Mixed Numbers and Improper Fractions

Topics for Today:

Fractions that have numerators that are as big as or larger than their denominators are called improper fractions.  We can covert between mixed numbers and improper fractions by using multiplication and division.  

Vocabulary:

improper fraction, mixed number

Sections Covered in Textbook:

3-8: Mixed Numbers and Improper Fractions (pages 164-167)

Resources & Tutorials:

1) What is a mixed number?

2) What is an improper fraction?

3) How do you turn a mixed number into an improper fraction?

4) How do you turn an improper fraction into a mixed number?

Comparing and Ordering Fractions

Topics for Today:

When comparing any two numbers, we must have them in a format that can be compared.  For fractions this means that we must have a common denominator to determine which part of a whole is greater than the other.

We discussed symbols of comparison today to include

• greater than (>)
• less than (<)
• equal to (=)
• not equal to (≠)

Vocabulary:

least common denominator, LCD

Sections Covered in Textbook:

3-6: Comparing and Ordering Fractions (pages 156-159)

Resources & Tutorials:

1) How do you put fractions in order using an LCD?

2) How do you compare fractions by finding a common denominator?

Simplifying Fractions

Topics for Today:

Today we discussed equivalent fractions. Equivalent fractions are different names for the same amount. We also used prime factorization to simplify fractions. Fractions that are in simplest form do not have any common factors in the numerator and denominator except for the number 1.

Vocabulary:

equivalent fractions, simplest form

Sections Covered in Textbook:

3-5: Simplifying Fractions (pages 151-155)

Resources & Tutorials:

1) Simplifying Fractions (Math Antics)

2) How do you reduce a fraction?

Prime Factorization

Topics for Today:

Today we discussed prime numbers and prime factorization.  A prime number is a number that has exactly two factors:  one and itself.  We used our divisibility rules from yesterday to help us break numbers down into their prime factors in preparation for simplifying fractions as well as finding common denominators.  Prime factorization is a technique that can be used for many mathematical purposes.  We also completed the Sieve of Eratosthenes to help us identify all the prime numbers between 1 and 100.  

Vocabulary:

prime factorization, prime number, composite number, Least Common Multiple, LCM,

Greatest Common Factor, GCF, multiple

Sections Covered in Textbook:

3-4: Prime Factorization 

Resources & Tutorials:

1) What is a Prime Number?

2) What are Prime and Composite Numbers?

3) How Do you Find Prime Factorization Using a Factor Tree?

4) Sieve of Eratosthenes

Divisibility Rules

Topics for Today:

Today we discussed the rules for divisibility.  A number is divisible by another if it can be divided by it with no remainder.  Knowing divisibility rules helps with simplifying fractions and prime factorization. 

Vocabulary:

divisible

Sections Covered in Textbook:

3-3: Divisibility Tests (pages 141-144)

Resources & Tutorials:

1)  What does divisibility mean?

2)  How do you check if a number is divisible by 2, 3, 5, 6, and 10?

Extras:

It's Amazing Worksheet (Number Theory)

Dividing Decimals

Topics for Today:

Today we reviewed how to divide decimals.  

The MAIN IDEA is that the divisor (the number we divide by) must be a whole number.  To make a decimal whole, we must multiply the divisor AND the dividend (the number we divide into) by the same factor of 10.  

Vocabulary:

divisor, dividend, quotient

Sections Covered in Textbook:

1-3: Multiplying and Dividing Decimals (pages 17-22)

Resources & Tutorials:

1) How do you divide decimals?

2) Dividing Decimals Class Notes

****Join Delta Math Class (click here)****

First Delta Math Review Assignment due Friday

Extras:

Decimals Board Game (online game)

Multiplying Decimals

Topics for Today:

Multiplication and division of decimals were the topics for today.  We also discussed some of the properties of multiplication.  The properties of equality are a set of rules that allow us to perform operations on equations without changing the truth of the equation.

Main Ideas:

Image credit: https://www.onlinemathlearning.com/multiply-decimals-2.html

Vocabulary:

identity property of equality, zero property, commutative property of multiplication, associative property of multiplication

Sections Covered in Textbook:

1-3: Multiplying and Dividing Decimals (pages 17-22)

Resources & Tutorials:

1) How do you multiply decimals?

Adding and Subtracting Decimals

Topics for Today:

We are getting back into the swing of things, and setting up classroom routines.  Today we did a bit of review of adding and subtracting decimals.

**Adding/Subtracting Decimal Numbers MAIN IDEA***
--> When adding or subtracting decimals, always line up the decimal points!

We also did a brief review of subtracting decimals using regrouping, as well as bringing in zeroes (called annexing) to make sure our numbers line up.   We also discussed a few of the properties of equality.

Vocabulary:

identity property of addition, commutative property of addition, associative property of addition

Sections Covered in Textbook:

1-2: Adding and Subtracting Decimals (pages 11-15)

Resources & Tutorials:

1) How do you add decimals?
2) How do you subtract decimals?

3) 1-2 Adding and Subtracting Decimals Class Notes

Extras:

Find those numbers!

Estimation Strategies

Topics for Today:

Today we discussed some strategies for estimating the answers to numeric expressions.  Students were asked to consider both how to estimate as well as the reasons why we use estimation.  We will spend a lot of discussion time this school year on number sense, and determining if our solutions to problems make sense. 

Image Credit: https://www.slideshare.net/Ms.DH/31-rounding-and-estimating-presentation

Vocabulary:

estimate, compatible numbers, sum, difference, product, quotient

Sections Covered in Textbook:

1-1: Using Estimation Strategies (pages 5 - 9)

Resources & Tutorials:

1)  How do you use front-end estimation to estimate a sum of several decimals?
2)  How do you estimate a quotient using compatible numbers?

Extras:
1) Guess It!  - Online Estimation Game