Learning to Love Math - Chapter 3

Chapter 3 - Examples of Differentiated Planning for Achievable Challenge

This is a continuation of Chapter 3, from a couple of weeks ago (I had my notes written, but it has taken me a while to type them!!). In the previous Chapter 3 post, I reviewed a couple of the examples of differentiated planning and activities that the author offered. In each example, students are learning the same basic concepts, but at different levels of challenge, which should lead to maximum success and should minimize their frustration.

This example is called Exploring Number Lines, and the author states that it is a helpful activity for both "explorers" and "map readers." As a preliminary activity, students explore number lines without any specific assignment; the author suggests using large number lines that can be rolled out on the floor. Students meet in groups and create KWL charts. In working with the number line, students will predict where they will end up with certain movements (2 places to the left, 5 places to the right, etc....on the positive side of the number line). As students move to a higher complexity, they will move toward exploring the negatives on the number line.

Another example she gives is related to understanding division, with the goal being the understanding of the concept of division as a way to break larger amounts into specific numbers of parts. The low-complexity group plays games/"sharing activities," in which students are given 10 manipulatives and are asked how they can be shared among their group of 5 members. Next students are given 15 items and asked if they can be shared evenly - if so, how? This activity continues, using different numbers of items and different numbers of group members.

The medium-complexity division
group (of 5 students) is given 100 pennies (or plastic pennies) and is asked to determine how many ten-cent pencils each group member could "buy" (equal number for each member). Students are then asked to determine how many 20-cent or 15-cent items could be purchased for each member.

The higher-complexity group would also work with ten and 20-cent items, would evaluate the worth of the items, and would use newspaper ads to find the unit rates of products.

A whole-class activity related to the division concept is to place students into groups of 3, give each group 7 large blocks, and ask them to determine how the blocks would be divided so that each person gets an equal share - the author states that this leads to the concept of fractions without necessarily calling them fractions.

All examples are very interesting! On to Chapter 4:)