Addition and Subtraction Strategies

Hi! Here are some of the strategies we have been using for adding and subtracting decimals:

Compensation is an addition strategy in which you adjust one of the addends to make it a friendly number by taking an amount from the other other addend.  This strategy works because of the Associative Property of Addition, which allows us to group addends in any way way we want. In the SmartBoard grab below, you will see how we used compensation to take .1 from 3.14 and group it with 2.9 to make 3 wholes. Our new expression was 3.04 (this was the previous 3.14) + 3 (the previous 2.9). 3.04 + 3 can easily be solved using mental math. Also, to the right, you can see how you could use compensation to adjust 16.18 + 5.94 to 16.12 + 6 = 22.12.

Our next two strategies are for subtraction. The first is using finding the difference by building up, and we can use an open number line to model this. Here we started by placing the subtrahend and minuend on the number line. Then we began at the subtrahend, and took jumps to get to to the minuend. Every times we took a jump, we record the distance traveled on top of the jump. We went from 1.83 to 2 (+.17), from 2 to 4 (+2), and from 4 to 4.67 (+.67). Then we added up the total distance traveled between the minuend and subtrahend and that was the difference.

The last strategy is called constant difference, and it is useful when the subtrahend is close to, but slight less than, a friendly number. In constant difference, we adjust both the minuend and the subtrahend by adding the same amount  to both (however much you need to make make the subtrahend friendly will determine this amount) in order to make a friendly expression. See below how we added .09 to the minuend and subtrahend of 5.03-2.91 to change it to 5.12-3= 2.12. Underlying this strategy is the concept that if the minuend and subtrahend both increase by the same amount, the difference between them will not change.

Division Strategy: Partial Products and Ratio Tables

With this strategy, we use a ratio table to build multiples of the divisor, starting with 1 set.  We can use place value, doubling, and halving to make 10, 2, and 5 sets of the divisor. We want to try to build a big "chunk" of the dividend using the ratio table, which we will then subtract from the remaining amount of dividend. We will continue to subtract sets of the the divisor from the dividend until we cannot subtract anymore sets. If we have any left over, this will be our remainder. We then add up all of the sets we made, and this is our quotient.

Here are some screenshots of this strategy

:

Using Open Arrays and the Distributive Property to Solve Division Problems

Using the Distributive Property is a  great strategy for solving division problems - and you can use an open array as a model. When you use an open array in division, the dividend is the area, the divisor is one side length, and you are solving for the other side length (this will be your quotient). You can use the Distributive Property to break the dividend into multiples of the divisor (this is really important because it allows you to divide easily by the divisor!),  and then add the distances along the unknown side to find the quotient.  I like to make a mini array with the area next to my large array to keep track of total area because I will be breaking it apart in my large array. Here are some screen shots from today's lesson - hope they help!

WELCOME FAMILIES!!!

I am so excited for the 2016-17 school year! It was wonderful to meet my new homeroom today. Please check back for updates, and/or follow this blog. I will post information about class and grade events and trips as well as math homework and review resources. Please email me if you have any questions or concerns.  I look forward to a great year! - Ms. Rached

5-306 Reflection

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5-307 Reflection

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Project Reflection

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Service Project Order Form

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Idea Lab

Congratulations!
You have now entered the Idea Lab phase of our Community Service project - where you will be brainstorming, researching and discussing ideas for your project to address our class issue. You will need to create a shared Google doc using the Idea Lab template. Fill out a separate template for each idea you have. I would like each group to have at least 3 ideas.  Please be detailed as possible with your supply lists (insert hyperlink to the websites where you found the prices). Idea templates are due on May 19.

STEM Match-Ups

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STEM Day Bios

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5-306 Research

Read this article  and this one (UNICEF) about children in poverty silently.

5-307 Research Part 1

Read "Effects of an Unhealthy Diet" and "Why Good Nutrition is Important" articles independently.

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: