fractions with bars, area model and number line 1mathematics learning, teaching and leading...

Fractions with

Bars, Area Model and Number Line

1Mathematics Learning, Teaching and Leading Collaborative

The Structure of Fractions

3.NF 1. Understand a fraction 1/B as the quantity formed by 1 part when a whole is partitioned into B equal parts;

1/61/6

B = 6

1/B1/6

0/6 1/6

Mathematics Learning, Teaching and Leading Collaborative

The Structure of Fractions3NF 1. Understand a fraction A/B as the quantity formed by A parts of size 1/B.”

1/b

1/61/6

1/B = 1/6

A= 44 parts of 1/6 = 4/6

A=0 and B=6 0/6 = 0

A=6 and B=6 6/6 = 1A = 4

B = 6 4/6


The Structure of Fractions

3NF 1. Understand a fraction 1/B as the quantity formed by 1 part when a whole is partitioned into B equal parts; understand a fraction A/B as the quantity formed by A parts of size 1/B.”

1/B = 1/12. The length of the blue line is A (in this case 4) parts of 1/B or 4 equal parts of 1/12; 1/12 + 1/12 + 1/12 + 1/12 = 4/12•1

Math Learning TLCMathematics Learning, Teaching and Leading Collaborative

The Structure of Fractions3NF 2a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.3NF 2b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

0/6 1/6 1=6/6

Starting at 0, 1/6 it is reproduced 6 times to get a long segment equal to 6/6 or 1.

The Main Topics of 4th Grade 4.NF

A big idea in 4th grade is the fundamental facts about equivalent fractions (a fraction is not changed when its numerator and denominator are multiplied by the same nonzero whole number.)

Spend time comparing, adding, and subtracting fractions with common denominators and the meaning of multiplying a fraction by a whole number.

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The square is vertically divided into three rectangles of equalarea, and 2/3 of the area is represented by the thickened rectangle.

n X a is equivalent to an X b b

4 X 2 = 84 X 3 = 12

2/3 = 8/12

The fraction value is not changed when its numerator and denominator are multiplied by the same nonzero whole number. Or why 2/3 = 8/12


(n × a)/(n × b) example: (4X2)/(4X3) = 8/12 2 = 4 X 2 2 = 8 3 4 X 3 3 12 2/3

If the square is vertically divided into three rectangles of equalarea, then 2/3 is represented by the thickened rectangle.

The 2/3 is now divided horizontally into 4 parts of equal area, making a total of 12 congruent parts. The thickened rectangle now has a value of 8 parts out of 12 total parts or 8/12.

4/4

2/38/12


Grade Four FractionsExamples from CCSS Content Standards for Mathematics1) Break apart a fraction into smaller fractions with the

same denominator, or bottom number, in more than one way. For example:

3⁄8 = 1 ⁄ 8 + 1 ⁄ 8 + 1 ⁄ 8 = 2 ⁄ 8+ 1 ⁄ 8

2) Explain why a fraction is equal to another fraction

3) Add and subtract mixed numbers (whole numbers mixed with fractions, such as 1 1/5) with the same denominators

4) Multiply a fraction by a whole number9Mathematics Learning, Teaching and Leading Collaborative

Mathematics Learning, Teaching, & Leading Collaborative

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Fraction BarsIndividual Work

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ . . .

•Lay the 1/4 bar on your desk and then find bars with more parts but with the same amount of shading. Write down a number sentence to describe your actions.

•Repeat this with the 1/2, 3/4, and 2/3 bars. When done, choose bars of your own choice, continue writing down number sentences that describe your actions.

•Be ready to share your thinking and noticings.


Fraction Bars: Work and discuss in pairs, and then in your small group. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ . . .

• Find the 1/2 bar. With your bars, show that

1/2 = 2/4 = 3/6 = 6/12 What do you notice?• Sketch a bar for 2/5. Divide the parts of your bar to show that 2/5 = 5/10.• Sketch a bar for 3/8. Divide the parts of your bar to show that 3/8 = 6/16.• What are some general methods you found for forming equivalent fractions? Be ready to report out to the large group.


Fraction Bars

4.NF.2 Compare 2 fractions with different numerators and different denominators . . . . . . .

Locate the 1/3 fraction bar and the 1/4 fraction.

Privately decide which fraction is greater and write down a number sentence that matches your thinking, using greater than or less then notation.


Fraction Bars

4.NF.2 Compare 2 fractions with different numerators and different denominators . . . . . . .

Locate and lay out the following pairs of fraction bars.

1/2 and 4/65/12 and 2/35/6 and 7/122/3 and 3/4

Write down a number sentence for each pair using greater than or less than signs.


Fraction Bars

Devise ways to use fraction bars to find these sums. Be ready to share your thinking.4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a) 1/5 + 2/5 =

b) 3/4 + 2/4 =

c) 3/6 + 4/6 =


Grade Five FractionsExamples from CCSS Content Standards for Mathematics1) Interpret a fraction as division of the numerator (the

top number) by the denominator (the bottom number)

2) Add and subtract fractions with different denominators

3) Multiply a fraction by a whole number or another fraction

4) Divide fractions by whole numbers and whole numbers by fractions


Fraction Bars

Devise ways to use fraction bars to find these sums. Be ready to share your thinking.5.NF.A Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

a) 2/3 + 3/4 =

b) 2/3 + 5/6 =

c) 3/4+ 3/12 =17Mathematics Learning, Teaching and Leading Collaborative

Fraction Bars

Devise ways to use fraction bars to find these differences. 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

a) 3/4 - 2/3 =

b) 5/12 - 1/6 =

c) 3/4 - 3/12 =

d) 1 ½ - ⅚ =



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StopGo to “What is the product of 4 x 2/3?


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Grade Five FractionsExamples from CCSS Content Standards for Mathematics1) Interpret a fraction as division of the numerator (the

top number) by the denominator (the bottom number)

2) Add and subtract fractions with different denominators

3) Multiply a fraction by a whole number or another fraction

4) Divide fractions by whole numbers and whole numbers by fractions



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The square is vertically divided into three rectangles of equalarea, and 2/3 is represented by the grey portion of the rectangle.

The square is horizontally divided into four rectangles of equal area, and 3/4 is represented by the grey portion of the rectangle.

Fraction MultiplicationMethod Two: Area Model 2/3 X 3/4


Now lay the 3/4 over the 2/3

Fraction MultiplicationMethod Two: Area Model 2/3 X 3/4


The shaded part of the rectangle is the part 3 X 2 = 6 (part) over the whole 4 X 3 = 12 (whole)

3 partsof equal area

Fraction MultiplicationMethod Two: Area Model

3/4

2/3


Fraction MultiplicationMethod Two: Area Model

3/5 X 2/3

The whole is 15 and the

part is 6 so the answer is 6/15


Method Two Area ModelFraction Multiplication 3 1/2 X 4 = 14

AND 4 X 3 1/2 = 14

Math Learning TLC

1 1 1 1/2

1 1 1 1/2

1 1 1 1/2

1 1 1

1/2

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ ½ + ½ + ½ + ½ = 12 + 4 (1/2) = 12 + 2 = 14


CCSS Math Task, Fraction Multiplication

Rob is calculating the area of this rectangle. His strategy is to multiply the whole numbers first and then multiply the fractions. Since 6 X 7 = 42 and 1/2 × 6 = 3, he concludes that the area of the rectangle is 42 + 3 = 45 sq. units.

Is he correct? If your answer is yes, explain why he correct. If you answer is no, write down the correct answer and tell why it is correct.

Math Learning TLC

7 1/2

6



29


30


31


32


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Fraction Multiplication, Method Three Egg Carton Fractions. Use your egg cartons and yarn to solve a selection (your choice) of the following.


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a) 1/4 of 2/3 e) 1/3 X 6/12

b) 1/3 of 2 f) 3/4 X 1

c) 3/4 of 1/3 g) 9/12 X 1/9

d) 1/4 of 1/3 h) 8/12 X 1/4


CCSS, 5th Grade

Stuffed with Pizza

Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eights of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Louis ate five-eights of the chees pizza. Louis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis, because Luis did not eat any pepperoni pizza. Luis says they ate the same amount of pizza. •Who is correct?•Show all your mathematical thinking.


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