MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Third Grade CurriculumFractions
Section 4 of 4Partitioning Wholes Amongst 2 or More Recipients
Suggested Number of Days: 3 Days
The suggested number of days includes instruction, practice, and mixed review time. Please review materials in advance to allocate days based on the resources provided.
Topic PageDay 1
Day 2
Day 3Class small
group rotation with Part III, Part
IV and Mini
Part I: Partitioning with Real World ExperiencesThe Quesadilla Question (Part 1)The Quesadilla Question (Part 2)Part II: Partitioning using PicturesExperience 1: Partitioning with Fractional PartsExperience 2: Partitioning with Wholes and FractionsExperience 3: Partitioning with Wholes and FractionsExperience 1: IMN Strips (5/page)Experience 1:Partitioning Pictures (4/page)Experience 2: IMN Strips (7/page)Experience 2:Partitioning Pictures (5/page)Experience 3: IMN Strips (7/page)Experience 3:Partitioning Pictures (4/page)Additional Practice ProblemsPart III: Partitioning with PicturesPart IV: Partitioning with Pattern Blocks
337991214192021222324
25-272829
NOTE: **Target Questions** are included for use in conjunction with the Teacher Notes. In the Practice Problems, some are marked with an “*”. It is suggested that you include these problems in your unit. There is also a model window pane problem on some target problems to use as a Guided Practice. Additional problems are also included as needed.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20151
Additional Resources:
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING WITH PICTURES 2014_RES.docx
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
FractionsPartitioning wholes between 2 or more recipients
TEKS: 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictoral representations of fractions with denominators of 2, 3, 4, 6, and 8; (Supporting)
3.3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictoral models, including number lines; (Readiness)
3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number (Supporting)
VOCABULARY: fraction, numerator, denominator, unit, unit fraction, partition, fair share, equivalent
Teacher Background: Partitioning is foundational for students to understand fractions, but understanding partitioning does not lead students simultaneously to a complete understanding of fractions. Partitioning a whole, or unit, into unit fractions, one piece (1/b) of an object separated into b pieces, allows these equal parts to be then shared among groups of 2 or more recipients as stated in the TEKS.
Student Background: Partitioning an object or set of objects is a real life experience most students have familiarity with, like partitioning a cookie in half so two people each get a fair share.
Materials: flour tortillas (paper circles can be used as a substitution), scissors, glue, manila or construction paper
Note to Teachers: Some pieces of the following experiences need to be cut by students, but you may choose to have the pictures pre-cut to facilitate timeliness of the lesson.
Part I: Partitioning with Real World Experiences
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20152
Additional Resources:
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING WITH PICTURES 2014_RES.docx
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
The Quesadilla Question (Part 1: Unit as one whole)
1. Have discussion with the class to see if they have ever had a quesadilla. Discuss that it is melted cheese, with meat and/or vegetables, inside a tortilla.
2. Have students sit at tables with 4 at each table or in groups of 4. If a group is not equal to 4, have them pretend there are other students in their group to equal 4.
3. Present this story to the students:
Today is National Quesadilla Day, Yeah! We are going to celebrate by sharing some quesadillas.
4. Give each table a sheet of large construction paper or manila paper. Give each table 2 tortillas, discuss that many quesadillas are made with a one tortilla on the top and one tortilla on the bottom with cheese and filling in the middle, but for the sake of this experience each tortilla will represent one whole quesadilla. Have students trace around each tortilla on the construction paper.
5. “How many quesadillas do we have?” (2) “How many people are going to eat these 2 quesadillas?” (4) “How should we share them?” (student responses may vary: cut them, split them, etc.) “We will have to cut, or partition them somehow so that everyone gets a share. But how should we cut the pieces?”(fairly or evenly)
6. “Let’s look at the first quesadilla. How many people are going to eat this quesadilla?” (4) “How many pieces should we partition it into?” (4) “Why?” ( so each of the 4 people gets one piece)“How should we partition the tortilla so that everyone gets a fair or equal piece?” Discuss the difference between cutting the quesadilla in 4 pieces using 3 vertical lines (not fair or equal) verses 1 vertical and 1 horizontal line (fair or equal) as demonstrated in the following picture. Fractions must have equal pieces.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20153
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
7. Have students first fold the tortilla in half then in half again to mark the tortilla into 4 fair shares. Then students can cut the tortilla into 4 pieces using scissors. Have them lay the pieces back on the construction paper circle.
8. “Now share the quesadilla at your table so everyone gets a fair amount, or everyone gets an equal amount of the one quesadilla.” Students share quesadilla. “How many pieces are in the quesadilla?” (4) “How many pieces does each person get of the one quesadilla?” (1) “So we could say that each person got what fraction of this quesadilla?” (one-fourth or 1
4 ) “One-fourth tells us that there are 4 pieces in the whole and you have 1 of those pieces, or 1
4 of the whole quesadilla.” Have each student keep their piece of tortilla.
9. “What about the second quesadilla? What should we do to it?”(Cut it into 4 equal pieces) “Why?” (So each person gets one piece)
10. Fold and cut the second tortilla and return it to the construction paper circle.
11. “Share this quesadilla at your table so everyone gets a fair amount, or everyone gets an equal amount of quesadilla.” Students share quesadilla. “How many pieces were in this quesadilla?” (4) “How many pieces did each person get?” (1) “So we could say that each
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20154
Note: Since most tortillas are not perfect circles, the pieces will be similar but not exact, equal pieces.
Shows fair shares or equal piecesDoes not show
fair shares or equal pieces
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
person got how much of this one quesadilla?” (one-fourth or 1
4 ) “But don’t you already have some
quesadilla?” (Yes) “You already had 14 and now you
have 14 more, so how much do you have now?”( 2
4 )
12. “Now we are going to record what each person at the table has.” Have one student from each table lay their pieces in the circle on the construction paper and trace their pieces next to each other. Label each as 1
4 and shade their 2
pieces one color. Then, have them write “their name has 24 ” ,
in the same color as the shading, next to the circle. The example is shown with a student named Nina.
13. Each student will complete the same process with a different color.
14. “What do you notice about what fraction of a quesadilla each person has?” (They all have the same amount). “Look at the shading. What do you notice about how much each person has shaded?” (Each person has one half of the one quesadilla shaded) “Each person
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20155
14
Ninahas24
14
14
14
14
14
14
14
Todd has24
Inahas24
David has24
14
Ninahas24
14
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
has 24 shaded which is the same as 1
2. Why are they the
same?” (24 covers the same amount as1
2) “What could we
say about 24∧1
2?”(they are equivalent) Demonstrate this if
necessary by cutting one tortilla into two equal pieces and compare the 1
2 and 24 (remember they will be similar but not
exact because tortillas are not exactly the same size). “Let’s record this on our paper.” Each person will record 2
4 is the
same as 12 of one quesadilla under their name.
15. “If 24 is the same as 1
2 then we can say they are equal
or equivalent. Let’s add that to our paper.” Add 24 = 1
2 to paper.
16. “Now let’s go back to think about our quesadillas. Each group got 2 quesadillas to share with 4 people.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20156
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
14
14
14
14
14
14
Todd has24
Inahas24
David has24
14
Ninahas24
14
24 =
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
14
14
14
14
14
14
Todd has24
Inahas24
David has24
14
Ninahas24
14
24 = 2
4 = 24 =
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
What fraction did each person get?”(each person got 24 or
12 of one quesadilla). “If we cut each quesadilla into 4 pieces, each person got 2 pieces or two-fourths of a quesadilla.”
The Quesadilla Question (Part 2: Unit as the set of tortillas)
1. Bring students to the floor. Hold up two tortillas. “Let’s look at things a different way. We still have 2 quesadillas that we need to share with 4 people.” Ask 4 students to come to the front of the room. “But now we need to look at the quesadillas together as a whole unit. I need to share them among 4 people, so how many total pieces do we need?” (4) “We need 4 pieces total, not 4 pieces each. To get a total of 4 pieces, what would we need to do?” (cut each into 2 pieces, 2 and 2 is 4) As a teacher demonstration, cut each tortilla into 2 equal pieces. “How many pieces do we have now?” (4) “If I give one piece to a student [give 1 piece to one of the students in the front of the room], how much of all of all of the quesadillas do they have?” (1 of 4 pieces) “They have 1 of 4 of the pieces or 1
4 of all the quesadillas.” Take back the piece and give one of the other students at the front of the room one piece of the quesadillas and ask what fraction they have of all the quesadillas? Continue with each of the 4 students at the front.
2. “Remember, we are not looking at just one quesadilla, we are looking at the two quesadillas together as a set. Each student has 1
4 of all of the quesadillas. Let’s use our paper at our tables to help represent this.” Have students return to their tables. Give each table white paper to lay over each of their drawings of the tortillas. Have them trace the circles on the white paper and cut them out.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20157
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Use one piece of tape to attach each white circle to the construction paper to create a flap.
3. “If each of you in the group of 4 are going to get some of all the quesadillas, how many total pieces do we need?”(4) “How are we going to cut our quesadillas?”(separate each into 2 equal pieces to get 4 total pieces) Draw a vertical line on each paper tortilla to cut it into halves.
4. “We are going to record how much of all the quesadillas each person at the table has. If you get 1 of 4 pieces, what fraction of all the quesadilla do you get?”(1
4 ) Have one student from each table write 14 of all the
quesadillas inside their piece of all the quesadillas and shade it the same color as they did previously. Continue with each student in the group.
5. “Each person gets 14 of all of the quesadillas. What
makes this example different from quesadillas we shared out previously?” (This time our unit is now two
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20158
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
14
14
14
14
14
14
Todd has24
Inahas24
David has24
14
Ninahas24
14
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
same as12
of one quesadilla
14
14
14
14
14
14
Todd has24
Inahas24
David has24
14
Ninahas24
14
14
of all thequesadilla
14
of all thequesadilla
14
of all thequesadilla
14
of all thequesadilla
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
quesadillas so our portion is 14 of all the quesadillas but before
it was 24∨1
2 of one quesadilla). “When we partition our wholes it makes a difference whether we are looking at partitioning each as a whole or if they all work together to make a whole unit, or whole set.”
Part II: Partitioning with Pictures
Teacher note: pre-cut whole pictures will facilitate the timeliness of the lesson
Experience 1: Partitioning Practice among two or more recipients with fractions
Partitioning pictures (TN Pg. 20) and IMN strips (TN Pg. 19) provided.
Recommendation: Use IMN horizontally to have enough space to draw the groups next to each other
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
1. Have students glue the IMN Strip onto the right side of their IMN.
2. Read Miguel story with class. “What do we know?” (3 sandwiches and 6 people) Pass out pictures of 3 sandwiches. “What could we do to represent Miguel and his 5 friends?” (Draw 6 people). “Or we could draw 6 circles that represent the 6 people to save time.” Draw 6 larger size circles to represent Miguel and his 5 friends. Label each circle: M, F1, F2, F3, F4, F5
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-20159
M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5 M F1 F2 F3 F4 F5
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
3. Have students cut out the three rectangles that the sandwich pictures are in.
4. “How many sandwiches do we have to share out?”(3) “How can we share 3 sandwiches to 6 friends?” (partition them into pieces) “How many pieces total do we need?”(6) “How do we know?” (6 people) “How can we make 6 pieces from 3 sandwiches?”(cut each sandwich in half or into 2 equal pieces) Show students how to fold each sandwich in half, label each half with a marker as being 1
2and cut along the creased line. “How many pieces of sandwich do we have now?”(6) “Do we have enough to share to each person?”(Yes) Have students share out the pieces in their IMN, one to each person and glue them down. “Each piece is how much of a sandwich?”(1
2) “Let’s look at the first question. What fraction of one sandwich did Miguel get?”(1
2) “Why?”(Each sandwich is cut in half, so
each piece represents 12 of one sandwich, and Miguel has one
of those pieces) Fill in answer on line of IMN strip.
5. “Now we need to look at the second question. What fraction of all the sandwiches did Miguel get? How is this question different?” (We are looking at all the
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201510
12
12
12
12
12
12
M F1 F2 F3 F4 F5
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
12 of a
sandwich
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
sandwiches as a set, not just one sandwich) “Let’s look at all the three sandwiches then. How many total pieces do we need?” (6) “How can we break up the sandwiches into 6 parts?”(cut each sandwich into 2 pieces)“If we were to use that number in a fraction, would it be our numerator or denominator?” (Denominator) “Why?” (It is the total number of pieces) “How many pieces does Miguel have?”(1) “Miguel has 1-sixth of the pieces then. How would we write that as a fraction?”(1 in the numerator and 6 in the denominator) “Let’s label Miguel as having 1
6 of all of the
sandwiches.” Label Miguel as having 16 . “How much does
each friend get?” (they each have one-sixth, or 1 of the 6 pieces of all the sandwiches) Label each friend with 1
6 . Fill in answer on line of IMN strip.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201511
12 of a
sandwich
16 1
6 16 1
6 16 1
6 of all thesandwiches
12
12
12
12
12
12
M F1 F2 F3 F4 F5
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 2: Partitioning among 2 or more recipients with wholes and fractions
Partitioning pictures (TN Pg. 22) and IMN strips (TN Pg. 21) provided.
Recommendation: Use IMN horizontally to have enough space to draw the groups and partition the pictures
Teacher note: Pre-cut whole pictures will facilitate the timeliness of the lesson.
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Begin the “Four-Step Problem Solving” process with students.Display the following problem.Suggestion: Complete the “Four-Step Problem Solving” process as an anchor chart for students to refer back to since the students will be focusing on sharing the manipulatives.
Main Idea Details / Known
Details / Known:* Please note the Details/Known is shown in two different ways. These are not the only ways, but students need to be able to show a representation that they can understand and explain.
Strategies:
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201512
Amount of cookies each twin
get
2 people sharing 5 cookiesor
sharing
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
1. “What are we sharing out?”(Cookies) “Into how many groups are we sharing?”(2) “Why?”(2 people, Yiselle and her twin brother, get them) “Let’s draw out those groups.” Draw two circles and label them as Y (Yiselle) and B (Brother). Note: the following pictures would be drawn in the strategies section.
2. “Now what do we need to share to our groups or people?”(Cookies) Pass out pictures of cookies in strips and have students quickly cut them out. “How many cookies do they have to share?”(5) “If we have 5 cookies and 2 people, could we start by sharing out whole cookies first?” (Yes) “Give each twin 1, how many cookies did we use?”(2) “Can we share out another whole cookie?”(Yes) “Give each twin another cookie. How many total cookies have we shared out?”(4) “What do we have left?”(1 cookie) “Could we just give this cookie to Yiselle or her brother?” (No, it would not be fair) “So what do we need to do?” (Cut it) “How many pieces do we need to cut it into?” (2) “Why?” (there are 2 people to share it with). Have students fold cookie in half and cut on the crease. “Each twin will get 1 of the 2 pieces, so what fraction of the last cookie will they receive?” (1
2) Have students label each half with the fraction, 12
and share it into each group.
3. “Are there any more cookies to share out to the twins?”(No) “Let’s look at what each twin got. How many
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201513
Y B
12
12
Y B
Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B Y B
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
cookies did Yiselle get?” (2 whole cookies and 12 of another)
Show students how this is recorded as 212.“How many cookies
did Yiselle’s twin get?”( 2 whole cookies and 12 of another)
Record under picture
How / Justify:
Shared whole cookies to each person Cut cookie in half and shared 1
2 to each person
Experience 3: Partitioning among 2 or more recipients with Wholes and Fractions
Partitioning pictures (TN Pg. 24) and IMN strips (TN Pg. 23) provided.
Recommendation: Use IMN horizontally to have enough space to draw the groups and partition the pictures
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Begin the “Four-Step Problem Solving” process with students.Display the following problem
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201514
12
12
Y B212
212
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Suggestion: complete as an anchor chart for students to refer back to since the students will be focusing on sharing the manipulatives.
Main Idea Details / Known
Details / Known: * Please note the Details/Known is shown in two different ways. These are not the only ways, but students need to be able to show a representation that they can understand and explain.
Strategies: (representations to be drawn in strategies section)
1. “What are we sharing out?”(gum) “Into how many groups are we sharing?”(3) “Why?”(3 people, Amelia, Josline, and Timothy) “Let’s draw out those groups.” Draw three grouping representations (circles). “What should we do to our groups so we don’t get confused?” (Label them)
2. “What are these three people sharing out?”(Gum). Pass out partitioning pictures and have students cut out the sticks of gum quickly. “Before we see if we need to partition anything, what should we check first?”(Can we share out wholes first) “Let’s see if we can share out any wholes first.” Have students share out pictures evenly. “How many wholes did each person get?”(one) “Is there anything left over?”(yes, 2 sticks of gum) “Turn to your neighbor and discuss if you
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201515
Portion sticks of gum each get
3 people sharing 5 sticks of gumor
sharing
A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T A J T
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
have enough to share these two pieces of gum fairly.” “What did you and your partner discuss?”(cannot share 2 wholes with three people).
3. “How can we split 2 pieces of gum with 3 people? What are we going to have to do?” (Student answers will vary) “If we know we have three groups, could we split each whole piece of gum into 3 pieces so everyone gets a part of one whole piece?”(Yes) “Let’s practice together on the first piece of gum.” Have students use a pencil to mark how the wholes would be partitioned. “How many pieces are in one whole piece of gum?”(3) “If someone got one of those pieces, what fraction would they get?” (1
3) “Let’s label
them then.” Have students label each portion as being 13.
“Who could get the first portion?”(Amelia) “Label it A for Amelia. Who could get the second portion?”(Josline). “How can we show that J gets this portion?” (Label it with a J) “And what should we do for the last piece?”(Label it T for Timothy) Discuss that the second whole should be done the
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201516
GUMGUM
GUMGUMGUM
A J T
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
same way. Have students work with their elbow partner to complete the second whole.
4. “Can we now share our wholes into 3 groups now?”(Yes) “Let’s cut our sticks of gum and share them out evenly to the three friends.” Have students glue down pictures after they have shared them to their three groups. “Let’s start by looking at Amelia. What does she have?”(1 whole, 1
3, and 1
3) “We should start with the whole since we shared that out first. Let’s label that one whole under the picture. How about these two fraction pieces, let’s label them under the whole too. Could we put these fraction pieces together to compose a new fraction?”(Yes, 1
3 + 13 = 2
3) Have students record this new composed fraction as well. Demonstrate how to write 12
3 under the picture. Have students complete Josline with their elbow partner and Timothy by themselves.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201517
J TT JA A13
13
13
13
13
13 GUMGUM
GUMGUMGUM
A J T
GUMGUMGUM
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
How / Justify: Shared out the wholes then partitioned each remaining
whole to share out to 3 people Found each person got 12
3 for their portion of the sticks of gum.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201518
13 A
13 A
13 J 1
3 T
13 J 1
3 T
1 whole 13+1
3=23
123
1 whole 13+1
3=23
123
1 whole 13+1
3=23
123
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 1: IMN Strip ( 5 per page)
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
Miguel made 3 sandwiches. He wanted to share them equally with himself and 5 friends.
What fraction of one sandwich did Miguel get? _____
What fraction of all the sandwiches did Miguel get? _____
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201519
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 1: Partitioning Pictures (4 per page)
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201520
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 2: IMN Strip ( 7 per page)
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201521
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Yiselle and her twin brother were splitting a package of cookies. There are 5 cookies in the package and they each want an equal amount. How much of the cookies will each twin get?
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201522
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 2: Partitioning Pictures ( 5 per page)
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201523
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 3: IMN Strip ( 7 per page)
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Amelia bought a pack of gum to share with herself and her two best friends, Josline and Timothy. It contained 5 sticks of gum. What portion of the sticks of gum will each person get?
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201524
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Experience 3: Partitioning Pictures ( 4 per page)
Practice Questions:
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201525
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
GUM
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Teacher Note: The practice questions provided on TN Pg. 26-27 provide additional practice for students to experience partitioning among 2 or more recipients. They are provided as an additional resource. Please assess your students to determine if they need to be used with your students, used as guided practice problems, used as partner practice, used as independent practice, used for small group instruction, etc.
The pictures on the following problems have been placed on the bottom of the page to allow students to cut them off and manipulate the pictures if necessary.
Students will complete the Main Idea, Details/Known, Strategies and How/Justify. The following shows what the strategies for each problem would look like.
Tobias cooked 7 ears of corn. He is sharing them with himself and his 5 family members. What fraction of the corn will each family member get?
Chance needed 2 containers of drink mix to make 6 gallons of punch. What fraction of the drink mix is in each gallon of punch?
Practice Question (Pictures provided at bottom, cut off if necessary)
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201526
11611
611611
611611
6
16
16
16
16
16
1111116
1
1616
1616
1616
1616
16
16
1616
26
26
26
26
26
26
161616161616161616161616161616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
1616161616161616161616161616161616161616161616161616161616
16161616161616161616161616161616161616161616161616161616161
61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616
16161616161616161616161616161616 1
6161616161616161616161616161616
1616161616
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Tobias cooked 7 ears of corn. He is sharing them with himself and his 5 family members. What fraction of the corn will each family member get?
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201527
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Practice Question (Pictures provided at bottom, cut off if necessary)
Chance needed 2 containers of drink mix to make 6 gallons of punch. What fraction of the drink mix is in each gallon of punch?
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201528
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
CoolKid Drink MixPunch Flavor
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
**Teacher note: It is suggested that on day 3 of Partitioning, use Part III, Part IV and the Mini as small group rotations.
Part III: Partitioning among 2 or more recipients Practice
Use file: MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING WITH PICTURES 2014_RES.docx
Use the Partitioning Practice with Pictures worksheet to allow students additional practice in partitioning pictures and labeling fractional parts.
Suggestion: Allow students to work with a partner for practice 1 and 2 and independently on 3 and 4.
Directions:1. Cut out pictures that correspond with Question 1.2. Share out wholes first. 3. Partition any remaining whole(s) into fractions that can be
shared evenly with each group. 4. Label all pictures with whole or fraction name.5. Glue pictures onto groups.6. Complete by filling in the blank in the statement below the
groups with the portion each group gets of the whole amount of objects.
7. Complete the remaining questions.
Example given for Question 1
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201529
14
141
4
14
1 14
1 14
1 14
1 14
1
1 14
1 1 1
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Part V: Partitioning with Pattern Blocks
Use File:MATH_3_A_3 FRACTIONS SECTION 4 OF 4 PARTITIONING WITH PATTERN BLOCKS 2014_RES.docx
Use the Partitioning Practice with Pattern Blocks worksheet to allow students additional practice in partitioning pictures and labeling fractional parts.
Suggestion: allow students to work with a partner for practice 1 and 2 and independently on 3 and 4.
Directions: (Question 1)
1. Have students identify a trapezoid in their pattern blocks. Have them place trapezoids inside the outline of the hexagon to determine how many trapezoids make a hexagon. (2)
2. Use the information to complete the information box to the right of the trapezoid picture.
3. Complete steps 1 and 2 for rhombuses and triangles.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201530
_____ trapezoids fit into a hexagon, so
1 trapezoid = _____ of the hexagon
2
12
MATH_3_A_2 FRACTIONS SECTION 4 OF 4 PARTITIONING 2014_LES.docx
Directions: (Question 2)1. Student uses rhombus Pattern Blocks to build a hexagon on the
hexagon outline2. Share out the rhombuses fairly into each group (represented by
the ovals). 3. Trace the rhombuses in each group once they are fairly shared
and label with the fraction part (1-sixth, because it is 1 rhombus of the 6 total)
4. Complete the missing blanks in the box below the groups.5. Complete steps 1-4 for number 3 and 4.
Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2014-201531
16
16
16
16
16
16
323