Maddy's Integer Operations

Modeling Integer Operations

During math, we reviewed by adding, subtracting, multiplying, and dividing integers. Here are some examples of what we did.

6 +  -4  = 2

First I started with six yellow (positive) chips, then added in four red (negative) chips, then crossed out the zero pairs. I ended up with two positive chips.

4 - -3  =

I started out with four positive chips, then we added three zero pairs, and crossed out the three red negative chips.

-4 * -2  =

I put eight zero pairs, knowing how many I had to cross out later on. Then I crossed out four pairs of negative two.

-8 ÷ 4 =

I started out with eight red negative chips, and divided them into four groups. There are two negative chips in each group.

Rules for adding, subtracting, multiplying and dividing integers: (Clearly explain the rules as you understand them here. Use math language.)

For multiplying and dividing integers, two positive numbers are positive, two negative numbers are positive, and if there is one positive and one negative, it is negative.

C Side vs. A Side B Blocks - Comparing Homework Times - Box and Whisker Plot

C Side and A Side:

C Side - B Block:

 

Mean: 76.8

Mode: 60

A Side - B Block:

Mean: 75

Mode: 45

How was the data similar?

Both the population size, median, maximum, minimum, outlier and third quartile are the same.

What was different in the 2 sets of data?

We discovered that the C side box plot didn’t have the top whisker, also, C siders had smaller outliers, 180, 135, 135, 120, and the A siders have larger, like 180, 180, 150, 150. However, the C side average is slightly larger than the A side average, as 76.8 > 75. Furthermore, the first quartile, and interquartile ranges are different.  

Were there any outliers?

Yes, the outliers for C and A side are 180, as they are much more than the other pieces of data.

Which class spends longer on their homework? PROVE IT!

C side B block spends more time on their homework. We know this because we used the three measures of center, mean, median and mode to prove this. C side’s mean is 76.8, whereas A side’s is 75, and 76.8 > 75. The median for both are 60 minutes, and the mode for C side is 60 minutes, which is longer than A side’s mode, which is 45 minutes.

How Tall is a Typical 6th Grader?

What is the height of a typical 6th grader at SAS?


The typical height of an average 6th grader is roughly 61 inches. I think this, because the median and the mode of the data of a typical 6th grader is 61 inches, and the mean of the data is 60.96 inches, which is very close to 61.

How does your own height compare?


My height (with sneakers on) is about 63 inches, and this is only two inches taller than the median, mode, and mean for the data of 6th graders. I don't think this is very precise, because without my sneakers, I am around 61 inches tall, but I think the data also shows the heights of 6th graders with their shoes on, too.

Does the height of 6th graders have a lot of variability? How do you know?

Yes, I think the height of 6th graders have a lot of variability. I know this because the minimum height is 52 inches, and the maximum height is 72 inches. The range, 72 minus 52, is 20 inches, which is a large gap.

Personal Finance Project

What did you already know?
I already knew a bit about using spreadsheets and I knew how to do some of the math. For example, for some questions I knew what to do and how to do it, but for others I needed help from Mrs. McComb.
What did you learn? (from the project? from your parents?)
I learned how to use tricks so that I didn't have to take a long time making the spreadsheet, and I learned how to make charts and graphs more. I also learned more about how to use percentages with problems like this, and I learned more about the pros and cons of keeping your money 'under your bed' instead of in a bank.

How might this affect what you do in the future?
This makes me more aware of how much more you can earn if you put your money in a bank instead of nowhere, and this also affects how I could use spreadsheets more effectively in the future.

What was your favorite part about the project? Least favorite part?
My favorite part of the project was watching the videos and learning different and quicker ways to using spreadsheets, and applying them to our own projects. My least favorite part was getting stuck a lot on questions I didn't know, because I haven't really don't anything like this project before, so I didn't know a lot.

Here's a link to our presentation: https://magic.piktochart.com/output/4771663-do-you-want-to-be-a-millionair

Dividing Fractions

¾÷⅛
You read the equation as how many ⅛'s there are in ¾.

3/4 ÷ 1/8 = 3/4 × 8/1 because 8/1 is the reciprocal of 1/8 meaning if multiplied together, it equals one. To find the reciprocal of a fraction, just switch the denominator to the numerator, and numerator to denominator. Only then you can multiply instead of divide.

Since 3/4 ÷ 1/8 has the same value as 3/4 × 8/1, you can just go ahead and write it out and multiply the numerators and denominators, then change the product from an improper fraction into a whole number or mixed number:

To make a model of 3/4 ÷ 1/8, make a rectangular bar, and divide it into quarters, and shade 3 quarters to show 3/4.

Next divide the bar into eighths, and to find the answer, count how many eighths there are in 3/4. 

There are 6 eighths in 3/4. 

¾÷⅛=6!

Student vs. Beast

Math Reflection, Fractions and Decimals

When is it more useful to use fraction or decimal notation?

You should fraction notation over decimal notation when the fraction notation is more convenient or when the decimal notation isn't easy to work with, or has many digits. For example, the 1/9 in decimal notation is 0.11111111111 which is much harder to work with, an 1/3 in 0.33333333333. You should use decimals when there are many digits, like .132435 instead of 132435/1000000.

When comparing two positive whole numbers with different numbers of digits, such as 115 and 37, the one with more digits is greater. Does this rule work for comparing decimals?

No, because 115 > 37, and .115 < .37

Fraction Comparison Reflection

You know how to compare fractions using cross products, LCD, and logical reasoning. When is it better to use one method over another?

You should use cross products when the fractions are small numbers and easy to work with:

You should use LCD (Least Common Denominator) when the denominators are different:

You should use logical reasoning when you can easily turn the fraction(s) into a benchmark fraction, or when you can see that one fraction is less than half, and the other is more than half, etc.

My Archaeology Google Site 2014

This is a link to my Archaelogy Google site that I made in Grade 6 Social Studies. I hope you learn something about the Terracotta Warriors!

Terracotta Warriors

My Favorite Number Project

For this assignment, I decided to make a blog.
Click here.

Gran, How Old Are You?

Using prime factorization helps answer the problem more efficiently because we know we need to find 5 numbers that multiplied together equals 111,111. So by finding the prime factorization, you can easily find the ages of Charlie, his siblings, and his mom. Also, when you find the prime factorization of 111,111 there are five numbers. One for each person. Using prime factorization also helps you know where to begin multiplying, and it helps you keep on track.

Investigation 2

How can you decide whether finding common multiples or common factors is helpful in solving a problem?

You can decide whether finding the common multiples or common factors by seeing if you have to multiply or find factor pairs. If your aim is to find bigger/greater numbers, than it's probably a common multiple problem. If you have to find a pair of smaller numbers, you probably have to find common factors.

http://www.ixl.com/math/grade-6/gcf-and-lcm-word-problems

For the question above, you have to find the LCM (Lowest Common Multiple) of 4 and 5.

For the 2nd question, you have to find the GCF (Greatest Common Factor) of 20 and 16.

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