H. Oliverius and N. Williams-Jones
CAMMP 2014
College of Education
Reading and Elementary Education
Day 1
Names: Allemeier, Auman, Canty, Cavalline, Gavin, Hong, Hart, Walley, Williams
Integrated, Thematic Problem Solving Unit: Piel’s Kitchen
Grade Level: 5th grade
Arithmetic Topic (operation): Fractions
HIERARCHY STEP # Building The Rorange Model/ Part –Whole Relationship
Teacher Input:
TW pass out c-rods to all students
TW walk students through the building of rorange model
TW go through the relationship of the fractions to one another: One Rorange=1 whole
2 dark green=1 whole rorange but 1 dark green is one of two equal parts
continue through the rest of the model.
TW Ask students problems below, work through them together.
TW allow students time to find as many equivalent fractions as possible
TW pass out materials to create dough
SW make dough
TW give students different fractions to mark out on their dough (4 equal parts, show me
¾) etc.
THEME PROBLEM # N/A
Summary Table
Action Language:
Open Number Sentence:
Manipulative:
Quantitative Solution:
Referential Meaning:
CONCRETE MANIPULATIVE: Cusienaire Rods- Rorange Model/ Dough
REPRESENTATIONAL MANIPULATIVE: n/a
TRANSITIONAL ACTIVITIES: Computer Activities
www.ixl.com/math-grade-/ fractions-review
www.internet4 classrooms.com
www.mrnussbaum.com
STUDENT PROBLEMS:
1. Find all the equivalents you can find of the following - 4/12; ½; 2/3
2. Compare 2/3 to 3/4, is 2/3 more, less or equivalent to 3/4
3. Compare ¼ to 1/3, is it more, less or equivalent to 1/3
4. Compare ½ to 1/3, is it more less or equivalent to 1/3
5. Compare 4/sixth to 2/3, is it more less or equivalent to 2/3
6. Is ¼ more, less or equivalent to 1/6
7. Is 3/12 more, less or equivalent to ¼
8. Is ½ more, less or equivalent to 3/6
9. Stephanie used 2/3 cup of chocolate chips to make cookies. She used ¾ cup of chocolate
chips to make brownies. Did she use more chocolate chips to make cookies or the
brownies?
10. Brad rides his bike ¾ mile every day. Jared rides his bike 4/6 of a mile every day. Who
rides their bike further?
11. Five out of six students went to the beach for summer break. Did more or less than half
of the students go to the beach for summer break?
12. 3 out of 12 students texted their friends to watch a video on Youtube of the dancing bear.
Did more than half or less than half call their friends to watch the video?
13. In a class of 12 students, 8 of them are girls. Are there more girls than boys in the class?
STUDENT ANSWER KEY:
No referential meaning exists for the following answers:
1.
Quantitative Meaning: 4/12 = 2/6= 1/3
½ = 2/4=3/6=6/12
2/3=4/6=8/12
2.
Quantitative Meaning: ¾ is more
3.
Quantitative Meaning: 1/3 is more
4.
Quantitative Meaning: ½ is more
5.
Quantitative Meaning: 4/6 is equivalent to
6.
7.
Quantitative Meaning: ¼ is more
Quantitative Meaning: 3/12 is equivalent to 1/4
8.
Quantitative Meaning: ½ is equivalent to 3/6
Referential meanings provided below:
9.
Quantitative Meaning: Stephanie used more chocolate chips to make brownies than
cookies.
10.
Quantitative Meaning: Brad rides his bike further
Referential Meaning: n/a
11.
Quantitative Meaning: More than half
Referential Meaning: students
12.
Quantitative Meaning: Less than Half
Referential Meaning: students
13.
Quantitative Meaning: More than half
Referential Meaning: students
Day 2
Names: Allemeier, Auman, Canty, Cavalline, Gavin, Hong, Hart, Walley, Williams
Integrated, Thematic Problem Solving Unit: Piel’s Kitchen
Grade Level: 5th grade
Arithmetic Topic (operation): Fractions
HIERARCHY STEP # Addition using Concrete Manipulatives
TW have students set up rorange model
TW review material from previous day, comparing fractions
TW introduce “two car train” and the addition action (joined with)
TW work through the problems with students
TW pass out trail mix manipulative and measuring spoons
SW have to complete problems (adding fractions) to figure out the measurements for the
recipe.
SW make the recipe
If students are ready for representational show them place value chart
THEME PROBLEM # A recipe for trail mix requires 1/2 cup raisins, 1/4 cup of chex mix, and 1/2 cup
M&M’s. How much trail mix does this recipe make all together?
Summary Table
Action Language: joined with
Open Number Sentence: ½ + 1/4 + 1/2
Manipulative: Rorange Model
Quantitative Solution: 1
Referential Meaning: cup of trail mix
CONCRETE MANIPULATIVE: cusinaire rods/ measuring cups and trail mix
TRANSITIONAL ACTIVITIES: Computer Activities
www.ixl.com/math-grade-/ fractions-review
www.internet4 classrooms.com
www.mrnussbaum.com
STUDENT PROBLEMS:
1.
2.
3.
4.
5.
6.
7.
8.
2/4 + 1/3=
½ + 1/12=
4/6+ 2/4=
2/4 + ½ =
1½+1½ =
2 ¾ + 1 1/3 =
John walked 1/2 of a mile yesterday and 3/4 of a mile today. How many miles has John walked?
Mary is preparing for an exam. She study 2/3 hours on Friday and 4/6 hours on Saturday, How many hours
she studied over the weekend.
9. Pearl has 22/3 cups of bananas and 3/4 cups of peaches. How many cups of fruit does she have?
10. Cindy has one and two-thirds cups of jelly beans in a bowl. She added two and a quarter cups of jelly beans
to the bowl. How many cups of jellybeans does she have?
STUDENT ANSWER KEY:
The following answers do not contain referential meanings:
1.
Quantitative Meaning: 10/12
2.
Quantitative Meaning: 7/12
3.
Quantitative Meaning: 14/12 or 1 2/12
4.
Quantitative Meaning: 1
5.
Quantitative Meaning: 3
6.
Quantitative Meaning: 3 7/12
7.
Quantitative Meaning: 5/4 or 1 ¼
The following answers contain referential meanings:
8.
Quantitative Meaning: 10/6 = 1 4/6 hours of studying
9.
Quantitative Meaning: 17/12 = 1 5/12 cups of fruit
10.
Quantitative Meaning: 3 11/12 cups of jelly beans
Day 3
Names: Allemeier, Auman, Canty, Cavalline, Gavin, Hong, Hart, Walley, Williams
Integrated, Thematic Problem Solving Unit: Piel’s Kitchen
Grade Level: 5th grade
Arithmetic Topic (operation): Fractions
HIERARCHY STEP # Subtraction using Concrete Manipulatives
TW have students build rorange model
TW review addition from the day before with some practice problems
TW explain the use of two car trains with subtraction (take away only)
TW work through problems with students
TW pass out fruit that is broken into fractions and wholes
SW create 2 word problems to share with the class in relation to their fruit, the class will
solve them together.
If students are ready to move to representational use place value chart
THEME PROBLEM # Sheila has 1 orange in her lunchbox. Her brother took 1/3 of her orange. How much of
the orange does Sheila have left?
Summary Table
Action Language: Take away
Open Number Sentence: 1/2 – 1/3
Manipulative: Cuisenaire Rods
Quantitative Solution: 1/6
Referential Meaning: cups of oranges
CONCRETE MANIPULATIVE: Cuisenaire Rods / Fruits
REPRESENTATIONAL MANIPULATIVE: n/a
TRANSITIONAL ACTIVITIES: Computer Activities
www.ixl.com/math-grade-/ fractions-review
www.internet4 classrooms.com
www.mrnussbaum.com
STUDENT PROBLEMS:
1.
2.
3.
4.
5.
6.
2/3- 1/3
¾-¼
6/12 - 1/12
2 3/4 – 1 1/2
1 3/6 – 1¼
3 2/3 – 2 1/12
Jack has to drive to his grandmother’s house which is 5 ¾ miles away. He has driven 3 ¼ mile so far. How
much further does he have to go?
8. Alice filled a bucket with 4/6 of a gallon of water. Later, she poured out 2/3 of a gallon of the water. How
much water is left in the bucket?
9. The chef of a pizza place used 3/12 of a package of pepperoni and 1/6 of a package of sausage. How much
more pepperoni than sausage did the chef use?
10. John has to walk home which is 3 ½ miles away. He stopped at the ice cream shop which is 2 ¼ the way
home. How many more miles does John have to walk?
7.
STUDENT ANSWER KEY:
The following answers do not contain referential meanings:
1.
2.
3.
4.
5.
6.
Quantitative Meaning: 1/3
Quantitative Meaning: 2/4
Quantitative Meaning: 5/12
Quantitative Meaning: 1 ¼
Quantitative Meaning: 1 3/12
Quantitative Meaning: 1 7/12
The following answers contain referential meanings:
7.
Quantitative Meaning: 2 2/4
Referential Meaning: miles to grandma’s house
8.
Quantitative Meaning: 0
Referential Meaning: water left in the bucket
9.
Quantitative Meaning: 1/12
Referential Meaning: more pepperoni
10.
Quantitative Meaning: 11/4
Referential Meaning: miles to his house
Day 4
Names: Allemeier, Auman, Canty, Cavalline, Gavin, Hong, Hart, Walley, Williams
Integrated, Thematic Problem Solving Unit: Piel’s Kitchen
Grade Level: 5th grade
Arithmetic Topic (operation): Fractions
HIERARCHY STEP # Multiplying using Concrete Manipulatives
TW have students build rorange model
TW review subtraction and addition of fractions
TW write a problem on the board and have students write an open number sentence.
TW explain that X = sets of so ½ x ¾ = ½ sets of ¾ how many in each set?
TW explain the the second number in the number sentence is the number of sets and the
third is the number in each set.
TW help students work through the problems below.
TW pass out bags of fruitloops
SW sort fruitloops and figure out what fraction of all of the fruitloops are red, blue, etc
then work through problems using that manipulative.
THEME PROBLEM # Katie has ½ of the red fruit loops left over from breakfast. On
Wednesday, she ate 1/3 of what she had left. How many red fruit loops did she eat on
Wednesday?
Summary Table
Action Language: sets of
Open Number Sentence: ½ x 1/3
Manipulative: cuisenaire rods
Quantitative Solution: 1/6
Referential Meaning: red fruit loops
CONCRETE MANIPULATIVE: Cuisenaire Rods/ fruit loops
REPRESENTATIONAL MANIPULATIVE: n/a
TRANSITIONAL ACTIVITIES: Computer Activities
www.ixl.com/math-grade-/ fractions-review
www.internet4 classrooms.com
www.mrnussbaum.com
STUDENT PROBLEMS:
1.
2.
3.
4.
5.
1/4 x 1/3
2/3 x 2/4
¼ x 1/2
3/12 x 1/3
¼ x 1/12
6. 7/12 x 1/4
7. On Friday night, John ate pizza for dinner and had 1/2 of the pizza left over. On Saturday, he ate 1/3
of what was left. How much pizza did John eat on Sunday?
8. A recipe for banana oat muffins calls for ¾ cup of nutmeg. You are making ½ of the recipe. How much
nutmeg should you use?
9. In Aaliyah's grade, 2/3 of the students have a sister. Of the students who have a sister, 1/2 also have
a brother. What fraction of the students in Aaliyah's grade have both a sister and a brother?
10. Justin operates an orange juice stand. On Monday he used 3/4 of a bag of oranges. On Tuesday he
used 1/10 as many oranges as on Monday. How many bags of oranges did Justin use on Tuesday?
STUDENT ANSWER KEY:
The following answers do not contain referential meanings:
1.
2.
3.
4.
5.
6.
Quantitative Meaning: 1/12
Quantitative Meaning: 4/12
Quantitative Meaning: 1/8
Quantitative Meaning: 3/36
Quantitative Meaning: 1/48
Quantitative Meaning: 7/48
The following answers contain referential meanings:
7.
8.
9.
10.
Quantitative Meaning: 1/6
Referential Meaning: pizza left
Quantitative Meaning: 3/8
Referential Meaning: nutmeg
Quantitative Meaning: 2/6
Referential Meaning: students have a sister and brother
Quantitative Meaning: 3/40
Referential Meaning: oranges used
Day 5
Names: Allemeier, Auman, Canty, Cavalline, Gavin, Hong, Hart, Walley, Williams
Integrated, Thematic Problem Solving Unit: Piel’s Kitchen
Grade Level: 5th grade
Arithmetic Topic (operation): Fractions
HIERARCHY STEP # Division using Concrete Manipulatives
TW have students build rorange model
TW review addition, subtraction and multiplication of fractions
TW go over action language for division and work the problems with students
TW then have students go over their recipe they brought in and give S different scenarios
in which they would have to ½ the recipe or double
THEME PROBLEM # Alan made 1/2 of a pound of trail mix. If he puts 1/6 of a pound into
each bag, how many bags can Alan fill?
Summary Table
Action Language: sets of
Open Number Sentence: ½ grouped into sets of 1/6 how many times
Manipulative: ½ / 1/6 =
Quantitative Solution: 3
Referential Meaning: bags of trail mix
CONCRETE MANIPULATIVE: Cuisenaire Rods
REPRESENTATIONAL MANIPULATIVE: n/a
TRANSITIONAL ACTIVITIES: Computer Activities
www.ixl.com/math-grade-/ fractions-review
www.internet4 classrooms.com
www.mrnussbaum.com
STUDENT PROBLEMS:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
¼ / 2/3
1/3 / ¼
¾ / 1/12
1 ½ / 1/3
2¼ / ¾
1 3/6 / 2/3
Ryan's bird feeder holds 3/4 of a cup of birdseed. Ryan is filling the bird feeder with a scoop that holds 1/8
of a cup. How many scoops of birdseed will Ryan put into the feeder?
A factory uses 1/10 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 1/5 of a
barrel of raisins. How many batches of granola bars did the factory make yesterday?
A cookie factory uses 1/4 of a barrel of oatmeal in each batch of cookies. The factory used 3/4 of a barrel of
oatmeal yesterday. How many batches of cookies did the factory make?
Gavin made 3/5 of a quart of hot chocolate. Each mug holds 3/10 of a quart. How many mugs will Gavin
be able to fill?
STUDENT ANSWER KEY:
The following answers do not contain a referential meaning:
1.
Quantitative Meaning: 3/8
2.
Quantitative Meaning: 1 1/3
3.
Quantitative Meaning: 9
4.
Quantitative Meaning: 4 1/2
5.
Quantitative Meaning: 3
6.
Quantitative Meaning: 2 3/12
The following answers referential meanings are listed below:
7
Quantitative Meaning: 6
Referential Meaning: scoops of bird feed
8.
Quantitative Meaning: 2
Referential Meaning: batches of granola bars
9.
Quantitative Meaning: 3
Referential Meaning: batches of cookies
10.
Quantitative Meaning: 2
Referential Meaning: quarts of hot chocolate