302 Research Directions Part 2

Spend 5 minutes discussing the article with your group.
Each person in your group will select one cause (agriculture, residencies, logging) or effect (climate change, global warming, habitat loss) of deforestation to research for the group research paper.
When you have all agreed on what these will be, please ask me for a form to fill out.

5-302 Research Directions Part 1

Please go to National Geographic Deforestation Article and read it independently.

Missing Dimensions Homework (2/22)

Hi! We reviewed the homework in class today, using a systemic guess-and-check strategy. Here are a couple of screen shots:

Area Model for Multiplying Fractions by Fractions

This model should be familiar to the students from our work with multiplying decimals.  Here is a screenshot from today:

Steps:

1. The first factor: Divide the square vertically by the second denominator (5), label the fraction at the bottom (4/5), and shade the fraction with the lighter of your 2 colors.

2. The second factor: Divide the square horizontally by the first denominator (6), label the fraction on the left (1/6), and shade only the intersection of the of the both factors with the second color.

3. Finding the product: The double-shaded region represents the product (4/30). The denominator of the product is the total number of cells, shaded and unshaded (30). 

** Sometimes students shade the entire second factor, all the way across, in step 2, before finding the intersection. While this is not incorrect, I have found that it can sometimes be more confusing.

Another problem:

* For this problem, we started by shading 4/5. Since multiplication is commutative, it does matter which factor you start with..

Using Constant Difference for Subtracting Mixed Numbers

We have been working on a new strategy, constant difference, for subtracting mixed numbers in which the fractional part of the minuend is less than the fractional part of the subtrahend. In the standard algoritm, you would have to regroup from the wholes and make an improper fraction in the minuend in order to subtract the fraction. In constant difference, the goal is to add an amount to the subtrahend (the amount being subtracted) in order to make it a whole number. Then you add the same amount to the minuend (the amount you are subtracting from) in order to keep the difference constant (the same). You now have a new minuend and a new subtrahend, and a much simpler equation to solve. Below is an example taken from class:

Using an Open Array to Model Decimal x Whole Number Multiplication

Here is a screen shot for how you could use an open array to model 18 x 8.7. First you would draw an array based on how many digits are in each factor (ie two digits x two digits would be a 2 x 2 array, 3 digits x 2 digits would be a 3 x 2 array). Then you would separate each factor by place value along the sides of the array, and solve for each cell of the array by multiplying the side lengths of the cells. Finally you would add all of the partial products in each cell together.

Here is one for 56.1 x 23, which is not as nicely color-coded:

Properties of Addition and Multiplication

For help with the properties of multiplication, including a quiz, click on the image below:

For help with the properties of addition, including a quiz, click on the image below: