Combine the thirds until you get 3 wholes and one third.) When you use fraction manipulatives to demonstrate why 5 × 2/3 equals 3 1/3, you are "proving" or demonstrating. But proofs in elementary and middle school don't have to be on the same level of rigor as later on.įor example, when you show students how and WHY multi-digit multiplication works (2 × 371 is the same as 2 × 300 + 2 × 70 + 2 × 1), you are proving, or "justifying" something. You as the teacher will want to convince your students that what YOU ARE telling them is indeed true. Proving before high school: justify and consider the "why"Ĭhildren can – and should – experience proofs before high school also. See also an example comparing a proof written in two-column form or written as text. And it is not enough to convince a fellow student, but any sufficiently educated rational person, such as your parents, your math teacher, and a mathematics professor.īut, the form of the proof or numbering your arguments is NOT the most important thing! You don't necessarily have to write proofs in 2-column format if you like writing them as plain text (prose) better. Then also you need to CONVINCE: to be logical in your reasoning. That is why we use "line segment AB" in text, instead of "this line." You probably had to spend some time figuring what I meant by "this line" and "that angle"!Ī proof needs to COMMUNICATE your thoughts clearly. But it isn't the best proof if it was written in a book. It is a fine proof if it was SPOKEN to someone while pointing to the various parts of the image. Well, the answer is, my proof above IS a fine proof – and yet it isn't. I mean, by SAS congruence theorem we know these two triangles are congruent."ĭo you think that is a proof? Is anything missing from it? So, looking at these triangles, there's a side that's as long as this side, there's an angle that is the same as this angle, and there's a side that is as long as this side. They are the same, I mean have the same measure, obviously, because they are formed in the two corners when these two lines cross each other, or you can also say they are 'vertical angles'. And now look at these two angles, here and here. And, since this is a midpoint, then this line is as long as this line. It's not drawn to scale or to be accurate. PROOF: "Look at this picture that I drew. PROBLEM: If E is the midpoint of BD, and AE is as long as EC, prove that the two triangles are congruent.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |