Day 41: Exposing Students to Limits

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and
V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.

The Learning Objective: Apply multiplication of fractions in order to find a limit.

Quote of the Day: “Spend time with people who constantly drain you, pull you in the wrong direction, or try to knock you down, and it will be almost impossible for your talent to take flight.” - John Maxwell

Agenda:

1. Jumpstart reviewing like denominators, unlike denominators, and multiplying fractions.
2. Review the homework. The most interesting problems asked students to find 1/4 of 154 and 1/3 of 120 in a word problem and then compare the amounts.
3. Physical example of a limit using our classroom.
4. Limits using a 64-square grid and continuously coloring half of the remaining unshaded grids and the questions which corresponded to this.
5. Starting the homework in class.

The Assessment: I was consistently circumventing the room during number four in the agenda and also checked homework during step one in the agenda. Overall I was encouraged by the homework results.

Homework: Tonight's homework was page 284 #4-11 and page 285 #14-16

My Glass Half-Full Take: I yelled onions twice today. The first time I got excited was when a student got a common denominator for 4, 10, and 7 compared the fractions and determined which fraction was greatest. Everyone else in the room that could solve it (including myself) multiplied one-fourth, three- tenths and, two-sevenths by 152, 160, and 147 respectively to see how many people were in each group. Then we determined that three-tenths of 160 was the biggest group. By finding a common denominator and changing the numerator, we'd get the same answer. It's always nice to have students sharing alternative ways for solving the problem - especially ways I never would have thought.

Another student eventually recognized that if a person continually walks half-way across a room they will mathematically never reach the wall.

One Thing to Do Differently: The activity we did today was done in partners. One of my colleagues did it in groups of six. I believe that would have worked much better. It would have been easier to facilitate giving colored pencils, and it also would have put the learning on the students instead of on me. I ended up being at the board for most of the block as it were and I believe students did not think as much as they should have. I also believe that perhaps ditching time to start on homework is better because the activity is deeper on Bloom's Taxonomy than our homework. Perhaps a simple assessment of three problems for homework will be a more appropriate way to give out homework in the future on this lesson.

Link of the Day: If you're looking for a hot button issue to talk about with Halloween in educational way, perhaps discussing the appropriateness of costumes would suit you.