Exploring Area, Polygons, and Geoboard Fractions

Transcription

Exploring Area, Polygons,
and Geoboard Fractions
Objectives To guide children as they explore finding areas
of
o irregular shapes, make polygons with trapezoids, and form
fractions on a geoboard.
Explorations
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Family
Letters
Assessment
Management
Teaching the Lesson
Key Concepts and Skills
• Divide shapes to model fractions as equal parts of a region or collection. Common
Core State
Standards
Interactive
Teacher’s
Lesson Guide
Curriculum
Focal Points
Ongoing Learning & Practice
1 2
4 3
[Number and Numeration Goal 3]
• Find area by counting square centimeters on grid paper. [Measurement and Reference Frames Goal 2]
Playing Beat the Calculator
Math Journal 2, p. 311
My Reference Book, pp. 124 and 125
1 calculator per child
Ongoing Assessment:
Recognizing Student Achievement
• Model polygons using pattern blocks and geoboards. Use an Exit Slip (Math Masters, page 415). [Geometry Goal 2]
[Operations and Computation Goal 1]
Key Activities
Exploration A: Children trace their hands and feet on centimeter grid paper
and determine the area of their handprints and footprints.
Math Boxes 10 7
Exploration B: Children build polygons and other shapes with trapezoids and
use Pattern-Block Templates to record their work.
Home Link 10 7
Math Masters, p. 317
Exploration C: Children divide shapes made on a geoboard into fractional parts.
Materials
Home Link 106
slate
Exploration A: Per partnership:
Math Journal 2, pp. 248 and 249
Exploration B: Per group:
trapezoid pattern blocks Pattern-Block Template triangle and rhombus
pattern blocks (optional)
Exploration C: Per partnership:
geoboard rubber bands
Differentiation Options
READINESS
Solving Equal-Parts Geoboard Problems
ENRICHMENT
Finding Fractional Parts
Advance Preparation
For the Math Message, make one copy of Math Masters, page 313 for every four children.
Teacher’s Reference Manual, Grades 1– 3 pp. 61, 62, 134–138, 158, 159
758
Unit 10
Decimals and Place Value
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Getting Started
Mental Math and
Reflexes
Write sets of numbers on the board.
Volunteers read the numbers aloud.
Have children record the median of each
set on their slates. Suggestions:
Math Message
Home Link 10 6
Follow-Up
Count squares to find the
area of each shaded figure.
Ask children to share some of the
making-change problems they made up
and solved.
349, 487, 204, 981, 500, 487, 210
487
2,581; 2,005; 3,096; 8,888; 5,210
3,096 3,096
1.
7
square centimeters
7
sq cm
2.
1 Teaching the Lesson
Math Message Follow-Up
NOTE Point out that there are two other
WHOLE-CLASS
ACTIVITY
ways to write square centimeter: sq cm and
cm2. Do not expect children to use the cm2
notation, but be sure to expose them to it.
(Math Masters, p. 313)
Review answers. Ask children to explain how they determined the
area for Problem 2. Some children may remember from Unit 9
that if more than _12 of a square centimeter is shaded, it is counted
as 1 square centimeter; if less than _12 of a square centimeter is
shaded, it is ignored. Children continue to use this rule in
Exploration A.
Teaching Master
Name
LESSON
10 7
Date
Time
Math Message
Name:
Name:
Count squares to find the area
of each shaded figure.
1.
1.
7
7
square
centimeters
Exploration A: Tracing Areas
of Handprints and Footprints
PARTNER
ACTIVITY
2.
PROBLEM
PRO
P
RO
R
OBL
BLE
B
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
L
VING
VIN
V
IIN
NG
square
centimeters
2.
7
7
sq cm
sq cm
(Math Journal 2, pp. 248 and 249; Math Masters, p. 314)
Partners help each other carefully trace one hand and one foot
(wearing a sock) on the centimeter grid pages. For the hand
tracings, children should keep their fingers close together. They
count all the whole square centimeters. If more than _12 of a square
centimeter is inside a tracing, it is counted as 1 square centimeter;
less than _12 of a square centimeter is ignored. Children trade
papers and check each other’s counts.
Name:
Name:
1.
1.
7
7
square
centimeters
square
centimeters
2.
2.
7
7
sq cm
sq cm
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Lesson 10 7
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Teaching Master
Name
LESSON
10 7
Date
As a follow-up, children can compare their actual hand and feet
sizes to those of other class members. As they make these visual
comparisons, ask them to predict which areas are about the same
and which are larger or smaller. If there is time, children can try
to predict areas of other small objects.
Time
My Handprint and Footprint Areas
Work with a partner.
1. Trace your partner’s hand onto his or her journal
page 248. When your hand is traced, keep your fingers
close together.
2. Count the number of whole square centimeters inside
your handprint.
If more than half of a square centimeter is inside your
handprint, count the whole square.
If less than half of a square centimeter is inside your
handprint, do not count the square.
Adjusting the Activity
Have children find the median values for all of the areas of the hands in
the class. Repeat for all of the areas of the feet in the class.
3. Record the area of your handprint at the bottom of that page.
4. Trace your partner’s foot onto his or her journal page 249.
(Keep your sock on your foot.)
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
5. Count to find the area of your footprint. Record the area of
your footprint at the bottom of that page.
6. Exchange journals and check each other’s counts. Count
again if you don’t agree with your partner.
Exploration B: Making
Follow-Up
Work in a small group. Compare your hand to other group members’
hands. Then compare your foot to others’. Predict the following:
Whose hand areas are about the same? Whose are larger?
Smaller?
Whose foot areas are about the same? Larger? Smaller?
SMALL-GROUP
ACTIVITY
Pattern-Block Worktables
PROBLEM
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SOLVING
SO
S
OL
O
LV
LV
VIN
IIN
NG
(Math Journal 2, p. 250; Math Masters, p. 315)
Compare your predictions to the areas you recorded.
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Children pretend that the trapezoid pattern blocks are small
worktables and that you, their teacher, want to make larger tables
by fitting the small trapezoid tables together. Children first make
some polygons and then try to make as many different-shape and
different-size tables as possible.
Student Page
Date
Children use trapezoids to build multiple shapes.
Time
LESSON
10 7
Using Pattern-Block Templates, children record their worktable
shapes on journal page 250. Group members compare reports to
try to find as many different worktable sizes and shapes
as possible.
The Area of My Footprint
ELL
Have children use small triangle or rhombus pattern blocks to make
more worktables.
A U D I T O R Y
T A C T I L E
Exploration C: Forming Fractions
V I S U A L
PARTNER
ACTIVITY
on the Geoboard
The area of each
is 1 square centimeter. Other ways to write square
centimeter are sq cm and cm2. Answers vary.
The area of my footprint is
square centimeters, or
sq cm.
229_262_EMCS_S_SMJ_G2_U10_57640X.indd 249
Children find their foot areas by counting whole
square units.
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(Math Journal 2, p. 251; Math Masters, p. 316)
Partners take turns. After one partner forms a shape on the
geoboard with one rubber band, the other partner tries to divide
the shape into 2 (or 3 or more) equal parts using other
rubber bands.
Unit 10 Decimals and Place Value
3/3/11 10:32 AM
Teaching Master
Children record results on journal page 251. The geoboard dot
paper on the journal page is for a 7 × 7 geoboard. If your children
are working with a 5 × 5 geoboard, have them outline a 5 × 5
dot array.
Name
Date
Time
10 7 Worktables
LESSON
Work in a group.
Materials
□ trapezoid pattern blocks
□ Pattern-Block Template (1 per person)
□ Math Journal 2, p. 250
Pretend that each red trapezoid pattern block
is a small table.
Your teacher wants to make larger worktables
by fitting these small tables together.
Try each of the following problems. Use a Pattern-Block
Template to record the tables you make on journal page 250.
1. Make a worktable shaped like a hexagon.
2. Make a worktable shaped like a triangle.
3. Use more than 1 block to make a worktable
shaped like a trapezoid.
4. Make a worktable shaped like a parallelogram.
5. Make another parallelogram worktable that has
twice the area of the one you just made.
6. Make any other worktable shapes that you can with
the trapezoids.
Children divide shapes into fractional parts on the geoboards.
Follow-Up
Compare your reports. Find all the different-size and
different-shape worktables that your group made.
ELL
Prepare several geoboard shapes ahead of time. Make most of the
shapes so that they can be divided into equal parts, but include a few shapes that
cannot be divided into equal parts. Have partners try to divide your shapes into
equal parts before they make their own.
A U D I T O R Y
T A C T I L E
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V I S U A L
2 Ongoing Learning & Practice
Playing Beat the Calculator
PARTNER
ACTIVITY
Teaching Master
(Math Journal 2, p. 311; My Reference Book,
pp. 124 and 125)
Name
LESSON
10 7
See My Reference Book, pages 124 and 125 for directions.
Children play Beat the Calculator to develop their recall of
addition facts. Using the Fact Power Table on journal page
311, children should record facts for which they can beat the
calculator by making a check mark in the box containing that fact.
Whenever they receive three check marks next to a particular fact,
they write the sum in that box to indicate that they know the fact
from memory. The Caller should select problems at random from
the Fact Power Table.
Date
Time
Geoboard Fractions
Materials
□ geoboard
□ rubber bands
□ Math Journal 2, p. 251
Work with a partner.
1. One partner makes a shape on the
geoboard with one rubber band.
Example:
2. The other partner tries to divide the
shape into equal parts using other
rubber bands. The equal parts
should be the same size and shape.
3. Take turns until each partner has
made 3 shapes.
4. Record some of the shapes you
divided on journal page 251.
Show the equal parts.
5. Record some shapes on the journal
page that you could not divide into equal parts.
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
Use an Exit Slip (Math Masters, page 415) to have children record the facts in
boxes for which they have at least one check mark. Children are making
adequate progress if they record all the facts from the Fact Power Table.
Work in a group.
6. Check one another’s work.
7. Discuss these questions:
Are shapes that can be divided equally special in some way?
What about the shapes that cannot be divided equally?
[Operations and Computation Goal 1]
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Lesson 10 7
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Student Page
Date
Math Boxes 10 7
Time
LESSON
INDEPENDENT
ACTIVITY
Math Boxes
10 7
(Math Journal 2, p. 252)
2. A pencil costs 95¢. An eraser
1. Draw at least one line of
costs 35¢ more than the
pencil. How much do the
pencil and the eraser cost
together?
symmetry.
Answer:
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 10-9 and 10-11. The skill in
Problem 6 previews Unit 11 content.
$2.25
Sample answer
60
3. Write as dollars and cents. Eight
in
4.
dollars and forty-three cents:
$8.43
$15.06
$50.17
5. Write <, >, or =.
1 hour
>
Home Link 10 7
Home Connection Children count squares to find the
areas of figures.
101 102
15 marbles are shared equally.
Each child gets 6 marbles. How
many children are sharing?
30 minutes
< 1 year
= 1 week
2
children
How many marbles are left
over?
3
INDEPENDENT
ACTIVITY
6. Use counters to solve.
3 months
7 days
97
Rule
+9
98
89
Answers vary.
fifty dollars and seventeen
cents:
45
88
56
fifteen dollars and 6 cents:
out
41
65
54
32
3 Differentiation Options
marbles
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INDEPENDENT
ACTIVITY
READINESS
Solving Equal-Parts
5–15 Min
Geoboard Problems
To explore dividing shapes into equal parts using a concrete
model, have children solve the geoboard problems on Math
Masters, page 318. Encourage children to share how they divided
the shapes.
Home Link Master
Name
Date
Teaching Master
Name
Time
10 7
Family
Note
Date
Time
10 7 Equal Parts
Area
HOME LINK
LESSON
In today’s lesson, your child found the area of shapes by counting square centimeters. As you
observe your child finding the areas below, check that he or she is counting squares that are
1
1
more than _
shaded as 1 square centimeter and not counting squares that are less than _
2
2
1
shaded. For Problem 4, see if your child has a suggestion for what to do if exactly _
of a
2
square is shaded. Remind your child that area is reported in square units. Other ways to
write square centimeters are sq cm and cm2.
69
Please return this Home Link to school tomorrow.
Count squares to find the area of each shaded figure.
Use a geoboard to solve each problem. Record what you
did below.
1. Make the square below on
2. Make the square below on
your geoboard. Divide the
square in half with a rubber
band. Record what you did
on the square below.
your geoboard. Divide the
square into 3 equal parts with
rubber bands. Record what
you did on the square below.
Sample answer
Sample answer
2.
1.
3. Make the square below
17
23
sq cm
3.
on your geoboard.
Divide the square into
4 equal parts with
rubber bands. Record
what you did on the
square below.
cm2
4.
4. Show four ways you can
divide this rectangle into
equal parts on a
geoboard. Record
your work below.
Sample answers:
Sample answer
11
9
square cm
cm2
Practice
5.
56
+ 29
85
6.
88
- 59
29
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Unit 10 Decimals and Place Value
3/21/11 11:56 AM
Teaching Master
ENRICHMENT
Finding Fractional Parts
INDEPENDENT
ACTIVITY
5–15 Min
To apply children’s understanding of fractions, have them draw
the WHOLE when a fraction of the WHOLE is given. Children use
a geoboard to complete Math Masters, page 319.
Name
LESSON
10 7
Date
Fractional Parts
Find the WHOLE for each fractional part shown. Record your
work on the geoboards for each problem.
1. This shape is worth
1
_
of the whole shape.
2
Draw the rest of the shape.
1
_
2. This shape is worth 3 of
Planning Ahead
For children’s Place-Value Books, you may want children to make
sturdy back covers out of posterboard, cardboard, or file-folder
stock. If so, you will need to prepare these covers before beginning
the lesson. Each child will also need five paper clips to hold pages
back when numbers are displayed.
1
2
Sample answer
the whole shape.
Draw the rest of the shape.
If you want to use a demonstration Place-Value Book in Lesson
10-9, use Math Masters, pages 330–336. Staple the pages of your
book together or, to allow for flipping of the pages, bind them with
an inexpensive spiral binding. (Most quick-copy stores can provide
this service.) You can also glue the digit pages to the pages of a
spiral notebook.
Time
1
3
Sample answer
1
_
3. This shape is worth 4 of
the whole shape. Draw the
rest of the shape.
1
4
Sample answer
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Lesson 10 7
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Exploring Area, Polygons, and Geoboard Fractions

Transcription

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