Chapter 6 Math Guide - Summit · PDF fileChapter 6 Math Guide I can model equivalent fractions...

$: Chapter 6 Math Guide - Summit · PDF fileChapter 6 Math Guide I can model equivalent fractions Start with your 1/3 shaded in. Draw one or more 2 6 Start with your 1/3 shaded in 1 3$
Chapter 6 Math Guide

I can model equivalent fractions

2

6

Start with your 1/3 shaded in

1

3

Start with your 1/3 shaded in. Draw one or more lines

across or up and down to create equal sections.

3

9

4

12

Start with your 1/3 shaded in. Draw one or more

lines across or up and down to create equal sec-

tions. This example has two lines going all the way

from top to bottom. It is broken up into 9 total sec-

tions and 3 of them are shaded. The same amount

is shaded, the pieces are just smaller and there are

more of them.

Start with your 1/3 shaded in. Draw one or more

lines across or up and down to create equal sec-

tions. This example has one line going all the way

from the top to the bottom. It also has one line go-

ing across each of the 1/3 sections. It is broken into

12 total sections and 4 of them are shaded. The

same amount is shaded, the pieces are just smaller

and there are more of them.

1 , 2 , 3 4

3 6 9 and 12 are all equal. They are equivalent fractions.


I can model equivalent fractions

1/3 1/3 1/3

1/6 1/6 1/6 1/6 1/6 1/6

1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

You can also use fractions strips to find

equivalent fractions and determine if frac-

tions are equivalent or not. If you follow

the line up and down, 1/3, 2/6, and 3/9

are all the same amount. This means they

are all equivalent fractions.

1/2 1/2

1/3 1/3 1/3

1/4 1/4 1/4 1/4

1/5 1/5 1/5 1/5 1/5

1/6 1/6 1/6 1/6 1/6 1/6

If you follow the lines, you can see that 1/2

is the same amount as 2/4. These are

equivalent fractions.

1/2 is not the same amount as 1/3 or 2/3,

so they are not equivalent.

1/3 is the same amount as 2/6. These are

equivalent fractions.

1/2 is also the same amount as 3/6. These

are equivalent fractions.

2/2, 3/3, 4/4, 5/5, and 6/6 are all the same

amount too. They are equivalent fractions

and all equal to one whole.

What other amounts are the same on the

fractions strips?

Online Resources:

*Think Central —> My Library —> Math —> Mega Math —> Fraction Action

—>Fraction Flare Up Level D

*Think Central —> My Library —> Math —> Interactive Student Edition —>

Chapter 6 —> Lesson 6.1

*Think Central —> My Library —> Math —> Math on the Spot Video Tutorial

—> Chapter 6 —> Lesson 6.1

*Cool Links —> Math: Model Equivalent Fractions Video

Link: https://www.khanacademy.org/math/arithmetic-home/arith-

review-fractions/equivalent-fractions-1/v/equivalent-fraction-models

*Cool Links —> Math: Equivalent Fractions with Area Models

Link: https://learnzillion.com/lesson_plans/9049-recognize-equivalent-

fractions-using-area-models

*Cool Links —> Math: Model Equivalent Fractions Practice

Link: https://www.ixl.com/math/grade-4/find-equivalent-fractions-using-

area-models

*Cool Links —> Math: Model Equivalent Fractions Practice 2

Link: https://www.splashmath.com/math-skills/third-grade/fractions/

equivalent-fractions-using-models



review-fractions/visualizing-equiv-frac/e/visualizing-equivalent-fractions



review-fractions/equivalent-fractions-1/e/equivalent-fraction-models-1


Link: http://harcourtschool.com/activity/elab2004/gr3/10.swf

*Cool Links —> Math: Model Equivalent Fractions Triplets

Link: http://www.mathplayground.com/Triplets/Triplets.html


I can create equivalent fractions and determine if fractions are

equivalent or not

Create equivalent fractions: If you multiply or divide the numerator and de-

nominator by the same number, you will create equivalent fractions. You

can choose to divide or multiply, but you must do the same to the numerator

and denominator. And you must multiply or divide by the same number.

1 (x 2)= 2 *The numerator and denominator were both multiplied

2 (x2) = 4 by 2, so 1/2 and 2/4 are equivalent fractions.

6 ( 2)= 3 *The numerator and denominator were both divided by

10 ( 2)= 5 2, so 6/10 and 3/5 are equivalent fractions.

Determine if fractions are equivalent: Check to see how the numerator and

denominator were changed between the fractions.

4 (x3)= 12 *The numerator was multiplied by 3 and the

5 (x2)= 10 denominator was multiplied by 2, so they are not

equivalent.

5 (x2)= 10 *The numerator was multiplied by 2 and the

10 ( 2)= 5 denominator was divided by 2, so they are not

equivalent.

Find the missing numerator or denominator: Determine how the numerator

or denominator changed from each fraction. Then do the same to the

missing spot.

2 8 *The numerator went from 2 to 8. This was done by

3 ? multiplying by 4. Do the same to the denominator.

3x4=12, so the missing number is 12. 2/3 = 8/12

=

Online Resources:



*Think Central —> My Library —> Math —> Math on the Spot Video Tutorials

--> Chapter 6 —> Lesson 6.2

*Think Central —> My Library —> Math —> Go Math Animated Math Models

—> Skill 23 Equivalent Fractions


—>Fraction Flare Up Level D

*Cool Links —> Math: Equivalent Fractions Target Game

Link: http://www.helpingwithmath.com/resources/games/

fraction_game4/equivalent01.html

*Cool Links —> Math: Equivalent Fractions Bingo

Link: http://www.abcya.com/equivalent_fractions_bingo.htm

*Cool Links —> Math: Equivalent Fractions Game

Link: http://www.mathplayground.com/Triplets/Triplets.html

*Cool Links —> Math: Equivalent Fractions Matching Game

Link: http://www.sheppardsoftware.com/mathgames/fractions/

memory_equivalent1.htm

*Cool Links —> Math: Least Common Multiple Snowball Fight Game

Link: http://www.fun4thebrain.com/beyondfacts/lcmsnowball.html

*Cool Links —> Math: Equivalent Fractions Target Game


equivalent_fractions_shoot.swf

*Cool Links —> Math: Equivalent Fractions Post Office

Link: http://www.wmnet.org.uk/files/Post_sorting_-_fractions_v2.swf


I can write a fraction in simplest form

Fractions written in simplest form are equivalent fractions. They are just a

specific equivalent fraction. Simplest form means the fewest possible pieces.

4 (1, 2, 4)

12 (1, 2, 3, 4, 5, 12)

4 ( 4) = 1

12 ( 4)= 3

6 (1, 2, 3, 6)

18 (1, 2, 3, 6, 9, 18)

6 ( 6) = 1

18 ( 6)= 3

5 (1, 5)

6 (1, 2, 3, 6)

Online Resources:

1. List the factors for both the numerator and the

denominator.

2. Find the greatest common factor (GCF).

3. You will divide the top and bottom by this GCF.

** 4/12 written in simplest form is 1/3


denominator.


3. You will divide the top and bottom by this GCF.

** 6/18 written in simplest form is 1/3


denominator.


If the only factor they have in common is 1, the

fraction is already in simplest form.

Online Resources:

*Think Central —> My Library —> Math —> Go Math Animated Math Models

—> Skill 24 Simplest Form



*Think Central —> My Library —> Math —> Math on the Spot Video Tutorial —>



—>Fraction Flare Up Level E

*Cool Links —> Math: Simplest Form Pacman Game


mathman_reduce_fractions.htm

*Cool Links —> Math: Simplest Form Practice

Link: http://www.mathplayground.com/fractions_reduce.html

*Cool Links —> Math: Simplest Form Practice 2


review-fractions/visualizing-equiv-frac/e/simplifying_fractions


Link: http://www.math-salamanders.com/simplify-fractions.html


Link: https://www.ixl.com/math/grade-5/write-fractions-in-lowest-terms

*Cool Links —> Math: Simplest Form Word Problems

Link: https://braingenie.ck12.org/skills/102613

*Cool Links —> Math: Simplest Form Video

Link: https://www.youtube.com/watch?v=as7ioM80K38

*Cool Links —> Math: Simplest Form Video 2

Link: https://www.youtube.com/watch?v=AtBUQH8Tkqc


I can find common denominators

Common denominators means the denominator is the same in two or more

fractions.

3/4 and 2/6

3

4 (4, 8, 12, 16, 20, 24, 28, …)

2

6 (6, 12, 18, 24, 30, 36, 42,…)

3 (x3)= 9 2 (x2)= 4

4 (x3)= 12 6 (x2)= 12

9/12 and 4/12 have common

denominators

1/3 and 2/5

1

3 (3, 6, 9, 12, 15, 18, 21, …)

2

5 (5, 10, 15, 20, 25, 30, 35,…)

1 (x5)= 5 2 (x3)= 6

3 (x5)= 15 5 (x3)= 15

5/15 and 6/15 have common

denominators

Online Resources:

1. List the first few multiples for each

denominator.

2. Find a common multiple from each list.

This common multiple will become the

new common denominator. Your list may

have more than one. Any of these

common multiples can be used unless

they specifically ask for the fewest pieces.

3. This common multiple becomes the new

denominator. Write new (equivalent)

fractions for each with this new common

denominator.


denominator.

2. Find a common multiple from each list.

This common multiple will become the

new common denominator. Your list may

have more than one. Any of these

common multiples can be used unless

they specifically ask for the fewest pieces.

3. This common multiple becomes the new

denominator. Write new (equivalent)

fractions for each with this new common

denominator.

Online Resources:





*Cool Links —> Math: Common Denominator Online Practice

Link: http://mrnussbaum.com/denominators/

*Cool Links —> Math: Common Denominator Online Practice 2

Link: http://www.aaamath.com/fra66j-lcd.html

*Cool Links —> Math: Least Common Denominator Online Practice

Link: https://www.ixl.com/math/grade-5/least-common-denominator

*Cool Links —> Math: Least Common Denominator Fruit Game


LeastCommonDenomimator.htm

*Cool Links —> Math: Least Common Denominator Video

Link: https://www.youtube.com/watch?v=pZEmFSP3Z0I

*Cool Links —> Math: Common Denominator Video

Link: https://www.youtube.com/watch?v=N-Y0Kvcnw8g


I can find equivalent fractions to solve word problems

*You can draw a picture or make a table to make connections and visualize

what you would do in real life. Be sure to always include labels.

Problem: Lincoln is organizing his toy shelves using bins. 3/4 of the bins will have action figures.

There will be no more than 12 total bins. What are two possible options for organizing his bins?

Start with the 3/4. Remember, the numerator is the part and the denomina-

tor is the whole. For this problem, 3 bins are action figures and there are 4 to-

tal. We want to find equivalent fractions to see what it would look like with

more bins, but still have 3/4 of those bins for action figures. Let’s draw a pic-

ture and find equivalent fractions to find our options.

3/4 6/8 9/12 12/16

Above are all equivalent fractions. We started with the 3/4 shaded in and

broke them into smaller pieces, but they are the same amount. 6/8 is a possi-

ble option. There would be 8 total bins and 6 of them would have action fig-

ures. 9/12 is also an option. There would be 12 bins, and 9 would have ac-

tion figures. 12/16 does not work because the problem says no more than 12

total bins. So, 6/8 and 9/12 are your answers.


I can find equivalent fractions to solve word problems

*You can draw a picture or make a table to make connections and visualize

what you would do in real life. Be sure to always include labels.

Problem: Micah is making superhero capes for his cousins. Each cape will have 5 superheroes,

and 3 of those superheroes are girls. If he has 7 cousins, what fraction of superheroes will be girls?

Start by drawing one cape and create a table to go along with what you

see. You can use basic shapes to represent the superheroes and the cape.

For example, I used triangles for the girls and circle for the boys. I added 1 for

number of capes, 3 for girl superheroes, and 5 for total superheroes. Then

draw a second cape and add the information to your table. I would do this

for at least 3-4 capes. If you notice a pattern, can you continue to fill in the

table without drawing all 7 capes. However, drawing all 7 capes is also a

great strategy.

As I started drawing my capes, I noticed the number of girls increased by 3

each time and the total increased by 5, so I continue to finish my table with-

out drawing all 7 capes.

Now, the problems asks for a fraction of superheroes that are girls. The table

shows 21 girls out of 35 total superheroes. This as a fraction is 21/35, so….

21/35 are girls

capes 1 2 3 4 5 6 7

Girls 3 6 9 12 15 18 21

Total

superheroes

5 10 15 20 25 30 35

Online Resources:

*Think Central —> My Library —> Math —> Go Math! Interactive Student Edi-

tion —> Chapter 6 —> Lesson 6.5

*Think Central —> My Library —> Math —> Math on the Spot Video Tutorial

—> Chapter 6 —> Lesson 6.5

*Cool Links —> Math: Equivalent Fractions Word Problems Video

Link: https://www.youtube.com/watch?v=1DHjWuSKeBo

*Cool Links —> Math: Equivalent Fractions Word Problems Video 2

Link: https://www.youtube.com/watch?v=-CdSCpju324


I can use benchmarks to compare fractions

Using benchmarks means comparing each fraction to a commonly known

fraction, such as 1/2. Remember 1/2 can be written many different ways as

equivalent fractions. This means you can use those equivalent fractions to

compare and determine if a fraction is less, greater, or equal to 1/2.

** 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14 = 8/16 = 9/18 = 10/20 **

Compare 3/4 and 2/8

Start with the 3/4. Find the 1/2 equivalent fraction that has the same

numerator or denominator as your fraction. With 3/4, the 1/2 fraction you

want to use is 2/4 because they both have a 4 as the denominator.

3/4 > 2/4 Having 3 of the same sized pieces is more than having 2 of those

Now do the same with 2/8. With 2/8, the 1/2 fraction you want to use is 4/8

because they both have an 8 as the denominator.

2/8 < 4/8 Having 2 of the same sized pieces is less than having 4 of those

Since 3/4 is greater and 2/8 is less, then….. 3/4 > 2/8

1/4 1/4 1/4 1/4

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

This fraction strip shows you that 3/4 is past the

1/2 mark. It is greater than 1/2.

This fraction strip shows you that 2/8 is before the

1/2 mark. It is less than 1/2.


I can use benchmarks to compare fractions

Using benchmarks means comparing each fraction to a commonly known

fraction, such as 1/2. Remember 1/2 can be written many different ways as

equivalent fractions. This means you can use those equivalent fractions to

compare and determine if a fraction is less, greater, or equal to 1/2.

** 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14 = 8/16 = 9/18 = 10/20 **

Compare 3/7 and 6/9

Start with the 3/7. Find the 1/2 equivalent fraction that has the same

numerator or denominator as your fraction. With 3/7, the 1/2 fraction you

want to use is 3/6 because they both have a 3 as the numerator.

3/7 < 3/6 The denominator of 7 means you are breaking them into smaller

pieces. Even though you have 3 of those pieces for each, the pieces for 3/7

are smaller, so 3/7 is smaller.

Now do the same with 6/9. With 6/9, the 1/2 fraction you want to use is 6/12

because they both have an 6 as the numerator.

6/9 > 6/12 The denominator of 9 means you are breaking them into bigger

pieces than if you were sharing/breaking them into 12 groups/pieces. Even

though you have 6 of those pieces for each, the pieces for 6/9 are bigger, so

6/9 is bigger.

Since 3/7 is less and 6/9 is greater, then .. 3/7 < 6/9

This fraction strip shows each amount has 3

pieces. However, because the pieces are smaller,

the 3/7 is smaller than the 1/2.

This fraction strip shows each amount has 6 pieces. However, because the pieces are bigger, the 3/7 is bigger than the 1/2

1/7 1/7 1/7 1/7 1/7 1/7 1/7

1/6 1/6 1/6 1/6 1/6 1/6

1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12

Online Resources:





*Cool Links —> Math: Compare Fractions Practice (Use benchmarks to solve)

Link: http://www.mathplayground.com/fractions_compare.html

*Cool Links —> Math: Compare Fractions Practice 2 (Use benchmarks to solve)

Link: http://www.mathgames.com/skill/1.12-compare-fractions-same-

numerator-or-denominator

*Cool Links —> Math: Compare Fractions Soccer-Choose Level 2 (Use bench-

marks to solve)

Link: http://www.fuelthebrain.com/games/comparison-shootout/

*Cool Links —> Math: Compare Fractions Tug of War Game (Use benchmarks

to solve)

Link: http://www.mathplayground.com/ASB_TugTeamFractions.html

*Cool Links —> Math: Compare Fractions with Benchmarks Video

Link: https://www.youtube.com/watch?v=41KGbHOrQA8

*Cool Links —> Math: Compare Fractions with Benchmarks Video 2

Link: https://learnzillion.com/lesson_plans/8881-compare-fractions-using-

the-benchmark-fraction-1-2

*Cool Links —> Math: Compare Fractions with Benchmarks Practice

Link: https://www.ixl.com/math/grade-5/compare-fractions-using-

benchmarks

*Cool Links —> Math: Compare Fractions with Benchmarks Practice 2

Link: https://www.ixl.com/math/grade-4/compare-fractions-using-

benchmarks


I can compare fractions

Use common denominators

2 1 3 x 1 = 2 1 x 3 = 3

6 2 6 x 1 = 6 2 x 3 = 6

6: 6, 12, 18, 24

2: 2, 4, 6, 8, 10, 12

Use common numerators

3 6 3 x 2 = 6 6 x 1 = 6

5 9 5 x 2 = 10 9 x 1 = 9

3: 3, 6, 9, 12, 15,

6: 6, 12, 18, 24

Online Resources:


denominator.

2. Find the least common multiple.

3. Write equivalent fractions for each with the

new (common) denominator.

4. Compare the fractions with the same

denominator. If they have the same

denominator, they are the same size

pieces. Use the numerator to compare. 2

pieces is smaller than 3 of those same sized

pieces. So, 2/6 is less than 1/2.

<


numerator


3. Write equivalent fractions for each with the

new (common) numerator.

4. Compare the fractions with the same

numerators. If they have the same

numerator, it means you have the same

number of pieces, but they are different

sizes The bigger the denominator, the

smaller the pieces are because you’ve

broken them up more. Think of having to

share with more people, you would get

less. The 6/10 is sharing with 10 people,

which means you’d get less than sharing

with only 9 people. The pieces for 6/10 are

smaller than the pieces in 6/9. So, 6/10 is

less than 6/9.

<

1/6 1/6 1/6 1/6 1/6 1/6

1/2 1/2

1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10

1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

Online Resources:


—>Fraction Flare Up Level F





*Think Central —> My Library —> Math —> Go Math! Animated Math Models

—> Skill 25 Compare Fractions

*Cool Links —> Math: Compare Fractions Practice

Link: http://www.mathplayground.com/fractions_compare.html

*Cool Links —> Math: Compare Fractions Practice 2

Link: http://www.mathgames.com/skill/1.12-compare-fractions-same-

numerator-or-denominator

*Cool Links —> Math: Compare Fractions Practice 3

Link: https://www.ixl.com/math/grade-3/compare-fractions

*Cool Links —> Math: Compare Fractions Soccer-Choose Level 2

Link: http://www.fuelthebrain.com/games/comparison-shootout/

*Cool Links —> Math: Compare Fractions Tug of War Game

Link: http://www.mathplayground.com/ASB_TugTeamFractions.html

*Cool Links —> Math: Compare Fractions Video

Link: https://www.youtube.com/watch?v=9me_tSRN2Z8

*Cool Links —> Math: Compare Fractions Video 2

Link: https://www.youtube.com/watch?v=KNdUJQ_qd4U

*Cool Links —> Math: Compare Fractions Pizza Game

Link: http://www.professorgarfield.org/KBKids/video/kbs2012.swf

*Cool Links —> Math: Compare Fractions Dirt Bike Game

Link: http://static.arcademics.com/games/dirt-bike-comparing-

fractions.swf


I can order fractions

Use benchmarks

2 4 7

4 6 10

Less:

1/2: 2/4

Greater: 4/6 7/10

4 7 4 x5 = 20 7 x 3 = 21

6 10 6 x5 = 30 10x 3 = 30

6: 6, 12, 18, 24, 30

10: 10, 20, 30, 40

Use common denominator

3 2 7 3x3= 9 2x4= 8 7x1= 7

4 3 12 4x3=12 3x4=12 12x1= 12

4: 4, 8, 12, 16, 20

3: 3, 6, 9, 12, 15, 18

12: 12, 24, 36, 48, 60

1. Start by comparing each fraction to the

benchmark 1/2. Put them into groups: less

than 1/2, equal to 1/2, and greater than

1/2

2. 2/4 is equal, it is the smallest fraction. 4/6

and 7/10 are in the same group. Now,

you compare those two fractions using a

common denominator or common numer-

ator.

3. List the first few multiples for the numerator

or denominator of each fraction. This ex-

ample shows the denominators.

4. Find the least common multiple and write

a new fraction with the new (common de-

nominator).

5. 21 is bigger than 20, so the order least to

greatest is… 2/4, 4/6, 7/10

1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14 = 8/16 = 9/18 = 10/20

1. List the first few multiples for the

denominator in each fraction.


3. Write equivalent fractions so all the

fractions have the new (common)

denominator.

4. Compare the numerators to put the

fractions in order. Remember, when the

denominator is the same, it means they

are the same size. If the numerator is

bigger, you have more of those same

sized pieces. 7 is the smallest, then 8,

then 9 So, the order for the fractions

least to greatest is… 7/12, 2/3, 3/4


I can order fractions

Use common numerator

3 2 6 3x2= 6 2x3= 6 6x1= 6

4 3 12 4x2= 8 3x3= 9 12x1= 12

3: 3, 6, 9, 12, 15

2: 2, 4, 6, 8, 10, 12

6: 6, 12, 18, 24

Online Resources

*Cool Links —> Math: Order Fractions Balloon Pop


Balloons_fractions1.htm

*Cool Links —> Math: Order Fractions Drag and Drop

Link: http://www.kidsmathgamesonline.com/numbers/fractions.html

*Cool Links —> Math: Order Fractions Video

Link: https://www.youtube.com/watch?v=HJIqhDSrYB4

1. List the first few multiples for the

numerator in each fraction.


3. Write equivalent fractions so all the

fractions have the new (common)

numerator.

4. Compare the denominators to put the

fractions in order. Remember, when the

numerator is the same, you have the

same number of piece, but the size is

different. The bigger the denominator,

the smaller the pieces are because

you’ve broken them up more. Think of it

as sharing. You are sharing with more

people, so you would get less. 12 would

be the smallest sized pieces, then 9, and

then 8. So, the order for the fractions

least to greatest is… 6/12, 2/3, 3/4

Online Resources:

*Cool Links —> Math: Order Fractions Video 2

Link: https://www.youtube.com/watch?v=N8dIOmk_lHs





*Think Central —> My Library —> Math —> Go Math! Animated Math Models

—> Skill 26 Compare and Order Fractions

*Cool Links —> Math: Order Fractions Online Practice

Link: http://www.topmarks.co.uk/Flash.aspx?b=maths/fractions

*Cool Links —> Math: Order Fractions Online Practice 2

Link: https://www.khanacademy.org/math/arithmetic/fraction-

arithmetic/arith-review-comparing-fractions/e/ordering_fractions

*Cool Links —> Math: Order Fractions Online Practice 3

Link: https://www.ixl.com/math/grade-4/order-fractions

*Cool Links —> Math: Order Fractions with Models

Link: http://www.softschools.com/math/fractions/games/

ordering_fractions/

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