cut down to size at high noon
cut down to size at high noon
intermediate
measurement/geometry
cut down to size
at high noon
by Scott Sundby
AFG302
ISBN-13: 978-1-59892-098-7
ISBN-10: 1-59892-098-7
AFG302
ISBN-10: 1-59892-098-7
W Y   nw
   i is i
Measurement
During the course of a day we estimate and measure
as we drive, shop, cook, and schedule our time. The
AfterSchool KidzMath story guides focus on the following important areas involving measurement: standard
units, measuring tools, and converting units.
Standard Units
In the United States we use the customary measuring system which includes inches, feet, and yards. The
“metric” measuring system used worldwide includes
centimeters, meters, and kilometers, and is based
on groups of ten. In the story guide activities, the
children measure length using both systems. It is
important that they become familiar with the common standard units and develop mental pictures for
judging and comparing size. (For example, the width
of a finger is about a centimeter.) Knowing the size
of standard units can also help children make more
reasonable estimates when they measure.
Measuring Tools
When using standard measuring tools like rulers,
the children will need guidance in how to use the
tools accurately–what the markings on the measuring tools mean and where to begin measuring. They
need to understand why each unit on a measuring
tool is the same size and why units must line up
with no space between them or overlap. When stanc u t d o w n t o s i z e at h i g h n o o n dard measuring tools are difficult to use in a particular situation, the children must learn to adapt their
tools or invent techniques that will work.
Converting Units
To solve measurement problems with standard units
children need to learn to convert standard units
within a measurement system (either metric or customary). (For example, the children find the number
of inches in two and half feet or the number of kilograms in 2500 grams.) The children can use their
knowledge of relationships between units to make
conversions. (For example, 12 inches is equal to 1
foot, 3 feet is equal to 36 inches, and 1 meter equals
100 centimeters.)
Geometry
Geometry allows children to describe, analyze, and
understand the physical environment. It also provides
important tools for solving mathematical problems.
The AfterSchool KidzMath Story Guides help children
develop geometry concepts in three important areas:
shapes, transformations, and spatial reasoning.
Shapes
Children need to develop precise ways to describe
and define two- and three-dimensional shapes (like
squares and cubes) and their parts (like angles and
lines) and to compare and classify them. They also
need to understand similarity (different size, same
shape). Children can think of similar shapes as those
that are related by “magnifying” or “shrinking.”
(For example, the triangles below are similar because
they are the same shape, but different sizes).
In the intermediate grades, children learn vocabulary to name and describe shapes. They are defined
on pages 21 and 22.
Transformations
Transformations are slides (translations), flips (reflections), and turns (rotations) of geometric objects.
Transforming shapes helps children understand that
such motions change a shape’s location or position,
but not its size or shape.
slide
flip
turn
Spatial Reasoning
Spatial visualization and reasoning involve an
intuitive feel for one’s surroundings and the objects
in them. They also help children recognize two- and
three-dimensional shapes and their attributes, and
relationships between shapes. The story guides develop children’s spatial reasoning in the following ways:
• Change the orientation of objects to create mental
pictures of two- and three-dimensional objects
and understand them better. (For example, if your
homework paper with a name in the upper-left
hand corner were turned 90 degrees clockwise, the
name would be in the upper right-hand corner.)
• Draw, build, compare, and analyze two- and threedimensional shapes. (For example, the children talk
about similarities and differences between buildings
they construct out of cardboard and paper.)
• Relate three-dimensional shapes to their twodimensional representations. (For example, the
children make three-dimensional airplanes from
two-dimensional diagrams.)
• Use maps and grids to apply geometry to the real
world. (For example, the children use two numbers
[or a letter and a number] and their corresponding
rows and columns to help them find locations,
identify paths, and find the distance between two
or more locations on a grid.)
down to size at
t
u
c
high noon
Cut Down to Size at High Noon illustrations copyright © 2000 by Wayne Geehan. Cover used by permission of Charlesbridge Publishing.
Everything seems normal in
the small frontier town of Cowlick—
until folks take off their hats!
The Story
Cut Down to Size at High Noon
by Scott Sundby
Charlesbridge Publishing, 2000
Reduce It!
Mystery Mural
Twist-O-Grid
(pp. 4–9)
(pp. 10–16)
(pp. 17–20)
The children use a grid to
make a picture smaller.
The children use grids to
enlarge the sections of a
“mystery mural.”
The children play a game
involving placing hands and
feet on a large game board.
To do this activity, you need
a large space like a gym or
outdoor area.
Yo u’ll n e e d:
• Copies of “Reduce It!”
page 7
• Pencils
c u t d o w n t o s i z e at h i g h n o o n Yo u’ll n e e d:
• Copy of “Mystery Mural,”
page 14
• Copy of “Mystery Mural
Layout,” page 15
• Pencils
• Marking pens
• 15–20 square sheets of
paper (81⁄ 2˝ × 81⁄ 2˝)
• Masking tape
Yo u’ll n e e d:
• Shower curtain or large
piece of plastic
• Dice
• Permanent marker
• Yard stick
• Masking tape
1
the Story
story Summary
New Words
Cowlick is a one-barber town until
Buzzsaw Bart shows up. Louie
Cutorze has a unique way of cutting
hair and so does Buzzsaw Bart.
The two barbers have a showdown
at high noon to see who will stay
and who will leave Cowlick. They
realize that they can learn from
each other and have a thriving
business working together.
The children may be unfamiliar with
these words. Discuss them when
they appear in the story. You will
find the definitions on page 21.
cowlick
voila
cranium
noggin
varmint
Before the story
Get Ready
1
The “talk about” sections
suggest questions and
discussion topics. You do
not need to ask all the
questions. Choose ones
that make sense for your
group of children.
The Leader’s Guide section “The Leader’s Role” will help you make
the most of the story guide activities. If you haven’t yet read it,
please do so.
2 Read the book to yourself before reading it to the children.
3 Think about the math and social questions you want to ask before,
during, and after the story. Write them on self-stick notes and put
them in the book where you will stop to ask the questions.
Introduce
Show the cover of the book and read the title.
ta l k
ab o ut
2
• What do you think this story might be about? Why do you say that?
• Why do you think part of the title is A Math Adventure?
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
during the story
Read the story aloud.
ta l k
ab o ut
After reading page 7, ask:
• Have you ever used this method to scale down a drawing (reduce it or make it smaller)? If yes, what did you do? Have you used a different method? What did you do? Why does Louie divide all his measurements by four?
• Why might you want to make a picture larger or smaller?
After reading page 16, ask:
• What do you think they are going to do at high noon?
• What else could Buzzsaw and Louie do to settle their differences?
after the story
ta l k
ab o ut
Point out the population totals in the illustration on page 32, and ask:
• Why do you think the population of Cowlick increased?
• What did Buzzsaw and Louie learn from meeting each other?
• What kinds of mathematics were the barbers using to scale up and
scale down the pictures (make them larger and smaller)?
c u t d o w n t o s i z e at h i g h n o o n 3
FPO
icon TK
Activity
1 Reduce It!
children work individually
MaTH SKiLLS
 Find locations on a grid
 Explore spatial relationships
 Explore similarity
In this activity, the children transfer shapes from
one set of squares to a smaller set. They explore
the concepts of similarity (same shape, different
sizes) and spatial relationships (the way shapes
fit together).
social SKiLLS
 Give help respectfully when asked
 Be persistent
Some children will struggle with this activity and
feel unsuccessful. Encourage them to ask for
help when they are frustrated. Discuss ways the
children can give and get help.
Before the activity
Gather the Materials
you’ll need
Consider what resources
(time, materials, space)
would be needed to do
this activity. Refresh your
memory of the math
skills by reading the
“What You Need to Know
About the Math in This
Guide” on the first page
of the guide.
For each child:
 Copy of “Reduce It!” page 7
 Pencil
Get Ready
1
Read and do the activity yourself before introducing it to
the children.
2 Think about the math and social questions you want to ask
before, during, and after the activity. Write them on a sheet of
paper to refer to during the activity.
4
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
Introduce
1
Explain that the children will reduce a picture of a hat (make it
smaller), using squares on a grid to help them. They will use the
numbers and letters on the grids to find corresponding squares and
transfer the picture from one grid to another. Specifically, they will:
• choose a square on the top grid that has part of the picture in it
• use the numbers and letters on the sides of the grid to find the
corresponding square on the bottom grid
• copy the lines, reducing them on the bottom grid
• repeat the process with all the picture squares until the hat
drawing is complete.
ta l k
ab o ut
• How can the numbers and letters help you draw your picture?
• What are you doing to help you transfer exactly what is in one square
into the other square?
• How can you ask for help if you need it? How can you help one another?
2 Have a child demonstrate reducing a few squares.
3 Distribute the materials and have the children begin the activity.
during the activity
Ask the children questions as they do the activity.
ta l k
ab o ut
• How did you find the correct square to transfer that part of the picture to?
• What can you do if you feel frustrated with this activity?
• How are you reducing your drawing?
• How can you help the children sitting around you?
c u t d o w n t o s i z e at h i g h n o o n 5
after the activity
Discuss the math and how the children worked together.
ta l k
ab o ut
• Do you think it is easier to enlarge or reduce? Why? What helped you?
• If you felt frustrated when doing this activity, what did you do?
• How did you use mathematics in this activity?
Changing the Activity
• Draw a picture on the “Grid: One-Inch Squares,“ page 9, and
have the children reduce it onto “Grid: 1⁄ 2-Inch Squares,” page 8.
• Have the children make a reduced drawing of your site’s logo.
6
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s

reduce it!
  i!
E
D
C
B
A
1
2
3
4
5
E
D
C
B
A
1
c u t d o w n t o s i z e at h i g h n o o n 2
3
4
5
© d e v e l o p m e n ta l s t u d i e s c e n t e r 7
grids: 1/2-Inch squares














A
A
1
2
3
4
5
6














A
A
1
8 2
3
4
© d e v e l o p m e n ta l s t u d i e s c e n t e r 5
6
1
2
3
4
5
6
1
2
3
4
5
6
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
grid: one-Inch squares







A
1
c u t d o w n t o s i z e at h i g h n o o n 2
3
4
5
6
© d e v e l o p m e n ta l s t u d i e s c e n t e r 9
Activity
2 Mystery Mural
group of 12 or fewer
MaTH SKiLLS
social SKiLLS
 Explore spatial relationships
 Explore similarity
 Give help respectfully when asked
 Ask for help when needed
In this activity, the children take the shapes
in each square and transfer them to another
square while making them larger. They are
exploring the concepts of similarity (same
shape, different sizes) and spatial relationships
(the way shapes fit together).
Some children may struggle with this activity and
may not feel successful. Encourage the children
to ask for help when they get frustrated and to
work together so that the shapes in their squares
match up.
Before the activity
Gather the Materials
you’ll need
This activity works
best with a group of
12 or fewer children.
Depending on the group
size, some children may
have to make more than
one square.
10




Copy of the “Mystery Mural Layout,” page 15
Tape
A few square pieces of paper (81⁄ 2˝ × 81⁄ 2˝ ) for demonstrating
Masking tape
For each child:




A square from “Mystery Mural,” page 14
An 81⁄ 2˝ × 81⁄ 2˝ square piece of paper
Pencil
Marking pen
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
Get Ready
1
2 Cut apart the “Mystery Mural” on the dotted lines. Practice enlarging
Read the activity before introducing it to the children.
a couple of the squares by drawing their image proportionally larger
on 81⁄ 2˝ × 81⁄ 2˝ squares.
3
4 Think about the math and social skills questions you want to ask
Think about where you might have the children put the mural up.
before, during, and after the activity. Write them on self-stick notes
or a piece of paper to refer to during the activity.
Introduce
1
ta l k
ab o ut
Explain that the children will work together to make a mystery
mural. The mural is such a mystery that they won’t know how it
will look until they have finished putting it together.
• What is a mural? Where have you seen a mural?
2 Explain that each child will be given a piece of paper with part of the
mural on it. Their job is to enlarge their piece of the mural onto a
larger square. After they are finished drawing, they will decorate their
squares and put all the pieces together to make one large mural.
3 Demonstrate how to enlarge a drawing. Pick one of the mural
pieces and draw the image on it onto an 8 1/2” square. As you
draw, talk about how you are making decisions. For example, if
you are enlarging square 10, you might say,
“There are three curving lines in this square. Two of
them are next to each other in the top left-hand corner
of the square. The outside one starts a little less than
1/4 of the way down the left side and ends a little more
than 1/4 of the way across the top. Another line scoops
around the corner. The other curved line is on the top
right-hand corner of the square. It starts about half way
across the square and ends almost at the corner.”
c u t d o w n t o s i z e at h i g h n o o n 11
4 Show the blank “Mystery Mural Layout.” Explain that this layout
shows how the pieces fit together.
ta l k
ab o ut
• If you have piece number 6, what other pieces need to fit with yours? (2, 5, 7, 10)
• How might you work with the children who have squares that touch
yours? Why is this important?
• If you need help, what might you say to someone?
5 Distribute the materials.
6 Have the children identify where their piece fits on the mystery
mural layout and identify the other pieces that need to fit with
theirs before they begin to work.
during the activity
1
ta l k
ab o ut
Ask the children questions as they do the activity.
• Who has the squares that are touching yours? How are you working
with them to make sure that your lines fit together?
• What is helping you draw the lines on your square?
• How can you give help respectfully to others?
After a child answers
a question, repeat the
answer back to make
sure you understand. (For
example, you might say,
“You said that you think
that it’s important to work
with the children who
have squares touching
yours so that the lines of
the drawing match from
square to square.”)
12
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
after the activity
1
Discuss the math and how the children worked together.
ta l k
ab o ut
• What helped you draw your square? What did you do when you got
frustrated?
• How did you ask for help when you needed it?
• What were the challenges and successes of working with the children
whose squares were next to yours on the mural?
2 Discuss and decide where to hang the mural.
ta l k
ab o ut
• About how much space will we need to put the mural up?
• Where can we put it up? Other ideas?
• What is a fair way to reach agreement about where to put the mural
if we can’t all agree?
• How will we make sure we have the pieces in order?
3 Have the children tape their pieces where you have decided to
mount the mural. Have them read the words.
ta l k
ab o ut
• What does mathematics counts mean? What are some ways that math
is important in our daily lives? Other ideas?
Changing the Activity
• Have the children make the mural even larger by using
12′′ × 12′′ squares
• Make a simple drawing on a photocopy of the “Mystery Mural
Layout” and have the children enlarge it.
• Make an enlarged mural of the site’s logo.
c u t d o w n t o s i z e at h i g h n o o n 13
mystery mural
1
5
9
14 2
m
3
4
m
a
e
t
h
i
t
c
a
c
6
7
8
s
n
u
ts
o
10
© d e v e l o p m e n ta l s t u d i e s c e n t e r 11
12
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
mystery mural layout
1
2
3
4
5
6
7
8
9
10
11
12
c u t d o w n t o s i z e at h i g h n o o n © d e v e l o p m e n ta l s t u d i e s c e n t e r 15
Grid: 1/2 -inch squares
16 © d e v e l o p m e n ta l s t u d i e s c e n t e r a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
Activity
3 Twist-O-Grid
group of 10 or fewer
MaTH SKiLLS
 Find locations on a grid
This activity gives the children practice locating
intersecting rows and columns on a grid—
an important skill in geometry.
columns
1
2
3
social SKiLLS
 Work together as a team
 Stay involved while waiting for a turn
The Children work as a team in this game.
Discuss ways the children can encourage one
another and what the group will do when a
team falls, ending their turn.
1
rows
2
3
Before the activity
Gather the Materials
you’ll need
Preparing the game
board may take some
time. Give yourself
plenty of prep time
and a chance for the
grid to dry.
 Shower curtain or large piece of sturdy plastic (about 6′ × 6′)
Number die
 Letter die (see Get Ready)
 Permanent marker
 Yard stick
 Masking tape
Get Ready
1 Read the activity.
2 Prepare the game board on a shower curtain or large piece of
plastic by making a six-by-six grid with numbers and letters along
the sides. Each square should be about 11′′ × 11′′.
c u t d o w n t o s i z e at h i g h n o o n 17
3
Prepare the letter die by covering the dots on a number die with
masking tape and writing one of the letters A–F on each side.
E
F
E
D
C
B
A
B
1 2 3 4 5 6
F
E
B
twist-o-grid game board
F
letter die
4 Think about the math and social questions you want to ask before,
during, and after the activity. Write them on self-stick notes or a
sheet of paper to refer to during the activity.
5 Choose a place to play where you can spread out the game board.
6 Decide how you will divide the children into two teams to play the
game. (Teams of three to five children work best.)
Introduce
1
2 Have the children decide fairly within each team who will go first,
Set up the game board and divide the group into teams.
At some ages, girls and
boys are uncomfortable
touching each other.
If this is an issue with
your group, create
single-sex teams.
second, and so on.
3 Decide fairly which team will go first, second, and so on.
4 State that the goal of the game is for all members of a team to
have all of their hands and feet on the game board without falling.
Explain and demonstrate the game, using two teams of three to five
children.
• Team 1 stands near the game board.
• The first player on Team 2 rolls the dice and calls out the
number and letter rolled.
• The first player on Team 1 puts a hand or foot in the square that
corresponds to the letter and number rolled.
• The second player on Team 2 rolls the dice, and the second
player on Team 1 puts a hand or foot on the square rolled.
18
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
• Team 1 players take turns placing hands and feet on the board
while Team 2 players roll the dice until all their hands and feet
are on the board or the group loses its balance and falls.
• Team 2 takes a turn on the game board while Team 1 rolls
the dice.
ta l k
ab o ut
E
F
E
D
C
B
A
B
F
1 2 3 4 5 6
• How can you encourage your team?
• How can you help your teammates so that your team can keep from
falling?
during the activity
Ask the children questions as they play.
ta l k
ab o ut
• How are you working together as a team?
• How are you staying involved while waiting for your turn?
• How did you decide which square to put your hand or foot in?
• Which square do you hope you get next? Why?
c u t d o w n t o s i z e at h i g h n o o n 19
after the activity
Discuss the math and how the children worked together.
ta l k
ab o ut
• What happened when a team’s turn was over? How did that feel to
everyone? Would you do it differently next time?
• How did you help one another?
• What mathematics were you using in this game? When have you
used this type of mathematics before?
20
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s
new words
math glossary
Cowlick: a lock or tuft of hair growing in a different direction
from the rest of the hair
Attribute: a characteristic of an object, such as the number
of sides it has
Cranium: (cray-nee-um) skull
Circle: a closed curve, every point of which is the same
distance from the center
Noggin: (nawgen) a person’s head
Varmint: (var-ment) a despised person or animal
Voila: (vwah-la) a French word used to call attention, to
express satisfaction or approval, or to suggest an appearance
as if by magic
Column: a vertical section of a chart or grid arranged in a
straight line
column
Customary Measuring System: a system of measurement
used in the United States that includes the units inches, feet,
and yards
Metric Measuring System: a decimal system of measurement used throughout the world (in this system liters are
used for volume, meters for length, and grams for weight)
Oval: a shape like an egg
Parallelogram: a closed shape with two pairs of parallel
sides
Pentagon: a closed shape that has five sides
Rectangle: a closed shape with two pairs of parallel sides
and four right angles
Row: a horizontal section of a chart or grid arranged in a
straight line
row
Scale Drawing: a drawing made by reducing or enlarging the
dimensions of an object proportionally
c u t d o w n t o s i z e at h i g h n o o n 21
math glossary
Similar: having same shape, but not necessarily the
same size
Spatial Relationships: how shapes relate to each other and
fit together
Square: a closed shape with four equal sides and four right
angles. A square is a special type of rectangle and parallelogram
Three-Dimensional: existing in three dimensions: having
length, width, and height
Transformation: a slide, flip, or turn of a geometric object
Trapezoid: a four-sided shape with one pair of parallel sides
Triangle: a closed shape with three straight sides and three
vertices (points)
Two-Dimensional: existing in two dimensions: having length
and width
Vertex (vertices): point where two lines meet to form an angle
vertex
Width: the distance along a line from one point to another
usually the dimension of an object from side to side
22
a f t e r s c h o o l k i d z m at h ™ s to r y g u i d e s