Learning to Love Math - Chapter 3

Chapter 3 - Examples of Differentiated Planning for Achievable Challenge

 I took notes on this chapter last week, on a bus ride to NYC (to see Aladdin!), but it has taken me until today to actually write this post:)

As the title of the chapter suggests, the author offers examples of differentiated planning and activities. In each example, students are learning the same basic concepts, but at different levels of challenge, which should lead to their maximum success and should minimize their frustration. There are several different examples, so I'll highlight a few in this post and the next.

The first activity, which involves working with shapes, is called "Draw My Shape," which the author says is a good activity for Map Readers. The steps for the activity are as follows:
1) pair student that have similar abilities in shape recognition and in naming shapes, OR pair a high mastery/low communication student with high communication/low mastery student
2) give each pair a set of manipulatives in a variety of shapes
3) the partners should sit opposite from each other with a divider between them so that they can't see each other's work
4) partner 1 gives verbal directions to partner two for how to draw a certain shape, and then the students switch
5) older students should be expected to use more descriptive, specific mathematical vocabulary.

A second activity involves estimating volume (with the goals of building estimation and prediction skills, adapting to new evidence, building math communication skills, number sense skills, and conceptual awareness):
The "low complexity" group follows this procedure:
1) the group is given a large pitcher of colored water
2) each group member fills an 8 ounce cup from the pitcher and predicts how high the water will reach when it is then poured into clear bottles that have different dimensions; students should mark their predictions with a marker before pouring and then discuss the result after pouring
3) student do the same thing with a second cup of water, making and marking new predictions before pouring

The "medium complexity" group, which the author labels as "Early Conceptual Thinking," does something similar to the first group, but they are expected to design the experiment themselves. They are given the materials and told that the goal is to make predictions, but are not given a procedure to follow. They are to keep group or personal records of their predictions, results, and explanations.

The "high complexity" group, labeled as " More Abstract Conceptual" would incorporate metric conversions and would look at the ounce markings on a measuring cup. In this case, students design  the experiment, complete it, and then pour the water from the 8 ounce into a metric cup. Students are expected to analyze, predict, test, adjust, and develop correlations about the relationship of cups, liters, ounces, and milliliters, as well as how to find conversion factors.

When finished, groups should share their findings with the rest of the class. Willis advises that homework should then be differentiated, based on the activities completed in class.

More examples next time...:)

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