What’s Goin’ On In Room 133

Posts Tagged ‘fractions’

OK, Colleagues – for those of you who could have found better success on that last test (in other words, if you scored less than 70%) , this is your opportunity to get a passing grade in the books for this lesson.   And for those of you who wanted a better score than you got, this is your opportunity to raise it to the next letter grade.  (It’ll look real good on that report card!)

Print out the following worksheets.   There are some fill-in the blank notes (use your text, interactive notes and the old noodle!).  There are a few questions to do on the worksheet themselves.  And, on the second page of each sheet, I have a list of questions from your textbook* that you have to tackle.   Complete everything and bring it in for credit – or extra credit, if you’re into that sort of thing ! 

7.1 Test Make-up Fractions Percents

7.1 Test Make-up Scientific Notation

Git ‘er dun – and git yer grade right!  

(*Enriched Math: these questions are in the blue textbook, so see me if you want in on this!)

It takes Zachery 2-3/4 hours to cut a lawn.  It takes Adam 3-1/8 hours to cut the same lawn.  How much faster is Zachery?

You have your sheet of fractions, Colleagues.  You need to annotate the decimal equivalent in the upper left corner and the percentage equivalent in the lower right corner of each fraction’s square.  (Sure hope you brought it home!  :0  If I find an e-version of the handout, I’ll post it here later this evening.)

Enriched Math Folks and anyone else up to the challenge:  We got to Scientific Notation and talked about using it for big numbers 93,000,000 miles between the earth and the sun.  And you also know that it can be used for small numbers too.  Can you figure out what the scientific notation is for any of the fractions on that sheet?  Hmmmm…

Rock on, Colleagues!    (Quiz tomorrow!)

That quote might be a little too early for you in your great literature studies, Colleagues, but it’s never too early – or too late – to see how to maintain the value of a fraction when you change the denominator.  Maybe this handy little link will refresh your memory banks.  Rock on!

Equivalent Fractions

(BTW – This is the kind of stuff you’ll find on the Great Links Abound page.  Make sure you mosey on over there from time to time!;) )

A 3-1/2 inch bolt is placed through a piece of wood that is 1-7/8 inches thick.  How much of the bolt is extending out?

A plumber needs to install a sink using pieces of pipe measuring 6-3/4 inches (read that as “six and three-quarters inches”), 10-2/3 inches, 5-1/6 inches and 3-1/8 inches. 

Find the total length of pipe needed to cut all the pieces.  (Rock on, Colleagues!)

The Decimal Point, that is?  We have looked at fractions and ratios and we now turn our attention to another fashionable form of a fraction, the dashing, the debonaire – the Decimal.  Yes, nation, even though this formidable fraction has been stripped of its elegant fraction bar, it is still considered a fraction, one that has gone through a unique transformation.  Yes, it has distinguished itself by actually dividing the numerator by the denominator – using long division, no less! – and for that we award it the noble Decimal Point.  The number that results from our division takes its place (or places) in our mathematical pantheon of heroes otherwise known as our base-10 system.  And the places that it holds are the tenths (1/10ths), the hundredths (1/100ths), the thousandths (1/1,000ths) and so on.

Wow, what would we ever do without it?  So take a look at page 556 in the text and run through questions 1- 28.  We’ll also have a few worksheets to keep ourselves in shape as we prepare to do the heavy lifting to come!

This is going out just to see how many folks are getting to the blog and what time they get there when they do!

Friday is early dismissal, but you will have a quiz on fractions as you come in.  Yes, I did say to bring your coloring pencils and pens.  After you are done with the quiz (it’s only 11 questions), I want you to use your imagination and show me what you know about fractions – the rules, the concepts, you’ve done it all in simplified form and expanded form and standard form, now show it to me in graphic form!  You’ll get a white sheet of printer paper for your final product, but use the instruction sheet to plan what you want to draw.  Put some thought into now and be creative!  Work on it through the rest of the period.  Turn it in at the end – if you really want to keep working on it at home, then you can bring it in Monday.  See you then!

Check out page 291, sport fans!  Tackle questions 33 and 39.  And take a look at “Keeping Things in Perspective” below. 

Essayons!

Ever hear that phrase?  Keeping things in perspective is like saying don’t get carried away.  Don’t take things too far.  Sort of like ‘keeping it real’.  Well, mathematically speaking, keeping things in perspective – or in proportion – is very much what we are dealing with now. 

If we look at a football field from end zone to end zone, we can see that it has a set distance – 100 yards, not counting the end zone-dance floor areas.  Well, suppose we were strapped in a helicopter high over the field and we took a perfectly flat (not tilted) photograph of the field looking straight down.  Our photo would show a perfect image of the football field with one major difference – it would be a LOT smaller than the field itself.  But you would be able to make out the features - the goal posts, the bleachers, the parking lots – because the photo would have everything in perspective.  Large areas on the ground (like the playing field) would take up more room on the photo, and smaller areas on the ground (like the press box or a seating section) would take up less room. 

Well, guess what?  That characteristic of perspective (proportion) can be expressed mathematically.  (You knew I’d get there, didn’t you?)  That characteristic is based on the concept of scale, just like the scale of a map – or an overhead photo!  The scale is the link between how big something is on the ground and how small it is on the map or photo.  Sometimes it is written in words such as “One inch equals thirty feet (ten yards),”  or it can be written using the equal sign  (1 inch = 30 feet) or even more often, the colon “:” sign (1 inch : 30 feet). 

Quite often, the mapmaker or the photo interpreter will set up the scale so that there are no words or units of measure in the description.  How?  Well, knowing our conversion values, we can see that the scale above translates into 1 inch = (30 ft x 12) inches which gives us 1 inch = 360 inches.  This means that 1 inch of measurement on the photo (say from one 10-yd line to the next) represents a total distance of 360 inches on the field (10 yards, right?).

And this is where proportion kicks in.  Because if 1 inch on the photo measures 360 inches across the same distance on the ground, then we also know that 1 foot of measure on the photo will represent 360 feet of distance on the ground.  And 1 centimeter of photo distance will represent 360 centimeters of ground distance.  And so on and so on.  So the scale can be written without any units of measure, such as “1 : 360″.  Written in this form, it is also called a ratio.  It can also be written as a fraction, so it could look like “1/360″.  Here it would be called a representative fraction. 

And guess what?  If it’s a fraction, then we use it the same way we’ve been using fractions all week!  Now that’s keeping it real!