Unit 7: 1.1 Finding Fair Shares
CCSS:
3.NF.1
SFO:
I will find equal parts of a whole and name them with fractions.
I will divide an area into equal parts.
I will name fraction parts with unit fractions.
EQ:
Why is it important to understand fractions when you are sharing things among multiple people?
Teacher Input:
1. Pass out M6 rectangles (“brownies” can use notecards if you want).
2. Explain that for the next few days they will be solving problems about sharing brownies.
3. Prompt the students to cut the brownie so that they can share it equally between two people.
4. Share student examples.
5. Have students explain what fraction of the brownie each person would get. Explain that a fraction is part of a whole.
6. Write ½ on the board and have students explain what the 1 and the 2 stand for. Use numerator and denominator vocabulary.
7. Have the students try to share the same brownie among more than two people. Rotate around the room as they work on it.
8. Use an example of a student who shared their brownie among three people, but didn’t use equal groups, and ask students if this was a fair way to share
the brownie.
9. Have students explain how they could prove whether the shares are equal or not.
10. Have the students determine what fraction of the brownie each person would get if it were shared among three people.
Independent
1. Have students complete Unit 7 pages 1 and 2.
Unit 7 Lesson 1.1
Finding Fair Shares
Objectives:
I will find equal parts of a whole and name them with
fractions.
I will divide an area into equal parts.
I will name fraction parts with unit fractions.
EQ: Why is it important to understand fractions when
you are sharing things among multiple people?
• We will be solving sharing problems the next
few days.
• Let’s just pretend these note cards that I pass
out are brownies…
• Use scissors to cut the “brownie” so that you
can share it equally between two people.
What Do You Notice?
• Let’s take a look at some brownies…
• What do you notice?
(This brownie can be
broken into two parts…
just click and drag.)
Now that I split my brownie, would this be a fair
way to share it?
How Do We Represent It?
• When we split a whole object into smaller, equal
pieces, we are creating fractions.
• A Fraction is a number that represents a part of a
whole.
• This is 1 whole brownie. If we were to split this
brownie into 2 pieces, what would we call one of those
pieces? What fraction would represent just one of
those pieces?
How Do We Represent It?
• Since the brownie is split into 2 pieces, one of the pieces would be
represented with the fraction…
1
Numerator
2
Denominator
OR
1/2
Numerator – the number above the line in a fraction that represents
how many pieces we are using or considering.
Denominator – the number below the line in a fraction that represents
how many pieces make up the whole.
(Elaborate)
1
1
2
2
Fractions Challenge
• Can you share the same brownie that you already cut with
more than two people?
• I will rotate around the room to monitor your progress (2-4
minutes).
• I noticed someone tried to share the brownie with three
people. Did this work? Why or why not? How can we
make it work?
• Let’s split this brownie into three equal pieces… What
fraction would each person get?
Guided Practice
• If you ate 3/8 of a pizza, shade the portion of
the pizza you ate.
• How much of this triangle is shaded?
Independent
• Complete Unit 7 pages 1 and 2 of
your investigations book.
Unit 7: 1.2 Making Fraction Sets
CCSS:
3.NF.1
SFO:
I will find equal parts of a whole and name them with fractions.
I will divide an area into equal parts.
I will name fraction parts with unit fractions.
EQ:
Why is it important to understand fractions when you are sharing things among multiple people?
Teacher Input:
1. Watch the Brainpop video on fractions.
2. Pass out 5 sheets of paper.
3. The students will cut each sheet into the following factions and label them: halves, thirds, fourths, sixths, eighths.
4. The students will place the fraction sheets in order from largest to smallest.
Independent
1. Have students complete Unit 7 page 5.
USE MAKING FRACTION SET PDF FILE.
Unit 7:1.3 More than one piece
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
-Power Point
-Blank 8x11” sheets of paper
-Fraction sets chart
-Student fraction sets from previous lesson
SFO:
-I can name fractional parts with fractions that have numerators.
-I can use representations to combine fractions that sum to 1.
Teacher Input:
-Explain to students that they will be folding paper to create different fractions. They will begin to identify fractions greater than 1.
-Fold an 8x11” piece of paper into fourths. Ask the students what fraction is each piece on the paper folded? They should recognize it is one fourth.
-Now cut a ¼ piece out of the paper
-Ask students what fraction was cut out. Label the cut piece with ¼. Now ask students how much you have left? Label the other sheet with ¾.
-Pass out 5 pieces of paper to each student.
-Tell students that they will make one sheet into halves, fourths, eighths, thirds, and sixths with a partner.
-Tell students that after they have folded the paper into fractional parts, they are not going to cut out all the pieces like they did last time. Instead they are
going to cut out only one piece. For each sheet they make, they will label the piece they cut out and also the piece that is left.
-Bring the class together and show students the fraction facts chart you created.
-Tell students that as they keep working with fractions they will use the chart to help us keep track of things we notice or discover that are true about
fractions.
-Tell students to work with a partner to see if they can use different fractions to make a whole.
-Write down fraction combinations students found that make a whole.
-Keep these lists posted throughout the unit.
Assesment:
Have students complete a ticket out where they write down 3 example of fractions that equal 1 whole.
Session 1.3
More Than One Piece
Review
1. What does the numerator in a fraction
stand for?
2. What does the denominator in a
fraction stand for?
3. Order the fraction strips below from
least to greatest.
I folded a piece
of paper into
fourths.
What fraction is
each of the
piece of paper I
have folded?
Now look at
the paper. I
cut a piece out.
What fraction
did I cut out
of the paper?
What fraction
do I have left?
3
4
1
4
With a partner you will add more
pieces to your fraction set
• Each student will receive 5 sheets of white paper.
• You will need to fold each paper into halves, fourths,
eighths, thirds, and sixths.
• After you fold the paper into fractional parts, you are
NOT going to cut out all of the pieces like you did last
time.
• Instead you are going to cut out only 1 piece as I did for
the fourths. For each sheet you make, you will label the
piece you cut out and also the piece that is left (Just as I
labeled the ¼ and ¾ when I did the fourths example).
• If you finish early, see if you can put all of the fractions
you cut out in order from least to greatest.
• You will have about 20 minutes to complete this with your
partner.
Fractions Chart
• We are going to create a fractions chart on chart
paper that we will record and keep track of things we
notice or discover that are true about fractions. We
will add to this throughout the unit and leave it
handing up in the room for you to refer to.
• Let’s refer back to the example I did with the
fourths. If I combine the two fractions ¼ and ¾ what
will I have? How could I write an equation that says
that one fourth and three fourths equals a whole?
• What other ways can you think of to make a whole
with fractions? With your partner use your fraction
sets to find different ways to make a whole. Be
prepared to share and record on our fractions chart.
Label your fractions chart with 2 sections. The first
section titled “Halves, Thirds, Sixths” and the other
titled “Halves, Fourths, and Eighths.”
Independent Practice
• Students will complete Unit 7 pg. 7
from their student activity book.
• Ticket Out: Give student a half sheet of
lined paper. Have students choose 3
things we recorded on our fraction
chart and illustrate them using pictures.
Unit 7 1.4: Sharing many things
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
-Powerpoint
-Notes
SFO:
- I can divide a group into equal parts and name the parts with fractions.
Teacher Input:
-In the previous sessions students worked with an area model for fractions, finding parts of a single whole. In this session they find fractions of groups of
objects.
-Tell students we have been finding fractions of rectangles, which are single objects that can be cut up into equal parts.
-It is also possible to find fractions of a group of things. Think about this: I have 12 marbles in my collection. I want to give my friend half of them. How many
marbles will I give to my friend?
-Allow students to consider this for a minute and then ask a few to explain how they thought about the question.
-Tell students that today they will be solving some problems about sharing 12 apples.
Have students complete student activity book pg. 8 and then compare with a partner.
Assessment:
Left side of interactive notebook
1.4 Sharing Many Things
Objective:
-I can divide a group into equal parts and name
the parts with fractions.
Big Idea: We have been learning how to find
fractions of a single whole. Today you will learn
how to find fractions of a group of objects.
Example
• I have 12 marbles in my collection. I
want to give my friend half of them.
How many marbles will I give to my
friend?
Draw a picture to solve.
Here’s a few other strategies
• Draw a box
• split it in half
• share the 12 things
between the two boxes.
• Count the number of
objects in one half.
So, ½ of 12 = 6
• Draw 12 objects and color
every second one (or
whatever your
denominator is).
• Count the number you
have colored in.
So, ½ of 12 = 6
Guided Practice
1) Oscar picked 12 apples. He gave 1/3 of the apples to Gil and
1/3 of the apples to Becky. How many apples did each of them
get?
2) Pilar picked 12 apples. She gave ¼ of the apples to Dwayne,
¼ of the apples to Murphy, and ¼ of the apples to Kelley. How
many apples did each of them get?
3) Chiang picked 12 apples. She gave 1/6 of the apples to each
of her 5 friends. How many apples did each friend get?
Let’s look at the answers…Number 1
• Draw a box
• split it in thirds
• share the 12 things
between the three boxes.
• Count the number of
objects in one third.
Oscar
Gil
Becky
So, 1/3 of 12 = 4
• Draw 12 objects and color
every third one (or
whatever your
denominator is).
• Count the number you
have colored in.
So, 1/3 of 12 = 4
Let’s look at the answers…Number 2
• Draw a box
• split it in fourths
• share the 12 things
between the four boxes.
• Count the number of
objects in one fourth.
• Draw 12 objects and color
every fourth one (or
whatever your
denominator is).
• Count the number you
have colored in.
Kelley
Dwayne
Pilar
Murphy
So, 1/4 of 12 = 3
So, 1/4 of 12 = 3
Can Someone Share their Work for Number 3?
• Draw a box
• split it in sixths
• share the 12 things
between the six boxes.
• Count the number of
objects in one sixth
• Draw 12 objects and color
every sixth one (or
whatever your
denominator is).
• Count the number you
have colored in.
Left Side Independent Practice
• Solve the following 5 problems in your notebook:
1. Jack brought 24 colored pencils to school. He wanted to
give ¼ of the colored pencils to each of his 2 friends. How
many did each friend get?
2. Sarah had 12 brownies. She wanted to give 1/3 of the
brownies to her teacher. How many did her teacher get?
3. Pedro bought 28 new CD’s. He gave ½ of them to his
brother. How many did his brother get? How many did he
have left over?
4. Jeremy’s mom went to the grocery store and bought a pack
of 30 water bottles. She was going to send 1/6 of the
water bottles to Jeremy’s class. How many was she going to
send to school?
5. Michelle picked 16 grapes. She decided to give 1/8 of the
grapes to her best friend Jackie. How many did Jackie get?
Challenge:
• Find 2/8 of 24
• Find 4/5 of 30
• Find 3/5 of 20
• Find ¾ of 36
Unit 7: 1.5 Sharing Several Brownies
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
- Index cards or sheets of paper that the students can cut to represent fractions.
- Chart paper
-Unit 7 page 11 of the student book.
SFO:
- I can divide a group into equal parts and name the parts with fractions.
- I can identify equivalent fractional parts.
-I can use fraction notation to record equivalencies (3/6 = ½)
-I can use mixed numbers to represent quantities greater than 1.
Teacher Input:
1. Display the activator problem on ppt (7 brownies divided among 4 people).
2. Ask the students to estimate how many brownies each person will get.
3. Pass out the recording sheet (Unit 7 page 11 of student book) and index cards and have the students solve the problem. (5-7 minutes)
4. Have three pairs of students briefly describe how they solved the problem. (try to select pairs that solved the problem in these ways: 1 + ½ + ¼, 7/4, 1¾)
5. While the students explain their solution, illustrate it on chart paper.
6. Have the class analyze the solutions and explain whether all people are getting fair shares in each solution.
7. Explain that seven fourths equals one and three fourths, so these are called equivalent fractions. (add to list of fraction facts)
8. Complete guided practice with the students.
Independent:
Have students create their own fair share problem, illustrate it on a blank paper, and solve it.
Assessment:
Independent assignment
Unit 7 Lesson 1.5
Sharing Several Brownies
Objectives:
I can divide a group into equal parts and name the
parts with fractions.
I can identify equivalent fractional parts.
I can use fraction notation to record equivalencies
(3/6 = ½)
I can use mixed numbers to represent quantities
greater than 1.
Review/Ten Minute Math
1. Spiral Review (CMS PPT)
2. Ten-Minute Math
What time is it on this clock?
If I start jogging at 1:06 and return 40
minutes later, what time will it be?
• 4 people are sharing 7 brownies. Estimate: How many
brownies will each person get?
• Using index cards, solve the problem. Record your
work in Unit 7 Page 11 of the student book.
Explain!
• Explain how you solved the problem while I
illustrate your solution on chart paper.
• Are all of these solutions correct?
• Are all four people getting equal shares in
each of these solutions?
• Does each solution mean the same thing,
even though each is written differently?
Equivalent Fractions
• Since 7/4 and 1¾ are equal, these are called
equivalent fractions.
• Can you think of some other equivalent
fractions? Let’s list some.
Guided Practice
Three people want to share 5 brownies. How
many brownies will each person get?
What equivalent fractions were found while
solving this problem?
Independent
• Use blank paper and create your own “sharing
multiple brownies” problem. (E.g. 4 people want to
share 7 brownies. How many brownies will each
person get?)
• Make sure your problem requires the use of
fractions. This isn’t simply division anymore
muahahahahaha!
• Be sure to illustrate the problem. After, solve the
problem on the back side of the sheet.
Unit 7 1.6: Assessment and 2.1 Making cookie shares
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
-Snap cubes or index cards (anything they can use to problem solve).
SFO:
- I can divide a group into equal parts and name the parts with fractions.
-I can divide an area into equal parts.
Teacher Input/Independent:
1. Have students complete Unit 7 pages 15 and 16. (they can use any manipulatives)
2. Rotate around the room and take notes: Can students create equal shares? Do students use fraction notation correctly to represent the equal
shares? Can students find fractional parts of a group represented by fractions with numerators greater than one?
3. Once they complete the sheets, consider #4.
4. Have students tell a story about ⅔ of 9. If they can’t create one spontaneously, come up with your own example.
5. Have the students explain how they figured out what ⅔ of 9 is. They can use manipulative while they share their solution.
6. Have students complete the mini-assessment (ppt) using blank paper.
Assessment:
Mini-assessment
Unit 7 Lesson 1.6
Sharing Four Brownies
Objectives:
I can divide a group into equal parts
and name the parts with fractions.
I can divide an area into equal parts.
Review/Ten Minute Math
1. Spiral Review (CMS PPT)
1. Ten-Minute Math
I wanted to school today. I left my
house at 7:45 and arrived at
school at 8:24. How long did it
take me to walk to school?
• Complete Unit 7 Pages 15 and 16 while I look
to see if you can…
Create equal shares?
Use fraction notation correctly to
represent the equal shares?
Find fractional parts of a group
represented by fractions with numerators
greater than one?
• Problem 4 asked you to find 2/3 of 9.
• Can you tell me a story about 2/3 of 9? If not,
I have this crazy story…
• How did you figure out what 2/3 of 9 is?
Show me using manipulatives.
(Pass out pattern blocks) - Let’s say this yellow
hexagon is a cookie. Can we make a cookie
that is the same size and shape using red
trapezoids, blue rhombi, or green triangles?
*Use the
physical
pattern
blocks,
these
won’t fit.
How many red trapezoids did it take to fill the
hexagon? How many blue rhombi? Green
triangles?
As I draw them in, let’s name the fraction!
*model drawing the
pattern blocks in and
labeling them with the
appropriate fraction.
1. Use Unit 7 page 18 of the student book.
2. Find 5 different combinations of red, blue,
and green pattern block that will cover the
hexagon.
3. Draw in the lines to represent these pattern
blocks, and label them with the correct
fraction name.
When the class is done, go to the next slide.
Here is one solution: (yeah, it looks funny…)
•
•
Let’s label each pattern block with the appropriate fraction.
Can you come up with an addition equation using these
fractions?
• Go ahead and write above each of your 5 combinations an
addition equation that represents the combination.
When the students are done, move on to the next slide.
Can you share some equations?
•
Can you identify which pattern block is half a cookie?
Can you use other pattern blocks to make half a cookie?
What equation can you use to represent that
combination?
•
Can you do the same for 1/3 of a cookie?
•
What about ¼ of a cookie?
• Fractions Quiz
Unit 7: 2.2 The Fraction Cookie Game
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
Pattern blocks
Fraction number cubes
M 14 - 16 Unit 7
SFO: I can combine / add fractions that have a sum of 1. I can identify equivalent fractional parts. I can combine fractions that equal other fractions.
Teacher Input: Today you will play a game where you will collect pattern block pieces to represent pattern block cookies. Have students trace hexagon
shapes onto paper to keep track of their cookies.
Play a few rounds with the students to model the game and rules. The objective of the game is to fill up your “cookies” first. Important rule: you must
always have as few pieces as possible when you’ve finished collecting cookie pieces on your turn. Example: I rolled ⅓ on my first turn, so I took a blue
rhombus. Then I rolled 2/6 on my second turn, so I took two green triangles. Do I have the fewest pieces possible in my cookie? How could I trade so that I
have fewer?
*Enrichment: to challenge students who are very successful with this game - create cookies made up of two hexagons equal to one whole.
Also, students can roll two fraction dice and add the two fractions before covering the cookies. See pages M15 Unit 7
-Students should play this game in pairs. If you have enough hexagon pattern blocks, student can use them instead of tracing the cookies onto paper. Each
time a cookie is complete, the player needs to either remove the hexagon, or put an “X” on that cookie on their sheet.
-Remind students to trade in their smaller fractions to make bigger ones and have the fewest number of pieces on each cookie.
-Discuss as a class, the kinds of trades they made while playing the game. Ask how much of the hexagon was filled, what was rolled, and how they solved
the amount of cookie to cover.
-Restate the student’s example using fraction names. For example: Kyla started with a red block and a green block. How can we name those pieces as
fractions? (½ and ⅙). How much of the hexagon did she already have? (⅔) What pieces did she need to make a whole cookie? (either one blue or two
greens) What fraction did she need to finish the cookie then? (½ or ⅓)
-Continue making the connections during the discussion between the blocks and the fractions.
-Introduce this as equivalent fractions. Ask the students if they can think of other equivalent fractions.
Make sure to add them to the chart.
Independent:
1. Unit 7 page 21 - students identify and order two sets of unit fractions
2. Unit 7 page 20 practice with multiplying sets
Assessment: observe students during the game - how they make trades; discussion and understanding of fraction names
The Fraction
Cookie Game
I can combine fractions to make a whole.
I can identify equivalent fractional parts.
I can name fractions that equal other fractions.
Object of the game: be the first to fill your cookies!
Materials: pattern blocks; fraction number cubes; hexagon cookies
1. Trace a dozen hexagon cookies onto a sheet of paper.
2. Roll a fraction number cube.
3. Take the amount in pattern blocks equal to the fraction rolled.
Place the blocks on a cookie.
4. Trade out your pattern blocks to have the fewest possible
covering your cookies.
5. Take turns rolling dice and filling your cookies.
6. The person who fills up all the cookies first, wins.
Example
I rolled ⅓ on my first turn. Then I rolled 2/6
on my second turn. Do I have the fewest
pieces? How could I trade so that I have
fewer pieces?
Another example:
I have ½ of a hexagon covered and I roll ⅚
what should I do?
Discussion:
Who can give us an example of when you
had to make a trade so that you would end
up with as few pattern block pieces as
possible? How much of a hexagon did
you start with? What did you roll? How
did you make the trade?
Equivalent Fractions
Fractions that are equal to one another, such
as one third and two sixths are called
equivalent fractions. On the left side of
your journal, make a list of equivalent
fractions.
Unit 7 Lesson 2.3 Assessment: Ways to Make a Share
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
-Student activity book pg. 23
SFO:
-I can use representations to combine fractions that sum to 1.
-I can identify equivalent fractional parts.
-I can use representations to combine fractions to equal other fractions
Teacher Input:
-Write the following equation on the board:
True or not true?
1/6+1/4=1/2
-Give students a few minutes to discuss in pairs and make any drawings or use any materials they might need. As students share, go around and notice what
they are saying.
-Bring the class back together and ask two or three pairs of students to share their thinking. When the class has come to an agreement wrap up the discussion
and introduce the students to the activity.
-For the remainder of the math time students will be working on Many Ways to Make a Share Activity and the Fraction Cookie Game.
-Students may work alone or with a partner to find fraction equivalencies on student activity book pg. 23.
-You can record more fraction equivalencies that students find on your class fraction chart.
-When students finish have them complete student activity book pg. 24 by themselves or with a partner.
-Students should play the fraction cookie game when they finish or for math workshop on this day!
Assessment:
Student Activity book pg. 23
-Students should be able to identify equivalent fractions (ie. 3/6 = ½)
-Students should also be able to find combinations of fractions that are equal to one and other fractions (ex. 3/6 + ½ = 1)
Use Lesson 2.3 Smart Notebook
Unit 7 Lesson 2.4 Making Half-Yellow Designs
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials:
-Student activity book pg. 25, notes, power point
SFO:
-I can use representations to combine fractions that sum to 1
-I can use representations to combine fractions to equal other fractions
Teacher Input:
-Complete review on slide 2 of powerpoint
-Show the students a design that looks like the one on pg. 81 of the teacher manual. Ask the students how much of the design is yellow. Next, tell them to
think of the design as a fancy cookie. If I eat the yellow part, how much of the cookie did I eat? What fraction would be the amount of the whole cookie I ate?
Give students a few minutes to consider the question in pairs.
-As the students share their thinking with the whole class, have them come up to the board and point of where they see the different halves of the design, or
to rearrange the pieces to show how the design is half yellow.
-Next show the students another design (pg. 82 of teacher manual) with all different colors. Is half of this design yellow, too? How can you tell? Again, give the
students time to work in pairs, and then bring them back together to share their thinking.
-Explain to students that we will call this kind of design a “Half-Yellow Design” because exactly half of it is yellow. The other half is made up of different colors
of pattern blocks.
-For independent practice students will make their own half-yellow design and then draw it on triangle paper.
Note: For students who are struggling you can get out pattern blocks for them to manipulate.
Assessment: Student’s independent practice in left side of notebook & exit ticket
Unit 7 Lesson 2.4 Making
Half Yellow Designs
Objectives:
-I can use representations to combine fractions
that sum to 1
-I can use representations to combine fractions
to equal other fractions
Review
• What fraction of the picture is shaded?
• What fraction of the picture is shaded?
• What is 1/6 of 24?
• The computer lab had 28 computers. 1/8 of the
computers were being used. How many computers
were available?
How much of this design is yellow?
Work with a partner and try to solve.
How did you know?
How
can you
tell?
Here’s another design. Is half of
this design yellow too?
Let’s review ways to make a whole
How many green triangles equal 1 whole?
Guided Practice
How much of the design is yellow?
Blue? Red? Green?
Guided Practice
How much of the design is yellow?
Blue? Red? Green?
Independent Practice
(Left Side)
• Open up your student activity book and rip out the
triangle pg. 25
• Use the triangle paper to draw your own 2 designs
using at least 1 of all the following shapes. Be as
creative as you would like. Use your colored pencils or
crayons to color code them.
• On an index card answer the following questions for
each design you created and then staple it into your
notebook.
How much of the design is yellow? Blue? Green? Red?
Exit Ticket
• What fraction of the design is shaded
yellow? Blue? Red? Green?
If you finish…
• Play the fraction cookie game
• Play a more challenged version of the cookie
game. Each person will roll the fraction dice 2
times. You will add those fractions together by
covering your hexagons with that amount of
shapes. You will then roll another dice and
subtract that amount of shapes from your
hexagons. The person to fill all of their hexagons
first with the least amount of shapes wins.
Equivalent Fractions
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials: Power point, notes
SFO:
-I can find equivalent fractions using pictures, multiplication, and division.
-I can determine whether two fractions are equal by drawing pictures.
Teacher Input:
-Complete review on slide 2 of Power point
-Activate prior background knowledge by having students brainstorm what they know about equivalent fractions.
-Introduce students to finding equivalent fractions by using pictures. Ask them the question: is ⅔ = ⅘? Have students draw fractions strips and
shade them to compare the fractions.
-Next introduce students to finding equivalent fractions using multiplication. Tell students that they can find equivalent fractions by multiplying
numerator and denominator by the same number. Find an equivalent fractions for ⅘.
-Last, show students how to find equivalent fractions using division. Have students find an equivalent fractions for 4/12. Make sure to tell students
that this strategy cannot always be used. They must be able to divide both numerator and denominator by the same number.
-Complete guided practice problems:
1. Does 5/6 = 7/8? Draw a picture to solve.
2. Does 1/3 = 2/6? Draw a picture to solve.
3. Use multiplication to find an equivalent fraction for 7/8.
4. Use division to find an equivalent fraction for 4/8.
5. Sally was following a recipe to make cookies. She needed to put in ¼ cup of oil. Instead she put in 3/12 cup. Did she follow the recipe
correctly?
-Next give students 3 options for a left side assignment:
Left Side Idea #1:
nCreate a three pocket foldable using 8x11” paper. On the front write “Equivalent Fractions” and on the inside label each pocket with picture,
multiplication, & division. You will need 2 index cards for each pocket or 6 total. On each index card solve the following equivalent fraction
problems:
Left Side Idea #3
Write a summary paragraph (5-7 sentences) explaining how to find equivalent fractions using all the methods you learned today. When you are
finished provide 1 example for each method.
Left Side Idea #4
Come up with 3 instances in the real world of when you would use equivalent fractions. Create a word problem for each and solve.
Assessment:
Left side of interactive notebook and exit ticket
Equivalent Fractions
Objectives:
-I can find equivalent fractions.
-I can identify whether a fraction is
greater than, less than, or equal to.
Review
1.
What fraction of the design is
shaded green? Yellow?
2.
What is 1/3 of 12?
What is 2/3 of 12?
3.
What do you know
about equivalent
fractions?
What is an equivalent fraction?
two fractions that name the same part of the whole
or that are equal.
Equivalent Fractions Brain Pop Video
Example:
4
6
2
3
Ways to find equivalent fractions
Example: Is 2/3 = 4/5?
 Draw a picture by lining up 2 fraction
strip boxes that are the same size.
Ways to find equivalent fractions
Example: Is 2/3 = 4/5?

Divide each fraction strip into the total
number of parts of each fraction by
looking at the denominator.
2
3
4
5
Ways to find equivalent fractions
Example: Is 2/3 = 4/5?

Shade in each fraction strip by looking at
the numerator to tell how much to shade.
2
3
4
5
Ways to find equivalent fractions
Multiply the numerator and
denominator by the same number (any
number). The larger the number you
multiply by, the more pieces you will
be dividing your fraction into.
 Example: Find an equivalent fraction
for 4/5.

x2
4
5
8
x2
10
Ways to find equivalent fractions

Divide numerator and denominator by the same number (Keep
in mind that you may not always be able to use this method. If
you cannot divide the numerator and denominator by the same
number then it means the fraction is already in simplest form
and you cannot use this method.

Example: Find an equivalent fraction for
4/12.
÷ 3
4
1
12
3
÷ 3
Guided Practice
1. Does 5/6 = 7/8? Draw a picture to solve.
2. Does 1/3 = 2/6? Draw a picture to solve.
3. Use multiplication to find an equivalent
fraction for 7/8.
4. Use division to find an equivalent fraction
for 4/8.
5. Sally was following a recipe to make
cookies. She needed to put in ¼ cup of oil.
Instead she put in 3/12 cup. Did she follow
the recipe correctly?
Independent Practice

Left Side Idea #1:
Create a three pocket foldable using 8x11” paper.
On the front write “Equivalent Fractions” and on
the inside label each pocket with picture,
multiplication, & division. You will need 2 index
cards for each pocket or 6 total. On each index
card solve the following equivalent fraction
problems:
Pictures
Multiplication
Division
1. Does 5/6 =
6/8?
3. Write an
equivalent fraction
for 4/5.
5. Write an
equivalent fraction
for 6/8.
2. Does 1/3 =
2/6?
4. Write an
equivalent fraction
for 3/8.
6. Write an
equivalent fraction
for 3/6.
Independent Practice


Left Side Ideas #3 & #4
Write a summary paragraph (5-7
sentences) explaining how to find
equivalent fractions using all the methods
you learned today. When you are finished
provide 1 example for each method.
Come up with 3 instances in the real
world of when you would use equivalent
fractions. Create a word problem for
each and solve.
Exit Ticket
1. Does 4/6 = 3/4? Solve & explain.
2. Does 3/6 = 4/8? Solve & explain.
3. Write 2 equivalent fractions for ¾.
4. Use division to write an equivalent fraction
for 4/8.
Comparing & Ordering Fractions (same denominators & different denomintors using only halves, thirds, fourths, sixths, eighths)
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials: Power point, notes, pattern blocks.
SFO:
- I can compare and order fractions with the same, and different, denominators (halves, fourths, eighths, thirds, sixths) using pattern blocks,
drawings, and a number line.
Teacher Input:
1. Pass out pattern blocks and blank paper.
2. Ask the students to determine if ⅔ or ⅚ is bigger using the pattern blocks.
3. Have students show their solutions.
4. Explain that a triangle is ⅙, and that two triangles (2/6) makes a rhombus (⅓). So four triangles (4/6) makes two rhombi (⅔). Thus, ⅚ > ⅔.
5. (Also on ppt) Model how this could be solved by drawing two rectangles. Draw a rectangle and split it into thirds. Shade ⅔ of this
rectangle. Then, draw another congruent rectangle directly under the first rectangle. Split this rectangle into sixths (make sure the thirds from
rectangle 1 lines up with the 2/6ths from rectangle 2). Shade 4/6 of this rectangle.
6. Ask the students to determine if ¾ or ⅝ is bigger. They may draw a rectangles to figure it out.
7. Have students show their solutions.
8. (Also on ppt) Model drawing a rectangle and splitting it into fourths. Shade ¾ of this rectangle. Then, draw another congruent rectangle
directly under the first rectangle. Split this rectangle into eighths (make sure the fourths from rectangle 1 line up with the 2/8ths from rectangle
2). Shade ⅝ of this rectangle.
9. Have students draw a number line and label 0 to the far left and 1 to the far right.
10. Explain to students that a number line can be split into parts just like a rectangle. Model splitting a number line in half, fourths, and then
eighths (it might help to draw a rectangle over the number line afterwards, with 0 being one side of the rectangle, and 1 being the other… just so
the students can see how it relates).
11. Ask the students to identify where ¾ and ⅝ would be labeled on the number line.
12. Have the students split another number line into thirds and sixths, then have them label ⅔ and 4/6 on the number line.
13. Show students how they can multiply both the numerator and denominator by a number to find common denominators to make comparing
fractions easier.
14. Work through the guided practice and have students fill in their notes.
Indendent:
- Display the independent work ppt slide. Have students construct two number lines on the left side of their interactive notebooks.
- Have them order the following fractions on one line: ⅓, 4/6, 3/3, ⅚, ⅔, ⅙
- Have them order the following fractions on the other line: ½, ¼, 6/8, ⅜., ¾, 2/2, 2/4, ⅞, ⅜.
- Bonus, have the students try to place these fractions on either number line: 15/16, 7/9.
Assessment: Left side.
Comparing and
Ordering Fractions
Objectives:
-I can compare and order fractions with
the same, and different, denominators
using pattern blocks, drawings, and a
number line.
Review
1.
CMS Daily Review
1.
Is 2/4 = 5/10? How do you know?
2.
Name a fraction that is equivalent
to 6/8.
Which is bigger?
Let’s use pattern blocks (hint: pass them out) to
determine if 2/3 or 5/6 is bigger.
You have a minute to figure this out. Here are some
questions to consider:
What pattern block is 1/3 of a hexagon cookie?
Since the fraction is 2/3, what does that mean?
What pattern block is 5/6 of a hexagon cookie?
Since the fraction is 5/6, what does that mean?
Which one is bigger?
Which is Bigger Explanation
So, how did you figure it out?
Here is what I did:
= 1/3
= 1/6
I know that two triangles (2/6) equals 1 rhombus (1/3). Which makes
sense because I know how to create equivalent fractions using
multiplication. So if 2/6 = 1/3, then 4/6 = 2/3. Well, I know that 5/6
is bigger than 4/6, so 5/6 must be bigger than 2/3. Or, another way
to say it would be 2/3 is less than 5/6.
Remember how to notate a comparison of numbers?
2/3 < 5/6
Using Boxes to Compare Fractions
We did something similar to this yesterday.
 In the first box I am going to split my box into
thirds, then shade in two parts. In the second
box, I’m going to split it into sixths, then
shade in five parts.

It is easy to see that 2/3 < 5/6 using the box
method.
Which is bigger?
Use the box method to figure out if ¾ or 5/8 is bigger.
You have a minute to figure this out. Here are some
things to consider:
Did I split the boxes into even parts?
Do some of the lines from both boxes match up?
Should they?
Which is Bigger Explanation
So, how did you figure it out?
Here is what I did:
I split the first box into fourths, then shaded 3 parts.
I split the second box into eighths, then shaded 5
parts.
It was very obvious that ¾ is greater than 5/8.
Can you notate that comparison?
Using a Number Line to Compare
Fractions
We are able to use a number line too!
 Here is my number line. You will notice I have 0
and 1 on the number line.
0
1

If I were to split this line in half, that point would
be what fraction? Let’s write that in.

If I were to split the line in fourths, what would I
need to label each point? Let’s write that in.
What about eighths?

Using a Number Line to Compare
Fractions

Now that we have our number line ready, let’s plot
¾ and 6/8.
0
1/8
¼
2/8
3/8
½
2/4
5/8
¾
7/8
6/8
4/8

Based on this number line, is ¾ or 5/8 bigger?
1
Using a Number Line to Compare
Fractions

Can we split this number line into thirds and
sixths?
0
1

Which is bigger, 2/3 or 4/6?

Why do you think halves, fourths, and eights work
really well together?

Why do you think thirds and sixths work well
together?
Enrichment: Skip If You Want

As we discussed, halves, fourths, and eighths work
well together. Thirds and sixths work well
together too.

But sometimes, we come across fractions that are
difficult to compare using pattern blocks, boxes,
or number lines. There is a method that we can
use though!

It would be extremely hard to figure out if 2/3 or
5/7 is bigger. It wouldn’t be nearly as hard if the
denominators were the same… in fact, if the
denominators were the same, all we would have to
do is compare the numerator. That’s kindergarten
stuff!
Enrichment: Skip If You Want

It just so happens that we can make 2/3 and 5/7
have the same denominator, or, common
denominators. Here’s how:

All you need to do is multiply the numerator and
denominator of 2/3 by 7, and the numerator and
denominator of 5/7 by 3.
2 x 7 = 14
3 x 7 = 21


<
15 = 3 x 5
21 = 3 x 7
Did you notice what we used to multiply the numerator and
denominator?
Can you believe it was that easy to get a common
denominator?
Independent Practice

Left Side (number line highly
recommended)
Using any strategy, order the following
fractions from least to greatest: 1/3,
4/6, 3/3, 5/6, 2/3, 1/6.

Using any strategy, order the following
fractions from least to greatest: ½, ¼,
6/8, 3/8, ¾, 7/8, 3/8.

Bonus: Can you place 15/16 in any of
these lists?
Fractions of a Set (more challenging problems such as 2/4 of a number instead of ¼)
CCSS:
3.NFA.1, 3.NFA.2, 3.NFA.3
Materials: worksheet.
SFO:
- I can determine fractions of a set with numerators that are greater than 1.
Teacher Input:
- Review finding fractions of set using the ppt.
- Explain that companies buy things in bulk. It would be silly for them to buy 346 single items. Instead, they buy a case or crate of those
items. When a shipment comes to their factory, they split the case or crate into parts and send those parts to different areas of the factory that
need them. They use language such as, “⅓ of the crate goes to the robotics department,” or, “⅚ of the case goes to storage.”
- (PPT) Model this method by drawing a rectangle. Explain that the rectangle represents a case or crate. Let’s say the crate holds 24 steel
bolts, and we need to send ⅓ of those bolts to storage. Draw a rectangle to represent the crate, and split the rectangle into thirds. Then, count
out 24 steel bolts evenly into each part of the crate.
- Have students answer how many bolts are in ⅓ of a crate.
- Ask students to explain how many bolts would be in ⅔ of a crate.
- (Guided Practice) Have the class solve the problem 6/8 of 72. Record each step.
Independent:
Have students complete the worksheet.
Assessment:
Worksheet
Fractions of a Set
Objectives:
-I can determine fractions of a set with
numerators that are greater than 1.
Review
1.
CMS Daily Review
1.
Compare these fractions 1/3 and
3/6?
2.
Compare these fractions ½ and 4/8.
Why Figure Out Fractions of a
Set of Objects?
When we group items together, sometimes it is easier
to talk about those items as one whole set (as long as
we know how many items are in that set!).
Doesn’t it make more sense to talk about 1 whole
create of apples, than to talk about the 346,436,853
individual apples that are packed in the crate?
Since we like to group items into a set to make it
easier on ourselves, we can use fractions to talk about
parts of that whole group.
Fractions of a Set (Box
Strategy)
So, how would we answer someone who asks, “What is 1/3 of 27
apples?”
Well, drawing a picture may help us…
Here is a box, and this box represents the crate holding the apples.
First, we want to split this box into thirds. Let’s do this now.
Now, in order to figure out how many apples go into 1/3, we need to
place an apple in each part of the crate until we reach 27. Now, look
at just one part of that crate. Since that one part is 1/3, we know
what 1/3 of 27 is.
Fractions of a Set (Box
Strategy)
Let’s try this again, but with a larger numerator. What is ¾ of 32?
First, draw your box. How many parts are we going to split the box
into this time?
Now, let’s draw an item in each box until we reach 32. How many items
are in each section of the box? Is that what the question is really
asking me?
Yes, the question is really asking how many items are in 3 sections of
the box! So, what is ¾ of 32?
Enrichment: Another Way
Well, some of you may have noticed a pattern…
1/3 of 27 is 9
¾ of 32 is 24
2/3 of 18 is 12
May you can use this short cut. When we want to find
a fraction of a set, we can just use division and
multiplication.
First, you want to divide the set by the denominator.
E.G. 2/3 of 18
18
3 = ____
Then, you want to multiply that by the numerator.
6 x 2 = ____
More Examples
What is 6/8 of 72?
____
____ = ____
____ x ____ = ____
Answer: ______
Independent Practice
Left Side
 Create a three-tab foldable. On the
front, write the following problems on
each tab:
5/6 of 24
3/8 of 40
¾ of 36

On the inside left, use any strategy to
solve the problem. On the inside right,
write the answer.
Fractions on a Number Line Lesson 1
CCSS:
3.NF.2.a
3.NF.2.b
SFO:
I can label fractions on a number line.
Teacher Input:
See PPT
*I can use my knowledge of fractions of an area to
place fractions on a number line.
Day 19
After lunch the friends notice a sale. Compare the crossed out prices to the new
sale prices. If all sale prices are calculated in the same way, what would the sale
price be on an item that originally cost $24? Use words and equations to explain
how you know.
$12
$21
$27
$3
$4
$7
$9
$1
Learn to plot fractions on a number line.
For the first two, use Firefox. All three show the same content.
 http://learnzillion.com/lessons/74-place-fractions-on-
a-number-line-1
 http://learnzillion.com/lessons/1729-identify-afraction-as-a-point-on-a-number-line-using-areamodels
 https://www.khanacademy.org/math/cc-third-grademath/cc-3rd-fractions-topic/cc-3rd-fractionsmeaning/v/fractions-on-a-number-line
0
1
Today we are going to use a number line to think about fractions between
0 and 1. What if I wanted to mark the spot for halfway between 0 and 1?
Where should I draw the line?
0
½
1
We now have divided the number line into two pieces. What fraction of
the whole number line is each piece?
If an ant is traveling on the line, starting from 0 and going to 1, how
many halves has the ant traveled when it starts at 0?
One student says the ant hasn’t traveled at all, so the ant has traveled
0 halves.
How many halves has the ant traveled when it gets to the mark we
drew between 0 and 1? How many halves has the ant traveled when it
gets to 1?
Here are two number lines. Mark 0/2, ½, and
2/2 just like we did before, on the first one.
Then divide the second number line into four
equal parts, or fourths.
0
0
½
¼
½
1
¾
1
To divide the number line into four equal parts, there are 3 lines
between 0 and 1. Why aren’t there 4 lines?
We have divided the number line into four equal parts. What
fraction is each of the pieces?
Work with a partner to label how many fourths the ant has traveled
when it arrives at each line. Then divide the last number line into
eighths and label them.
0
½
0
0
¼
1/8
¼
1
½
3/8
½
¾
5/8
¾
1
7/8
1
If the ant travels half the distance from 0 to 1 on the number line divided
into fourths, how many fourths has it traveled? What if the ant traveled
half the distance on the number line divided into eighths? How many
eighths has it traveled?
When we place fractions on a number line, we need to remember that
fractions are parts of a whole.
Fractions are more than zero, but less than one.
We need to determine the number of sections so we can identify the
fractions.
Count the number of sections between the lines on the number line below.
How many sections are there? 5
Each line is 1 part, or 1 section. See if you can name the fraction for each
line. Work with a neighbor.
0
1/5
2/5
3/5
4/5
1 or
5/5
Count the sections and then label the fractions below:
0
0
1/6
¼
2/6
2/4
3/6
3/4
4/6
5/6
1
6/6
CMS Number Line Fractions - Lesson 2
Materials: (See 3rd grade number line unit 2013 is google docs)
- Cuisenaire Rods
Number Line Handout
Standards:
3.NF.2.a
3.NF.2.b
SFO:
Before:
Give each group a set of Cuisenaire Rods and give each student a blank 12cm number line. 12 cm should also be the distance of a red rod and an orange rod when they are joined.
Labeling one-half on the number line
Can you find the rod in which two of them would cover the entire number line? (dark green). If two of these rods are needed to cover the distance between 0 and 1, what fraction should we write at the end of the
first rod? (one half).
Labeling one-fourth on the number line
Can you find the rod in which four of them would cover the entire number line?
What fraction would we write here (point to end of first rod) How do you know?
Based on our number lines what is the relationship between fourths and halves?
Ask students to leave line c blank for now and continue labeling lines d and e in the same manner above.
When students are finished ask, “What do you notice about the thirds and sixths? If I only had thirds, could I mark sixths? If I only had sixths, could I mark fourths?
Tell students to think about the relationship between halves and fourths, and thirds and sixths, to mark line c with eighths.
Pose several of the following questions in a “think, pair, share” format
• What number is halfway between zero and one? (it’s important to refer to fractions as numbers since many students believe that fractions are not really numbers).
• What number is halfway between zero and one-half?
During:
Tell students you have created some question cards. Put a card at each station and have students move around the room with a partner/small group and respond.
Make sure to watch students as they work so that you can lead the discussion at the end of the lesson. Look for patterns in student thinking, or errors/misconceptions.
Questions to ask as students are working:
What is the question asking you to do?
How can you use the rods to help you with this task?
How do you know that you are correct?
Things to observe:
What process do students use while solving the tasks?
How do they explain or communicate about their use of the rods?
After:
Gather students back together to discuss a few of the station questions. Ask several students to show their representations. Have students turn and talk to their partner as well as share with the whole class.
Evaluation:
During the lesson, make sure to observe and listen to students as they reason about each of the tasks that they work on.
All of the student work can be used to examine students’ mathematical reasoning.
Fractions on a Number Line
Lesson 2
Objective:
• I can label fractions on a
number line using Cuisenaire rods.
Video (Optional)
• Learn Zillion Fractions on a Number Line Video
• Can you find the rod in which two of
them would cover the entire number
line? If two of these rods are needed to
cover the distance between 0 and 1,
what fraction should we write at the
end of the first rod?
• Can you find the rod in which four of them
would cover the entire number line?
• What fraction would we write here (point to
end of first rod) How do you know? What
fraction should we write at the end of each
rod?
• Based on our number lines what is the
relationship between fourths and halves?
• Can you find the rod in which eight of
them would cover the entire number
line? What fraction would we write at
the end of each rod?
• Can you find the rod in which three of
them would cover the entire number
line? What fraction would we write at
the end of each rod?
• Can you find the rod in which six of
them would cover the entire number
line? What fraction would we write at
the end of each rod?
• What do you notice about the thirds
and sixths? If I only had thirds, could
I mark sixths? If I only had sixths,
could I mark fourths?
• What is the relationship between thirds
and sixths.
Think – Pair - Share
• What number is halfway between zero and
one?
• What number is halfway between zero and
one-half?
• Is 99/100 greater or less than 1?
• Is 2 1/3 greater or less than 1?
Activity
• With a partner you will answer these questions that I
have on your notes. I will give you 10 minutes to complete.
I will then write these questions on white 8x11” paper and
put them around the room. You and your partner will have
5-10 minutes to go around the room and write your
answers to the questions. Whether you have the same
answer or a different answer than what is already on the
sheet, write it down anyway!
What other numbers are the same as one-half?__________
What number is one-fourth more than one-half? __________
What number is one-sixth less than one? __________
What number is one-third less than one? __________
What number is halfway between zero and one? __________
Which number is closest to zero? __________
Which number is closest to one? __________
What would you call a number halfway between zero and one
twelfth? _____
Left Side
• Draw 3 blank number lines in your
notebook. Plot these 3 fractions and
after you plot it write 2-3 sentences
explaining how you knew where to plot it
on the number line.
1. 1/8
2.
4/6
3.
2/3
CMS Number Line Fractions - Lesson 3
Materials: (In CMS Number Line Unit)
- Two-Unit Number Line
Standards:
3.NF.2.a
3.NF.2.b
SFO:
I can represent fractions on a number line that extends from 0 to 2.
Before:
Show students a number line from 0-2. Only the whole numbers should be marked. Ask, what are some numbers between 1 and 2? Note: The purpose of this question is just to get them thinking.
You do not need to get correct answers at this time.
During:
Hand out to each student a copy of a number line identical to the one used earlier.
Yesterday, we determined which rod was ½ of our number line. Which rod was that?
How many of those will we need to cover this number line? Why?
Generate a discussion around counting by ½. If we counted around the room what are some numbers that we would say? As students respond they should say one-half, two-halves, three-halves.
Pause there.
Ask students, can we have three-halves? Turn and talk with your partner and decide if three-halves is possible. What does three-halves look like?
Have some students share what they think about three-halves. Ask students so show what they are thinking by drawing both a picture (area model of a rectangle or circle) and a number line.
Ask, On this number line (two-unit number line) where would we put all of the numbers that we say when we count by one-half?
Note: At this point, it’s ok if students don’t identify numbers between 1 and 2 as mixed number. This lesson is to give them additional practice counting starting with a unit fraction. The idea that 3/2
= 1 ½ will come up later in this unit.
Have students mark halves, fourths, and eighths on the same number line. If time allows give them another number line and have them mark the thirds and sixths on their two-unit number lines.
Then have students work through the 8 stations and respond to each question (similar to Lesson 2 in this unit).
After:
Bring students back together. Ask students, What other numbers did you find that were equal to one?” Allow some student to respond, then say, On a post-it, draw a representation for one of these
fractions.
As students finish their drawings, have them put them on the board. What do you notice? How can all of these be equal to 1?
Explain to students when we find numbers that have the same value, we call them equal. When we find fractions that have the same value, we call them equivalent. Is this equation true? Are all of
these equivalents? 12/12 = 2/2 = 1
After turning and talking with their partner, have students generate an exit ticket that shows 3 equivalent fractions. Make sure students draw a representation and an equation.
Evaluation:
During the lesson, make sure to observe and listen to students as they reason about each of the tasks that they work on.
All of the student work can be used to examine students’ mathematical reasoning.
CMS Number Line
Fractions – Lesson 3
Objective: I can represent fractions on a number
line that extends from 0 to 2.
Review
1. CMS Daily Review
2. Justin ate 2/3 of a pizza. Darren ate 5/6 of a pizza. Who
ate more? Represent this using an expression.
3. Enrichment: Jaime ate 9/13 of 39 Oreos. How many
Oreos did Jaime eat?
 Video
What Do You Know?
What are some numbers between 1 and 2?
0
1
2
Yesterday, we determined which rod was ½
of our number line. Which rod was that?
How many of those will we need to cover
this number line? Why?
What Do You Know?
What are some numbers between 3 and 4?
2
3
4
Yesterday, we determined which rod was ½
of our number line. Which rod was that?
How many of those will we need to cover
this number line? Why?
Counting by Halves on
the Number Line
-
First, let’s count around the room by ½.
-
Wait, is it possible to have 3/2? What does it look
like?
-
Let’s plot ½, 2/2, 3/2, and 4/2 on this number
line.
0
1
- Now, let’s plot fourths and eighths.
2
Partner Work
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
Answer the following the questions
1. What other numbers are equal to one and one half?
_____ _____
2. What number is one-fourth more than four? _____
3. What number is one-sixth less than two? _____
4. What number is one-third more than five? _____
5. What number is halfway between two and one-half,
and three? ___
6. What numbers are the same as one-half? _____
7. What number is one-half more than three? _____
8. What number is one-sixth more than two? _____
50
55
60
Discussion

What other number did you find that were
equal to one? Draw a representation for
one of these fractions on a post-it. Put
your post-it on the board.

What do you notice? How can all of these
be equal to 1?

Is this equation true? Why or why not?
12/12 = 2/2 = 1
50
55
60
Left Side

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Directions: Create a 4 tab foldable. On the
outside of the foldable write the fractions below
and draw a picture that represents each. On the
inside left draw a number line and plot it. On the
inside right, create a word problem with that
fraction in it.
 ¾
1½
6/8
2¾
Example: 2 ¾
0
1
2
3
Jack and his family ate
pizza for dinner. Jack ate 2
¾ slices. His sister Sara ate
1 ½ slices. How much did
they each altogether?
CMS Number Line Fractions - Lesson 4
Materials:
- Pre-cut 4-inch lengths of dry spaghetti or yarn.
- Worksheet in doc.
Standards:
3.NF.3.a
3.NF.3.b
SFO:
I can partition a number line accurately.
Before:
Igor Vovkovinskiy has the longest foot in the world, but doesn’t have shoes that fit! Watch the video clip to see what Reebok is doing to help.
Watch the following video clip about the shoe-size of the tallest man in the world: http://www.telegraph.co.uk/news/newsvideo/weirdnewsvideo/9246505/Americas-tallest-mangets-measured-for-size-21-trainers.html
http://www.telegraph.co.uk/news/newsvideo/weirdnewsvideo/9246505/Americas-tallest-man-gets-measured-for-size-21-trainers.html
Hold up a length of spaghetti. Say, “This piece of spaghetti represents ¼ of Igor Vovkovinskiy’s shoe. With a partner, I would like you to show me how long Igor’s entire shoe
is. Avoid telling students how to re-create his shoe size. Instead, provide lengths of spaghetti, paper, and tape. Allow students time to work out a solution. Not all students will
want to use 4 pieces of spaghetti; some may just use one piece, draw it and repeat. Using different colored pieces of spaghetti will allow students to see the parts clearly.
As students work, circulate to see how they are solving the task. Do they understand that they need 4 pieces? For students who are struggling, you may want to ask, “If this
piece of spaghetti represents half of your shoe, how could we find the length of your entire shoe?” Look for a few examples to use during the discussion.
Discussion:
After students have worked, gather them for a discussion. Tape an example of Igor’s shoe
on the board that looks like this:
1/4
2/4
3/4
4/4
Ask students, what do you think about this example? Is there anything wrong with it?
Ask a few students to share how they might fix this example. See note For students who are having trouble seeing that the fraction names a specific point on a line, you might say, “When Igor puts his foot ¼ of the way down, where would his foot
land?”
After: Ask students to complete the handout : Draw the Finish Line
Evaluation:
During the lesson, make sure to observe and listen to students as they reason about how to create the whole when given a unit.
CMS Number Line
Fractions – Lesson 4
Objective: I can represent fractions on a number
line that extends from 0 to 2.
Review
1. CMS Daily Review
2. What number is one-sixth more than one?
3. What number is one-eighth less than one?
4. What number is three-fourths less than two?
Feet Too Big for Shoes
Igor Vovkovinsky has the longest foot in the
world, but doesn’t have shoes that fit! Let’s
watch this video to see what Reebok is doing
to help:
www.telegraph.co.uk/news/newsvideo/weirdne
wsvideo/9246505/Americas-tallest-man-getsmeasured-for-size-21-trainers.html
- This pre-cut piece of yarn represents ¼ of
Igor’s shoe. Use yarn, rulers, paper, anything
to re-create his show size.
Discussion
-
I’m going to borrow one of your examples
and tape it to the board. (Try to use one
that could be more accurate)
-
What do you think about this example?
Is there anything wrong with it?
How might you fix this example?
Independent
-
Complete the worksheet.
CMS Number Line Fractions - Lesson 5 (two-day workshop)
Materials:
-Make a giant “dinosaur fossil” out of bulletin board paper (it would be great if it could be laminated, or reinforced somehow. It has be jumped on by several
people. Use tape to outline it on the floor.)
-Notes
-Center directions
-Center notes for students to record work
(Read lessons 5 and 6 prior to lesson in CMS Number line unit.)
Standards:
SFO:
*I can place a fraction on a number line.
*I can identify what the fraction represents.
*I can compare fractions and find equivalent fractions on a number line.
*I can measure with a ruler marked with fourths and halves.
Before:
CMS review
Review vocabulary
Do the warm up.
During: go over the directions for the dinosaur fossil center.
-Demonstrate jumping less than half way across the print.
-Ask students to estimate the distance you jumped.
-Repeat by jumping further the second time.
-Ask for an estimate again.
-Go over expectations for each center.
After: As the students are working in the areas, observe and question their thinking.
Homework:
teacher generated
-use the sheet sent, or make your own.
CMS Number Line Fractions - Lesson 6 (two-day workshop)
Continue with the workshop from yesterday.
Gather the students into a group and lead a discussion about their thinking and process.
Discuss the answers and have students explain how they got the answers.
Discuss how to organized the data from jump the dinosaur fossil. (Use a line plot.)
No Homework.
Number Line Workshop
Days 5 and 6
*I can place a fraction on a number line.
*I can identify what the fraction represents.
*I can compare fractions and find equivalent fractions on a
number line.
*I can measure with a ruler marked with fourths and halves.
EOG Review Question

Day 24

Mr. Doyle shares 1 roll of bulletin board paper
equally with 8 teachers. The total length of the
roll is 72 meters. How much bulletin board
paper does each teacher get?
Vocabulary

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

Unit
Distance
Whole
One half
One fourth
Estimate
Between
Warm Up Task

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
Given the part, what is the whole?
Compare your drawing with a neighbor.
Is it identical? Is it similar?
What do you notice?
This is ¼ of the mystery shape. Add on to make
the whole shape.
Warm Up Task




Given the part, what is the whole?
Compare your drawing with a
neighbor.
Is it identical? Is it similar? What
do you notice?
This is ¾ of my mystery
line. Draw my whole
line.
Independent Activities

The following slides give a brief overview of the
stations you will work at today.
Jump the length of a Dinosaur Fossil




You will watch the teacher do a trial jump.
“How far do you think the teacher jumped?”
Watch the teacher jump again.
“How far has the teacher jumped?”
Ant Races



Some ants are having a race. Determine which
ant is the winner for each race.
Place and record where each ant has traveled.
Show the position on the line.
Who walked the furthest? Write a number
sentence using <, >, or = to compare.
Who walked the furthest?




The entire length of your sentence strip
represents a 4-mile race.
Draw a line and label where mile 1 would be.
Do the same for miles 2 – 4.
Draw and label all of the halves on your number
line.
Place each person where he/she stopped
walking. Answer the questions.
End of day 6



How could we use a number line to organize the
data for jumping a dinosaur fossil?
What would we have to do first?
Once the data is organized, create a line plot.
Lesson #7: Making and using a Ruler
Standard:
3.MD.4.
3.NF.2
SFO:
I can make a ruler and measure objects using my knowledge of fractions.
EQ:
How does a ruler make use of fractions?
Before:
Give students “inch bricks” Say, “yesterday, we measured how far we could jump using a dinosaur fossil. Today, we are going to measure items using this
‘inch brick”. Tell students to find some things that are about ½ inch long/tall (eraser, cap of marker, fingernail) etc. They may want to mark the ½ inch point
using a blue or black pen before they begin.
Next, ask students to mark ¼ inch on their brick in red pen. Ask, how do you know that’s ¼? Are there any other fourths? Have students mark remaining
fourths.
During:
Explain to students that although we often measure things to the nearest half or quarter inch, we don’t often find things to measure that are less than an
inch. How can that be? Allow students time to discuss (students should realize that fourths are not only found between 0 and 1).
Tell students they are going to make a ruler with a partner using inch bricks. Ask, who knows how many inches are in a foot? How many inch bricks will we
need?
Allow partners time to make their rulers. They will want to mark the half and quarter inches (it will be easier for students to see if they use a blue/black pen for
halves and red for fourths).
Have students begin measuring things around the room to the nearest half and quarter inch.
After:
Hand out a traditional ruler and give partners time to compare the ruler they made with a standard ruler.
Ask “What do you notice?” (students may notice that the rulers they made are not exactly the same length)
Ask “What do the shortest marks between whole numbers mean on the standard ruler? What do the longest marks mean?”
Ask partners to measure a few small items in their desk with their ruler, and then with the standard ruler.
Ask, “which ruler is easier to use? Why? Which is more accurate?”
CMS Lesson # 7
Making and Using a Ruler
Objectives:
- I can measure objects to the nearest
half and quarter inch.
Review
• Compare the following fractions using <, >, =:
2/3
3/4
• What is 2/3 of 21?
• Pass out “inch bricks” (inch graph paper) to
students.
• Last lesson, we measured how far we could
jump using a dinosaur fossil. Today, we are
going to measure items using this ‘inch brick”.
Tell students to find some things that are
about ½ inch long/tall etc. Mark the ½ inch
point using a blue or black pen.
• Next, mark ¼ inch on your brick in red pen.
How do you know that’s ¼? Are there any
other fourths? Have students mark remaining
fourths.
• Although we often measure things to the nearest half or
quarter inch, we don’t often find things to measure that are
less than an inch. How can that be? Allow students time to
discuss.
• You are going to make a ruler with a partner using inch
bricks. Who knows how many inches are in a foot? How
many inch bricks will we need?
• Allow partners time to make their rulers. You will need to
mark the half and quarter inches (it will be easier for
students to see if they use a blue/black pen for halves and
red for fourths).
• You will measure items around the room. See next slide for
your recording sheet.
• Hand out a traditional ruler and give partners
time to compare the ruler they made with a
standard ruler.
• What do you notice?
• What do the shortest marks between whole
numbers mean on the standard ruler? What
do the longest marks mean?
• Measure a few small items in your desk with
your ruler, and then with the standard ruler.
• Which ruler is easier to use? Why? Which is
more accurate?
Lesson #8: Measuring Bugs (this lesson may take 2 days)
Standard:
3.MD.4.
SFO:
I can measure objects using my knowledge of fractions.
EQ:
Why is it important to understand fractions when measuring things?
Before:
On a Smartboard or overhead (you can print the page and put on a transparency) show the following http://www.studyzone.org/testprep/math4/d/inch4l.cfm
Choose a few things to measure as a class ask the students to determine the length to the nearest half or fourth of an inch. Ask questions like, “Should we
measure this item to the nearest half or quarter inch? Where does the end of this object fall?”
During:
Explain to students they will be measuring the length of the bugs to the nearest half and fourth of an inch. They will then create a line plot of their data.
(For the teacher; the bugs measure..
¼ inch: red ant, housefly
½ inch; honey bee, lady bug
¾ inch; mosquito, field grasshopper, three-lined hoverfly
1 ¼ inches; mayfly
1 ½ inches; praying mantis, dragonfly, katydid
2 ½ inches; daddy long leg
3 ½ inches; yellow cellar slug
4 ½ inches; goliath beetle
After:
Show students how to make a line plot. Ask them to plot the bug data with their partner. Once finished, ask questions such as, “How many bugs measured ¾
of an inch? How many bugs were longer than 1 ½ inches?” Questions should not require students to add or subtract fractions.
CMS Fraction Unit Lesson #8
Measuring Bugs & Creating a Line Plot
Objectives:
-I can measure objects to the nearest quarter and half inch.
- I can create a line plot to represent data using fractions.
Measuring Review
• http://www.studyzone.org/testprep/math4/d
/inch4l.cfm
• http://www.funbrain.com/measure/ - Choose
medium inches
Measuring Bugs
• You will be measuring the length of the bugs to the nearest half and
fourth of an inch. You will decide whether you should measure to the
nearest half or fourth an inch based on which the bug is closest to.
You will rotate around the room to different bugs. After you measure
record your findings on your recording sheet. This will go on the right
side of your notebook.
Name of Bug
Length to the nearest ½ or ¼ inch
Left Side:
• You will create a line plot using the data you
have collected.
• Include a title for your graph
• Draw a line plot
• Create 3 questions to go with your line plot
and answer them.
Example: How many bugs were longer than 3 ½
inches?
Left Side: Create a Line Plot with Your Data
What is a line plot?
• A line plot is a graph that
shows frequency of data
along a number line. It is
best to use a line plot
when comparing fewer
than 25 numbers. It is a
quick, simple way to
organize data.ine plot?
Reading a Line Plot
Complete the Line Plot
Check your answers…
The bugs measure…
• ¼ inch: red ant, housefly
• ½ inch: honey bee, lady bug
• ¾ inch: mosquito, field grasshopper, three-lined
hoverfly
• 1 ¼ inches: mayfly
• 1 ½ inches: praying mantis, dragonfly, katydid
• 2 ½ inches: daddy long leg
• 3 ½ inches: yellow cellar slug
• 4 ½ inches: goliath beetle
Exit Ticket
Directions: Measure each bug to the nearest half or quarter inch.