### 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:) ### Memory Wheels - First Day, Last Day, and Any Day in Between!

This post has been moved to:  http://www.cognitivecardiowithmsmm.com/blog/memory-wheels-first-day-last-day-and-any-day-in-between

### Math Class - First Day Activity

Rectangle of pentominoes Many 6th graders seem to have a pretty negative attitude about math, so I try to do something interesting to "grab" them during our first class. Last year, during the first math class, we spent part of the period working with pentominoes. Before working with the pentominoes, however, we played a name game so we could learn each others' names (I find it impossible to start anything else if I don't know some names, and fortunately, I learn them fairly quickly). rectangle outline For the activity, I divided the students into groups of 3 or 4. The directions for the activity were not complicated - the task was to make a rectangle, using all of the pentominoes. I gave students an outline of the rectangle, as pictured to the left, so they would know the correct size of the rectangle. The squares in the grid are each one inch. The rectangle is 5 squares (inches) wide and 13 inches long (13 inches includes the row that has the "Pent

### How Much Math Homework??

I am very curious about math homework in middle school, from a teacher perspective:     How much math homework do you give?     What kind of homework do you give?     How do you go over it in class? Let me explain why I ask these questions. I have taught 6th grade math for eight years, and every year, my goal is to "perfect" the homework issue. My basic issue is that I feel that I spend too much time going over it (not necessarily every day, but often). In the past, we have reviewed homework in the following ways:    1. going over answers as a class    2. self-checking answers that are on the board and sharing any questions    3. partner-checking and then verifying    4. choosing only a few problems to check When I taught elementary school (for 12 years), I never seemed to have this problem....we had 60 minutes for class and I never struggled to fit everything in. But at middle school, we have 44 minutes (minus time to switch for classes), and I just haven't fo