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GROUP NORMS AND HOUSEKEEPING

Logistics:

Phone Calls

Rest Rooms

BreaksLunch

PunctualitySharing

Group Norms:Participate

Listen with an open mind

Ask questions

Work toward solutionsLimit side bars

Fifth Grade Big Idea 2Day 1

Develop an understanding of and fluency with

addition and subtraction of fractions and

decimals.

Big Idea 2 Benchmarks

Share 3 donuts between 5 people.

When equally shared, each person gets ⅗ of a donut.

Fractions

The idea of breaking a whole into parts, sharing the parts, and providing names for those parts is the fundamental concept in the development of fraction knowledge.

There are four ways that fractions are used to represent application situations: part of a whole, part of a set, indicates division, and ratio.

Extensive research and observational data demonstrate that few students understand fractions. Therefore major changes must be made in the approach to teaching fractions.

1st meaning: Part/whole:

You take the “whole” and split it into equal parts.

Example 1: A baseball game has nine innings. Seven have been played. What fraction of the game has been played?

Example 2: This class has 19 students. Eighteen are females. What fraction of the class is female?

Three Meanings of a Three Meanings of a FractionFraction

Quotient Implies “division”

Example 1: Pizza for a group of friends: $12 ÷ 3 people (or $ 12/3 each)

Example 2: 3 doughnuts, 5 kids. How much of a doughnut does each kid get?

How could they do the above? (Different from part-whole splitting)

22ndnd Meaning of a Fraction: Meaning of a Fraction:

Ratio: Conceptually different and doesn’t imply dividing a whole into parts or division.

Example.: 1 week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

Weekend days to school days is 2:5 or 2/5.Weekend to whole week is 2:7 or 2/7.

33rdrd Meaning of a Fraction: Meaning of a Fraction:

Fractions—For these problems, circle the greater Fractions—For these problems, circle the greater number of each pair and tell number of each pair and tell the strategiy you the strategiy you

used.used.

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9

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7

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5

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11

7

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6

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23

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4

6

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2

6

Then: Change 5⅔ to an improper fraction, and Change to a mixed number.

1.

2.

3.

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8

9

1.

2.

3.

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4

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When the whole numbers are different, you only have to compare the whole numbers.

When the whole numbers are different, you only have to compare the whole numbers.

When the numerator is the same, look at the size of the pieces in the denominator.

When the numerator is the same, look at the size of the pieces in the denominator.

Strategies to Compare/Order Fraction

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11

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3

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•Use benchmark numbers•Use benchmark numbers •Compare missing pieces•Compare missing pieces

Strategies to Compare/Order Fraction

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3

8 >

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6

10Think: 3 is less than half of the denominator so the fraction is less than ½.

Think: 6 is more than half of the denominator so the fraction is more than ½.

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8

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4

5Think: 1/8 is missing to make a whole.

Think: 1/5 is missing. Since 1/5 is a larger missing piece than 1/8 then ….

Revisit these fractions. Compare the strategy Revisit these fractions. Compare the strategy you used previously with one you used this time.you used previously with one you used this time.

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7

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5

4€

11

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6

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23

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Then: Change 5⅔ to an improper fraction, and Change to a mixed number.

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Comparing Fractions

An article by Go Math co-author Juli Dixon, PhD., “An Example of Depth...”.

MA.5.A.2.1Represent addition and subtraction of

decimals and fractions with like and unlike denominators using models, place value or

properties.

MA.5.A.2.2Add and subtract fractions and decimals fluently and verify the

reasonableness of results, including in problem situations.

Models to Add and Subtract Fractions

Manipulatives for Like and Unlike Denominators

Kathy had 2 yards of

ribbon. She gave yard

of her ribbon to Matt. How

much ribbon did Kathy

have left?

The oval track at the horse

race is mile around, but

the horses run for 1

miles during the race. What

length of the track will the

horses run twice?

Fractions Stories…Fractions Stories…

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8

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Real-Life Application of Fractions

You need exactly 1-cup of water for the dessert you are making. You can only find the cup, cup and

cup measuring cups.

How many different ways can you measure out 1-cup of water?

€

1

8

€

1

4

€

1

2

Write stories to support the following:

3/4 + 5/8

4/5 - 1/2

1 1/6 + 2/3

Now it’s your turn to tell Now it’s your turn to tell the story…the story…

MA.5.A.2.1FCAT 2.0 Test Spec.Item

Why Show Fractions in Simplest Forms?

Less pieces and a clearer visualization of the part whole relationship

There were 80 swimming pools at a local store. If of the pools were sold during one hot summer day, how many pools were left for sale after that day?

Jose spent of his money on concert tickets. If he had $200.00 to begin with, how much does he have left?

Singapore Model Drawing Examples

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Answer: B

MA.5.A.2.1FCAT 2.0 Sample Test Questions

MA.5.A.2.3Make reasonable estimates of fraction and

decimal sums and differences, and use techniques for rounding.

When asked this question, only 24% of 13-When asked this question, only 24% of 13-year olds and only 37% of 17-year olds year olds and only 37% of 17-year olds could estimate correctly.could estimate correctly.

Consider this Consider this concerning data…concerning data…

Estimate + .Estimate + .

a)a) 11 b) 2b) 2

c) 19c) 19 d) 21d) 21€

12

13

€

7

8

Consider the highly technical paper Consider the highly technical paper plate…plate…

•What else can you What else can you show me?show me?

•What should I show What should I show you?you?

•Can we use this for Can we use this for decimals?decimals?

1/2 + 2/51/2 + 2/5

2/6 + 3/112/6 + 3/11

2 1/13 + 6/72 1/13 + 6/7

3 4/5 + 1 1/33 4/5 + 1 1/3

1 7/8 - 1/21 7/8 - 1/2

Estimate the Estimate the following:following:

MA.5.A.2.4Determine the prime

factorization of numbers.

Divisibility Rules

How Do We Know They Are Prime?

Composite numbers can be placed into varying types of rectangles

Prime numbers cannot

Let’s look at that…

Composite Numbers

6 2415

Prime Numbers

7 17 29

Prime NumbersEratosthenes’(ehr-uh-TAHS-thuh-

neez) Sieve

276 BC - 194 BC

•Eratosthenes was a Greek mathematician, astronomer, geographer, and librarian atAlexandria, Egypt in 200 B.C. •He invented a method for finding prime numbers that is still used today.•This method is called Eratosthenes’ Sieve.

Eratosthenes’ Sieve

A sieve has holes in it and is used to filter out the juice.

Eratosthenes’s sieve filters out numbers to find the prime numbers.

Definition

Factor – a number that is multiplied by another to give a product.

7 x 8 = 56

Factors

Definition

Prime Number – a number that has exactly two factors.

77 is prime because the only numbersthat will divide into it evenly are 1 and 7.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Let’s use a number grid from 1 to 100 to see how prime numbers were discovered.

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Remove the number 1. It is special number because 1 is its only factor.

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Leave the number 2 and remove all its multiples.

2 3 5 7 9

11 13 15 17 19

21 23 25 27 29

31 33 35 37 39

41 43 45 47 49

51 53 55 57 59

61 63 65 67 69

71 73 75 77 79

81 83 85 87 89

91 93 95 97 99

Leave the number 3 and remove all its multiples.

2 3 5 7

11 13 17 19

23 25 29

31 35 37

41 43 47 49

53 55 59

61 65 67

71 73 77 79

83 85 89

91 95 97

Leave the number 5 and remove all its multiples.

2 3 5 7

11 13 17 19

23 29

31 37

41 43 47 49

53 59

61 67

71 73 77 79

83 89

91 97

Leave the number 7 and remove all its multiples.

2 3 5 7

11 13 17 19

23 29

31 37

41 43 47

53 59

61 67

71 73 79

83 89

97

The PRIME Numbers!

GROWING A

FACTOR TREE

Can we grow a tree of

the factors of 180?

180Can you think of one

FACTOR PAIR for 180 ?

This should be two numbers that multiply together to give the

Product 180.

You might see that 180 is an EVEN NUMBER and that

means that 2 is a

factor…

2 x = 180� ?

OrYou might

notice that 180 has a ZERO in

its ONES PLACE which means it is a

multiple of 10.

SO…10 x = 180�

OrYou might

notice that 180 has a ZERO in

its ONES PLACE which means it is a

multiple of 10.

SO…10 x = 180�

10 x 18 = 180

10 18

180

10 18

We “grow” this “tree” downwards since that is how

we write in English (and we are not

sure how big it will be. We could run out of paper if we grew upwards).

NOW

You have to find

FACTOR PAIRS

for 10

and18

10

52

180

18

6 3

2 x 5 = 10 6 x 3 = 18

Find factors for 10 & 18

ARE

WE

DONE

???

2 3 32

5

10

2 6

180

18

3

5

Since 2 and 3

and 5 are PRIME

NUMBERS they do not grow “new branches”. They just

grow down alone.

Since 6 is NOT a prime number - it is

a COMPOSITE NUMBER - it still

has factors. Since it is an EVEN

NUMBER we see that:

6 = 2 x

Answer: C

FCAT 2.0 Sample Test Question

FCAT 2.0 Test Spec.Item

MA.5.A.6.1Identify and relate prime and

composite numbers, factors and multiples within the context of

fractions.