Grouping Fractions According to Landmarks

After creating 40 fraction cards in class, we organized them into groups based on connections we made about them after analyzing relationships between numerators and their denominators. By doing this, we were able to make many generalizations about fractions.

#1- Fractions that have "0" as a numerator equal 0. (Zero parts are named, or shaded.)

#2- Fractions that have a numerator which is exactly one-half of its denominator equal 1/2. 2 is half of 4, so 2/4 = 1/2.

We also added to this observation by saying that since the numerator is half the denominator, IF WE DOUBLE THE NUMERATOR IT WILL EQUAL THE DENOMINATOR.

#3- Fractions that have a numerator equal to its denominator equal 1 whole. If 8 out of 8 parts are shaded, the whole is shaded, therefore, 8/8 = 1 whole.
Those first three groupings were easy to make, as you can imagine. When placing fractions BETWEEN LANDMARKS, though, our generalizations became more advanced!

Here we have two fractions that fall BETWEEN 0 and 1/2. In this case, the numerators are "less than half" of the denominators BUT "greater than zero".

For example, with 2/6, half of 6 is 3, but fewer than 3 parts (only 2) are shaded; therefore, the fraction is LESS than 1/2.

Here we have three fractions that fall BETWEEN 1/2 and 1 whole. In this case, the numerators are "more than half" but "less than equal to" to denominator.

For example, half of 8 is 4, therefor 4/8 = 1/2.

If I have the fraction 5/8, since 5 is more than 4 (half the denominator), then the fraction is greater than 1/2.

We are now beginning to explore decimal and percent equivalents for fractions in class- new, powerful strategies to add to our tool belts when we compare fractions! Math is FUN when there are multiple ways to solve problems and justify our reasonings!

What do you think about fractions, decimals, and percents? Leave a comment!

Love,

Mrs. Phillips

Tips for Raising Your Current Math Average

Progress Reports went home today. How are you feeling about your current average in math?

Are you interested in raising your average for this nine weeks now that we are at the halfway point? What can you do THIS WEEK to get started?

Well, we have two math assessments this week, as well as a Fraction Design project that was just assigned- these will be three upcoming important math grades toward this nine week's math average. There will also be a math homework assessment next Friday, based on Week 13 (last week), Week 14 (this week), and Week 15 (next week) topics.

So, here are some tips on RAISING that math average, or KEEPING it right where you want it!

TIP #1- Quiz yourself or have a family member quiz you. For tomorrow's EDC quiz, review your EDC purple folder tonight - the month of November elements. The assessment will be based directly in alignment with the notes and skills that you practiced all month each day (if you have an overall grasp of each element and how we approached the math content each day, you should be just fine on tomorrow's quiz). Can you explain the Calendar for November to a family member? Can you identify all four quadrilaterals? Do you know which have right angles, and which have acute/obtuse angles? Do you know which are parallelograms (all opposite sides parallel)? Skim over each element for the month and ask yourself general questions like the ones I just shared with you. Also, check to see that your notes are accurate and thorough. Any mistakes should be corrected from when we discussed the work as a whole group in class. If you have incorrect or incomplete work, you should really reflect on how well you are engaging and spending your time in class applying yourself as an ACTIVE LISTENER! Hopefully, you will be pleased in looking at your work knowing that you put forth your best effort each and every day!

TIP #2- Review your notes and study guides. There will be another assessment this Thursday on our current unit of focus, Different Shapes, Equal Pieces. We will work through a review/study guide in class on Wednesday. In addition to reviewing that, we will also give you a "Comparing Fractions' reference sheet in class tomorrow. You will need to study these Tuesday and Wednesday night to review for this important test.

By the way, can you answer the following?

Fractions are instructions to do what?
What is half of one-half? half of one-third? half of one-fourth?

When the denominator doubles, what happens to the area/size/value of the fraction?

Which is larger, two-fifths or two-thirds?

TIP #3- Start Planning Now! Fraction Project guidelines were passed out today on a yellow sheet. You were encouraged to take notes on an example that was given in class (using Fruit Loops). How thorough are your notes? Are you going to plan ahead now for this project, or might you wait until the night before this project is due to begin working on it? (Remember, it will be due on Tuesday, December 16th). Start planning NOW! Also, don't forget to have FUN! This is an exciting and creative project, so enjoy it!

TIP #4- Complete homework INDEPENDENTLY and USE PREVIOUS NOTES to help you when you get stuck! With the week 14 homework, look back at last week's notes and see how successfully you completed that work. Don't ask for much help on this week's homework; rather, use your class notes from last week to complete this week's homework when you need a reference. Then, after you are finished, you can ask a family member to go back and check over your work to give you feedback. Remenber, this is YOUR homework!

Four great tips on how to achieve your very best on the next four assigned grades in Math for this nine weeks. :-)

Put forth your best effort in all that you do! We are proud of you!

Love,

Ms. Phillips