Today's estimation was the length of the song Oye Como Va by Santana. Most students estimated that 1/3 of the song was over, so take 1:26 and multiply it by 3. I made sure in each class students explained to me what to do with 3:78, the product. Most said subtract 60 seconds and add a minute. I made an analogy that if someone was 5 feet 1 inch tall, we don't say they are 4 feet 13 inches tall. They realized how silly that sounded. I basically referenced place value and that once the base was 60 it increased the hour by 1.
|Digging deep into interpreting time.|
Then I had students take out their data sheets from friday, textbook, and composition book. I had volunteers give me examples of 2 acute, 2 obtuse, 2 right, and 2 non triangles. We then analyzed the side lengths that did not form a triangle. I didn't take a picture of the definition, but I made sure in most classes that we investigated side lengths of 4, 6, and 10. I remember last year some students mistakenly thought that if the sum of 4 and 6 was equal the long side it could be possible. That is not true, and is easy to demonstrate with the squares with those side lengths. Therefore...
Three side lengths of squares will not form a triangle if the sum of the small and medium sides is less than or equal to the side length of the large square. Conversely, three squares will form a triangle if the small and medium side lengths is greater than the long side. They had discovered the triangle inequality theorem. Students had been introduced to it last year, and some even remembered it from a certain 6th grade teacher (cough Miss Wong cough).
I had them copy the 3 statements below from the next problem, and then volunteer and complete the sentences as a group. This picture doesn't show the examples.
|The first class work problem was 5, 6, 7. They confirmed it was a triangle, and then squared all the sides, added the small and medium squared sides, and it was greater than the longest side squared, so an acute triangle. 2, 11, and 15 wouldn't form a triangle because the sum of 2 and 11 is not greater than 15.|
|Proving a right triangle.|
|One of our students who supports Kumon.|
|We didn't get time to review all of these, and we will tomorrow.|