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Getting Started
Mental Math and Reflexes
Math Message
Pose problems like the following as children write the answers
on slates. They may use tool-kit clocks as needed.
Using your ruler, draw a line segment
1 minute ⫽
seconds 60
1 hour ⫽
minutes 60
1
ᎏᎏ hour ⫽
2
minutes 30
1
ᎏᎏ hour ⫽
4
2
ᎏᎏ hour ⫽
4
3
ᎏᎏ hour ⫽
4
1
ᎏᎏ hour ⫽
3
1
ᎏᎏ hour ⫽
12
1
ᎏᎏ hour ⫽
6
3
that is 1ᎏ4ᎏ inches long on your slate.
1
minutes 20
minutes 5
minutes 10
Divide the line segment into ᎏ4ᎏ-inch segments.
1
How many ᎏ4ᎏ-inch segments are there?
Home Link 8 7 Follow-Up
䉬
minutes 15
Go over the answer to Problem 5. The
minutes 30
ᎏ
ᎏᎏ
diagram shows 2 wholes and ᎏ
12 (or 3 )
of a whole. The corresponding mixed number, then, is
minutes 45
ᎏ
ᎏᎏ
2ᎏ
12 (or 2 3 ).
1
4
4
1
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
1
4
If an overhead projector is available, use it to go over the solution.
1
Lead children to the conclusion that since there are seven ᎏ4ᎏ-inch
7
7
segments, the line segment is ᎏ4ᎏ inches long. ᎏ4ᎏ inches is another
3
name for 1ᎏ4ᎏ inches.
䉴 Writing and Solving Fraction
1
4
1
4
1
4
1
4
3
1
14
Math Message solution
Adjusting the Activity
1
You and the children make up stories involving fractions of sets.
Children solve the problems in any way they can—using pennies
or counters, drawing pictures or doodles, and so on. You might
want to begin with stories such as the following:
●
1
4
0
WHOLE-CLASS
ACTIVITY
Number Stories
1
4
Extend the line segment ᎏ4ᎏ inch.
Think of the line segment as part of a number
line from 0 to 2. With children, label the points
1
that are ᎏ4ᎏ inch apart.
AUDITORY
䉬
KINESTHETIC
䉬
TACTILE
䉬
VISUAL
3
Andy bought 24 stamps for his stamp collection. ᎏ4ᎏ of the
stamps were from the United States. How many stamps were
from the United States? 18 stamps
Possible solution strategy: Take 24 coins or counters and divide
them into 4 equal sets. Each set consists of 6 counters and is
1
1
ᎏᎏ of the total, so ᎏᎏ of 24 ⫽ 6. Three sets consist of 18 counters and
4
4
3
3
are ᎏ4ᎏ of the total, so ᎏ4ᎏ of 24 ⫽ 18.
0
1
4
2
4
3
4
1
2
3
1 14 14 14 2
Extending the line segment
Ongoing Assessment: Informing Instruction
Watch for children who are having difficulty solving problems with fractions of
sets. Remind them that the denominator (the bottom number in a fraction) tells
the total number of equal groups, and the numerator (the top number in a
fraction) tells the number of equal groups being considered. Children count the
objects in the number of groups given by the numerator to solve the problem.
Have children use manipulatives to act out each problem.
Lesson 8 8
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●
Ruthann read 12 books in the last 4 months. Three were
3
1
ᎏᎏ
nonfiction. What fraction of the books were nonfiction? ᎏ1ᎏ
2 or 4
of the books On average, how many books did she read per
month? 3 books
Possible solution strategy: Three out of 12 books is equivalent to
3
ᎏᎏ of the total. Take 12 counters and divide them into 4 sets of
12
1
3. Each set is ᎏ4ᎏ of the total. To find the average number read
per month, divide 12 by 4.
●
3
Kiko has done ᎏ5ᎏ of the math problems. What fraction of the
2
math problems does she still have to do? ᎏ5ᎏ of the problems
Possible solution strategy: Suppose Kiko has 5 problems to
3
solve. She solved ᎏ5ᎏ of the problems—3 problems. This leaves
2
2 problems still to be solved. Two out of 5 problems is ᎏ5ᎏ of the
problems.
●
2
5
Which would you rather have— ᎏ3ᎏ of a can of lemonade or ᎏ6ᎏ of a
5
can of lemonade? Assuming you like lemonade, ᎏ6ᎏ of a can
Possible solution strategy: Use Fraction Cards to compare the
2
4
fractions, or reason as follows: ᎏ3ᎏ is equivalent to ᎏ6ᎏ, which is less
5
5
2
than ᎏ6ᎏ. Therefore, ᎏ6ᎏ is more than ᎏ3ᎏ.
●
1
It took Nathan 1ᎏ4ᎏ hours to do his homework. How many
minutes did he spend on homework? 75 minutes
1
1
Possible solution strategy: 1 hour ⫽ 60 minutes, ᎏ4ᎏ hour ⫽ ᎏ4ᎏ of
1
60 minutes, or 15 minutes. Therefore, 1ᎏ4ᎏ hours ⫽ 60 minutes
⫹ 15 minutes ⫽ 75 minutes.
●
1
Tamekka had 20 books to put into her bookcase. She put ᎏ2ᎏ of
1
the books on the top shelf and ᎏ2ᎏ of the remaining books on the
second shelf. How many books did she still need to put into the
bookcase? 5 books What fraction of the total number of books is
1
that? ᎏ4ᎏ of the total
1
Possible solution strategy: ᎏ2ᎏ of 20 ⫽ 10, so she put 10 books on
1
the top shelf, which left 10 books to be shelved. She put ᎏ2ᎏ of the
remaining 10 books on the second shelf—that’s 5 books. She
put a total of 10 books ⫹ 5 books, or 15 books, into the
bookcase which left 5 books to be shelved.
After working through a few examples, ask volunteers to make up
stories for the class to solve.
Adjusting the Activity
Make up additional fraction number stories as appropriate before
children solve problems independently. Use similar number stories in future
Minute Math+ sessions.
A U D I T O R Y
690
Unit 8 Fractions
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
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䉴 Solving Fraction Stories
PARTNER
ACTIVITY
(Math Journal 2, pp. 200 and 201)
Children work with a partner or independently to complete
journal pages 200 and 201.
Ongoing Assessment:
Recognizing Student Achievement
Journal page 201
Problems
10–13
夹
Use journal page 201, Problems 10–13 to assess children’s progress toward
solving problems involving fractional parts of a collection. Children are making
adequate progress if they are able to successfully complete Problems 10–13.
Some children may successfully complete Problems 14–16.
[Number and Numeration Goal 2]
Student Page
Date
Student Page
Time
LESSON
Date
Fraction Number Stories
8 8
䉬
8 8
䉬
Solve these number stories. Use pennies, counters, or draw
pictures to help you.
1.
There are 8 apples in the package.
Glenn did not eat any. What fraction
of the package did Glenn eat?
3.
Anik bought a dozen eggs at the
supermarket. When he got home, he
1
found that ᎏᎏ of the eggs were cracked.
6
How many eggs were cracked?
4.
I had 2 whole cookies. I gave you ᎏᎏ
4
of 1 cookie. How many cookies did I
have left?
2
2
Chante used ᎏᎏ of a package of
3
ribbon to wrap presents. Did she use
3
more or less than ᎏᎏ of the package?
5.
There are 10 quarters. You have 3.
I have 2. What fraction of the
quarters do you have?
1ᎏ34ᎏ
6.
3
ᎏᎏ
10
2
ᎏᎏ
10
or
7.
or
cookies
1
ᎏᎏ
3
1
Neither;
1ᎏ12ᎏ
⫽
1ᎏ24ᎏ
Math Journal 2, p. 200
夹
夹
10. 6
ᎏᎏ
12
12. 3
ᎏᎏ
12
夹
夹
14. ᎏ3ᎏ
4
1
ᎏᎏ
2
Dorothy walks 1ᎏᎏ miles to school.
2 2
Jaime walks 1ᎏᎏ miles to school.
4
Who walks the longer distance?
8.
Sample answers:
7
ᎏᎏ
12
1
One day, Edwin read ᎏᎏ of a book.
3
1
The next day, he read another ᎏᎏ of
3
the book. What fraction of the book
had he read after 2 days?
What fraction of the quarters do
we have together?
5
ᎏᎏ
10
Draw eggs in each carton to show the fraction.
Example:
What fraction of the book did he
have left to read?
1
ᎏᎏ
5
continued
Sample answer: Jerome gave 2 new pens to
his little sister. If the package had 10 pens in
it, what fraction of the pens did he keep for
8
himself? ᎏ1ᎏ0 of the pens
eggs
2
ᎏᎏ
3
What fraction of the quarters do
I have?
Fraction Number Stories
Write a fraction story. Ask your partner to solve it.
1
4
less
9.
2.
0
ᎏᎏ
8
Time
LESSON
Twelve children shared
2 medium-size pizzas equally.
What fraction of 1 whole pizza
did each child eat?
ᎏ1ᎏ
6
or
ᎏ2ᎏ
12
1
16. Julie drank ᎏᎏ of a glass of juice.
4
Draw an empty glass.
Shade in the glass to show how much
juice is left. Write the fraction.
11. 4
ᎏᎏ
12
13. 1
ᎏᎏ
2
15. ᎏ1ᎏ
3
3
–
4
of the
glass of
juice is left.
Math Journal 2, p. 201
Lesson 8 8
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2 Ongoing Learning & Practice
䉴 Reviewing the Line Plot
WHOLE-CLASS
ACTIVITY
Routine
(Student Reference Book, pp. 79–81)
Use pages 79–81 in the Student Reference Book to review data
landmarks. On the board, prepare a line plot with stick-on notes
using this data: 42, 42, 43, 45, 45, 46, 46, 46, 46, 47, 47, 48, 48,
48, 48, 48, 50, 51, 53. To provide a context for children, suggest
that the line plot shows the arm span measures in inches of a
class of third graders.
Number
of
Children
42 43 44 45 46 47 48 49 50 51 52 53
Number of Inches
Line plot of 3rd grade arm spans
Ask children to identify the maximum arm span 53 inches, the
minimum arm span 42 inches, the mode 48 inches, and the range
11 inches from the line-plot data. Next, ask children to think of
another way to find the median without removing the stick-on
notes from the line plot. If no one suggests it, have volunteers
cross out the first and last stick-on note from each end of the line
plot over and over until one remains—this is the median arm
span. 47 inches
Number
of
Children
42 43 44 45 46 47 48 49 50 51 52 53
Number of Inches
The median arm span is 47 inches.
Have children imagine that you will put all the stick-on notes in a
container and draw one out at random without looking. To
practice comparing chances for two different events, pose the
following:
●
692
Unit 8 Fractions
Compare the chance of drawing a note that says 42 with the
chance of getting a note that says 50. There is a greater chance
of drawing 42 than 50. Explain how you figured it out. There
are two 42s and only one 50.
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Student Page
●
Compare the chances of drawing 42 and 47. The chances are
equal because there are two 42s and two 47s.
Date
●
8 8
Compare the chances of drawing 46 and 48. There is a greater
chance of drawing 48 because there are five 48s and four 46s.
Compare the chances of drawing 48 or a number larger than
48. There is a greater chance of drawing 48 because there are
five 48s and only three numbers larger than 48.
Math Boxes
䉬
1.
●
Time
LESSON
2
3.
Draw two ways to show ᎏᎏ
2.
6 feet ⫽
2
yards
1
1ᎏ2ᎏ
Sample answers:
1
3
1
1ᎏᎏ
2
feet ⫽ 18 inches
1ᎏᎏ yards ⫽
yards ⫽
4
54
feet
inches
246
22–24
3.
Use simple drawings to show all of
the possible ways you can take
2 blocks from the bag.
4.
4
ᎏᎏ
5
Tara frosted of the cupcakes.
What fraction of the cupcakes
1
ᎏᎏ
5
is not frosted?
1
䉴 Math Boxes 8 8
䉬
Did she frost more or less than ᎏᎏ
2
of the cupcakes?
more
INDEPENDENT
ACTIVITY
If there were 20 cupcakes in all,
how many did she frost?
16 cupcakes
(Math Journal 2, p. 202)
5.
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-6. The skill in Problem 6
previews Unit 9 content.
Show two ways a team can score
37 points in a football game.
6.
Sample answer:
7
points
6
points
3
points
2
points
3
2
1
3
2
1
2
1
Will, Wes, Sam, and Ameer want
to share $25 equally. How much
money will each person get?
Answer:
Write a number model:
Writing/Reasoning Have children draw or write an
4
answer to the following: In Problem 4, is ᎏ5ᎏ more or less
1
4
1
than ᎏ2ᎏ? How do you know? Sample answer: ᎏ5ᎏ is more than ᎏ2ᎏ
because 4 of 5 equal parts is bigger than 1 of 2 equal parts.
䉴 Home Link 8 8
䉬
Use your calculator. Pretend the
division key is broken. Solve this
problem.
(3 ⫻ 7) ⫹ 6 ⫹ (2 ⫻ 3) ⫹
(2 ⫻ 2) ⫽ 37; (2 ⫻ 7) ⫹
(3 ⫻ 6) ⫹ 3 ⫹ 2 ⫽ 37
$6.25
16 17
Math Journal 2, p. 202
INDEPENDENT
ACTIVITY
(Math Masters, p. 262)
Home Connection Children solve fraction number stories
like those in the lesson. They solve multidigit addition
and subtraction problems.
3 Differentiation Options
Home Link Master
Name
ENRICHMENT
䉴 Solving Math Curse
SMALL-GROUP
ACTIVITY
15–30 Min
Number Stories
HOME LINK
88
䉬
Family
Note
Date
Time
Fraction Number Stories
In class we have been solving many kinds of fraction number stories. If some of these Home
Link problems seem difficult, encourage your child to model them with pennies or draw
pictures to help solve them.
22–24
Please return this Home Link to school tomorrow.
Solve these fraction stories. Use pennies, counters, or pictures to help.
To apply children’s understanding of fraction concepts, read
Math Curse and identify and solve the fraction problems in the
story. Have children write their own fraction number stories based
on daily activities, like those in Math Curse. The class can then
discuss and solve these stories. Consider assembling the stories
into a class book.
1. Elizabeth bought a dozen eggs. She dropped her bag on the
2
way home, and ᎏᎏ of the eggs broke. How many eggs broke?
3
3
1
2. Katie mowed ᎏ4ᎏ of the lawn before lunch. What
8
eggs
ᎏᎏ
fraction of the lawn did she have to finish after lunch? 4 of the lawn
1
3. Donnie lives 1 mile from school. One day he walked ᎏᎏ of the way to school
2
when he remembered he had to return home to get a book.
When he finally made it to school, how far did he walk in all?
2
miles
4. Sheridan made 4 trays of cookies. She took 2 trays to school for her
3
classmates. She took ᎏᎏ of a tray of cookies to her
ᎏ1ᎏ
4
teacher. How many trays of cookies did Sheridan have left?
14
trays
5. Jackson needed 2 pints of milk for his recipe. If he had one gallon of milk
in the refrigerator, how much did he use?
ᎏ1ᎏ
(Hint: 1 gallon ⫽ 4 quarts, and 1 quart ⫽ 2 pints) 4 gallon
EXTRA PRACTICE
䉴 Minute Math+
SMALL-GROUP
ACTIVITY
5–15 Min
To offer children more experience with fractions, see the following
pages in Minute Math+: pp. 86, 90, 92, and 155.
Practice
Unit
Write these problems on the back of this page. Solve and
show your work.
6. 2,083 ⫹ 4,678 ⫽
7. 6,714 ⫺ 3,806 ⫽
8. 4,762 ⫹ 4,762 ⫽
6,761
2,908
9,524
Math Masters, p. 262
Lesson 8 8
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693