equivalent fractions - 3rd grade australian math...

$: Equivalent Fractions - 3rd Grade Australian Math Bearsthirdgradeaustralianmathbears.weebly.com/.../equivalent_fractions.pdf · Computer: Khan Academy 3rd grade mission I Can: Fractions$
Equivalent Fractions

Day 1

Whole Numbers as FractionsWhole numbers can be written as fractions.

If I asked you to write the number 3 as a fraction, how

would you do it?

Problem of the DayDaniah went on a walk. The trail she walked on was 3

miles long with mile markers at every ⅙mile. She

stopped for a break at a mile marker that said 9/6. Draw a

number line, and plot a point where she stopped for a

break.

Whole Numbers as FractionsWhat does the denominator of a fraction tell us?

What does the numerator of a fraction tell us?

If the denominator of a fraction is 1, how many pieces are

in the whole?

If the denominator is 1, the numerator tells us how many

wholes there are.

Whole Numbers as Fractions9/1 can be read as “nine wholes”.

How would you say 15/1?

How could you write 12 wholes as a fraction?

What whole number does 3/3 represent? Why?

Plotting Whole Numbers on a Number LineDraw a number line from 0 to 6 like the one below.

With your team, plot the following fractions on that

number line:

Plotting Whole Numbers on a Number LineDraw a number line from 0 to 3.

Independently, draw a picture to represent each of the

fractions below, then plot them on your number line:

3/3 2/2 3/1 2/1

Independent Practice/CentersComplete the fractions activity sheet. When you are finished, go

to your center for the day.

Computer: Khan Academy 3rd grade mission

I Can: Fractions

I-pods: Multiplication Fluency

Partner Work: Draw a picture or number line to represent a fraction. Swap with your partner, and represent the fraction a different way. Use fractions that represent whole numbers.


Day 2

Problem of the day Solve using model drawing.

Adventure Toys is planning to give away 12

rocket kits each day for the next 3 days. How

many more rocket kits will Adventure Toys

need to give away if they already have given

away a half of a day’s worth of toys?

VocabularyFraction

Part or Numerator

Whole or Denominator

Equidistance

Equivalent

Bar Model

What does equivalent and bar model mean?Equivalent means equal.

So when we say equivalent fractions, we mean two or

more fractions that are equal

Bar Model is a pictorial representation of a fraction

using bars or rectangles.

Ex.

Equivalent fractions--bar bodelEx. If I have the fractions 2/4 and 1/2,

they are equal.

Take a look at the drawings to the right.

Notice that although the whole in each

fraction is different, the areas that are

shaded are equal and the areas that are

unshaded are equal as well. Notice that

the bars are beside one another vertically

(up and down) and not horizontally (side by

side). These bar models help prove that

2/4 and 1/2 are equivalent fractions.

How to draw a bar model1.Draw a long bar or rectangle

2.Divide the rectangle into sections that equal the whole

in the fraction

3.Shade in the number of sections that equal the part in

the fraction

If we wanted to draw a bar model for 1/5, it would look like

this…

Bar modelIf we wanted to draw a bar model for 6/9, how would it look?

equivalent fractions--bar modelsIf I want to compare the fractions 2/3 and 8/12 I would do it

like this…

The bar above represents what fraction?


How do you know that 2/3 and 8/12 are equal?

Guided practice w/ equivalent fractions--bar modelsIf I want to compare the fractions 3/6 and 1/2 I would do it

like this…




Guided practice w/ equivalent fractions--bar models cont...If I want to compare the fractions 2/2 and 4/4 I would do it like this…




Both 2/2 and 4/4 can also be written as equal to what number?

You try!Using the bar model, show how 1/2 is equal to 7/14.

Do not forget the bar model 3-step process…

1.Draw a long bar or rectangle


in the fraction


the fraction

You try!Using the bar model, show how 2/3 is equal to 6/9.

Do not forget the bar model 3-step process…

1.Draw a long bar or rectangle


in the fraction


the fraction

Lesson REviewToday we discussed what equivalent, equivalent fractions, and

bar model mean. We also used the bar model to help us prove

how two fractions can be equivalent. On Thursday we will

continue to work with equivalent fractions, but we will be

learning how to prove fractions are equivalent using the

circle model.

Independent practice and centersComplete the fractions activity sheet. When you are

finished, go to your center for the day.


I Can: Fractions


Partner Work: Draw a picture or number line to represent a fraction. Swap with your partner, and represent the fraction a different way.


Day 3

Problem of the DayFranklyn orders a pizza from Pizza Hut. He knows that

when they slice the pizza into 8 slices he can eat 2 slices,

or 2/8 of the pizza. When the pizza is delivered, Franklyn

finds that they only cut the pizza into 4 slices. If he wants

to eat the same amount as 2/8 of the pizza how many

slices and what fraction of the pizza should Franklyn eat?

Draw a picture to prove your answer.

Equivalent Fraction ReviewWatch this video

to review what

we learned

yesterday and

learn more about

equivalent

fractions!

http://youtube.com/v/N1X0vf5PUz4

http://youtube.com/v/N1X0vf5PUz4

Equivalent Fractions- Circle ModelYesterday, we learned about representing equivalent

fractions with the bar model. Today, we are going to

practice creating and representing fractions with a circle

model.

Draw a circle with ½ shaded like this one:

How can you create circles that represent fractions

equivalent to ½?

Reminder: Fraction models MUST have equal parts!

Equivalent Fractions- Circle ModelList fractions that are equivalent to ½.

What do you notice about all of the denominators?

Equivalent Fractions- Circle ModelWhen you create equivalent fractions, the numerator and

denominator are multiplied by the same number. If the

original denominator is 2, the denominators for all

equivalent fractions will be even because they are multiplied

by 2.

Equivalent Fractions- Circle ModelCreate circle models to find fractions that are equivalent to

1/3.

What do you notice about all of the denominators?

Equivalent Fractions- Circle ModelIf the original denominator is 3, the numerators and

denominators for all equivalent fractions will be multiples of

3.

Creating Quick Equivalent FractionsIn order to quickly create equivalent fractions, simply

multiply the numerator and denominator by the same

number. Let’s create equivalent fractions for ¼:

Creating Quick Equivalent FractionsOn your own, try creating quick equivalent fractions for

1/10.

Are My Fractions Equivalent?There is a foolproof way to determine whether or not

fractions are equivalent! It’s called cross-multiplication.

If you are comparing two fractions, multiply the numerator

of the first fraction by the denominator of the second

fraction. Then, multiply the denominator of the first fraction

by the numerator of the second fraction. If the products are

equal, the fractions are equivalent. Let’s look at a model to

understand cross-multiplication better...

Cross-Multiplication

Pizza PartyYou must have 1 whole pizza at all times.

-When I say go, rotate around the room to try to make an

equal trade with a partner. Make sure you can prove that

the fractions you trade are equivalent.

-Record each trade on your “I gave, I got” sheet.

Pizza PartyWhat were some of the trades you made?

I gave... I got...

Independent Practice/CentersComplete the fractions activity sheet. When you are finished, go

to your center for the day.


I Can: Fractions


Partner Work: Draw a picture to represent a fraction. Trade with your partner and create equivalent fractions.


Day 4

Problem of the Day◼ Mr. Reed ate 4/8 of a pizza. How much pizza is

left? Write 2 equivalent fractions that represent your answer.

Key VocabularyFractionNumeratorDenominatorWholeEquivalent FractionMultipleCross Multiplication

I Do: Demonstrate how each of these fractions are equivalent.

3/4 and 6/8:

I Do: Demonstrate how each of these fractions are equivalent.

⅓ and 2/6

Learning Activity 2-We Do

2/4 is equivalent to ? /8

Learning Activity 2-We Do

⅔ is equivalent to ?/6

Learning Activity 3-You Do

¼ is equivalent to ?/8

Learning Activity 3-You Do

2/6 is equivalent to ?/3

Exit ticket:

How can you represent equivalent fractions with both bar models and circle models?


Day 5


The Khan Academy Extraordinaires team masters

an average of 11 skills a day. If it has been

8 days, about how many skills have the Khan

Academy Extraordinaires team mastered?

VocabularyFraction

Part or Numerator


Equidistance

Equivalent

Number Line

Equivalent fractions on a number lineJust like two or more fractions have to be used in a bar model or

circle model to show if they are equivalent, the same thing must

happen when using a number line.

Ex. 1 If I want to see if 1/3 and 3/6 are equivalent on a

numberline, I would draw two number lines of the same length and

place them beside one another vertically. Next, I would plot one

fraction per number line, to see where my plotted fractions line

up. It would look like this…

Equivalent fractions on a number line cont...Based on where our plotted fractions are on each of their number

lines we can see that because their tick marks do not line up, they

are not equal.

Equivalent fractions on a number line cont...Ex. 2 If I want to see if 1/2 and 3/6 are equivalent on a

numberline, I would draw their number lines like this…

Are 1/2 and 3/6 are equivalent?

How can you prove your answer?

equivalent fractions on a number line cont...Let’s plot the fractions 1/2 and 1/4 on the number lines

below and see if they are equivalent fractions.

Are the 1/2 and 1/4 equivalent?

How do you know?

equivalent fractions on a number line cont...Let’s find the fractions for these number lines and determine if any of the plots on these number lines are equivalent.

What is my whole for the fractions that will be listed on my 1st number line?

What is my whole for the fractions that will be listed on my 2nd number line?

What is my whole for the fractions that will be listed on my 3rd number line?

What is my whole for the fractions that will be listed on my 4th number line?

equivalent fractions on a number line cont...What are the other two fractions listed on my 1st number line?

What are the other five fractions listed on my 2nd number line?

What are the other three fractions listed on my 3rd number line?

What are the other five fractions listed on my 3rd number line?

What points are equivalent from the four number lines above?

Guided practice w/ equivalent fractions on a number lineLet’s plot the fractions 1/5 and 4/6 on the number lines


Are 1/5 and 4/6 equivalent?

How do you know?

Guided practice w/ equivalent fractions on a number lineLet’s plot the fractions 1/2 and 4/8 on the number lines


Are the 1/2 and 4/8 equivalent?

How do you know?

yOU TRY!Find the fractions for these number lines and determine if any of the plots on these number lines are equivalent.

What is my whole for the fractions that will be listed on my 1st number line?

What is my whole for the fractions that will be listed on my 2nd number line?

What is my whole for the fractions that will be listed on my 3rd number line?

What is my whole for the fractions that will be listed on my 4th number line?

yOU tRY!What is the other fraction listed on my 1st number line?

What are the other four fractions listed on my 2nd number line?

What are the other three fractions listed on my 3rd number line?

What are the other seven fractions listed on my 4th number line?

What points are equivalent from the four number lines above?

Lesson REviewToday we worked with equivalent fractions on a number line.

Tomorrow we will be comparing fractions on a numberline to

fractions in a visual or pictorial model.




I Can: Fractions



Day 6: Equivalent FractionsComparing Fractions On a Number Line To

Visual Models

Problem of the Day

Draw a pictorial model to help you solve the problem below.

Madalynn ate 1/4 of a pizza. If there were 12 slices, how many slices are left?

Key Vocabulary

• Fraction

• Part or Numerator

• Whole or Denominator

• Equidistance

• Equivalent

• Number Line

Learning Activity #1-I Do

Learning Activity #2-We Do

• Plot 4/6 on the number line below.

• Shade in the equivalent to 4/6 in the boxes below.

• Cross multiply to check your answer.

0 1

Learning Activity #2-We Do

• Plot 4/8 on the number line below.

• Shade in the equivalent to 4/8 in the boxes below.


0 1

Learning Activity #3-You Do

• Plot 3/4 on a number line (equidistance).

• Shade in an equal number of eighths on a visual model (equal parts).



• Shade in 2/6 on a visual model (equal parts).

• Plot the equivalent fraction to 2/6 on a number line with thirds (equidistance).



• Plot 1/2 on a number line (equidistance).

• Shade in an equal number of sixths on a visual model (equal parts).


Independent Practice• Complete the worksheet on

your own.

Centers• Computers: Khan Academy 3rd

grade mission

• I-pods: Multiplication fluency

• I Can: Fractions

• Partner work: Draw a picture or number line to represent a fraction. Swap with your partner, and represent the fraction a different way.

Exit Ticket• Use a number line to plot 3/4.

Make an equivalent fraction with a visual model that has 8 equal parts.


Day 7


Ashley's web design business made $28

yesterday. She decided to save 1/4 of her

earnings and spend the rest on supplies. How

much money did Ashley save?

VocabularyFraction

Part or Numerator


Equidistance

Equivalent

Number Line

Mixed Number

Comparing number lines and visual modelsWhen comparing number lines with a visual model, we work with two

or more fractions two different ways.

One way is plotting the fraction on a number line and the other way

is pictorial either by the circle model or the the bar model

Ex. Below, 2½ is shown pictorially and on a number line

OR

number lines and visual models

Let’s show 1⅗ on a number line and pictorially

Comparing number lines with a visual model--word problems cont...Solve the word problem below and compare your

answer pictorially

La’Nya and Ta’Nya run track. At their track

meet La’Nya runs 1¼ miles in two minutes and

Ta’Nya runs 1¾ miles in three minutes. What is

the total distance that La’Nya and Ta’Nya ran

together?

equivalent fractions on a number line cont...Now let’s compare fractions using two number lines

Look at the plotted points on each of the number lines.

To see which fraction is greater, use your highlighter and draw a line

from zero on each number line to the plotted point.

Which number line has the larger distance from zero to the plotted

point?

*** Another way to see which fraction is largest is to see Which plotted

point is closer to the number 1.

Guided practice with number lines and visual models

Solve the word problem below and show your answer pictorially and on a number line.

Makayla is celebrating her birthday. Her mom buys ice cream for her party. If Makayla and her guests eat 2 tubs of ice cream and ⅓ of another tub, how much ice cream was eaten at Makayla’s birthday?

Guided practice with Comparing number lines with a visual model--word problemsSolve the word problem below and compare your answer

pictorially and using a number line.

Mr. Moss and Mr. Hegedus played golf at Adventure Landing.

If Mr. Moss putted a golf ball that traveled a distance of

2⅜ yards and Mr. Hegedus putted a golf ball that traveled a

distance of 2⅙ yards, who putted their golf ball the

furthest?

You try!Solve the word problem below and compare your answer

pictorially (bar model or circle model) and using a

number line.

Mr. Cox and Mr. Reed had a contest for who can hold their

breath underwater the longest. Mr. Cox held his breath

underwater for 1⅖ minutes. Mr. Reed held his breath for 1¾

minutes. Who held their breath underwater the longest?

Lesson REviewToday we learned how to compare fractions pictorially and on

a number line. Tomorrow we will take everything we’ve

learned about fractions in the past several weeks and do a

review for your assessment on Friday.




I Can: Fractions



Equivalent FractionsReview Day


Mr. Reed made 3 pans of biscuits. He split

each pan in half. He gave five halves to his

students, and he kept the rest for his

family. What fraction of the biscuits did he

keep for his family?

Review Activity There are problems posted around the room

that are similar to problems you will see on

the assessment tomorrow. Solve each problem,

and record your answer on your bubble sheet.

Remember to look for equivalent fractions!

When you are finished, you may get an ipod

and practice your multiplication facts.

equivalent fractions - 3rd grade australian math...

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