understanding fractions - 3rd grade australian math...

Understanding Fractions

Day 1

Problem of the dayMalik scored 8 points in each of the 4 quarters of the basketball game. Cameron scored a total of 19 points in the game. How many points did Malik and Cameron score altogether?

Key vocabularyNumerator-The top number in a fraction.

Denominator-The bottom number in a fraction.

Part-This is the numerator (a portion of the total).

Whole-This is the denominator (the total).

I do...Naming Fractions

There are 3 parts shaded, so the numerator (top number) will be 3.

There are 4 total parts (shaded and not shaded), which is the whole. This means that 4 is going to be the denominator (bottom number).

The fraction is 3 (pronounced three-fourths) 4

We do...Naming fractions

1. How many parts are shaded? 2. Is this the numerator or denominator?3. How many total parts (shaded and not shaded) are there?4. Is this the numerator or denominator?5. What is the fraction?

You do...Naming fractions

1. What is the numerator (parts shaded)?2. What is the denominator (total parts shaded and not

shaded)?3. What is the fraction?

I do...recognizing parts and wholes

1. I need to make 4 total parts, since the denominator (bottom number) is 4.

1 2 3 4

2. I need to shade in 1 of the parts, since the numerator (top number) is 1.

1 2 3 4

The fraction is 1 4

We do...recognizing parts and wholes

1. How many total parts do I need to make?

The denominator (bottom number) is 6, so I need to make 6 total parts.

1 2 3

4 5 6

2. How many parts do I need to shade?

The numerator (top number) is 5, so I need to shade in 5 parts.

1 2 3

4 5 6

The fraction is 5 6

You do...recognizing parts and wholesThe fraction is 3 8

More practice (Complete with your group)Name the fraction of shaded parts:

1.

Recognize the part and whole.

1. Shade in 5 8

Name the fraction of unshaded parts:

2.

Name the fraction of shaded parts:

3.

Recognize the part and whole.

2. Shade in 2 3

Independent practiceFront: Match the shaded portion of each figure to the correct fraction.

Back: Write the fraction based on how much of the figure is shaded.

Back: Shade in the correct amount of parts on each figure based on the given fraction.

Independent practice and centersComplete the fractions on a number line 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 to represent a fraction. Swap with your partner and name the fraction.

Exit Ticket▪ Explain the difference between the numerator and the

denominator.


Day 2

Problem of the dayMrs. Pillsbury has 10 boxes of brownies. Each box contains 6 brownies. If Mrs. Pillsbury burned 7 brownies on accident, how many brownies does Mrs. Pillsbury still have that are not burned?

What is a fraction review (halves)● A number represented by a part and a whole

○ Ex. “one half” or 1/2○ The “1” in the fraction represents the part○ The “2” in the fraction represents the whole○ On a number line (a line with tally marks that represent numbers)

it looks like this…

OR

● We read the number line like this…○ zero, one-half, one OR zero, one-half, two-halves

***The whole can be represented as “1” or the total number of parts over the total that makes the whole

Other Vocabulary● Tick Mark

○ A mark on a number line used to indicate a number or fraction

● Plot○ A dot or circle over a tick mark on a number line

● Equidistance○ or spaced out evenly

Fractions on a number line (fourths)How do we graph the fraction 1/4 on a number line?

● 1st: draw a number line that looks like this...○

● 2nd: draw a tick mark for zero on the far left like this…○

● 3rd: draw a tick mark for the whole on the far right like this...○ In this case it is “1” or “4/4”

OR

Fractions on a number lineWhy do we put “1” sometimes for the whole?

● When the part we are talking about in a fraction is equal to the number of parts that make up the whole, it equals “1” ○ Ex. the figure below shows that there are 4 parts to this

circle and those same 4 parts create the whole circle or 1 full circle, so we can say 4/4, or 1

= =

Fractions on a number line (fourths) continued ● 4th: Determine how many more tick marks you need on your number

line by counting forwards from the “0” on your number line until you get to your whole, making sure your numbers remain as fractions○ In this case our fraction is 1/4 which means our whole is

4/4. So we would count forward like this...■ 0… 1/4… 2/4… 3/4… 4/4

○ On the number line it looks like this (notice all the tick marks are equidistance or spaced out evenly)...

Fractions on a number line (fourths) continued5th: Place a plot on the number line to show which fraction you are looking for (in this case our fraction is “one fourth”)…

● What pattern do you see?

Fractions on a number line 5-step process1. Draw the number line (if it is not already drawn for

your)2. Draw a tick mark for zero to the far left of the number

line3. Draw a tick mark for the whole to the far right of the

number line4. Count from zero to your whole on the number line to find

the number of additional tick marks needed5. Fill in your additional tick marks and fractions on your

number line and plot the fraction you are looking for

Fractions on a number line (eighths)Watch me use the 5-step process to graph the fraction 5/8

Step 5

Guided practice w/ fractions on a number line (fourths)Plot the fraction 3/4 on the number line

Step 1

Step 2

Step 3

Step 4

Step 5

Guided practice w/ fractions on a number line (eighths)Plot the fraction 1/8 on the number line

Step 1

Step 2

Step 3

Step 4

Step 5

Your turn 1!Plot the following fraction on a number line (remember the 5-step process)

Your Turn 2!Plot the following fraction on a number line (remember the 5-step process)

Lesson REviewToday we reviewed what a fraction is and worked with halves, fourths, and eighths. Tomorrow we will continue to work with fractions, but we will focus on thirds and sixths.



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 dayAt the Taco Shack, you can buy a meal for $4. Mr. Jordan needs to buy 7 meals. If he has $21 dollars, how much more money will Mr. Jordan need to pay for 7 meals?

Vocabulary review● Number Line● Fraction● Tick Mark● Plot● Whole● Part● Equidistant

Fractions on a number line 5-step process ReviewWhat is the 5-step process for plotting a fraction on a number line?

Fractions on a number line 5-step process1. Draw the number line (if it is not already drawn for you)2. Draw a tick mark for zero to the far left of the number

line3. Draw a tick mark for the whole to the far right of the

number line4. Count from zero to your whole on the number line to find

the number of additional tick marks needed5. Fill in your additional tick marks and fractions on your

number line and plot the fraction you are looking for

Plotting thirds on a number lineNow we are going to use the 5-step process for plotting fractions on a number line to help us plot thirds, or a fraction whose whole is “3”

We are going to plot 2/3

What is the part?

What is the whole?

What is another name for part?

What is another name for whole?

Plotting thirds on a number line continuedLabel the pictures in the correct order by writing a 1, 2, 3, 4, or 5 beside each one to show the order I should complete the process for plotting 2/3 on a number line

Plotting sixths on a number line continuedLabel the statements in the correct order by writing a 1, 2, 3, 4, or 5 beside each one to show the order I should complete the process for plotting 3/6 on a number line

Let’s plot itNow let’s actually plot 3/6 on a number line and pay close attention to the location of 3/6 on the number line… what do we notice about 3/6 on the number line?

Guided practice w/ plotting thirds on a number linePlot the fraction 1/3 on a number line

● After I draw my number line, what comes next?

Guided practice w/ plotting thirds on a number linePlot the fraction 5/6 on a number line

● After I draw my number line and draw a tick mark for zero, what comes next?

You Try!Plot the following fraction on a number line (remember the 5-step process)

Lesson REviewToday we reviewed what a fraction is and worked with thirds and sixths. Tomorrow we will continue to work with fractions, but we will focus on using pictures to represent fractions.



I Can: Fractions




Day 4

Problem of the day Jasmine ordered a pizza that had 8 slices. She ate 2 pieces, Saran ate 3 pieces, and Diego ate 1 piece. Carlos ate the rest. What fraction of the pizza did Carlos eat? Draw a picture or number line to represent this problem.

Representing fractionsSo far, we have learned two major ways to represent a fraction. What are they?

Representing fractionsWe can represent ¾ as a picture or on a number line:

Picture:

Number Line:

Representing fractionsWe can represent ¾ as a picture or on a number line:

Picture: This circle has 4 pieces total, so the denominator is 4. 3 pieces are shaded, so the numerator is 3.

Number Line: The number line goes from 0 to 4/4, which is 1 whole. The whole is split into 4 equal sections, so the denominator is 4. The dot is after the third section, so the numerator is 3.

Matching fractionsDraw a number line to match this picture. What fraction does it represent?

Matching fractionsDraw a picture to match this number line:

Matching fractionsDraw a number line and a picture to represent ⅔.

Mixed NumbersA mixed number is a combination of a whole and a fraction. These are mixed numbers:

Mixed NumbersFor this number, we would have 5 wholes and 1 third. Our wholes should still be divided into thirds.

Mixed NumbersThis can also be represented as a number line.

Mixed NumbersWhat fraction does this picture represent?

Mixed NumbersWhat fraction does this number line represent?

Mixed NumbersDraw a picture and number line to represent this fraction:

Representing fractionsI will give you a set of cards. Some cards have fractions, some have the word form, some have number lines, and some have pictures. Your job is to work with your team to create sets of four cards that represent the same fraction. When you finish, raise your hand. If you are correct, you may get started on your independent practice for today.

Independent Practice/ CentersComplete the fraction worksheet for independent practice. When you are finished, go to your center for the day.


I Can: Fractions



DAY 5PARTITIONING A NUMBER LINE

PROBLEM OF THE DAY

• BRADLEY ATE 1/8 OF A PIZZA. JOZIAH AND

MARCUS EACH ATE 2/8 OF THE PIZZA. HOW

MUCH PIZZA WAS LEFT?

KEY VOCABULARY

• FRACTION

• NUMERATOR

• DENOMINATOR

• WHOLE

• NUMBER LINE

• TICK MARKS

DIRECT INSTRUCTION

• UNDERSTANDING HOW TO PARTITION A NUMBER LINE

• THE DENOMINATOR OF THE FRACTION WILL TELL

YOU HOW MANY SECTIONS TO PARTITION ON THE

NUMBER LINE.

• NOTE: SECTIONS ARE NOT THE TICK

MARKS...THEY ARE THE SPACES BETWEEN TICK

MARKS.

DIRECT INSTRUCTION

• YOU ALWAYS MAKE 1 LESS TICK MARK THAN WHAT THE DENOMINATOR IS…

• THE TICK MARK WITH THE WHOLE NUMBER COUNTS AS 1 OF YOUR

TICK MARKS.

• YOU CAN COUNT THE SECTIONS BETWEEN THE 2 WHOLE NUMBERS

TO MAKE SURE THAT THERE ARE THE SAME AMOUNT OF SECTIONS

(NOT TICK MARKS) BETWEEN THE 2 WHOLE NUMBERS.

• EXAMPLE: IF THE DENOMINATOR IS 4, YOU WOULD MAKE 3 TICK

MARKS. THE 4TH TICK MARK IS ALREADY THERE AT THE WHOLE

NUMBER.

DIRECT INSTRUCTION

• YOUR TICK MARKS NEED TO BE SPREAD OUT EVENLY BETWEEN THE

2 WHOLE NUMBERS.

• REMEMBER FRACTIONS ARE EQUAL SIZED PARTS. THE TICK

MARKS ON A NUMBER LINE NEED TO BE SPREAD OUT EVENLY,

SO THAT THE SECTIONS ARE EQUAL IN SIZE.

• THE AMOUNT OF SECTIONS PARTITIONED IS THE DENOMINATOR FOR

EACH TICK MARK.

DIRECT INSTRUCTION

• LABEL THE NUMERATOR OF THE 1ST TICK MARK WITH A 1 AND CONTINUE

TO INCREASE BY 1 UNTIL YOU REACH THE WHOLE NUMBER.

• THE LAST TICK MARK BEFORE THE WHOLE NUMBER SHOULD BE A

DIFFERENCE OF 1 BETWEEN THE NUMERATOR AND DENOMINATOR.

• EXAMPLE: IF THE DENOMINATOR WAS 4, THEN THE LAST

NUMERATOR BEFORE THE WHOLE NUMBER WOULD BE 3.

• EXAMPLE: IF THE DENOMINATOR WAS 8, THEN THE LAST

NUMERATOR BETWEEN THE WHOLE NUMBER WOULD BE 7.

WHOLE GROUP-I DOPARTITION THE NUMBER LINE INTO 4 EQUAL PARTS.

REMEMBER: WHERE THE WHOLE NUMBER (1) IS COUNTS AS ONE OF

YOUR TICK MARKS, SO THIS MEANS MAKE ONE LESS THAN WHAT IT

SAYS.

NOTE: THERE ARE 4 SECTIONS BETWEEN THE 0 AND 1. WE ONLY MADE

3 TICK MARKS. ALSO, THE TICK MARKS ARE SPACED EVENLY.

0 1

0 1

WHOLE GROUP-I DO

LABEL EACH TICK MARK WITH THE CORRECT FRACTION.

NOTE: THE DENOMINATOR IS 4 FOR EACH TICK MARK, BECAUSE THAT’S

HOW MANY SECTIONS WE PARTITIONED THE NUMBER LINE INTO. THE

NUMERATOR STARTS AT 1 ON THE 1ST TICK MARK AND CONTINUES. THE

LAST TICK MARK BEFORE THE WHOLE HAS A DIFFERENCE OF 1

BETWEEN THE NUMERATOR AND DENOMINATOR (3/4).

0 1¼

2/4

¾

WHOLE GROUP-WE DO

PARTITION THE NUMBER LINE INTO 8 EQUAL PARTS.

GUIDING ?’S:

1. HOW MANY TICK MARKS DO I NEED TO MAKE?

2. IS THERE ANYTHING ELSE I SHOULD KNOW ABOUT THE TICK MARKS?

0 1

GUIDED PRACTICE-WE DO

HERE’S WHAT YOUR PARTITIONED NUMBER LINE SHOULD LOOK LIKE.

0 1


NOW, WE NEED TO LABEL EACH TICK MARK WITH THE CORRECT FRACTION.

GUIDING ?’S:

1. WHAT IS THE DENOMINATOR GOING TO BE FOR EACH OF THE TICK MARKS

THAT I MADE?

2. WHAT IS THE NUMERATOR GOING TO BE FOR EACH TICK MARK…EXPLAIN.

3. ARE THERE ANY OTHER THINGS THAT I SHOULD REMEMBER WHEN

LABELING THE FRACTIONS?

0 1


HERE’S WHAT YOUR LABELED NUMBER LINE SHOULD LOOK LIKE.

6/ 8

5/ 8

3/ 8

0 14/8

1/ 8

2/ 8

7/ 8

GUIDED PRACTICE-YOU DO

1. PARTITION A NUMBER LINE INTO 5 SECTIONS.


• PARTITION A NUMBER LINE INTO 3 SECTIONS.


• PARTITION A NUMBER LINE INTO 10 SECTIONS.

INDEPENDENT PRACTICE

• COMPLETE THE PARTITIONING A NUMBER LINE WORKSHEET.

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

• EXPLAIN HOW MANY TICK MARKS YOU WOULD MAKE IF YOU WERE

PARTITIONING A NUMBER LINE INTO 6 EQUAL PARTS.


Day 6

Problem of the day Dontae had some skittles. ⅜ were purple. He had the same number of orange as purple. The rest were yellow. What fraction of each color did he have?

Moving fractions on a number lineNumber lines have many variations. Sometimes when we move fractions on a number line, we don’t start at 0. We can start at a different whole number, or even another fraction.

Sometimes number lines start at a high number and move to a lower number.

Sometimes a number line is too long to count by ones, so we have to divide a number line into larger pieces.

Moving fractions on a number lineLet’s solve this problem that has a longer number line:

The Centerville Cougars football team was 60 yards from the end zone. The opposing team tackled the football player about halfway from the end zone. About how many yards from the end zone was he when the player got tackled? Draw a number line to show the point where he

was when tagged out.

Moving fractions on a number lineWhat if he got tackled when he was only 1/3 of the way to the end zone?

What if he got tackled when he was 2/3 of the way to the end zone?

Guided practiceSerai and Joseph are hiking on a trail at Umstead State Park. The trail they want to hike is 3 miles long. There are signs to mark each 1/4 of a mile along the trail. Create a number line with tick marks at each ¼ mile.

Guided practiceOn the trail, there are water stops at every 1/2-mile sign. Label each 1/2 mile sign with a W for water.

Guided practiceThere are benches every 3/4 of a mile along the trail. Label the number line every 3/4 of a mile with a B to show where the benches are.

Guided practiceSerai stops for water at the 7/4-mile sign. Label the 7/4 sign with a S.

Guided practiceJoseph stops to rest at the 11/4-mile sign. Label the 11/4 sign with a J.

Independent practice and centersComplete the fractions activity sheet. When you are finished, go to your center for the day.


I Can: Fractions




Day 7

Problem of the day Solve using model drawing.

Ashley cut a length of rope into 10 pieces. Each piece measured 10 centimeters. What was the length of the rope before it was cut?

Vocabulary● Fraction● Part● Whole● Add● Sum

Fractions in a word problem● Just like writing a fraction, a word problem where a fraction

can be created includes a part and a whole. Here is an example…○ Laurice sees a crate of 12 apples. She asked her mom to buy

5 of the apples. What fraction of the apples did Laurice want her mom to buy?

1) The whole is 12 (There are 12 total apples that Laurice sees)2) The part is 5 (Laurice asked her mom to only buy 5 apples out of

the total amount)3) The created fraction is “five twelfths” or 5/12

Fractions in a word problem cont...● Here is another example…

○ Billy’s mom bought a bag of flour that weighs 10 pounds. She will use 3 pounds to make pancakes. What fraction of the bag of flour will she use to make pancakes?

1) The whole is 10 (There are 10 total pounds in the bag of flour)2) The part is 3 (Billy’s mom will only use 3 pounds of the total

pounds of flour)3) The created fraction is “three-tenths” or 3/10

Fractions in a word problem with addition● How about one more...

○ The Hill family bought a citrus cream pie with 8 equal slices. If Grandma Hill ate 1 slice of cream pie and Grandpa Hill ate 3 slices of cream pie, how many slices of cream pie did Grandma and Grandpa Hill eat altogether?

1) What is the whole? 8 (The citrus cream pie has a total of 8 slices)2) What is the part that Grandma Hill ate? 13) What is the part that Grandpa Hill ate? 34) What is the created fraction for Grandma Hill? 1/85) What is the created fraction for Grandma Hill? 3/86) What is the sum of what Grandma Hill and Grandpa Hill ate? 1/8 + 3/8 = 4/8

Fractions in a word problem with addition cont...● Here’s more practice...

○ Freddy helps his baby brother put together a puzzle with giant pieces. If Freddie puts together 6 pieces of the puzzle and his baby brother puts together the remaining 5 pieces of the puzzle, what fraction do they each put together?

1) How can we figure out the whole? Add together the pieces Freddie and his baby brother put together(6 + 5 = 11)

2) What is the part Freddy put together? 63) What is the part Freddy’s brother put together? 54) What is the created fraction for Freddy? 6/115) What is the created fraction for Freddy’s brother? 5/11

Guided practice for Fractions in a word problem● Let’s try this one...

○ Vanessa and her parents bought one big block of cheese that was divided into 6 equal pieces. If 1 of the 6 pieces of the block of cheese is used for lasagna, what part of the block of cheese is being used for lasagna?

1) What is the whole?2) What is the part?3) What is the created fraction?

Guided practice for Fractions in a word problem with addition cont...

● How about one more...○ Lisa’s mom baked a cake and cut it into 9 equal slices.

If Lisa eats 2 slices and Lisa’s mom eats 3 slices, how many total slices of cake do Lisa and her mom eat altogether?

1) What is the whole?2) What is the part that Lisa ate? 3) What is the part that Lisa’s mom ate? 4) What is the sum of what Lisa and her mom ate?

You TryAubry is allowed to drink 7 cups of milk a day. She had 2 cups of milk today for breakfast. What fraction of cups of milk has Aubrey drank for today?

1) What is the whole?2) What is the part?3) What is the created fraction?

You TryMs. Eaton has a bag of Kit Kat Miniatures. She eats 9 pieces with lunch and shares the remaining 7 pieces with Mrs. Hinton. What fraction do each of them eat?

1) What is the whole?2) What is the part that Ms. Eaton ate? 3) What is the part that Mrs. Hinton ate? 4) What is the created fraction for Ms. Eaton?5) What is the created fraction for Mrs. Hinton?

Lesson REviewToday we reviewed how to create a fraction from a word problem and how to add two fractions in a word problem together to get a fraction sum. Tomorrow we will continue to work with fraction word problems.



I Can: Fractions




Day 8

Problem of the day Solve using model drawing.

Mr. Reed ate 2/8, Ms. Valles ate 1/8 of the pizza, and Ms. Eaton ate 1/8 of the pizza. How much pizza was left??

Vocabulary● Fraction● Part● Whole● Add● Sum

Fractions in a word problemThere are 12 slices in a large pizza. Alejandro ate 4 slices and Reggie ate 3 slices. What fraction of the pizza is left?

Fractions in a word problemThere are 100 yards on a football field. How many yards does a quarterback throw the ball if he throws it 3/10 of the distance of the field?

Fractions in a word problemThere are 10 pieces of candy in a jar. If Heaven and Destiny each ate 2 pieces and Anthony ate 1/2 of the amount of candy. What fraction of the candy did they eat?

Fractions in a word problemThere are 50 multiplication facts on a sheet. How many problems have you answered if you have completed ⅖ of them?

Fractions in a word problemKisinda spent $3 on a notebook, $2 on a ink pen, and $1 on an eraser. She had $10, what fraction of the money did she spend?

Fractions in a word problemSebastian spent $2 on a bag of Doritos, $1 on a Mountain Dew, and another $1 on a Snickers. He had $5, what fraction of the money does he have left?

Fractions in a word problemMr. Reed bought a 20 lb bag of candy. He wants to keep 1/4 of the candy at home and the remaining amount at school. How many pounds of candy will he bring to school?

Fractions in a word problemYaritza ordered a large pizza that had 8 slices. She ate 1 slice and Jamiyah ate 2 slices. What fraction of the pizza was left?



I Can: Fractions



Exit TicketExplain a real-world example when you would have to find fraction sums.

understanding fractions - 3rd grade australian math...

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