Students enter silently according to the Daily Entrance Routine. They are asked to take their homework out and check their answers using the worked out answers displayed on the board. While students take 2-3 minutes to check I walk around to find a student sample whose work is correct but looks different than the sample on the board. We review the work displayed on the board and students get to share their understanding and solution for each problem.
I'm specifically looking for problems like #3 where the commutative and associative properties can be used in different ways to solve this problem. In the example I provided on the answer sheet attached, I used the commutative property to group the whole number together and the fractions together. I was interested in finding a student who did not use the commutative property and instead use the associations already preset, combining the first pair of numeric terms (-44 - 3/8) and the second pair (95 - 5/8) separately. Thus:
(-44 - 3/8) + (95 - 5/8)
-44 3/8 + 94 3/8 = 50
I found one such student and while their horizontal numeric expressions had fewer steps as she simplified, her "arithmetic" steps included two horizontal mixed fraction operations. During the previous lesson we reviewed the difference between using numeric expressions to show work and completing arithmetic steps on the margin to aid neat simplifying of the expressions.
After the student put up the work, we were able to discuss, with the help of the class, the pros and cons of both of our solutions.
This HW check is also a great opportunity to catch common mistakes such as dropping negative signs in the simplifying of expressions or adding/subtracting fractions involving carrying and borrowing incorrectly. These are some common errors I continue to look out for.
Khanacademy is known for its success with autodidacts and independent learners. I learned about this program while surfing the net looking for a tool students could use at home, providing me data of their activity so that I could recommend skills to continue practicing at home. This site does all that, and more. Learnzillion includes some coaching and data assessment resources, but the main reason I like this site is the user friendliness of its videos.
On this first day of introducing students to the sites, we will focus on signing up and learning how to navigate the site. I will need students to add me as their coach to both sites. For more information on "coaching at khan, go here. and More more on Learnzillion, go here. It is also important to mention that students will need parental consent to have these accounts. These and other links including walk-throughs are provided below:
Students are provided a “how to” sign-up sheet for two websites: khanacademy.org and learnzillion.com. Everyone is given headphones to view the videos on each website. We will focus on signing up for Khan Academy and completing the recommended tasks. I set these tasks previously for each student according to the results in their most recent quiz. For example, those who need to review integer operations will see recommendations for these topics and exercises for when they log on to each site.
On khanacademy you can recommend skills for students to practice from the coaching tab. I recommended the same lesson to all students (adding fractions with different signs) and expected them to complete it during class. The exercise problems also include some subtraction. I gave all students this task because I wanted to assess whether watching the video would improve skills for students.
I ask students to look at the projected image of the class energy points. This is a “real time” view on the website of the average amount of points being earned by students in the class. According to Khan Academy:
Energy points measure effort on Khan Academy. Learners earn more energy points for pushing the edge of their knowledge. They are not a measure of mastery or ability.
I use this text to explain to students that energy points measure how hard you’re trying to improve. Students are motivated because they see instant progress on the board. I ask a group to stop working for about 3-4 minutes and alert the class to notice how the progress is affected when some stop. Students are better able to make the connection between effort and success when they can reap immediate benefits or see immediate change in the positive direction. The graph provided by khanacademy can do this.