa or division is the inverse operation of multiplication and vice versa.  

Thus using fact families help students learn their basic facts, builds their confidence and knowledge of basic number facts while developing a solid foundation of algebraic thinking.  Consequently, students have an easier time when they begin solving one and multiple step equations because they are already familiar with the concept of inverse operations. 

In addition, the use of fact families helps students build more flexibility into their number sense because they are exposed to seeing more than one operation at a time.  Now, there is some argument that learning each operation individually is better because they are more fluent with the facts but due to COVID, many students did not accomplish the fluidity so they need scaffolding.  

I think using fact family triangles with middle and high school students is a really awesome way of scaffolding.  It helps them see the relationships they might have missed and it allows them to build number sense.  Let me know what you think, I'd love to hear.  Have a great weekend.