Learner Activities

What makes a great activity? Certainly one that is engaging and motivating. Chapter 5 discusses two types of learning approaches: direct instruction and inquiry-based learning. Activities can be either. Basically "direct instruction" activities are where it is clear what skills need to be acquired and it is clearly layed out how to acquire them. The focus is on gaining proficiency not quelching curiosity. Inquiry-based is where the ends aren't quite clear; where you need to be curious and find out what type of answer you need before even finding it. For instance, if the topic is slope-intercept, a direct instruction activity focuses on teaching what slope and the y-intercept are. It states the facts, then works on the skills necessary for proficiency. An inquiry-based approach is if a student comes to an understanding through exploration-- like looking at real life examples of a changing rate; like phone rate plans for example.
Obviously the latter seems more engaging, however, procedural proficiency is definitely necessary. It is difficult to differentiate procedures in math, but topics can be explained in a variety of ways, and at a slower pace, for those learners who need more processing time. The more interactive, curiousity-sparking activities are more easily differentiate-able, especially with on-line actitivites, where for instance you can't move on to the next level until you've demonstrated enough proficiency. The activity grows in complexity as the student gets better at their own pace.

The topic for my curriculum web is slope and y-intercept. These websites I found to be helpful. I put them in order of when they would come into play in instruction. The first offers an introduction, the second is for the learning, and the third is for the assessment. The level of interactivity goes from least to most.

http://www.math-play.com/Slope-Intercept/Slope_Intercept.html
This one might be a little boring- not a game-, but it is interactive and a helpful introduction to this topic. It allows students to change the slope and the y-intercept and see the resulting line. It also asks probing questions for the students to start thinking about the consequences of changing the slope and the y-intercept.

http://www.mathwarehouse.com/algebra/linear_equation/slope-intercept-form.php
This website is nice because the students can use it at home to help them self-teach, or it can be used in class. It has boxes to click on for the answer. Therefore, you could put the site up on a smart board, and give the class time to work out the problems, then click on the automated response. It also has the sliding line, so students can control slope and y-intercept, and not only see the line created, but also a table of values.

http://hotmath.com/hotmath_help/games/kp/Karappan_Poochi_Sound.swf
O wow! This site is AMAZING! It is a fun game for kids. Basically, cockroaches crawl across the screen in a straight line. There are three rounds- first is the easiest, find the y-intercept; second, find the slope; and third, find the equation of the line the cockroaches crawl on. Once you type it in, a laser shoots them and they die. It is timed, so after a few minutes, you lose that turn and have to try again. You need to reach a certain proficiency to be able to move on. It is challenging and fun!!!! So easy for differentiation- since you move on as you get better.