Just to let you elementary people know, I used the idea of fact families with my sophomores the other day. We've started Trig, and it's not uncommon to have an equation like sin 36 = 12/x. I explained to them that it's a real pain to have a variable in the denominator. Then I reminded them of their fact families: how if 2 = 6/3, then 3 = 6/2 because 2(3) =6. As a result, they could rewrite the original equation as x = 12/sin36, and simply take out their calculators. So, to all those teachers who did a great job of teaching their kids to internalize the basics, I offer you my thanks.

lol..Yes, I was good until I got to the second sentence as well! Very nice, Alice! We love our fact families. Of course, next year I will be teaching Singapore Math, and it's my understanding they use different terminology.

Alice, although I post very little, I actually base a lot of my math teaching off of you. :thumb: I have always loved Math, but I know I've seen you post several times about difficulties with an elementary teacher saying something not entirely true and it backfiring later in high school. Things I do in my 4th Grade classroom: 1) fact practice EVERY day 2) rarely say never 3) if I do tell them they can't do it, I specifically tell them: you are NOT allowed to do this in 4th grade because you're not prepared for it yet, BUT as you get older these things are possible and often required: For Example: reading division equations properly (they often read backwards which would give a decimal), negative numbers, graphing in the positive coordinate plane only, and I'm sure more I can't think of right now. Often I will show them how it is possible (just once) and tell them although they don't understand it now, they will in middle school or high school. Sorry for the rambling, but I just wanted to say thank you :thanks: as an elementary school teacher, who has never taught above 4th, for the inisght of a high-school teacher and how I can improve my teaching to prepare these kids for better experiences later in school.

No idea what you're talking about. Sin? Sin?! Honestly, I so did not get that far in my math journey. But I'm glad you were able to use fact families to do whatever it is you were doing.

You have inspired me for when I introduce my algebraic expressions unit in the near future. Thanks, Alice.

So true! What a delightful way to open my Monday morning! Mrs. Hodge, how wonderful that you open their eyes to things that are possible, even if they're currently beyond the grasp of your kids. In my mind, that's what teaching is all about: opening their eyes to the possibilities. For anyone who is curious, here's the quickie explanation: You teach your kids that in similar triangles, corresponding sides are in proportion. Someone, somewhere along the way, actually figured out what that ratio was for each angle. In a right triangle, the Sine (abbreviation: sin) of an acute angle is the ratio of the length of leg opposite that angle to its hypotenuse. The Cosine (cos) of an acute angle is the ratio of the length of the leg adjacent to it to the hypotenuse. The Tangent (tan) of an acute angle is the ratio of the length of the opposite leg to the adjacent leg. So, for example, sin 30 = 1/2 because in a right triangle with a 30 degree angle, the side opposite the 30 degree angle is always half the hypotenuse. You can find the rest of the angles using the sin, cos and tan keys on a scientific calculator.

One of my kiddos "discovered" multiplication/division families today. (We haven't talked about how they're related yet, we only concretely divided actual objects so far.) He was so excited!