Math 5Unit Review

Instructor: Mrs. Tew Turner

In this lesson we will review for the unit

assessment and learn test taking strategies.

Math Warm-up

Double each of the following. Do them mentally.

1. 43

2. 27

3. 85

(Pause Lesson to work)

Math Warm-up - ANSWER

Double each of the following. Do them mentally.

1. 43 86

2. 27 54

3. 85 170

(Pause Lesson to work)

In this unit you learned about fractions.

Today we will review all that you have learned, as well as go over test taking strategies.

Vocabulary Reviewfraction – a symbol, such as ¾, used to describe one or more parts of a whole that is divided into equal parts. A fraction can name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers.

Vocabulary Review

numerator - the number above the fraction bar in a fraction

denominator - the number below the fraction bar in a fraction

12 denominator

numerator

Vocabulary Review

dividend- the number to be divided. 24 ÷ 4 = 6

divisor- the number that a dividend is divided by.24 ÷ 4 = 6

Vocabulary Review

quotient - the number that is the result of dividing. 24 ÷ 4 = 6

6 is the QUOTIENT!

Vocabulary ReviewEquivalent fractions: have the same value, even though they may look different.Unlike denominator: Unlike denominator is the bottom number in a fraction that is not the same as another fraction. Common denominator: Denominators must be the same to be common.

Vocabulary Review

Greatest Common Factor: The greatest number that is a factor of 2 or more given numbers.Example: 18=2 x 3 x 3

24=2 x 2 x 2 x3Find the prime numbers!Benchmark fraction: Common fractions used for estimating, such as ½, ¼, ⅓, ⅔, & ¾.

Vocabulary Review

Multiple: a number that contains another number repeatedly without a remainder, example 5 is a multiple of 25. Prime: a number that can bedivided evenly only by 1 and itself.Composite: a number that can bedivided evenly by numbers otherthan 1 or itself.

Least Common Denominator: (LCD), The least common multiple of the denominators of two or more fractions.

Vocabulary Review

Least Common Multiple: (LCM), the least number that is a common multiple of two or more numbers.

Vocabulary Reviewmixed number – a whole number and a fraction Ex.

Vocabulary Reviewimproper fraction – a fraction whose numerator is greater than or equal to its denominator (the fraction is 1 whole or more)Ex.

Fractions as Division Review

Al, Lisa, Nico, and Laura are making a picture. They will share 3 rectangular strips of colored paper. What fraction represents the part of a whole strip of paper each will get?

1 whole 1 whole 1 whole

Find 3 ÷ 4

One way to divide 3 wholes into 4 equal parts is to first divide each whole into 4 equal parts. Each part is ¼ of a whole.

1 whole 1 whole 1 whole

Find 3 ÷ 4

Rearrange the quarter pieces so that each person gets 3 of the ¼ pieces. Each gets ¾.

Lisa

Nico

Laura

Al

Give each answer as a fraction:

1. 1 ÷ 2

2. 9 ÷ 10

3. 3 ÷ 4

Finding Equivalent Fractions Review

Write 2 equivalent fractions. Use multiplication for one and division for the other.

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom would still be whole numbers.

Simplifying Fractions Review

Simplifying fractions , also known as, reducing or putting into lowest terms, means to make the fraction as simple as possible. They are still the same or equivalent but written with a different fraction name, as ½ = 2/4.To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers equally.

Fractions in Simplest Form

If a number is a factor of two numbers, it is called a common factor.The greatest common factor (GCF), of 2 numbers is the greatest or largest number that is a factor of both numbers.4 was the greatest common factor for both 12 & 20. 2 is a factor but we still did NOT have simplest form until we divided it by 4 (the largest factor).

Simplify the fraction. common factor = common

multiple

4 ÷ 2 = 2 10 2 5

3 (Is this fraction in simplest form?) 5 Can the numerator & denomInator

be divided by a whole number?

Simplest Form

YES

(It was not in simplest form as it could be divided by ‘2’ for both the numerator & denominator.)

NO

Greatest Common Factor

The greatest common factor (GCF), of 2 numbers: 20 & 3020: 1, 2, 4, 5, 10, 2030: 1, 2, 3, 5, 6, 10, 15, 30The GCF of 20 & 30 is 10. Or 10 is a multiple of both numbers.

Fractions in Simplest FormGuided Practice

Adding and Subtracting Fractions Review

When you don’t know the equivalent fraction to use when adding or subtracting fractions with unlike denominators you will have to change one or all the fractions to share a common denominator. Find the common denominatorwe need to find the least common multiple or the least common denominator to do this.

1. Find the common denominator

This just means all the fractions have the same denominator.

Why is this important to adding and subtracting fractions?Before you can do these operations the fractions must share a common denominator.

2. Find the least common denominator.This is the same as finding the least common multiple of the denominators.As ¼ =2/8 (4 is a multiple of 8)Find the LEAST (smallest) common multiples of both denominators to see what can be the shared denominator.

Example of Least Common Multiple

1/3 List the multiples of 3: 3, 6, 9, 12, 15, 1/6 List the multiples 6: 6, 12, 18, 24, …The least common multiple is 6. Now what do you do?

Example of Least Common Multiple

1/3 List the multiples of 3: 3, 6, 9, 12, 15, 1/6 List the multiples 6: 6, 12, 18, 24, …The least common multiple is 6. Now what do you do?

1 = 2 (What was multiplied by both the 3 6 numerator and denominator to get 2/6? 2 was.)

1x2=2 3x2=6

What Did We Do?

The trick was to list the multiples of each denominator, then find the Least Common Multiple!

Easy as ....

The Steps!Here are the steps to follow:Find the Least Common Multiple of the denominators (which is called the Least Common Denominator). Change each fraction (using equivalent fractions)to make their denominators the same as the least common denominator. Then you add (or subtract) the fractions, as you wish!

Mixed Numbers and Improper Fractions Review

You know that 20 ÷ 9 = 20

9

This is an improper fraction because the numerator is greater than the denominator.

Improper fractions can be rewritten as mixed numbers!

You can write 20 ÷ 9 as a mixed number.

You know that 20 ÷ 9 = 20

9Step 1: Divide the numerator by the denominator.

9 20 18 2

2

You can write 20 ÷ 9 as a mixed number.

You know that 20 ÷ 9 = 20

9Step 2: Write the remainder as a fraction. 9 20 18 2

2The divisor is the denominator!

2 29

Write as an improper fraction.

229

Step 1: Multiply the denominator of the fraction by the whole number.

x2 x 9 = 18

2 29

Write as an improper fraction.

2 29

Step 2: Add the numerator of the fraction.

229

x

18 + 2 = 20

+

Write as an improper fraction.

2 29

Step 3: Write using the same denominator.

20 9

2 29

Write as an improper fraction.

2 29

2 29

= 20 9

Write the improper fraction as a mixed number, or the mixed number as an improper fraction.1. 2.

3 38

25 4

Adding and Subtracting Mixed Numbers and Improper Fractions

Review

What is 2 + 3 ?34

12

Step 1: Convert to improper fractions

234

x

+

312

x

+

= =114

72

What is 2 + 3 ?34

12

=x2

114

72

Step 2: Convert fractions to have common denominator (if needed)

LCM: 4- 4,8,12 2- 2,4,6

x2 14 4

What is 2 + 3 ?34

12

=114

14 4

Step 3: Add the numerator because it is an addition problem.

+25

What is 2 + 3 ?34

12

=114

14 4

+25 4

Step 4: Write the new numerator over the denominator

What is 2 + 3 ?34

12

25 4 25 ÷ 4 = 6 r. 1

1 4

6

Step 5: Write the improper fraction as a mixed number

What is 2 + 3 ?34

12

1 4

6

Step 6: Simplify the fraction

This is already in simplest form.

Using Benchmark Fractions to Estimate Review

Which benchmark is nearest?38

Which benchmark is nearest?38

3/8 is less than ½ because it is less than 4/8. 3/8 is greater than ¼ because it is greater than 2/8. In fact, it is halfway between ¼ and ½.

How can benchmarks help you estimate the sum of two fractions?

Think about it with this problem.12

58+

Is the sum between 0 and 1 or between 1 and 2?

12

58+

Is the sum between 0 and 1 or between 1 and 2?

Since 5/8 is greater than ½, the sum would be between 1 and 2.

Quick Check

Estimate the sums and describe your thinking.

Word Problems Review

Lesson ReviewWhen working on Word Problems:

•Read each problem twice, twice.•Underline key words.•Underline the information you need to solve a problem.•Circle any data that is provided.•Choose your solution strategy.•Solve and show your work.•Check your answer.

Hoping to be named Salesperson of the Month, Braden called the names from 2 2/5 pages of the phone book last week. This week, he called the people listed on another 5 2/5 pages of the same phone book. How many pages worth of people did Braden call in all?

In your Math NotebookIndependent Practice

Test Taking Strategies(Write these in your Math Notebook)

•Read each problem twice.•Underline key words.•Underline the information you need to solve a problem.•Circle any data that is provided.

Test Taking Strategies(Write these in your Math Notebook)

•Solve the problem.•Show your work as you solve the problem.•Check your work.•Use estimation to check if your answer is reasonable.

Today you reviewed for the unit assessment and learned about test taking strategies.

Good Work with this

lesson.