module 10 fractions - PBworks
Transcript of module 10 fractions - PBworks
Revised 3/31/04 321
SAN DIEGO CITY SCHOOLS
Instructional Module to Enhance the Teaching of
H A R C O U R T
Math
California Edition
Grade 2
Module 10 - Revised
Number Sense and Fractions
– WORK IN PROGRESS –
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D
C
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Harcourt Math – Grade 2 MODULE 10
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Harcourt Math – Grade 2
11 Days
Key Mathematical Concepts: • Identify groups • Build, read, and write numbers • Compare and order numbers • Identify equal parts • Identify and compare fractions • Compare parts of a whole • Solve problems
Chapter 23 Parts of a Whole Lesson 23.1: Explore Fractions Lesson 23.2: Unit Fractions Lesson 23.3: Other Fractions Lesson 23.4: Compare Unit Fractions Lesson 23.5: Fractions Equal to 1
Chapter 24: Parts of a Group Lesson 24.1: Explore Fractions Lesson 24.2: Unit Fractions Lesson 24.3: Other Fractions Lesson 24.4: Compare Parts of a Group Lesson 24.5: Problem Solving Assessment
Harcourt Math: Grade 2
Module 10: Number Sense and Fractions Days 139 - 149
11 Days
Day 1 Unit 5 Lesson 23.1
Day 2 Unit 5 Lesson 23.2
Day 3 Unit 5 Lesson 23.3
Day 4 Unit 5 Lesson 23.4
Day 5 Unit 5 Lesson 23.5
Day 6 Unit 5 Lesson 24.1
Day 7 Unit 5 Lesson 24.2
Day 8 Unit 5 Lesson 24.3
Day 9 Unit 5 Lesson 24.4
Day 10 Unit 5 Lesson 24.5
Day 11 Unit 5 Assessment
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GRADE 2 Order of Units
2003-2004 School Year TRADITIONAL CALENDAR
September October
Module 1: Addition and Subtraction Strategies and
Facts, Place Value, and Graphing. Chapters 6, 1-4, 5
25 days
October
Module 2: Geometry Chapters 17 and 18
11 days
October
November
Module 3: Money and Time Chapters 7 and 9
12 days
November
Module 4: 2-Digit Addition and Subtraction Chapters 11-13
16 days
December
Module 5: Measurement Chapters 19 and 20
13 days
January February
Module 6: 2-Digit Addition and Subtraction Chapters 14 - 16
19 days
February
Module 7: Number Sense and Fractions Chapters 21 and 22
11 days
February
March
Module 8: Multiplication and Division Chapters 28 - 30
16 days
March April
Module 9: 3-Digit Addition and Subtraction Chapters 25 and 26
16 days
April Module 10: Number Sense and Fractions Chapters 23 and 24
11 days
April May
Module 11: Money and Time Chapters 8 and 10
11 days
May Module 12: 3-Digit Addition and Subtraction Chapter 27
10 days
Days to be used throughout the year (at teacher’s discretion) when more time is necessary to make meaning of a concept.
9 days
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GRADE 2 Order of Units
2003-2004 School Year YEAR ROUND CALENDAR
September October
Module 1: Addition and Subtraction Strategies and
Facts, Place Value, and Graphing. Chapters 6, 1-4, 5
25 days
October
Module 2: Geometry Chapters 17 and 18
11 days
October
November
Module 3: Money and Time Chapters 7 and 9
12 days
November
Module 4: 2-Digit Addition and Subtraction Chapters 11-13
16 days
December
Module 5: Measurement Chapters 19 and 20
13 days
January February
Module 6: 2-Digit Addition and Subtraction Chapters 14 - 16
19 days
February March
Module 7: Number Sense and Fractions Chapters 21 and 22
11 days
March April
Module 8: Multiplication and Division Chapters 28 - 30
16 days
April May
Module 9: 3-Digit Addition and Subtraction Chapters 25 and 26
16 days
May June
Module 10: Number Sense and Fractions Chapters 23 and 24
11 days
May June
Module 11: Money and Time Chapters 8 and 10
11 days
June July
Module 12: 3-Digit Addition and Subtraction Chapter 27
10 days
Days to be used throughout the year (at teacher’s discretion) when more time is necessary to make meaning of a concept.
9 days
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DAY 1 UNIT 5: Number Sense and Fractions
Chapter 23: Parts of a Whole LESSON 23.1 TE, P. 335A
LESSON FOCUS: Explore Fractions CALIFORNIA STANDARD:
Number Sense 4.1 Recognize, name and compare unit fractions from 1/12 to 1/2.
PURPOSE OF LESSON:
Learn the meaning of fractions of a whole.
ROUTINE: Materials: • Timer • Two sheets of acetate/acetate clocks from Module 3, Lesson 9.1
Suggestion: Throughout the Day • Set a timer to ring “on the hour.” Write both the analog and
digital times. Students make observations at the end of the day.
Suggestion: Approximating Time • Use the acetate clock. Approximate time to the hour by
using the one-handed clock. Move the circle to show times such as the following: “about 4 o’clock”, “halfway between 1 and 2 o’clock”, “a little past 8 o’clock.” Use approximate language.
LAUNCH: Materials: • Cuisenaire rods (see Note) OR • Pattern blocks (see Note)
Rod Relationships • Give students time to explore the rods. Introduce
“equivalent” and “equal parts.” • Ask them to find equivalent relationships: rods of the same
color that can be put together, end-to-end so that they are equal in length to other rods (e.g., 2 whites = 1 red, 2 reds = 1 purple).
• Ask students to find how many yellow rods are equal to an orange rod (2). Have a student prove the following: “The yellow rod is half a long as the orange rod.”
Note: If Cuisenaire rods are unavailable, introduce Launch and Explore, Day 2, Lesson 23.2, providing two days for students to explore fractions using pattern blocks
EXPLORE: Materials: • Cuisenaire rods
Fraction Rods • Have students find all the other pairs of halves they can. • Have students do the same with thirds (e.g., three whites =
1 light green; the white rod is 1/3 the light green rod), fourths (e.g., 4 red rods = 1 brown rod; the red rod is 1/4 the brown rod) and fifths (e.g., 5 red rods is = 1 orange rod; the red rod is 1/5 the orange rod).
• Students can find relationship equal to more than one rod (e.g., 2 black rods = 1 orange + 1 purple).
PRACTICE: As time allows: Pp. 335 and/or 336. SUMMARIZE: Closure:
• Revisit purpose of the lesson with students. • Prove that 2 red rods is 1/2 a brown rod. What is the
whole? How many reds equal 1 brown?
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HOMEWORK: Materials: • Homework: Paper Folding worksheet
Suggestion: Have students fold a sheet of paper into two equal parts. Have them repeat with other sheets of paper, folding one into three, one into four and one into eight equal parts. Discuss with an adult: Are the parts equal? How many parts in the whole?OR Pp. 335 and/or 336
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Homework: Paper Folding
1. Fold a sheet of paper into two equal parts.
Are the parts equal?
How many parts in the whole?
2. Fold a sheet of paper into three equal parts.
Are the parts equal?
How many parts in the whole?
3. Fold a sheet of paper into four equal parts.
Are the parts equal?
How many parts in the whole?
4. Fold a sheet of paper into eight equal parts.
Are the parts equal?
How many parts in the whole?
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DAY 2 UNIT 5: Number Sense and Fractions
Chapter 23: Parts of a Whole LESSON 23.2 TE, P. 337A
LESSON FOCUS: Unit Fractions CALIFORNIA STANDARD:
Number Sense 4.1 Recognize, name and compare unit fractions from 1/12 to 1/2.
PURPOSE OF LESSON:
Learn how to identify fractions that represent 1 part out of any number of equal parts of a whole.
ROUTINE: Materials: • Timer • Two sheets of acetate/acetate clocks from Module 3, Lesson 9.1 • Cuisenaire rods
Suggestion: Throughout the Day • Set a timer to ring “on the half hour.” Write both the analog
and digital times. Students make observations at the end of the day.
Suggestion: Clock Hand Relationships • Use the overhead clock. Approximate time to the hour by
using the one-handed clock. • Move the circle to show times such as the following: “about 4
o’clock”, “halfway between 1 and 2 o’clock”, “a little past 8 o’clock.” Use approximate language.
• Using the same model, placing the larger circle on first (making a clock with two hands) or another type of “teaching clock”, talk about what happens to the big hand as the little hand moves from hour to hour.
• Focus the discussion on what happens when the hour hand is halfway between hours. Discuss where the minute hand would be if the hour hand is a little before or past (approximately 15 minutes) an hour.
Discussing Homework • Have students share folded paper from Day 1, Lesson 23.1.
Begin with those papers that are folded into two equal parts; discuss “one-half” and “1/4. “
• Ask students what relationships they see between the sheets of paper and the Cuisenaire rods (Explore, Day 1, Lesson 23.1).
• Discuss how the size of the “whole” changes but the name of each equal part (“one half”) does not. Repeat with other papers/rods/relationships. It is very important to ask yourself, “What is the whole.”
LAUNCH: Materials: • Pattern blocks
• Pattern Block Relationships • Give students time to explore the pattern blocks. Review
“equivalent” and “equal parts.” • Ask them to find equivalent relationships: blocks of the same
color that can be put together so that they are equal to the size of the yellow hexagon (e.g., two red trapezoids, three blue rhombi, six green triangles).
• Ask students to find how many trapezoids are equal to a hexagon (2). Have a student prove the following: “The trapezoid is half the size of hexagon.” Discuss:
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• If the yellow hexagon is one whole, what fractional part of one is a blue rhombus (1/3)? Have a student prove the following: “The blue rhombus is one third the size of hexagon.”
• If the yellow hexagon is one whole, what fractional part of one is a green triangle (1/6)? Have a student prove the following: “The green triangle is one sixth the size of hexagon.”
• Discuss how the size of a fractional part is dependent upon the size of the whole. During Explore, the size of the whole will change.
EXPLORE: Materials: • Pattern blocks
Fraction Pattern Blocks • Have students find other fractional relationships (e.g., a
green triangle is 1/2 a blue rhombus, a green triangle is 1/3 a red trapezoid, a blue rhombus is 1/3 a yellow hexagon).
• Have students trace blocks and label with fraction words (e.g., one-half) or symbols (e.g., 1/2).
PRACTICE: As time allows: Pp. 337 and/or 338. SUMMARIZE: • Discuss the fractional relationships between Cuisenaire
rods, pattern blocks and folded paper. • Emphasize how the size of the fractional part is dependent
upon the size of the whole (e.g., the triangle has a value of one-third when the trapezoid is the whole but it has a value of 1/6 when the hexagon is the whole). Identifying the “whole” is very important.
Closure: Revisit purpose of the lesson with students. HOMEWORK: Materials: • P. TR 90
Suggestion: • Students cut out and cut apart circles and look for
relationships. • Students write about how these fraction circles relate to their
experiences with Cuisenaire rods, pattern blocks, and folded paper. Students will need these circles for a later assignment.
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DAY 3 UNIT 5: Number Sense and Fractions
Chapter 23: Parts of a Whole LESSON 23.3 TE, P. 339A
LESSON FOCUS: Other Fractions CALIFORNIA STANDARD:
Number Sense 4.2 Recognize fractions of a whole and parts of a group.
PURPOSE OF LESSON:
Learn to identify, model, and record fractions that represent more than 1 equal part.
ROUTINE: • Timer • Two sheets of acetate/acetate clocks from Module 3, Lesson 9.1
Suggestion: Throughout the Day • Set a timer to ring “on the quarter hour.” Write both the analog
and digital times. Students make observations at the end of the day.
Suggestion: Clock Hand Relationships • Use the overhead clock. Continue to focus the discussion on
what happens when the hour hand is halfway between hours. • Discuss where the minute hand would be if the hour hand is a
little before or past (approximately 15 minutes) an hour. LAUNCH: Materials: • A packet of five 3x18 inch strips of construction paper, in five different colors per student • Pair of scissors per student OR • P. TR 92
Fraction Kits • Model the following:
1. Take a strip of a specific color (all students should use the same color). Label strip “one whole.”
2. Take another strip, fold it in half, and cut it into two pieces. Label each piece 1/2. Discuss label.
3. Take another strip of a specific color. Fold and cut into into four pieces. Label each piece 1/4. Discuss label.
4. Take another strip of a specific color. Fold and cut into 8 pieces. Label each piece 1/8. Discuss label.
Note: P. TR 92 can be used as an alternative, if necessary. However, having students constructing their own Fraction Kits is more meaningful.
EXPLORE:
Fraction Kit Relationships • Students explore relationships between the strips. • Give students time to explore the fraction strips. Review
“equivalent” and “equal parts.” • Ask them to find equivalent relationships: strips of the same
color that can lie put together so that they are equal to the length of another color.
• Students discuss and write about their explorations. Students discuss and write about how the strips are related to Cuisenaire rods, pattern blocks, and folded paper.
PRACTICE: As time allows: Pp. 339 and/or 340. SUMMARIZE: • Students share their written work. They discuss the
relationships they observed in their Fraction Kits. • Students discuss how Fraction Kits are similar to and different
from other fraction models they have used. Closure: revisit purpose of the lesson with students.
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HOMEWORK: Materials: • A packet of five 3x18 inch strips of construction paper, in five different colors per student OR • P. TR 92
Suggestion: Students make a Fraction Kit at home using construction paper or P. TR 92.
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DAY 4 UNIT 5: Number Sense and Fractions
Chapter 23: Parts of a Whole LESSON 23.4 TE, P. 341A
LESSON FOCUS: Compare Unit Fractions CALIFORNIA STANDARD:
Number Sense 4.1 Recognize, name and compare unit fractions from 1/12 to 1/2.
PURPOSE OF LESSON:
Learn to compare unit fractions of a whole
ROUTINE: Materials: • Timer • Clock with moveable hands
Suggestion: Throughout the Day • Set a timer to ring “at five minute intervals” at different points
throughout the day. • Write both the analog and digital times. Students make
observations at the end of the day. Suggestion: Counting by Five Minute Intervals • Do Counting by Five Minute Intervals, TE, P. 125A. Rather
than focusing on the minute hand pointing on the 7, encourage students to express that it is about 35 minute after the hour.
• Suggest that students always look at the hour hand to learn the approximate time, and then focus on the minute hand.
LAUNCH: Materials: • Pattern blocks • Fraction Kit • Fraction die spinner 1/2, 1/2, 1/4, 1/4, 1/8, 1/8 or Pattern Block die spinner 1/2, 1/2, 1/3, 1/3, 1/6, 1/6 ( P.TR 107), per pair of students
Comparing Fractions • Review the fractional relationships in the pattern blocks,
considering the yellow hexagon as “1” or “one whole.” • Have students discuss the fraction “name” for the green
triangle (1/6), blue rhombus (1/3), and red trapezoid (1/2). • Students compare the fractional parts, writing less than and
greater than statements. (Note: Students may experience confusion because 3 is less than 6, yet 1/3 is greater than 1/6.
Example: 1/3 > 1/6 1/2 < 1 2/3 > 1/2 Introduce: Cover Up • Introduce Cover Up for two partners. The winner is the person
that covers up the whole first, with no overlapping pieces. • Players take turns rolling the fraction die (or spinning the
spinner). On each turn, players take the size piece that comes up on the die or spinner.
• Students must roll exactly what is needed to fill up the whole. EXPLORE: Materials: • Fraction Kits • fraction die (or spinner) per pair of students
Cover Up • Students play Cover Up.
PRACTICE: As time allows: Pp. 341 and/or 342.
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SUMMARIZE: • Discuss: What did you learn from playing Cover Up? What
greater than/less than statements can you make about the pieces you used to play the game (i.e., 1/4 is less than 1/2)?
Closure: • Revisit purpose of the lesson with students.
HOMEWORK: Materials: • Teacher’s Resource Book P. 107 • Fraction Kit/P. TR 92
Suggestion: • Students practice collaboratively playing Cover Up by
themselves or with an adult. • Students will need spinner for another assignment. OR Pp. 341 and/or 342
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DAY 5 UNIT 5: Number Sense and Fractions
Chapter 23: Parts of a Whole LESSON 23.5 TE, P. 343A
LESSON FOCUS: Fractions Equal to 1 CALIFORNIA STANDARD:
Number Sense 4.3 Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.
PURPOSE OF LESSON:
Learn to identify the fraction for the whole.
ROUTINE: Materials: • Timer • Clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring at different points throughout the day. • Write both the analog and digital times. Students make
observations at the end of the day. Suggestion: Predicting Readings • Shown an analog clock, students predict what a digital clock
will look like and vice versa. LAUNCH: Materials: • Cuisenaire rods • Pattern blocks • Fraction Kits • Folded paper
Equal to One • Show students the yellow hexagon as “one whole”; on top,
arrange six green triangles in the shape of the hexagon. • Discuss the fraction represented by one triangle (1/6) and
the fraction represented by one whole (6/6). • Take one triangle away; ask students what has been
removed (1/6) and what remains (5/6). • Repeat with rhombi. Discuss the fraction represented by one
rhombus (1/3) and the fraction represented by one whole (3/3). Take one rhombus away; ask students what has been removed (1/3) and what remains (2/3).
• Repeat with trapezoids. Discuss the fraction represented by
one trapezoid (1/2) and the fraction represented by one whole (2/2). Take one trapezoid away; ask students what has been removed (1/2) and what remains (1/2).
• Repeat this process with the other models that have been
used (Cuisenaire rods, and Fraction Kits). Discuss different ways to represent one whole with materials and symbols.
EXPLORE: Materials: • Fraction Kits • Fraction die/spinner per pair of students (see Day 4)
Cover Up • Students play Cover Up. Today, students write different
equations equal to one (recording the pieces used to cover the whole).
Example: 1/2 + 1/4+ 1/8 + 1/8 = 1
PRACTICE As time allows: Pp. 343 and/or 344
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SUMMARIZE: Discuss:
• What are different ways to combine fractions to make one whole?
Closure: • Revisit purpose of the lesson with students.
HOMEWORK: • Fraction Circles (P. TR 90) • 6-section spinner (P.TR 107), (label sections: 1/2, 1/2, 1/4, 1/4, 1/8 and 1/8)
Suggestion: • Students label Fraction Circles with fraction
names and collaboratively play Cover Up with an adult.
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DAY 6 UNIT 5: Number Sense and Fractions
Chapter 24: Parts of a Group LESSON 24.1 TE, P. 349A
LESSON FOCUS:
Explore Fractions
CALIFORNIA STANDARD:
Number Sense 4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole.
PURPOSE OF LESSON:
Learn the meaning of fractions of a group
ROUTINE: Materials: • Timer • Clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring at different points throughout the day. Write
both the analog and digital times. • Students make observations at the end of the day. Suggestion: Predicting Readings • Shown an analog clock, students predict what a digital clock will
look like and vice versa. LAUNCH: Materials: • A six-pack of soda • A four-pack of juice boxes • A five-pack of gum • A three-pack box of crackers OR • Other sets of objects
Introduce: Fractions as Part of a Set • Use a six pack of soda. Tell students, “Pretend that I drink one
can of soda. I can write a fraction to represent what part of the six-pack I drank.”
• Write one-sixth and 1/6. Discuss: • What does the ‘6’ refer to? • What does the ‘1’ refer to? • Why does this notation make sense? • What if I drank 2, 3, 4, 5, 6 sodas? Write the fraction in words and symbols. • If I drank 1 soda, how can I write a fraction to represent the sodas I didn’t drink? 2 sodas? 3 sodas? 4 sodas? 5 sodas?
• Write the fraction in words and symbols. • Repeat this process with other sets of objects.
EXPLORE: Materials: • A six-pack of soda • A four-pack of juice boxes • A five-pack of gum • A three-pack box of crackers
Fractions as Part of a Set • Students choose sets of objects. On the right side of at folded
sheet of paper, students draw pictures that represent all and parts of a set; on the left side of the paper, students record words and fractions that represent all and parts of the set.
Words Pictures Two-fifths of the gum is chewed. 2/5 Three-fifths of the gum is not chewed. 3/5
PRACTICE: As time allows: • Students share their fraction pictures with classmates. • Classmates try to guess the fraction that is represented in
pictures.
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SUMMARIZE: Discuss:
• How do fractions representing parts of a set (e.g., cans of soda from the parts of a set model) relate to fractions representing parts of a whole (e.g., triangles on a hexagon from the parts of a whole model)?
Closure: • Revisit purpose of the lesson with students.
HOMEWORK: Materials: • Homework: Parts of a Set worksheet
Suggestion: • Students look at home for objects that typically come in sets. • Students record pictures, words and fractions that represent all
and parts of the sets. • Students bring in sets to share with classmates.
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Homework: Parts of a Set Directions: Look for objects that usually come in sets. Record pictures, words and fractions to show all and parts of that set. Repeat with other sets. Bring in sets to share with your classmates.
Pictures Words Fractions
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DAY 7 UNIT 5: Number Sense and Fractions
Chapter 24: Parts of a Group LESSON 24.2 TE, P. 351A
LESSON FOCUS: Unit Fractions CALIFORNIA STANDARD:
Number Sense 4.2 Recognize fractions of a whole and parts of a group.
PURPOSE OF LESSON:
Identify, model, and record equal parts of groups.
ROUTINE: Materials: • Timer • Clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring “at five minute intervals” at different points
throughout the day. Write both the analog and digital times. • Students make observations at the end of the day. Suggestion: Counting by Five Minute Intervals • Do Counting by Five Minute Intervals, TE, Pg. 125A. Rather
than focusing on the minute hand pointing on the 7, encourage students to express that it is about 35 minute after the hour.
• Suggest that students always look at the hour hand to learn the approximate time, and then focus on the minute hand.
LAUNCH: Materials: • 12 two-color counters (or lima beans painted on one side) per student
Sharing Homework • Students share homework from Day 6, Lesson 24.1. Students
discuss fractions that could represent all and parts of the sets of objects students have brought in to share.
Fractions with Two-Color Counters • Give students directions:
1. Divide the counters into three equal groups, all showing the yellow side.
2. How many groups? (3) 3. What fractional part of the whole set is represented by
one group? (1/3) 4. How many counters are in 1/3? (4) 5. Flip the counters over in one group. What fractional part
of the whole set is red? (1/3) What fractional part of the whole set is yellow? (2/3)
6. How many counters are in 1/3? (4) 2/3? (8) • Rearrange the counters into two equal groups.
1. How many groups? (2) 2. What fractional part of the whole set is represented by
one group? (1/2) 3. How many counters are in 1/2? (6) 4. Flip the counters over in one group. What fractional part
of the whole set is red? (1/2) What fractional part of the whole set is yellow? (1/2)
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• Rearrange the counters into six equal groups. 1. How many groups? (6) 2. What fractional part of the whole set is represented by
one group? (1/6) 3. How many counters are in 1/6? (2) 4. Flip the counters over in one group. What fractional part
of the whole set is red? (1/6) What fractional part of the whole set is yellow? (5/6)
5. How many counters are in 1/6? (2) How many counters are in 5/6? (10)
• Rearrange the counters into four equal groups.
1. How many groups? (4) 2. What fractional part of the whole set is represented by
one group? (1/4) 3. How many counters are in 1/4? (3) 4. Flip the counters over in one group. What fractional part
of the whole set is red? (1/4) What fractional part of the whole set is yellow? (3/4)
5. How many counters are in 1/4? (3) How many counters are in 3/4? (9)
EXPLORE: Materials: • 12 two-color counters per student
More Fractions with Two-Color Counters • Students show a set of counters with 2/6 of their yellow sides
showing. • Students find as many solutions as they can, using 12 counters
or less. • Students draw and write about what they have shown.
PRACTICE: As time allows: • Students compare work with a partner and/or complete Pp.
351 and/or 352. SUMMARIZE: • Students share solutions from Explore with their classmates.
Closure: • Revisit purpose of the lesson with students.
HOMEWORK: Materials • 12 two-color counters per students • Homework: Fractions with Two-Color Counters worksheet
Suggestion: • Students use counters at home. They find different solutions
for 1/2, 1/4, and 1/3, using all or part of their counters. • Students draw, write and record fractions to show how they
used the counters.
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Homework: Fractions with Two-Color Counters Directions: Use 12 two-color counters. Find different solutions for 1/2, 1/4 and 1/3, using all or part of your counters. Draw and write about how you used the counters.
Fraction Drawing Writing
1/2
1/4
1/3
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DAY 8 UNIT 5: Number Sense and Fractions
Chapter 24: Parts of a Group LESSON 24.3 TE, P. 353A
LESSON FOCUS: Other Fractions CALIFORNIA STANDARD:
Number Sense 4.2 Recognize fractions of a whole and parts of a group.
PURPOSE OF LESSON:
Learn to identify fractions of a group that represent more than one equal part.
ROUTINE: Materials: • Timer • Clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring at different points throughout the day. Write
both the analog and digital times. • Students make observations at the end of the day. Suggestion: Predicting Readings • Shown an analog clock, students predict what a digital clock
will look like and vice versa. LAUNCH: Materials: • Color tiles per student: 12 red, 12 blue, 12, green, 12 yellow
Fractions with Color Tiles • Give students directions:
1. Make three equal groups of color tiles, each group a different color. 2. What fractional part of the whole set is represented by
one group? (1/3) 3. How many counters are in 1/3? (4) 2/3? (8) 4. Make two equal groups, each group a different color.
What fractional part of the whole set is represented by one group? (1/2)
5. How many counters are in 1/2? (6) 6. Make four equal groups of color tiles, each group a
different color. 7. What fractional part of the set is represented by one
group? (1/4) 8. How many color tiles are in 1/4? (3) 2/4? (6) 3/4? (9)
EXPLORE: Materials: • Color tiles
More Fractions with Color Tiles • Students make a set of tiles that is 2/6 yellow. • They find as many solutions as they can, using 12 tiles or less. • Students draw and write about what they have shown.
PRACTICE: As time allows: Pp. 353 and/or 354. SUMMARIZE: • How does today’s activity relate to what the lesson with two-
color counters? (Day 7, Lesson 24.2) Closure: • Revisit purpose of the lesson with students.
HOMEWORK: • Students write story problems about fractions that name parts of groups.
• For example: Keisha has 10 chocolate chip cookies and 10 oatmeal cookies. What fraction of the cookies are oatmeal? (1/2)
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DAY 9 UNIT 5: Number Sense and Fractions
Chapter 24: Parts of a Group LESSON 24.4 TE, P. 355A
LESSON FOCUS: Compare Parts of a Group CALIFORNIA STANDARD:
Number Sense 4.2 Recognize fractions of a whole and parts of a group.
PURPOSE OF LESSON:
Learn to compare fractions of a group.
ROUTINE: Materials: • Timer • Clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring “at five minute intervals” at different points
throughout the day. Write both the analog and digital times. • Students make observations at the end of the day. Suggestion: Counting by Five Minute Intervals • Do Counting by Five Minute Intervals, TE, P. 125A. Rather
than focusing on the minute hand pointing on the 7, encourage students to express that it is about 35 minute after the hour.
• Suggest that students always look at the hour hand to learn the approximate time, and then focus on the minute hand.
LAUNCH: Materials: • Snap cubes
Model: Comparing Parts of a Group • Students use counters to model the following:
• Use 12 snap cubes. Make 1/3 red and 2/3 blue. Which is greater: 1/3 or 2/3? How do you know? • Use 12 snap cubes. Make 1/4yellow and 3/4green. Which is greater: 1/4 or 3/4? How do you know? • Use 12 snap cubes. Make 2/6 red and 4/6 blue. Which is greater: 2/6 or 4/6? How do you know?
EXPLORE: Materials: • Familiar manipulatives (snap cubes, color tiles, two–color counters) • Homework from Day 8, Lesson 24.3
• Students exchange homework papers. • Students solve each others story problems and record
solutions using words, numbers, and/or pictures.
PRACTICE: As time allows: Pp. 355 and/or 356 SUMMARIZE: Closure:
• Revisit purpose of the lesson with students. How do you know that 2/3 is greater than 1/3? How do you know that 1/2 is greater than 1/4?
HOMEWORK: Materials: • P. FA 98 • Six pennies • A cup
Suggestion: Family Involvement Activities, P. FA 98.
Harcourt Math – Grade 2 MODULE 10
Revised 3/31/04 344
DAY 10 UNIT 5: Number Sense and Fractions
Chapter 24: Parts of a Group LESSON 24.5 TE, P. 357A
LESSON FOCUS: Problem Solving: Making a Model CALIFORNIA STANDARD:
Mathematical Reasoning 1.2 Use tools, such as manipulatives or sketches, to model problems.
PURPOSE OF LESSON:
Make a model to solve problems.
ROUTINE: Materials: • timer • clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring at different points throughout the day. Write
both the analog and digital times. • Students make observations at the end of the day. Suggestion: Predicting Readings • Shown an analog clock, students predict what a digital clock
will look like and vice versa. LAUNCH:
Story Problems with Fractions • Write the following story problem on the board or overhead:
At the bake sale, 3 children bought and shared one brownie. How much did each child get?
• Ask students to think about how they would figure out the problem.
• Ask them to share their strategies with the class. Model, or have students model, ways of representing their strategies with pictures and words.
• Connect fractional notation to the students’ solutions. EXPLORE: Materials: • “Brownies” (equal size paper “brownies”, 21 “brownies” per student; if using worksheet 2 ½ copies per student)
Sharing Brownies • Present the following problem to students:
If I gave each group of four children four brownies to share, how much would each child get?
• Discuss: Sharing equally.
• If I gave each group of four children one brownie to share, how much would each child get?
• If I gave each group of four children two brownies to share, how much would each child get?
• If I gave each group of four children three brownies to share, how much would each child get?
• If I gave each group of four children five brownies to share, how much would each child get?
• If I gave each group of four children six brownies to share, how much would each child get?
• Students use paper “brownies”. Students glue down each person’s share and record the fraction to represent how much each person got.
Harcourt Math – Grade 2 MODULE 10
Revised 3/31/04 345
PRACTICE: As time allows: Pp. 357 and/or 358 SUMMARIZE: • Students present Sharing Brownies solutions to their
classmates. Closure: • Revisit purpose of the lesson with students.
HOMEWORK: Materials: • Brownies Worksheet (equal size paper “brownies”, 8 “brownies” per student; if using worksheet, 1 copy per student
Suggestion: • Students solve the following problem and record their solutions
with words, numbers and pictures: Eight people are sharing 12 brownies. How much did each person get, if everyone got a fair share?
Harcourt Math – Grade 2 MODULE 10
Revised 3/31/04 346
“Brownies”
Harcourt Math – Grade 2 MODULE 10
Revised 3/31/04 347
DAY 11 UNIT 5: Number Sense and Fractions
Chapters 23 and 24: Parts of a Whole and Parts of a Set Assessment
TE, P. 345/359
LESSON FOCUS: Assessment CALIFORNIA STANDARD:
Number Sense 4.2 Fractions of a whole and parts of a group.
PURPOSE OF LESSON:
Check understanding of concepts, skills and problem solving from Chapters 23 and 24.
ROUTINE: Materials: • timer • clock with movable hands
Suggestion: Throughout the Day • Set a timer to ring “at five minute intervals” at different points
throughout the day. • Write both the analog and digital times. • Students make observations at the end of the day. Suggestion: Counting by Five Minute Intervals • Do Counting by Five Minute Intervals, TE, P. 125A. Rather
than focusing on the minute hand pointing on the 7, encourage students to express that it is about 35 minute after the hour.
• Suggest that students always look at the hour hand to learn the approximate time, and then focus on the minute hand.
LAUNCH: Materials: • Cuisenaire rods • Fraction Kits • Color tiles • Snap cubes • Pattern blocks • Sets of familiar objects • Two-color counters • “Brownies”
Review • Discuss the models used in the fraction activities addressing
parts of a whole and parts of a set.
EXPLORE: Materials: • Cuisenaire rods • Fraction Kits • Color tiles • Snap cubes • Pattern blocks • Sets of familiar objects • Two-color counters • “Brownies” • Snap cubes
Sample Problems • Give students sample problems similar to those on Pp. 345,
346, 359 and 360. • Let students use familiar materials to model solutions to the
problems. • Provide students opportunities to share solution strategies with
their classmates.
PRACTICE: As time allows: Pp. 345, 346; 359, 360.
Harcourt Math – Grade 2 MODULE 10
Revised 3/31/04 348
SUMMARIZE: Closure:
• Revisit purpose of the lesson with students. Open ended questions:
• What have you learned about fractions? Chart responses. HOMEWORK: Suggestion:
• Family Involvement Activities pages FA 94 and/or FA 100.