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13.19 Fractions
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Author: David Riddick
Date Created: 8/9/2003 9:01:06 PM PST
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Grade/Level:
4
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Students:
27 Students. 14 boys and 13 girls. 4 EO's; 6 IFEP's; 3 RFEP's; 14 ELD3-4:
GATE class - advanced learners
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Subject Area(s):
Mathematics
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Concept(s):
Students will learn to compare and order fractions with denominators in the
halves, thirds, fourths, and twelfths.
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State
Academic Content Standard(s):
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 CA- CCTC: Aligned CSTP's and TPE's
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• Standard : CSTP: Standard for Planning Instruction and Designing
Learning Experiences for all Students
TPE: D. Planning Instruction and Designing Learning Experiences
for Students
CSTP Description: Teachers plan instruction that draws on and values
students’ backgrounds, prior knowledge, and interests. Teachers establish
challenging learning goals for all students based on student experience,
language, development, and home and school expectations. Teachers
sequence curriculum and design long-term and short-range plans that
incorporate subject matter knowledge, reflect grade-level curriculum
expectations, and include a repertoire of instructional strategies.
Teachers use instructional activities that promote learning goals and
connect with student experiences and interests. Teachers modify and
adjust instructional plans according to student engagement and
achievement.
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• CSTP Key Element : Designing short-term and long-term plans to foster
student learning.
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 Question : make decisions about
organizing curriculum to allow enough time for student learning,
review, and assessment?
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CA- California K-12 Academic Content Standards
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• Subject : Mathematics
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• Grade : Grade Four
By the end of grade four, students understand large numbers and addition,
subtraction, multiplication, and division of whole numbers. They describe
and compare simple fractions and decimals. They understand the properties
of, and the relationships between, plane geometric figures. They collect,
represent, and analyze data to answer questions.
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• Area : Number Sense
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• Sub-Strand 1.0: Students understand the place value of whole numbers
and decimals to two decimal places and how whole numbers and decimals
relate to simple fractions. Students use the concepts of negative
numbers:
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Standard 1.5: Explain different
interpretations of fractions, for example, parts of a whole, parts of a
set, and division of whole numbers by whole numbers; explain
equivalents of fractions (see Standard 4.0).
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Standard 1.7: Write the fraction
represented by a drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction to a simple decimal
on a number line.
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Objective(s):
Cognitive: Students will know how to compare and order fractions.
Observable: Students will use manipulatives, drawings, pictures, and create
posters to explain their understanding of how to compare and order fractions.
Criteria: Given a list of 10 pairs of fractions, students will circle the
greater fraction in the pair with an accuracy of 75%.
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Prerequisite Background Skills/ Knowledge:
Student should know a fraction of 4/4 is equal to a whole. Among like
denominators, the closer the numerator is to the denominator in value, the
closer the fraction is to one whole.
The names of the fractional parts are determined by the number of fair shares
making up the whole: halves - two fair shares; thirds - three fair shares;
fourths - four fair shares; twelfths - twelve fair shares.
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Vocabulary/Language Skills:
Listening: Students listen to verbal instructions given during directed
lesson. ELD students are given help by peer tutors as teacher speaks.
Speaking: Students participate in directed lesson by raising hands and
answering questions.
Writing: Students will take notes and write in their Math notebooks.
Reading: Students read from math textbook and Handouts
Vocabulary: numerator, denominator, greater than, less than, halves, thirds,
fourths, twelfths
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Materials:
1) Pencil & Paper
2) Transparencies
3) Transparency pen
4) Math Textbook
6) Handout "Compare and Order Fractions"
7) Handout "Quiz - Compare and Order Fractions"
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Classroom Management:
During directed lesson, students are seated in assigned seats, which are
2-person desks.
I will give out extra credit points for students who participate and
cooperate with lesson.
Extra credit points for actively engaged students
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Models of Instruction:
Unguided Inquiry
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Procedure
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Open:
As an attention getter, pull out a carton of one dozen eggs. Taking one egg
out of a box of a dozen, ask the students for the fraction that would
describe 1 egg out of a dozen. Write 1/12 on the board.
Take another 2 eggs out of the box and ask the students for the fraction that
would describe the 3 eggs. Write 3/12 on the board.
Which fraction is larger, 1/12 or 3/12?
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Input:
1st: Give students the objective and the standard for the lesson: Compare and
order fractions with denominators in the halves, thirds, fourths, and
twelfths.
Explain how the following are expressed as a fraction. The denominator distinguishes
how the fraction is read.
halves - /2
thirds - /3
fourths - /4
twelfths - /12
2nd: Review the denominator is the number "down" from on the
fraction. The numerator is the "number" above the fraction.
3rd: (Day One) Students will use area models to examine which is larger, 1/3
or 1/4.
They will divide a piece of graph paper into three equal parts using
horizontal lines, and color in the bottom third with a light color.
Ask them to name the fraction that represents the colored-in section.
They will divide the same piece of paper into four equal parts using
horizontal lines and color in the bottom quarter with a dark color.
Ask them to name the fraction that represents the new colored-in section?
With the 1/4 drawn within the 1/3, the students consider which is larger, 1/3
or 1/4.
Demonstrate where the fractions would be situated on a number line.
4th: (Day Two) Students will use length models to compare fractions.
They will draw number lines from 0 to 1 marked off at 1/4 intervals.
Have them highlight the locations of 1/2 and 3/4 on the line.
Ask them which is larger, 1/2 or 3/4.
Pass out handout: "Compare and Order Fractions"
Students will work in cooperative groups to analyze and determine which pair
of fractions is greater.
High achieving students may create a poster visually explaining how to
distinguish which fraction is greater.
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Guided Practice:
Demonstrate where the fraction 1/4, 1/2, and 3/4 would be on a number line.
Explain one part of large denominator is less in value than one part of small
denominator. Visually draw a pizza slice comparing 1/3 to 1/4. Would 1/12 be
greater than 1/3?
Demonstrate were the fractions from the handout would be on a number line.
Direct pairs of students to explain and analyze why one fraction is greater
than another.
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Independent Practice:
In pairs, students devise and record strategies to explain how to compare and
order fractions.
Students will use area models to examine which is larger, 1/3 or 1/4.
Students will use length models to compare fractions.
Students will compare fractions with the same denominator.
Students will complete a Quiz - "Compare and Order Fractions."
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Close:
In a grand conversation, students will reflect on strategies that work best
for them.
Students will discuss how to compare and order fractions and what they
learned.
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Assessment/
Reflection
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Assessment:
Students will circle the greater fraction from a list of 10 pairs of
fractions to demonstrate understanding of comparing and order fractions with
a 75% accuracy.
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Reflection:
The objective of the lesson was achieved. Students were able to circle the
greater fraction from a list of 10 pairs to demonstrate understanding of
comparing and ordering fractions. This was the first fraction lesson I
instructed with my class. I was delighted to find they had a solid conceptual
understanding of fractions. The anticipatory set engaged students to
understand the concept of denominator and numerator. The denominator
represents the total number of parts in a whole. The dozen eggs illustrated this.
The numerator was represented as I took one egg out of the dozen. I asked
students what fraction of the dozen is represented in my hand.
I was surprised to see the class as a whole had a basic understanding of how
to compare and order fractions. Their level of understanding was far above
what I had anticipated. As a class, we discussed strategies and connections
to compare and order fractions. One rule I found extremely powerful was
coined, “The Thomas Rule.” Thomas came up with a rule to compare two fractions.
If the numerator of a fraction is the same, the fraction with the higher
denominator will be smaller. For example, 1/4 is greater than 1/12.
This lesson proved to me the significance of the anticipatory set. The “hook”
at the beginning of the lesson is vital to engage students. Short and Long
term plans must stem from a powerful anticipatory set.
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