Decimal and Fraction Concepts – Grade Three
Ohio Standards
Connection:
Number, Number Sense and Operations
Benchmark B
Recognize and generate equivalent representations for whole numbers, fractions and decimals
Indicator 7
Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or parts of a set; e.g.; 3 of 10 marbles are red can also be described as
3
10
and 3 tenths are red.
Benchmark A
Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.
Indicator 2
Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: d. Explain the concepts of tenths and hundredths using physical models, such as metric pieces, base ten blocks, decimal squares or money.
Mathematical Processes
Benchmark
I. Represent problem situations in a variety of forms (physical model, diagram, in words and symbols), and recognize when some ways of representing a problem may be more helpful than others.
Lesson Summary:
In this lesson, students recognize and use fraction and decimal concepts and notations as related ways of representing parts of a whole or parts of a set. Students explain the concepts of tenths, using physical models. Students apply skills in problemsolving situations. At this point, third graders are expected to recognize decimals as they write amounts of money and are expected to read 0.6 as six-tenths. They should understand 6
10
is six-tenths.
Estimated Duration: Two - Three hours
Commentary:
Decimals make it possible to use the place value system to represent fractional parts (Burns, 1992). This lesson reinforces the concept of fractional parts and introduces decimals as another representation of fractional parts. Using familiar fractions and physical models, students make connections among the two representations in a concrete method. It is important for students to use appropriate terminology when reading decimals to reinforce the place value concept. For example, they should read 0.3 as “three-tenths”, rather than
“zero point three”. Students should write and reflect on definitions and topics covered by this lesson in their mathematics notebooks or journals. Continue to develop decimal concepts for hundredths and by comparing values of fractional parts.
Pre-Assessment:
•
Distribute Decimal and Fractions Concepts Pre-
Assessment, Attachment A.
•
Have students complete the survey in teams or pairs in which they discuss the response first, then write the response individually in their own words.
•
Discuss responses as a class, asking for their reasoning.
Scoring Guidelines:
Assess students’ prior knowledge and experience with fractions and decimals. Consider how students’ responses to questions show readiness and progress in meeting the grade level expectations. Categorize students’ levels of understanding using the rubric guidelines.
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Decimal and Fraction Concepts – Grade Three
Ready for Instruction
Explains and identifies fractions and compares the parts (numerator and denominator). Identifies and creates models for given fractions.
Identifies a fraction and may or may not compare its parts. Shows some understanding in representing fractions using visual models with minor flaws.
Identifies a fraction. Flaws in understanding about the parts and representations of fractions are evident.
Post-Assessment:
Distribute Decimal and Fraction Concepts Post-Assessment, Attachment B, to each student after completion of instruction.
Scoring Guidelines:
See Answer Key, Decimal and Fraction Concepts Post-Assessment, Attachment C, for answers and rubrics.
Instructional Procedures:
Part One
1.
Complete Pre-Assessment.
2.
Elicit a definition of the word fraction from the pre-assessment class discussion, making sure that students know that fractions are both parts of a whole and parts of a set. Begin focusing on fractions as representing a part of a whole. Distribute the rectangle divided into ten parts.
See Tenths Grids, Attachment D .
3. Explain that the rectangle grid is one whole. Have students use three different colors of crayons or markers to shade in each section the color of their choice. Have a model of the rectangle on the overhead or board.
4. Ask students how they can represent the part of the rectangle that is shown by each of the colors. Model an example to guide students’ thinking. For example, “I colored 4 parts red, so how can I write the amount that is red? Can I just write 4?” Allow time for students to share their ideas with their partners or teams.
5. Discuss their ideas as a class and allow students to share how they might represent it. They may come up with 4 out of 10, 4
10
or four-tenths. Share all ideas, and then have each student write his/her own representation for each color.
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Decimal and Fraction Concepts – Grade Three
6. Walk around and informally assess students’ work. Have students share their representation with partners or their team.
7. Have students create a table in their notebooks or journals. If they have no journals or notebooks, consider stapling paper together to make booklets for the unit on fractions and decimals. Use the smaller tenths grids from Tenths Grids , Attachment D, or have students draw their own.
1
10
2
10
5
10
10
10 one-tenth two-tenths five-tenths ten-tenths, one whole
*Use this table for mixed numbers in the next part.
8. Introduce vocabulary by asking students to explain what a fraction is. After some discussion have the class come up with a definition. Be sure to have the definition include that a fraction is a number that represents part of a whole or part of a set.
Have students record the definition in their math notebooks or journals.
9. Ask the students how they decide which number is on the top and on the bottom of the fraction line. Elicit definitions as a class for “numerator” and “denominator.” After further discussion have students record definitions and examples. For example:
• denominator - the number below the fraction line that represents the total number of equal parts. For example: If there are 3 marbles, and 1 is red, the fraction of marbles that
1 is red would be written as . The 3 represents the total number of marbles.
3
• numerator - the number above the fraction line that represents how many equal parts are described. For example: A cake is cut into 8 pieces, and you eat 2 of them. The part of the
2 cake you ate as a fraction would be
8
. The 2 is the numerator that represents the number of pieces you ate. The 8 represents the number of equal parts.
10. Pose the question, “What if I changed the rectangle to a square that had 10 rows of 10 and shaded 4 squares? Display the 10-by-10 grid. Have partners share with each other how we might represent the shaded part now. Discuss as a class how 4 shaded areas on this grid is different from the previous rectangle before.
11. After several examples of different parts of a whole being shaded, have students practice writing the portions both as a fraction and in words.
12. Hold up a dime or display an illustration on the overhead. a. Ask students to describe what part of a dollar is a dime (one-tenth). Show a rectangle and explain this represents one dollar.
3

Decimal and Fraction Concepts – Grade Three b. Ask students for the number of dimes needed to have one dollar. (10) Model by placing
10 dimes or circles in the shape of a rectangle to represent a dollar bill. c. Restate that a dime is one-tenth of a dollar, since there are 10 dimes to make a dollar.
Ask,
•
What part of a dollar is seven dimes? (seven-tenths)
•
What part of a dollar is 3 dimes? (three-tenths)
•
If I have one-half of a dollar, how many dimes do I have? (five)
•
What part of a dollar is (5) five dimes? (five-tenths).
13. To close the lesson, have students respond in their journals recalling the meaning of the terms fraction, numerator, and denominator. Have students create examples in their journals and share with the class.
Part 2
14. Focus on fractions as parts of sets. Begin by asking for 10 student volunteers to come to the front of the classroom. Tell the class that this group is one set. Have the students make statements about parts of the set. Write all responses on the board or chart paper. For
3 example,
10
of the students are girls, or three of the ten are girls, or three-tenths are girls.
Continue until all students have had the chance to make a statement about parts of the set.
15. Continue the concept of parts of a set by using manipulatives. Distribute 10 objects (buttons, color tiles, colored counters, pattern blocks, etc.) to each student. Have individuals represent
6 the parts of a set in fractions and words. For example, six-tenths (
10
) of the counters are red.
Students then write statements and share them with their partners or teams. Informally assess student performance by asking questions like, “How did you know the number that was the numerator? What about the denominator? If I changed the number of objects in the set to eight, how would your representation change?”
16. Extend the concepts with mixed numbers. a. Pose the problem situation
The teacher bought 6 pizzas for the class party. Each pizza was cut into 10 slices. After the party, there was 12 slices left. How much pizza was left? b. Have the students use counters to represent the situation. Ask questions to guide students.
•
How many slices makes a whole pizza? (10)
•
Are there enough slices left to make a whole pizza? (yes)
•
How many slices are left? (2)
•
How would you describe the remaining pizza? (One and two-tenths)
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Decimal and Fraction Concepts – Grade Three
17. Model writing a mixed number representing the amount of pizza remaining. Display two grids. Shade the entire first grid and two of the 10 columns in the second grid.
18 Ask students to write a fraction that represents the shaded parts. Allow partners or teams to discuss first, then share ideas with the class. Record the student responses in a visible location.
19. Elicit responses from the class that indicate that the first grid with all parts shaded represents
10 one whole,
10
and the second grid represents two-tenths. Display in words and fraction
2 form one and two-tenths and 1
10
20. Emphasize how to read the mixed number as one and two-tenths to prepare for using a decimal point.
21. Have students determine what fraction of the pizza was eaten by the class. They need to determine that 48 slices were eaten. Have them build a representation and conclude that four and eight-tenths pizzas were eaten.
22. Provide additional problem situations for students to solve. Have them build models and represent the fractional parts in words and symbols. Discuss reasoning for the symbolic notation of the fractions.
23. Have students identify or draw representations of fractions and mixed numbers in a mathematics journal. For example, give a visual representation of a mixed number and have students describe it in words or symbols or give a mixed number and have the students draw a visual representation. Collect the journal and student work to informally assess progress.
Determine future instruction based on data gathered from journal entry.
Instructional Tip:
Allow team sharing by giving each team a transparency sheet and overhead marker. Assign one student to record results, then when teams share, they can put the transparency on the overhead for the class to see.
Differentiated Instructional Support:
Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s).
•
For the students showing evidence of not meeting expectations, provide support individually or in small groups. Present them with a variety of manipulatives to see fractions as numbers that represent parts of a whole or parts of a set. Make sure students can identify the fractional part orally and written as both a fraction and in words.
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Decimal and Fraction Concepts – Grade Three
•
Allow students who demonstrate evidence of exceeding the standard, to create games and activities to reinforce fraction concepts. They may make flashcards or games that others could use to match pictures of fractional parts to the fraction or decimal words. In addition, these students can act as peer tutors or study buddies for those having difficulty meeting the standard.
Home Connections:
•
Students add entries to their Picture, Fraction and Decimal table.
•
Have students work on a fraction flipbook in which they draw pictures of fractions and represent them in words and numbers, too.
Materials and Resources:
The inclusion of a specific resource in any lesson formulated by the Ohio Department of
Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site’s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students.
For the teacher: attachments, overhead sheets and overhead markers, manipulatives (buttons, colored tiles, colored counters, or pattern blocks)
For the student: whiteboards/chalkboards (if available), three colors of crayons/markers, copies of attachments
Vocabulary:
• denominator
• fraction
• mixed number
• numerator
Technology Connection:
Use software that allows students to create fractional parts, name them, and relate them to decimals of tenths.
Research Connections:
Burns, Marilyn. About Teaching Mathematics: A K-8 Resource . Sausalito, Ca: Math Solutions
Publications, 1999.
Pask, Gordon. Conversation, Cognition and Learning.
New York: Elsevier, 1975.
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Decimal and Fraction Concepts – Grade Three
Attachments:
Attachment A, Pre-Assessment
Attachment B, Post-Assessment
Attachment C , Answer Key, Decimal and Fraction Concepts Post-Assessment
Attachment D , Tenths Grids
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Decimal and Fraction Concepts – Grade Three
Name_______________________________ Date__________________________
Directions: Answer the following questions to show what you know about decimals and fractions.
1.
What is a fraction? Give an example.
______________________________________________________________________________
______________________________________________________________________________
__________________________________
2.
Shade three-tenths of the grid below.
____________________________________
4. Which fraction model shows one-tenth shaded?
How do you know? __________
___________________________________________________________________________
A. B.
C.
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Name_______________________________ Date__________________________
Directions: Answer the following questions to show what you know about decimals and fractions.
1.
Which picture shows
3
8
of the circle shaded?
2. What fraction of the set is shaded?
○ ○ ○ ○ ○ ○ ● ● ● ●
6
A.
10
B.
10
4
C.
4
10
3.
A bag contains 10 marbles. Three of the marbles are red. Which choice correctly shows how to represent the number of marbles out of the bag that are red?
A. 3 tenths or
10
3
B. 10 thirds or
4. Which fraction represents seven-tenths?
A.
10
7
B.
7
10
10
3
C. 3 tenths or
10
5. Which mixed number represents two and 9 tenths
7
C.
100
3
A.
9
2
10
B. 9
2
10
C.
9
2
100
9
6. Choose the decimal for
10 from the choices below.
A. 10 ninths B. 9 tenths C. 1 tenth
8

7.
T hree dimes is what fraction of a dollar?
9 .
A . 30 tenths B. 10 tenths C. 3 tenths
8-10.Write a fraction and decimal to represent the shaded part of each grid.
8 .
Fraction
D ecimal
Fraction
D ecimal
1 0.
Fraction
D ecimal
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Decimal and Fraction Concepts – Grade Three
11. Use the space below to describe to a classmate what a fraction is. Include in your description the math terms “numerator” and “denominator.” You may use examples in your written description.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
12. Draw a picture that shows the mixed number
3
2 . Then write in words how you read the
10 mixed number.
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Decimal and Fraction Concepts – Grade Three
Total Possible points is 18
(Multiple Choice items 1 point each)
1. A
2. C
3. C
4. B
5. A
6. B
7. C
3
8. Fraction
10
Decimal 3 tenths
6
9. Fraction
10
Decimal 6 tenths
8
10. Fraction
10
Decimal 8 tenths
10

11. Descriptions may vary. Use the rubric to assess the descriptions.
Score Description
4 The response is clear, easy to understand, and includes that:
• a fraction is a number that represents part of a whole or part of a set
• a numerator represents the part of a fractional model
• a denominator represents the whole of a fractional model
• an appropriate example
3 The response includes that:
• a fraction is a number that represents part of a whole or part of a set
• a numerator is the number above the fraction line and/or that is the number of parts/objects
• a denominator is the number below the fraction line and/or the total number of equal parts of a whole and/or number of things in the set
• provides an appropriate example containing minor flaws
2 The response includes that a fraction is part of something, but may or may not include both parts of a set. The meanings of numerator and denominator are vague or reversed.
1 The response attempts to explain the meaning of fraction, numerator, and denominator.
The meanings are incorrect or unclear and show little or no understanding.
0 No attempt
12. Use the scoring guideline to assess model and written description.
2-point response Illustrates the mixed number and writes in words “Two and three tenths”
1-point response Illustrates mixed number incorrectly or written response is incorrect or the words are incorrect
0-point response No attempt or both parts are incorrect
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