Today PJ and I discussed Ratios that can be reduced. We talked about an athlete who made 18 basketball shots and made 12 of them. The question asked if she continued to shoot at this rate, how many baskets would she make on her next 6 shots? We set up the ratio 18:12 and PJ recognized it could be reduced by 6 to 3:2. Then we said if there are 6 shots, we would have multiplied the 3 by 2, so we must multiply 2 by 2 to get the number of baskets made would be 4. Then we took the experiment outside for our findings. PJ shot the basketball 10 times and made 5 baskets. I shot the ball 10 times and made 7 baskets. We put our data together to make 20:12. I asked PJ what the reduced ratio would be and he said 5:3. Then I asked him, if we made 30 more shots at this rate, what would our number of baskets be. PJ realized it should be by 18 baskets!
Today Aiden and I continued working with triangles. We started with given conditions of a 40 degree angle, and side lengths of 5 and 6 units. We drew a triangle and considered if this was the only possible triangle we could draw. We noticed that if we "swung" one of the legs inward, we could still preserve it's length but it would create a triangle with a different shape this time. We compared this exercise with one we saw yesterday where the conditions given implied there was only 1 possible triangle that could be created. We then discussed a 30-60-90 right triangle and I asked Aiden what types of triangles could be created with these conditions. We agreed that the triangle could be enlarged or reduced, but the shape would stay the same. If we oriented it differently by reflecting or rotating it, the position would change, but the actual shape would remain the same. We determined that all 30-60-90 triangles are proportional to each other by some scale factor. Instead of moving onto 8.4 (that will take a whole class period), we decided to practice some of the problem types we've seen recently. We pulled up a problem with a scale factor drawing of a living room blue print. We practiced using proportions and cross multiplication to solve for the missing sides. Aiden did excellently today!
Today Carson and I met on Teams. We covered a lot of content and Carson did a great job. We discussed polynomials and how to classify them by degree (constant, linear, quadratic, cubic, etc.) and number of terms (monomial, binomial, trinomial, etc.). Carson and I did an activity where I showed him an example of each type and then labeled it with the correct classification. Then I gave Carson problems to practice on his own. We discussed how to put the polynomials in standard form first, then choose the highest degree we see with the number of terms to classify. Next we discussed how to add and subtract polynomials. We discussed the importance of combining like terms and distributing the negative when appropriate.
