EM07TLG2_G3_U08_L03.qxd
1/17/06
10:38 AM
Page 660
Getting Started
Mental Math and Reflexes
Math Message
Have children write numbers from dictations on slates.
Then they identify digits in given places.
Hank said, “I shared 24 pieces of candy with my
friends.
Write thirty-two hundredths. Underline the digit in the tenths
place. 0.32
Write five hundredths. Circle the digit in the tenths place.
0. 0 5
Write two and nine-tenths. Write an X through the digit in
the tenths place. 2.9
Write four hundred six thousandths. Circle the digit in the
thousandths place. Write an X through the digit in the tenths
place. 0.40 6
1
1
1
I gave ᎏ2ᎏ of the candy to Kim, ᎏ3ᎏ to Juan, and ᎏ4ᎏ to Moira.”
Explain how you know Hank made a mistake.
Home Link 8 2 Follow-Up
䉬
Briefly review answers. Have children share their
strategies.
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Children share their answers. Hank could not possibly have done
what he said. He would have had to give 12 pieces of candy to Kim
1
1
(ᎏ2ᎏ of the candy), 8 pieces to Juan (ᎏ3ᎏ of the candy), and 6 pieces to
1
Moira (ᎏ4ᎏ of the candy). This adds up to 26 pieces, which is more
than he had to give.
䉴 Exploration A: Finding Relationships
Student Page
Date
Time
LESSON
Fractions with Pattern Blocks
83
䉬
Exploration A
Work with a partner.
Materials
ⵧ pattern blocks
ⵧ Pattern-Block Template
Part 1
Cover each shape with green
pattern blocks. What fractional part of
each shape is 1 green pattern block? Write the fraction under each shape.
1
2
1
6
1
3
Part 2
Cover each shape with green
pattern blocks. What fractional part of each
shape are 2 green pattern blocks? Write the fraction next to each shape.
2
3
2
—
10
2
1
—
—
6 or 3
2
1
—
—
8 or 4
Math Journal 2, p. 185
660
1
or —
5
Unit 8 Fractions
PARTNER
ACTIVITY
among Shapes
(Math Journal 2, pp. 185–187)
Children use green pattern-block triangles and blue pattern-block
rhombuses. Various shapes are displayed on journal pages
185–187. Children find what fractional part of each shape is
covered by one or two triangles and one or two rhombuses. Some
shapes on journal pages 186 and 187 cannot be tiled entirely by
rhombuses, but children can solve these problems by rediscovering
that a pattern-block rhombus has the same area as two triangles.
Children are reminded on journal page 187 that the number
under the fraction bar (the denominator) names the number of
equal parts into which the whole shape is divided. Children record
their fractions and use their Pattern-Block Templates to draw how
the blocks were used to divide the shapes.
For a follow-up activity, partners in each group can compare their
fractions and use the blocks to check their answers. In some cases,
more than one fraction is correct.
EM07TLG2_G3_U08_L03.qxd
1/17/06
10:38 AM
Page 661
Student Page
䉴 Exploration B: Taking Apart
INDEPENDENT
ACTIVITY
and Putting Together Squares
(Math Masters, pp. 242 and 243)
Date
LESSON
83
䉬
Time
Fractions with Pattern Blocks
continued
Part 3
Cover each shape with blue
pattern blocks. What fractional part of
each shape is 1 blue pattern block? Write the fraction under each
shape. If you can’t cover the whole shape, cover as much as you can.
Think: Is there another block that would cover the rest of the shape?
Children work independently or with a partner to find ways to cut
two same-size squares into pieces and reassemble the pieces into a
single square.
The solution involves cutting each square into same-size triangles.
The most efficient way is to cut each square along one of the
diagonals. The pieces can then be reassembled as shown below.
1
5
1
4
1
3
2
3
Math Journal 2, p. 186
One solution for Exploration B
Another solution for Exploration B
The squares can also be cut into 8 or 16 same-size triangles, but
this makes it more difficult to reassemble them into a square. It is
not possible to solve the problem by cutting the squares into
smaller squares. Have children share strategies as time allows.
Teaching Master
Name
LESSON
83
䉬
Date
Student Page
Time
Taking Apart and Putting Together
Exploration B
Materials
Date
LESSON
83
䉬
Time
Fractions with Pattern Blocks
continued
Try This
䊐 Math Masters, p. 243 (2 squares)
Part 4
䊐 scissors
Cover each shape with blue
pattern blocks. What fractional part of each shape
would 2 blue pattern blocks cover? Write the fraction under each shape.
䊐 glue or tape
䊐 paper
There are two squares on Math Masters, page 243. Your task is to cut
each square into pieces, and then to put all the pieces from both
squares together to make one large square. DON’T START YET!
䉬 Plan what you will do before you cut. It is possible to solve the puzzle
by cutting each square into 2 pieces. You can also solve the puzzle
by cutting each square into more than 2 pieces.
䉬 Cut only on the dashed lines.
䉬 Use all of the pieces.
䉬 Don’t leave any empty spaces between the pieces.
䉬 Don’t overlap any pieces.
1
2
䉬 Glue or tape your finished square onto a full sheet of paper.
䉬 Now cut out the two squares on Math Masters, page 243 and solve
the puzzle.
2
3
4
9
Part 5
Use your Pattern-Block Template to show how you divided the shapes in
each section. Remember: The number under the fraction bar names the
number of equal parts into which the whole shape is divided.
Follow-Up
Get together with the rest of the group.
䉬 Compare your answers.
䉬 Use the blocks to check your answers.
䉬 Decide whether more than one fraction can be correct.
Math Masters, p. 242
Math Journal 2, p. 187
Lesson 8 3
䉬
661
EM07TLG2_G3_U08_L03.qxd
1/17/06
10:38 AM
Page 662
Student Page
Date
䉴 Exploration C:
Time
LESSON
8 3
䉬
Dressing for the Party
Dressing for the Party
Exploration C
Work in a group of four.
Materials
ⵧ
ⵧ
ⵧ
ⵧ
SMALL-GROUP
ACTIVITY
Math Masters, p. 244 (Pants and Socks Cutouts)
scissors
tape
blue, red, green, and black crayons or coloring pencils
Problem
Pretend that you have 4 pairs of pants: blue, red, green,
and black. You also have 4 pairs of socks: blue, red,
green, and black. You have been invited to a party. You
need to choose a pair of pants and a pair of socks to
wear. (Of course, both socks must be the same color.)
For example, the pants could be blue and both socks black.
(Math Journal 2, pp. 188 and 189; Math Masters, p. 244)
Children work in groups of four to find all possible color
combinations of pants and socks when 4 pairs of pants and
4 pairs of socks come in 4 different colors. To support English
language learners, discuss the different uses of the word pair.
How many different combinations of pants and socks
are possible?
Strategy
Use the cutouts on Math Masters, page 244, and crayons to help you
answer the question.
Before you answer the question, decide on a way for your group to
share the following work.
䉬 Color the pants in the first row blue.
䉬 Color the pants in the second row red.
䉬 Color the pants in the third row green and those in the fourth row black.
䉬 Color the socks in the same way.
䉬 Cut out each pair of pants and each pair of socks.
䉬 Tape together pairs of pants and pairs of socks to show different
outfits. Check that you have only one of each outfit.
Math Journal 2, p. 188
Children color, cut out, and tape together as many different-color
outfits as possible. There are 16 different combinations.
(Additional pants and socks are included on Math Masters, page
244 in case of mistakes.)
Have children within each group share the work equally. When
they have made all possible combinations, each group writes a
report on journal page 189 describing how they found the answer.
2 Ongoing Learning & Practice
Student Page
Date
8 3
䉬
Dressing for the Party
1.
How many different combinations of
pants and socks did your group find?
2.
Is this all of the possible combinations?
3.
How do you know?
continued
16 combinations
yes
Sample answer: Each color of pants is paired
with each color of socks.
How did your group divide up the work?
Answers vary.
5.
How did your group solve the problem?
Answers vary.
Math Journal 2, p. 189
662
SMALL-GROUP
ACTIVITY
(Math Masters, p. 449; Student Reference Book, p. 295)
Time
LESSON
4.
䉴 Playing Multiplication Bingo
Unit 8 Fractions
Children play Multiplication Bingo introduced in Lesson 7-3 to
practice multiplication facts. See the rules for Multiplication Bingo
(All Facts) on page 295 in the Student Reference Book.
EM07TLG2_G3_U08_L03.qxd
1/17/06
11:15 AM
Page 663
Student Page
䉴 Math Boxes 8 3
INDEPENDENT
ACTIVITY
䉬
(Math Journal 2, p. 190)
Date
Time
LESSON
8 3
䉬
1.
Math Boxes
Double the amounts.
$1.10
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 8-1. The skill in Problem 6
previews Unit 9 content.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 4
夹
$2.50
$10.50
$12.50
$25.00
3.
5
8
5
It has
It has
Use Math Boxes, Problem 4 to assess children’s progress toward
understanding that parentheses affect the order in which operations are carried
out. Children are making adequate progress if they successfully complete 2 of
the number sentences. Some children may be able to successfully complete all
of the number sentences.
5 ⫻ 90 ⫽
5 ⫻ 900 ⫽
24 ⫽ 3 ⫻ 8
2,400 ⫽ 30 ⫻ 80
24,000 ⫽ 300 ⫻ 80
夹
40 ⫽ 3 ⫹ 7 ⫻ 4
edges.
vertices.
square
116
䉬
16 17
2
5
Color ᎏᎏ of the rectangle.
12 apples per bag.
6.
How many apples in 3 bags?
36 apples
What fraction is not colored?
䉴 Home Link 8 3
( )
( )
(4 ⫻ 8)⫹(2 ⫻ 2)⫽ 36
4 ⫻(8 ⫹ 2)⫻ 2 ⫽ 80
31 ⫽ 3 ⫹ 7 ⫻ 4
faces.
[Patterns, Functions, and Algebra Goal 3]
Writing/Reasoning Have children write an answer to the
following: In Problem 2, how does knowing that 5 ⫻ 9 ⫽ 45
help you know that 5 ⫻ 900 ⫽ 4,500? Sample answer:
5 ⫻ 900 is 100 times as much as 5 ⫻ 9, or 4,500.
Put in the parentheses needed to
complete the number models.
4.
What is the shape of its base?
5.
45
450
4,500
5⫻9⫽
This drawing shows a
square pyramid.
It has
Solve.
2.
$2.20
$5.00
$21.00
$25.00
$50.00
ᎏ3ᎏ
5
How many apples in 4 bags?
48 apples
22 23
66 67
Math Journal 2, p. 190
INDEPENDENT
ACTIVITY
(Math Masters, p. 245)
Home Connection Children solve problems involving
fractions. Explain that they may use pennies or counters
to model the problems.
3 Differentiation Options
Home Link Master
Name
READINESS
䉴 Solving Pattern-Block Puzzles
Time
Fraction Number Stories
Family
Note
Your child may benefit from modeling the number stories with pennies or counters. Help
your child think about the problems as stories about equal shares or equal groups.
䉬
INDEPENDENT
ACTIVITY
Date
83
HOME LINK
Please return this Home Link to school tomorrow.
5–15 Min
(Math Masters, p. 246)
Solve each problem. Tell someone at home how you did it.
Draw a picture on the back if it will help.
1. Lucy was playing a card game with 2 friends.
To provide experience with fractions of regions, have children
cover pattern-block shapes with smaller pattern blocks. They
record their work on Math Masters, page 246.
They were playing with a deck of 21 cards.
Lucy dealt ᎏ31ᎏ of the deck to each person.
How many cards did Lucy get? 7 cards
2. Jonathan bought 12 pencils. He gave
1
ᎏᎏ
2
of them to his brother
and ᎏ14ᎏ of them to his friend Mike.
How many pencils did he give to Mike?
3
pencils
3. Gerard was reading a book with 40 pages.
He read 10 pages in an hour.
ᎏ1ᎏ
What fraction of the book did he read in an hour? 4
or
10
ᎏ
ᎏ
40
4. Melissa was reading a book with 50 pages.
She read 10 pages in an hour.
What fraction of the book did she read in an hour?
ᎏ1ᎏ
5
or
10
ᎏ
ᎏ
50
Follow the instructions below.
5. Draw 15 small circles. Circle
3
ᎏᎏ
5
of them.
6. Draw 12 small circles. Put an X through
3
ᎏᎏ
4
of them.
Math Masters, p. 245
Lesson 8 3
䉬
663
EM07TLG2_G3_U08_L03.qxd
1/17/06
10:38 AM
Page 664
Teaching Master
Name
LESSON
83
䉬
Date
Time
PARTNER
ACTIVITY
ENRICHMENT
Pattern-Block Puzzles
䉴 Exploring with Tangrams
You will need your Pattern-Block Template and pattern blocks.
1. Cover the hexagon with triangle blocks. Use your template to trace
the shapes on the hexagon.
15–30 Min
(Math Masters, p. 435)
1
Shaded part ⫽ ᎏ
234
6
Shade 1
To further explore relationships among polygons, have children
use tangrams to make a variety of shapes. Read the book
Grandfather Tang with the children. When you have finished the
story, have children choose one of the tangram puzzles in
the book to solve. They should record their solutions on a
half-sheet of paper.
.
5
6
Part
not shaded ⫽ ᎏ
234
2. Cover the hexagon with blue rhombus blocks. Use your template to
trace the shapes on the hexagon.
1
Shaded part ⫽ ᎏ
234
3
Shade 1
.
2
3
Part
not shaded ⫽ ᎏ
234
template to trace the shapes on the polygon.
1
Shaded part ⫽ ᎏ
234
5
Shade 1
.
4
5
Part
not shaded ⫽ ᎏ
234
246
Math Masters, p. 246
Copyright © Wright Group/McGraw-Hill
3. Cover the polygon with triangle and blue rhombus blocks. Use your
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
䉴 Minute Math+
5–15 Min
To offer children more experience with fractions, see the following
pages in Minute Math+:
Basic Routines: p. 12–Levels 2 and 3
Counting: p. 35–Level 3
Operations: p. 40
Teaching Master
Name
Tangram Puzzles
Math Masters, p. 435
664
Unit 8 Fractions
Date
Time