Revisiting Fraction Operations

Topics for Today:

Welcome back!  Hopefully everyone had a relaxing and fun break.

We started back gently today with further review of fraction operations.  To help with mastery, students were assigned a quiz correction assignment in Delta Math to work on the types of problems they missed on their quizzes.  

Image credit: http://clipart-library.com/clipart/88585.htm

Vocabulary:

None

Sections Covered in Textbook:

No new material was covered today - we spent time reviewing instead.

Resources & Tutorials:

If they need help, students should revisit blog entries from November 10th through 15th.  

Dividing Fractions and Mixed Numbers

Topics for Today:

We are almost done working through fraction operations and today we discussed dividing fractions.  

MAIN IDEA

• We don’t really “divide” fractions – we multiply by the inverse also known as the reciprocal. 
• Just like with multiplication, mixed numbers must be converted to improper fractions before we may begin.
• Once we rewrite the problem as multiplication, we then just follow the rules of multiplying fractions.
• When multiplying fractions . . .We take out common factors in the numerator and denominator,
• Next, we multiply numerators, and then
• We multiply denominators.
• Final answers should always be in simplest form.
• Some remember the process as   KEEP --- CHANGE --- FLIP

Vocabulary:

reciprocal

Sections Covered in Textbook:

4-5: Dividing Fractions and Mixed Numbers (pages 207-212)

Resources & Tutorials:

1)What is the reciprocal rule of dividing fractions?

2) What is a reciprocal?

3 How do you divide fractions?

4) How do you divide mixed numbers?

5) Dividing Fractions and Mixed Numbers Class notes

Multiplying Fractions and Mixed Numbers

Topics for Today:

We are moving right along with fraction operations. Today we discussed multiplying fractions and mixed numbers.  There is no need for a common denominator when multiplying.  We do have to convert any mixed numbers to improper fractions before we can perform the multiplication.  Because multiplying numbers can make our answers get very big, very fast, we first want to divide out common factors in the numerator and denominator before we multiply. 

Vocabulary:

multiply fractions

Sections Covered in Textbook:

4-4: Multiplying Fractions and Mixed Numbers

Resources & Tutorials:

1) How do you multiply fractions?

2) How do you multiply a whole number by a fraction?

3) How do you multiply mixed numbers?

4) Multiplying Fractions and Mixed Numbers Class notes

Adding and Subtracting Mixed Numbers

Topics for Today:

Adding and subtracting mixed numbers was our topic of today.  To add or subtract mixed numbers, we must still have a common denominator for the fractional component.  There are times when we must regroup after adding or before subtracting, depending upon our problem.  

Sections Covered in Textbook:

4-3: Adding and Subtracting Mixed Numbers (pages 197-201)

Resources & Tutorials:

1)  How do you add mixed fractions with the same denominator?

2) How Do You Subtract Mixed Fractions with the Same Denominator?

3) How Do You Subtract Mixed Fractions with Different Denominators by Regrouping?

4) Adding and Subtracting Mixed Numbers Class notes

Adding and Subtracting Fractions

Topics for Today:

Today we began working on operations with fractions by adding and subtracting.   

The MAIN IDEA when combining fractions is the pieces of the whole must be the same shape and size to be able to add or subtract (need a common denominator).  We used the skills we built in the last unit to find the least common denominator (which is the least common multiple of the numbers that appear in the denominators of our fractions.  

Vocabulary:

Sections Covered in Textbook:

4-2: Adding and Subtracting Fractions (pages 192-196)

Resources & Tutorials:

1) How do you find a common denominator and a least common denominator?

2) How do you add fractions with the same denominator?

3) How do you add fractions with different denominators?

4) How do you subtract two fractions with the same denominator?

5) How Do You Subtract Two Fractions with Different Denominators?

6) Adding and Subtracting Fractions Class Notes

Estimating with Fractions and Mixed Numbers

Topics for Today:

Today we discussed estimating operations with fractions in preparation for doing the actual arithmetic in the lessons that will follow.  We used benchmarks (values used as reference points) to help determine how to round fractional pieces to find our estimates.  We used number sense to figure out when to round fractions up or down based upon their closeness to the fraction of 1/2.  We also revisited the concept of compatible numbers to help with estimating division problems.  

Vocabulary:

benchmark

Sections Covered in Textbook:

4-1: Estimating with Fractions and Mixed Numbers (pages 187-190)

Resources & Tutorials:

1) Estimating Mixed Numbers

2) Estimating with Fractions and Mixed Numbers Class notes

Unit 2 Review - Day 2

Topics for Today:

Today we played a game of Money Grab to finish up our review of Unit 2.  Students should make sure their notebooks are fully organized prior to joining class on Friday.  Notebooks will be collected at the beginning of class, and no class time on test day will be allocated for organizing - this task needs to be completed prior to coming to class on Friday.  

Resources & Tutorials:

Money Grab Questions and Answers

Answers to Chapter 2 Review Sheet (from yesterday)

Unit 2 Review

Topics for Today:

Today we played we spent time working on our notebooks and reviewing for our Unit 2 Test on Friday.  We will continue our review tomorrow.  Students can find the table of contents for any unit on the Table of Contents Page of this blog.  

Topics for this unit include:

* Divisibility (rules for 2, 3, 4, 5, 6, 8, 9. and 10)

* Prime Factorization (factor trees)

* Greatest Common Factor (GCF)

* Least Common Multiple (LCM)

* Simplifying Fractions

* Mixed Numbers & Improper Fractions

* Changing Fractions to Decimals and Decimals to Fractions

* Comparing and Ordering Rational Numbers

Vocabulary:

See page 178 in your textbook

Sections Covered in Textbook:

Chapter 3 Sections 3-3 through 3-10 (skip 3-7) - Pages 141-179

Resources & Tutorials:

Unit 2 Review Sheet

Rational Numbers

Topics for Today:

You have seen rational numbers your entire life, but have referred to them as fractions.  The word "rational" contains the word "ratio", which is just a comparison of numbers by division.  In our lesson on Friday, we discussed that a fraction is really a division problem with the vinculum (fraction bar) serving as a division symbol.  

Any number that can be expressed as a fraction is rational, and includes repeating and termination decimals that are both positive and negative.  Any number on the number line that can be put into the form of a fraction is rational.  

Vocabulary:

rational number

Sections Covered in Textbook:

3-10: Rational Numbers (pages 173-176)

Resources & Tutorials:

1) What is a rational number?

2) Comparing Rational Numbers

3) Ordering Rational Numbers

4) Rational Numbers Class Notes