Fractions Describe Parts of a Whole
Fractions Describe Parts of a Whole
Objectives
Students will develop a primary understanding of parts of a whole. Previous experiences of sharing are connected to the use of physical materials and visual models (drawings and diagrams). Students will:
- construct models to represent fractional parts of a whole.
- experience fractions using different representations, such as area models (circles, rectangles, pattern blocks, etc.), sets (chips), and lengths (fraction strips, Cuisenaire rods).
- learn to use various models to solve problems.
Essential Questions
How are relationships represented mathematically?
How can mathematics support effective communication?
How is mathematics used to quantify, compare, represent, and model numbers?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
- How is mathematics used to quantify, compare, represent, and model numbers?
- How can mathematics support effective communication?
- How are relationships represented mathematically?
- What does it mean to estimate or analyze numerical quantities?
- What makes a tool and/or strategy appropriate for a given task?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- Elementary and Middle School Mathematics: Teaching Developmentally by John Van de Walle. Heinemann, 2009.
- Piece = Part = Portion by Scott Gifford. Tricycle Press, 2008.
- Funny & Fabulous Fraction Stories (Grades 3–6) by Dan Greenburg and Jared Lee. Scholastic Teaching Resource, 1999.
- The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta and Robert C. Bolster. Cartwheel Books, 1991.
- http://www.gamequarium.com/fractions.html (multiple fraction games)
- http://www.fractionbars.com/BarsAndCardsGame/
- http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html?from=grade_g_2.html (naming fractions)
- Requires Adobe Flash Player
- http://nlvm.usu.edu/en/nav/frames_asid_103_g_2_t_1.html?from=grade_g_2.html (visualizing fractions)
- Requires Adobe Flash Player
Formative Assessment
-
View
Multiple-Choice Items:
- Which represents one-half shaded?
- Which shows two brownies shared equally among four children?
- Choose the fraction that best represents the shaded portion of the square.
- What fraction of the shapes are circles?
- What fraction of the school supplies are pencils?
- What fraction of the stars are shaded?
- What fraction of the squares are shaded?
- What fraction of the fruits are bananas?
- What fraction represents the circles that are shaded?
Multiple-Choice Answer Key:
1. A
2. B
3. D
4. D
5. A
6. D
7. C
8. C
9. A
Short-Answer Items:
- Peter has six chocolate bars that he wants to share equally with himself and three of his friends at lunch. How much will each person get when four of them share the six chocolate bars equally? Using a picture, show how you solved the problem and explain what you did.
- A pitcher was filled with eight glasses of water. Juan poured three glasses of water for himself.
Using a fraction and drawings, explain how much water is left in the pitcher.
- Tammy had a tennis lesson from her brother. Her brother brought a basket with 18 tennis balls. When Tammy was finished with her lesson there were 7 balls left in the basket. Write or use drawings to help explain the fraction of tennis balls used in Tammy’s lesson.
Short-Answer Key and Scoring Rubrics:
- Peter has six chocolate bars that he wants to share equally with himself and three of his friends at lunch. How much will each person get when four of them share the six chocolate bars equally? Using a picture, show how you solved the problem and explain what you did.
Each person will get
chocolate bars. (Explanations may vary. Since there are six whole chocolate bars, each person can have one. That leaves two full chocolate bars. If you cut each of the leftover chocolate bars in half, that gives four halves. Then each person can get a half plus a whole chocolate bar. That means each person will have chocolate bars).Points
Description
2
- Mathematics is correct.
- Written explanation and drawing are complete and detailed.
- Student demonstrates thorough understanding of fractions.
1
- Mathematics is correct but does not have a written explanation OR mathematics has errors but a written explanation is given.
- Drawing may not be present.
- Student demonstrates some understanding of fractions.
0
- Mathematics is incorrect or contains many errors.
- Written explanation/drawing is missing or erroneous.
- Student does not demonstrate an understanding of fractions.
11. A pitcher was filled with eight glasses of water. Juan poured three glasses of water for himself.
Using a fraction and drawings, explain how much water is left in the pitcher.
Since Juan used
of the water in the pitcher, 
of the water is left. Pictures should demonstrate that three glasses of water are gone, while five glasses remain.Points
Description
2
- Mathematics is correct.
- Written explanation/drawings are complete and detailed.
- Student demonstrates thorough understanding of fractions.
1
- Mathematics is correct but does not have a written explanation OR mathematics has errors but a written explanation is given.
- Student demonstrates some understanding of fractions.
0
- Mathematics is incorrect OR only the number of glasses remaining is given with an explanation or drawing, and the response does not use fractional form.
- Written explanation/drawings are missing or erroneous.
- Student does not demonstrate an understanding of fractions.
12. Thomas had a tennis lesson from his brother. His brother brought a basket with 18 tennis balls. When Thomas was finished with his lesson there were 7 balls left in the basket. Write or use drawings to help explain the fraction of tennis balls used in Thomas’s lesson.
Thomas used
of the balls in the basket. Pictures should demonstrate that 11 out of 18 balls were used, while 7 balls were not used.Points
Description
2
- Mathematics is correct.
- Written explanation/drawings are complete and detailed.
- Student demonstrates thorough understanding of fractions.
1
- Mathematics is correct but does not have a written explanation OR mathematics has errors but a written explanation is given.
- Student demonstrates some understanding of fractions.
0
- Mathematics is incorrect OR only the number of balls used is given with an explanation or drawing, and the response does not use fractional form.
- Written explanation/drawings are missing or erroneous.
- Student does not demonstrate an understanding of fractions.
Performance Assessment:
Tiffany and her grandmother are planning a vegetable garden. One plan for the garden is shown below.
- What fraction of the garden plan is tomatoes and lettuce? Explain how you got your answer using words, fractions, and drawings. Write your answer in the answer box below.
- What fraction of the garden plan is corn and carrots? Explain how you got your answer using words, fractions, and drawings. Write your answer in the answer box below.
- Are the fractions for A and B the same? Explain why they are the same or show how the garden plan could be changed to make the fraction of tomatoes and lettuce the same as the fraction of carrots and corn.
Challenge Question (optional; not included in scoring rubric):
- Tiffany loves tomatoes and her grandmother loves green beans and corn. Explain how Tiffany could adjust the sections of the garden so the fraction of tomatoes is equal to the fraction of green beans and corn, without getting rid of any of the types of vegetables.
Performance Assessment Key:
Tiffany and her grandmother are planning a vegetable garden. One plan for the garden is shown below.
- What fraction of the garden plan is tomatoes and lettuce? Explain how you got your answer using words, fractions, and drawings. Write your answer in the answer box below.
Tomatoes and lettuce make up
of the garden. Support will vary…- What fraction of the garden plan is corn and carrots? Explain how you got your answer using words, fractions, and drawings. Write your answer in the answer box below.
Corn and carrots make up
of the garden. Support will vary…- Are the fractions for A and B the same? Explain why they are the same or show how the garden plan could be changed to make the fraction of tomatoes and lettuce the same as the fraction of carrots and corn.
The fractions in A and B are not the same. Explanations will vary…
Challenge Question (optional; not included in scoring rubric):
- Tiffany loves tomatoes and her grandmother loves green beans and corn. Explain how Tiffany could adjust the sections of the garden so the fraction of tomatoes is equal to the fraction of green beans and corn, without getting rid of any of the types of vegetables.
Explanations will vary…
Performance Assessment Scoring Rubric:
Points
Description
4
- Mathematics is correct with complete work shown.
- Written explanation/drawings are thorough, detailed, and clear.
- Student displays excellent understanding of the questions, mathematical concepts, and processes.
- Student meets or performs beyond the problem requirements.
3
- Mathematics is correct with some work shown.
- Written explanation/drawings are thorough and clear.
- Student displays good understanding of the questions, mathematical concepts, and processes.
- Student meets all of the problem requirements.
2
- Mathematics is mostly correct with minimal or no work shown.
- Written explanation/drawings is present but lacks detail or is difficult to read.
- Student displays partial understanding of the questions, mathematical concepts, and processes.
- Student meets some of the problem requirements.
1
- Mathematics is incorrect with some work shown.
- Written explanation/drawing is present but lacks detail or is difficult to read.
- Student displays little understanding of the questions, mathematical concepts, and processes.
- Student does not meet the majority of the problem requirements.
0
- Mathematics is incorrect with no work shown.
- Written explanation/drawings are not present.
- Student displays no understanding of the questions, mathematical concepts, and processes.
- Student meets none of the problem requirements.
Final 05/10/2013
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