Changing Area

CHALLENGE QUESTION!

If the area of one figure to another increased 81 times, how many times greater is the perimeter of this new, larger similar figure?

*Hint* Remember the 'rule' we discussed in class.

Perimeter!

Perimeter is the distance around a figure. You can find perimeter by adding all of the side lengths together, or by using a formula. For example, the formula for perimeter of a square is 4s (4 x side length), and the formula for perimeter of a rectangel is 2l + 2w (2 x length + 2 x width). If the shape is irregular, you simply have to add all sides together!

**TRY THIS CHALLENGE QUESTION**
Find the greatest perimeter possible when 6 identical unit squares are arranged to form a closed figure. Adjacent squares (neighboring squares) must share an entire side. You will probably have to draw out six squares and either cut them out or manipulate them on your paper until you find the arrangement with the greatest perimeter :)

Symmetry

Symmetry is everywhere! It's in nature, architecture, shapes, letters, etc.

A figure has line symmetry if it can be folded or reflected so that each of the two parts are congruent. The line of reflection is called the line of symmetry.

Below is an example of symmetry in nature.

source http://farm2.static.flickr.com/1258/813779861_48acd71741.jpg

Symmetry in architecture!

Where do you see symmetry in the world around you?

Triangles

Triangles are tough shapes. They are the most frequently used shape in architecture because they provide such strong support. Triangles cannot be deformed without changing the length of one it's sides or if one of it's joints break.

Notice how the Golden Gate Bridge is constructed with many triangles to give superior strength and durability.

You may not have recognized this, but many bike frames are built using triangles as the primary shape. Mountain bikes and BMX bikes take a lot of beating from their riders during trail riding and trick jumps, but the triangular frame provides the strength needed to support this force!

Share some examples of where you find triangles at use in the world around you. This may be in your home, school, searching on the Interent, etc.

Geometry and Architecture

Hey guys! Branching off of our discussion today, see if you can identify more geometric vocabulary from the video that is linked below.

http://www.thefutureschannel.com/dockets/hands-on_math/abcs_of_architecture/

Click on the link and watch the video. Try to find (visual) and listen (auditory) for the words we discussed in class or any other words that relate to geometry. Leave a comment with your findings! Feel free to watch some of the other videos on how geomtry is used in the world around us :)

Pencil Problem...

Mr. Foster is ordering classroom supplies. He orders enough pencils for every student and then adds 20% more for extras (in case some students lose theirs :). If Mr. Foster has 75 students, what is the total number of pencils he needs to order?

Use the PERCENT PROPORTION to solve this problem. Tell how you set it up and explain the steps for solving:)

Percent Question

If a sales tax rate is 7%, find how much you would have to pay in sales for every $1.00 you spend, for every $10.00 you spend AND for every $100.00 you spend. Give three answers and try to explain how they are related. 

Similar Figures

Similar figures that are the same shape but different size. Also, the ratios of the lengths of the corresponding sides are proportional. Knowing this, decide if the two figures pictured below are similar. Tell why or why not in your comment. Be sure to make ratios with corresponding sides! 

Proportions

Use the following chart to create proportions and answer the questions.

1. How many cups of mix would it take to make 50 pancakes? Show the proportion on your comment.

2. How many cups of water would it take to make 20 pancakes? Show the proportion on your comment.

**Challenge** How many pancakes did I make if I used exactly 4 cups of water?

If you forget how to solve a proportion, follow this example by Harrison!

Unit Rate Question

?Question, Question?

Suppose your friend receives $10.50 each week in allowance if she cleans her room every day. What is the unit rate she receives for cleaning her room every day? 

Be sure to label your answer specifically so it represents a unit rate. 

Equivalent Ratios

Equivalent Ratios-are ratios taht name the same compairson . You can find and equivalent ratio ratio by mutlplying or dividng both terms of a ratio of the same number.

Selena block 1

Unit Rates

Unit rates are helpful for finding the best deal on a product at a store. For example, a store may be selling fish food in a variety of brands. How do you know which brand is the best deal? Find the unit rate of each product and compare the answers!

Here we go! Brand A sells 3oz of fish food for $3.79. Brand B sells a similar kind at a price of $2.58 for 2oz. Is Brand A or Brand B a better deal?

Erin will tell you how to find the best deal using the unit rate!

divide 3.79 by 3 and you'll see that the unit cost is $1.26 an oz.( Brand A)

Divide 2.58 by 2, you get $1.29 an oz. (Brand B)

even though brand A costs more, it is a better deal per oz.!!!!!

Ratios and Snack Time

After completing some assignments for my Instructional Design class I decided I needed a snack. So, I went for a banana with peanut butter on it. While I was putting the p.b. on the banana I noticed something very interesting on the label. Check out the picture and see if you can find what was so interesting.



Can you think of/find anywhere else in the "real world" that ratios are used. Check out the web if you need to and post a comment with your findings!

Chapter 7 Introduction

We are now beginning Chapter 7, Proportional Relationships. This chapter covers ratios, rates, proportions, similar figures, and percent problems. This chapter is strong in the Number, Number Sense Standard with emphasis on Indicators 4, 5, 9, 14 and 15.

So what are ratios anyway? Ranika will tell you about them....read on:

A ratio compares two numbers. Ratios can be written in 3 ways.
EX: 5 to 7 5:7 and as a fraction 5/7.

n n n n t t n n

The ratio for n to t is 6:2, which can be reduced to 3:1.

RANIKA BLK 2

Ordered Pairs

Ordered pairs (X,Y) are directions for plotting a point on a coordinate grid. They can both be positive, both negative, or a mixture of positive and negatives.

QUESTION: What quadrant would the ordered pair (-2, -8) fall in? Leave a comment with the answer!

Line Plot, Frequency Table, Histogram

Chapter 6 moves on into new types of graphs. Line plots and frequency tables are fairly easy to create while histograms require a bit more attention to detail. Histograms are quite similar to bar graphs but there are some differences. Can you tell me what makes a bar graph and a histogram different? Leave a comment with your answer!

A frequency table shows the tally marks for a particular category as well as the number, or frequency.

Neatness will improve, but for now here is an example of a histogram.

Bar Graph

Winter Break is over, so to introduce bar graphs we conducted a survey of gifts students recieved. We picked four categories that seemed to capture the most popular gifts. Here are the results. Also, today was nice becuase every student was able to use the AirLiner in one class setting, which is unusual. Each student was given the chance to put a tally mark next to the gift/s that they recieved. When all students recorded their results we had one student create a bar graph to display the data.

A very nice bar graph! Title, lables and appropriate intervals on the scale.