Fractions and Decimals

Topics for Today:

Today we talked about converting fractions to decimals and vice versa.  A fraction is simply a division problem with the denominator serving as the divisor.  Any fraction can be converted to a decimal by dividing the denominator into the numerator.

For changing decimals to fractions, the process is simple.  Take for example 0.2. 

1.  Say it

2.  Write it

3.  Simplify it

Also, there are some common fraction/decimal equivalents that should be committed to memory.  They are: 

Vocabulary:

terminating decimal, repeating decimal

Sections Covered in Textbook:

3-9: Fractions and Decimals (pages 168-172)

Resources & Tutorials:

1) Convert a fraction to a decimal

2) Convert a decimal to a fraction

3) Fractions and Decimals Class Notes

Extras:

Fraction Reaction

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?

5) Mixed Numbers and Improper Fractions Class Notes

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?

3) Comparing and Ordering Fractions Class Notes

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?

3) Simplifying Fractions Class Notes

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

5) Class Notes on Prime Factorization

Extras:

Website for Prime Enrichment

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?

3)  Divisibility Class Notes

Extras:

It's Amazing Worksheet (Number Theory)

Guess, Check, and Revise Strategy

Topics for Today:

Today we explored some story problems.  Students typically are not excited about story problems until they see and solve enough of them to start recognizing patterns.  One of the main focuses of the mathematics program at Field School is to help students organize problems and apply them to patterns we have worked with together.

Today we used the guess, check, and revise strategy which is very useful especially for students who have not had a thorough Algebra I course.  For this strategy, students take the information from the problem and try combinations until they satisfy the other conditions in a problem.  Organizing the guesses into a table keeps the work organized.

Vocabulary:

guess, check, and revise

Sections Covered in Textbook:

None - this lesson was pulled from other materials

Resources & Tutorials:

1) How to solve an equation by guessing and checking.
2) Learn Guess and Check (not a video).

3) Guess, Check, and Revise Class Notes

Extras:

Another Ken Ken Puzzle