Unit 2Fraction Operations

Pre-Alg.

Bell Ringer

Concept Builder:Review strategies for adding and subtracting fractions and mixed numbers.Direct Instruction or

Explorations:

1. Notes on fraction/mixed number +/-

2. Practice

Independent Work/hw:WorksheetAssessment:Teacher obs.

9/20

DCN # 150

Unit 2: Fractions!

Bellringer

1. Name two fractions equivalent to 3/4

2. Write in standard form

5.06 x 10-7

3. Volume = ____2. 0.000000506

3. 65.28 in3 3.2 ”

5.1”

4”

Review of fractions-

What is a fraction?

We all learned that a fraction was part of a whole.

That’s true but fractions are also-

1. A ratio of two numbers2. An incomplete division problem 3. A way to compare two numbers

1 2

3

If one slice is eaten what remains?

2/3 ?

A new way to think about fractions

27 52 Both have the digit 2 but the 2 has a differentvalue in 27 than in 52. It’s place value is larger!

2/3 2/12Would you rather have 2/3 of a pizza or 2/12? Both numbers have a 2 in them!

The 2 has a different valuehere as well!

Numerator Digit Denominator Place Value

The 2 has a different valuehere.

Eating an equal amount of the same size of pizza sliced into 12 pieces.

3 Slices 12 Slices

If you still eat 1/3 of the pizza, what is left onthe 12 slice pizza? How many smaller slices?

2 = ? 3 12

2 x 4 = 3 x 4 12

8

Same problem worded differently….

Two thirds of seventh graders write withmechanical pencils. If we select 12 seventh graders at random, how manywould prefer to write with a mechanicalpencil?

2 = ? 3 12

2 x 4 = 3 x 4 12

8

Adding and subtracting fractions and mixed numbers

7

32

3

29

1. Find a common denominator

+

21

9

21

14

2. Add the fraction and whole numbers.

21

2311

3. Reduce your answer12

221

Renaming in subtraction

54

52

31. Borrow from the whole

number.2. Add the denominator to

the numerator to make the new numerator.

3. Subtract.

7

23

5

Bell Ringer

Concept Builder:Review strategiesnumbers. for multiplying fractionsDirect Instruction or

Explorations:

1. Check HW

2. Round Robin problems

Independent Work/hw:

Assessment:Teacher obs.

9/21

DCN # 149

Multiplying Fractions

Bellringer

1. 8 2/5 – 5 5/7 =

2. Write in scientific notation 304000000

3. Compare √ 34 _____ 650%

1. 2 24/35

2. 3.04 x 108

3. <

Multiplying with numbers greater than 1 result in products larger than their factors. For example-

3 x 4 = 12

Think “3 sets of 4 equals 12 ”

Multiplying with fractions less than 1 result in products smaller than one or more of their factors. For example- ½ x 4 = 2 ½ x ¼ = 1/8

Think “ ½ set of 4 equals 2”

X = OF

Multiplying fractions and mixed numbers.

1. Reduce first if possible

2. Multiply the numerators

3. Multiply the denominators

1514

73

x 2

1

1

5

1 x 2 = 2

1 x 5 = 5

Multiplying mixed numbers

1. Change mixed numbers to improper fractions.

2. Reduce if possible

3. Multiply numerators and denominators.

9

147

1295

175

1 xx 4 2

1 3

32

238

Bell Ringer

Concept Builder:Understand the meaning of multiplying fractions; applying the multiplication algorithmDirect Instruction or

Explorations:

1. Demonstrate fraction division using modeling

2. Notes on the algorithm

3. Class practice text

pp 144 problems 1-27

Independent Work/hw:WorksheetAssessment:Teacher obs.

9/22

DCN # 148

Dividing Fractions

Bellringer

1. Under what conditions can I multiply a number by a fraction and get a larger number? Explain.

2. 1/5 – 5/6 =

3. 3 1/4 + 7 4/5 =

4 ÷ ½ = 8One way to divide fractions. . .

Another way …

81

8

22

18

2

1

2

8

2

1

1

4

2

14

Dividing fractions and mixed numbers 1. Change any mixed

numbers to improper fractions.

2. Keep, change, flip to make it a multiplication problem.

3. Reduce first if possible and multiply.

3

22

3

87

8

3

78

7

3

78

7

3

12

Multiplicative inverse

A number multiplied by it’s multiplicative inverse equals 1. For example:

15

5

5

15

16

6

2

3

3

2

*Also called the reciprocal

In the operation of division, multiplying with the divisor’s multiplicative inverse results in the same answer. For example, 4 ÷ 2 = 4 x ½

Why is this important?

So when you have a division problem with fractions or mixed numbers, keep change flip and make it a multiplication problem.

The easiest way . . .

Bell Ringer

Concept Builder: Multiplying mixed numbers by applying the multiplication algorithmDirect Instruction or

Explorations:

1. Check HW

2. Drill and kill problems

Independent Work/hw:WorksheetAssessment:Teacher obs.

9/23

DCN # 147

Multiplying and Dividing

Fractions

Bellringer

1. Quickly estimate: 783 ÷ 37

2. 2/5 – 5/7 =

3. Estimate √199

800/40=20783/37=21.2

-11/35

199 is between perfect squares196 and 225 or14 < √199 < 15 but closer to 14 than15 so estimate 14.1 or 14.2

Bell Ringer

Concept Builder:Applying the multiplication and division algorithmDirect Instruction or

Explorations:

1. Check homework

2. Amateur Arch.

Independent Work/hw:

Worksheet

Assessment:Teacher obs.

9/28

DCN # 145

Multiplying and Dividing Fractions

Bellringer:

Place in order from least to greatest

| -5 + 3 | -17 -√3 9 x 10-3

Bell Ringer

Concept Builder: Applying the multiplication and division algorithm to fractions and mixed numbersDirect Instruction or

Explorations:

1. Review fraction operations on desk

2. Word problems in groups

Independent Work/hw:WorksheetAssessment:Teacher obs.Quiz grade

9/29

DCN # 144

Multiplying and Dividing Fractions

Bellringer: Test Review

1. Choose the correct answer for

A. 2 ½ B. - 2 ½ C. 3 29 /32 D. - 3 29 /32

2. Choose the correct answer for

A. 5 B. -5 C. 12 2 /4 D. - 12 2 /4

3.

4. What is 4/7 of 28?

5. Babs had 12 ½ yards of ribbons that she cut into pieces ¾ yd. long. How many pieces did she have?

5

4

8

13

96

51

8

58

Renaming in subtraction