MATHEMATICS
STANDARDS
A PA R E N T ’ S H A N D B O O K
O U R
C H I L D R E N ,
K - 5
Published by the Pittsburgh Council on Public Education
Community Champions for Children’s Achievement
2
What your child should be learning:
INTRODUCTION
WHAT SHOULD MY CHILD BE LEARNING?
The elementary mathematics curriculum
taught in your child’s school is “Everyday
Mathematics.” That means the classroom
activities and assignments for kindergarten
through fifth grade should reflect those
described in this handbook.
“Everyday Math” is designed to encourage
children to think mathematically and to
develop confidence and familiarity with math
concepts and skills by using numbers and
activities that have meaning in children’s
lives. Children learn about inches and centimeters by measuring their own hands, for
example. They discover negative numbers by
reading an outdoor thermometer and charting
the daily temperature. They may find an
average of the lengths of their classmates’
shoes. And they find decimal numbers in a
handful of real coins. In kindergarten through
third grades, classroom routines reinforce this
everyday learning (see “Classroom Routines”).
At all grade levels, students play a variety of
math games that give them plenty of practice
using numbers.
Everyday Math, which is based on research
about how children learn, is structured
differently from the math many parents
learned in elementary school. It does not
involve presenting a skill or concept to
students, expecting them to master it within a
certain time period, and then moving on.
Instead, a teacher introduces a mathematical
idea that children will come back to again and
again before they leave elementary school. For
example, kindergarten students may work with
their teacher to make a simple graph showing
how many children in the class have a birthday
each month. A fifth grade student may
demonstrate the same skills in gathering and
graphing data in much more sophisticated
ways, by designing a survey, administering it to
classmates, and interpreting and graphing the
results.
In keeping with the structure of the curriculum,
teachers also have different ways of assessing
Everyday Math students throughout the year.
Because young children’s learning is gradual
and their progress tends to be uneven, teachers
rate their work as:
• “Beginning”—The student is not able to
complete the task independently. He/she
shows little understanding of the concept or
skill.
• “Developing”—The student shows some
understanding, but needs reminders or suggestions to complete the task without errors.
• “Secure”—The student is able to apply the
concept or skill without any help.
CLASSROOM ROUTINES
In grades K-3, classroom routines and daily
activities show students how math is used in
everyday life and help them practice skills,
such as:
• Calendar activities. Students practice
PROBLEM-SOLVING TASK
FOR GRADES 1-3:
MAKING APPLE JUICE
As a rule of thumb, you need 3 apples
to make 1 glass of apple juice.
• About how many apples would
you need to make 2 glasses of
juice? ...To make 3 glasses of
juice? ...A glass of juice for each
person in this classroom?
• If we have 1 dozen apples, about
how many glasses of juice could
we make?
• If we have 2 dozen apples, about
how many glasses of juice could
we make?
recognizing numbers on a calendar. (“What
is the date of the third Tuesday? How many
days are in September?”)
• Taking attendance. Each day, children
record the number of students who are
present and the number who are absent.
These numbers can be used to create “number
stories” (word problems) and graphs.
• Documenting the weather. Students record
the temperature every day in both
Fahrenheit (68°) and Celsius (20°). The class
discusses what type of weather they are
having that day—sunny, cloudy, rainy,
snowy—and documents it with a colored
square on a number line or graph. This
information can be used to find patterns in
temperature or weather. In third grade,
students chart sunrise and sunset times and
graph changes in the length of daylight
during the school year.
• Number line activities. For many activities,
students refer to the number line that circles
the room, counting off the days of the
E x ample of s e c on d gr ade w or k w it h t e ac he r ’s c omme n t s
Introduction
1
3
CONTENTS
After deciding what approach—or combination
of approaches—to use, students plan and
carry out their strategies to solve the problem.
WHAT IS IN THIS HANDBOOK?
school year. For example, the teacher may
say, “Today is the thirty-eighth day of school.
How many ways can we show 38?” Students
can also refer to the number line when they
recite facts as a class, such as rote counting by
ones forward and back from given numbers
or “skip-counting” by twos (2, 4, 6…), fives
and tens. Reviewing out loud helps students
remember facts they are learning.
• Daily schedule. The daily schedule provides
opportunities for students to practice telling
time and to develop strategies for solving
problems about time. “If music class starts
at 10:30 and ends at 11:10, how long is
music class?” “How many minutes until
lunch time?”
PROBLEM-SOLVING
Problem-solving is a key component of
Everyday Math at all grade levels (see the
example on page two). Students make important
decisions about how to solve problems, rather
than just following steps that they have been
shown to find an answer. They learn to
choose from a range of strategies, including:
• Describing a computation problem as a
“number story” (word problem)
• Using objects (laying out counters to
represent three times three, for example)
• Drawing a picture (drawing six birds and
four worms to find out how many birds
won’t get a worm, for example)
• Using relation symbols, such as “2+2=4,”
“10-3=7”
In this handbook, you will find an outline of
the math standards—goals and expectations
for students—for each grade level. To show
the types of activities that build these skills
and concepts, information for each grade level
includes a sample of student work, an
example of a game students play, and an
example of a homework assignment. In
grades one and two, the example of student
work has a related “rubric” (a grading or
scoring guide). On page 18, you will also find
a glossary with definitions of words that may
be used by your child’s teacher in the context
of the Everyday Math curriculum, or that may
be part of homework assignments.
This handbook is only an outline to be used
as a resource by parents. For more information
about grade-level goals or the Everyday
Math curriculum, ask your child’s teacher or
principal.
A note about the games. The games included for
each grade level are samples, to show how the
games relate to skills and concepts students
are learning. (In the classroom, the teacher
gives students game directions verbally.) The
descriptions here can also serve as guidelines
for playing at home. Ask your child to show
you how to play “Name that Number,”
“Broken Calculator,” or another favorite
game.
A note about homework assignments. Examples
of homework assignments are presented here
to illustrate the goals of the curriculum. They
are not exact copies of assignments your child
may bring home. Homework assignments in
kindergarten through third grades that
involve home activities are called “Home
Links.” In fourth and fifth grades, they’re
called “Study Links.”
INTRODUCTION ........................................ 2
STANDARDS BY GRADE LEVEL:
Kindergarten ................................................ 4
Grade one .................................................... 6
Grade two .................................................... 8
Grade three ................................................ 10
Grade four .................................................. 12
Grade five .................................................. 14
WHY HAS MATH INSTRUCTION
CHANGED? .............................................. 17
GLOSSARY .................................................. 18
© 2002 Pittsburgh Council on Public Education
A copy of the official registration and financial information of
the Pittsburgh Council on Public Education may be obtained
from the Pennsylvania Department of State by calling toll free,
within Pennsylvania, 1/800/732-0999. Registration does not
imply endorsement.
Pittsburgh Council on Public Education
13 Pride Street
Pittsburgh, PA 15219
This handbook was produced by the Pittsburgh Council on
Public Education (PCPE) in cooperation with the Pittsburgh
Public Schools. Thank you to Dr. Diane Briars and Yvonne
Comer Holbrook of the PRIME (Pittsburgh Reform in
Mathematics Education) team; Anne McFeaters, education
consultant for the Pittsburgh Public Schools; teachers Karen
Shepherd at Grandview Elementary School, Melissa Butler and
Melanie Karabinos at Knoxville Elementary School, Sandra
Boyd and Ellen Smith at Linden Academy, Colleen Pilarski and
Dr. Susan Smith at Phillips Elementary School; PCPE Board
member Dr. Idorenyin Jamar; Gretchen Underwood, who
contributed to the handbook as a Carnegie Mellon University
graduate student; and parents Vivian Ross, Laura Schwartz,
Patty Scoratow, and Sylvia Steele. The photographs are of
children at Woolslair Elementary School in Pittsburgh,
Pennsylvania.
4
What your child should be learning:
KINDERGARTEN GOALS
K I N D E R G A R T E N
G R A D U A T E S
NUMBERS
Count to 110 or higher by 1s, 5s, and 10s.
“Skip count” by 2s to 30 (two, four, six, eight…).
Count backward from 10 to 0.
Read and write numbers from 0 to 100 or
higher.
Know the values of a penny, a nickel, a dime
and a quarter.
S H O U L D . . .
to give to her group. How many more pencils must she find?”
• “Tom has 7 cookies. Carla has 5 cookies. Who
has more cookies? How many more cookies?”
• “There are orange sections for snack today.
Keisha, Greg and Mike have 6 orange
sections to share equally. How many orange
sections can each child have?”
Verbally explain or use objects or pictures to
show how a problem was solved.
ADDING AND SUBTRACTING
Make “number families”—combinations of
numbers that add up to the same number—
up to the 5 number family. (For example, the
“3 number family” is 0+3=3, 1+2=3, 2+1=3,
3+0=3.)
PROBLEM-SOLVING
Using pictures or objects, solve simple “number stories” (word problems) that involve:
• Counting. “How many students are in class
today? How many snacks do we need to
give one snack to each person?”
• Adding. “Zack had 9 pennies. Then he
earned 2 more pennies. How many pennies
does Zack have now?”
• Subtracting. “Zack had 11 pennies. He spent
6 pennies. How many pennies does Zack
have now?”
• Matching. “There are 6 birds and 4 worms.
How many birds won’t get a worm?”
Create simple number stories for numbers
less than 20.
Using pictures or objects to model the problem, solve more complex problems such as:
• “Shakeia has 2 pencils. She needs 6 pencils
MEASURING
Compare sizes of objects. Which is bigger,
heavier, taller, longer?
Tell time to the hour, using a clock with hands
and a digital clock.
SAMPLE HOMEWORK
Make a “number family” for the
number 5.
Example:
The number family for 5 is all the
combinations with a sum of 5—0+5,
1+4, 2+3, 3+2, 4+1, 5+0.
COLLECTING AND GRAPHING DATA
Make simple bar or picture graphs. For example, the class might graph students’ birthday
months using pictures of birthday cakes.
Make observations and answer questions
about simple graphs. (“How many students
have a birthday in January? Are there more
birthdays in January or more birthdays in
June?”)
Kindergarten
MATHEMATICS
SAMPLE OF STUDENT WORK
SAMPLE GAME
“MONSTER SQUEEZE”
Assignment:
Record and graph students’
heights.
Explanation:
With the teacher, students
measure and record their
heights and the teacher
graphs the information. As
a class, they discuss the
results.
Tools: Two pictures of monsters, a 0-10
number line (“0-1-2-3-4-5-6-7-8-9-10”)
Number of players: 2 or more
Rules: Place the monsters at either end of
the number line. The
teacher or a student
thinks of a number
between 0 and 10.
Another player guesses the number. The
first player says,
“Your number is too
large” and moves the
right-hand monster to
cover the guessed number, or “Your
number is too small” and moves the
left-hand monster to cover the guessed
number. The other player(s) keep
guessing until the correct number has
been “squeezed” between the two monsters. Players take turns thinking of a
number and moving the monsters.
Example: Ms. Brown thinks of the
number 4. Ken guesses 7. Ms. Brown
says, “Your number is too large” and
places the monster on the 7. Ken
guesses 2. Ms. Brown
says, “Your number is
too small” and places
the other monster
on the 2. Ken sees
that the number is
between 2 and 7
and he correctly
guesses 4. Now it’s
his turn to think of a
number.
5
6
What your child should be learning:
FIRST GRADE GOALS
F I R S T
G R A D E
G R A D U A T E S
NUMBERS
Count, read and write numbers from 0 to
1,000.
Count by 2s, 5s, and 10s forward and backward, with and without a calculator.
Recognize the largest and smallest number
that can be made with two or three digits.
(“What is the largest number I can make with
the digits 5, 3, and 8? 853. What is the smallest
number? 358.”)
Name numbers as even (2, 4, 6…) or odd (3, 5, 7…).
Count combinations of pennies, nickels and
dimes and add the amounts (Two nickels plus
one dime equals 20 cents. Three nickels plus
one penny equals 16 cents). Show equal values with coins (one dime equals two nickels,
or 10 pennies, or one nickel and five pennies).
Use the symbols for greater than (3>1), less
than (3<10), and equal to (4+1=3+2).
Write own telephone number and address.
ADDING AND SUBTRACTING
Begin to memorize basic addition and subtraction facts (5+5=10, 5-2=3).
S H O U L D . . .
Using a number chart, add and subtract 10
and multiples of 10 from given numbers
(40+10=50, 40+20=60).
2
1
11 12
21 22
31 32
41 42
51 52
61 62
71 72
81 82
91 92
101 102
3
13
23
33
43
53
63
73
83
93
103
4
14
24
34
44
54
64
74
84
94
104
6
5
15 16
25 26
35 36
45 46
55 56
65 66
75 76
85 86
95 96
105 106
8
7
18
17
28
27
38
37
48
47
58
57
68
67
78
77
88
87
98
97
107 108
9
19
29
39
49
59
69
79
89
99
109
0
10
20
30
40
50
60
70
80
90
100
110
Number Chart
Show different ways of expressing a two-digit
number (30+6=36, 40-4=36, 10+10+10+5+1=36;
|||| ||||=10; D [dime] + Q [quarter] =35).
PROBLEM-SOLVING
Solve one-step addition and subtraction
“number stories” (word problems).
Create simple addition and subtraction
number stories. (“Five birds were sitting in a
tree. Two flew up into the air. How many are
in the tree now?”)
Solve addition and subtraction problems with
more than one step using pictures or objects.
(“I have 20 books. I gave Kim 10 of them.
Then I lost two. How many do I have now?”)
Verbally explain or show how the problem
was solved, using pictures or objects.
PATTERNS AND MATHEMATICAL
REASONING
Find missing numbers in a pattern (2, 4, 6, __,
10, __, 14, 16).
Find patterns (such as odd and even numbers,
multiples of 2, 5 and 10) on a number line
(< 1-2-3-4-5 >) and a number chart.
Recognize and follow number patterns to
solve problems.
Create and continue visual patterns with
pattern blocks (▲ ▲ ▲ ▼ ▲ ▲ ▲…).
GEOMETRY
With straws and twist ties, make simple 2dimensional shapes such as triangles,
rectangles, and squares.
MEASURING
Order objects by length—from shortest to
longest, for example.
Order objects by weight—from heaviest to
lightest, for example.
Read a thermometer to find the daily
temperature.
Tell time to the hour, half hour, and quarter hour.
COLLECTING AND GRAPHING DATA
Use tally marks ( |||| | ) to record data.
Make simple bar or picture graphs.
Make observations and predictions from
simple bar or picture graphs. (“Today’s
temperature is higher than yesterday’s.
Tomorrow it might be even higher.”)
First Grade
MATHEMATICS
SAMPLE HOMEWORK
SAMPLE GAME
Count a handful of coins for someone at home. Record the total.
“BEAT THE CALCULATOR”
SAMPLE OF STUDENT WORK AND RUBRIC (SCORING GUIDE)
Tools: Calculator, pair of dice or deck
of cards
Number of players: 3
NUMBER STORY
Assignment: Write a number story (a word problem) and show your answer using words
and pictures.
Rubric:
Secure (able to apply the concept or skill on their own): The number story includes a question,
a “number model” that answers it (2+2=4, for example), a picture illustrating this, and a
“unit box” (a box indicating the object or item being counted, in words or a picture). The
student created the story and answered the question correctly without needing assistance.
Developing (in the process of developing understanding): The number story contains most of
the elements described above, but not all. For example, the unit box may have been omitted, the picture may not adequately represent the number story, or the student may have
answered the question numerically without actually writing the question to be answered
(as in this example).
Beginning (just
starting to explore a
concept or skill): The
number story is not
complete and/or the
elements don’t
support each other.
For example, the
units in the drawing
don’t match the
numbers the student
has written. The
student needed a
great deal of help to
complete the task.
Rules: One player is the “Caller,” a
second player is the “Calculator,” and
the third player is the “Brain.” The
“Caller” uses the dice or draws two
cards from the deck to create an
addition problem. The “Calculator”
solves the problem with a calculator
while the “Brain” solves it without a
calculator. The “Caller” decides who
solved the problem first. Students take
turns playing each role.
Example: Dawnita, the “Caller,” rolls a
6 and a 2 with the dice. Jonathan, the
“Calculator,” enters the problem into
his calculator (6+2) while Tyler, the
“Brain,” tries to solve the problem
mentally. Tyler quickly raises his hand
and tells Dawnita that the answer is 8.
7
8
What your child should be learning:
SECOND GRADE GOALS
S E C O N D
G R A D E
G R A D U A T E S
S H O U L D . . .
NUMBERS
Add 3 one-digit numbers mentally.
Count by 2s, 5s and 10s forward and backward from any two- or three-digit number
(54, 52, 50, 48…).
Memorize basic addition and subtraction
facts.
Identify “place value” in three-digit numbers.
For example, in 387, 3 is in the 100s place, 8 is
in the 10s place and 7 is in the 1s place:
387=300+80+7.
Write two-, three-, and four-digit numbers
when they are read out loud. (“Seven
hundred twenty four” = 724.)
Read two-, three-, and four-digit numbers.
(724 = “Seven hundred twenty four.”)
“Shade in” a fractional part of a whole and
name the part that is shaded-in.
Complete a “Frames-and-Arrows” puzzle
with someone at home. (See the Glossary
on page 18 for more information.)
Multiply numbers by 1 and by 10 (1x7=7,
10x7=70).
Know the values of a penny, a nickel, a dime,
a quarter, a half-dollar, and a dollar. Show
coins for a given amount, using pennies, nickels, dimes and quarters.
Solve “number stories” (word problems)
involving money. (“I had two dollars and my
mom gave me a quarter. How much do I
have?” “I spent 75 cents on candy. I paid with
one dollar. What’s my change?”)
Show equal values with coins. (One quarter
equals five nickels, or two dimes and one
nickel, or two dimes and five pennies.)
Use a calculator to add and subtract money
amounts, as decimals (.25+.36=.61).
one-third
SAMPLE HOMEWORK
PROBLEM-SOLVING
PATTERNS AND MATHEMATICAL
REASONING
Recognize patterns and relationships between
numbers, such as odd and even, or multiples
of two, five and ten, or doubling or halving a
number. (See the sample homework.)
ADDING, SUBTRACTING, MULTIPLYING
Make up number stories for a given equation.
(“Write a number story for 78+22=100.”)
Understand that there are many ways to show
a number. (50 can be shown as 25+25, 100-50,
10x5, two quarters. 125 can be shown as
100+25, 175-50, 50+50+25.)
Solve multi-step problems. (“I bought two
apples for 50 cents each. I also bought a
banana for 35 cents. How much did I spend? I
paid with two dollars. What’s my change?”)
Identify common 3-dimensional shapes such
as prisms, cylinders, cones and spheres.
Write addition “turnarounds” (4+3=3+4) for
given facts. Write “extended” addition facts
(since 4+3=7, then 40+30=70, and
400+300=700).
Solve simple multiplication problems (“There
are three baskets. Each basket has five eggs.
How many eggs in all?”) using common
strategies such as:
Find the perimeter (the sum of the length of
Make up “fact families” (the fact family for 4,
3, 7 is 3+4=7, 4+3=7, 7-4=3, 7-3=4). Make up
“extended” fact families (30+40=70, 40+30=70,
70-40=30, 70-30=40).
• Drawing a picture
Use a calculator to add 3 or more two-digit
numbers (17+24+56=97).
• Making a table
GEOMETRY
Using a ruler or straight-edge, draw a line
between two given points (a “line segment”).
perimeter
• Creating a model using objects
area
• Guessing and checking the answer
• Looking for a pattern
Second Grade
MATHEMATICS
the sides) of a shape by counting units.
Find the area (the measurement of the inside
of a shape) by counting units.
MEASURING
Tell time to five-minute intervals.
Measure objects in inches, feet, centimeters,
decimeters and meters, using a ruler, a tape
measure, a yardstick or a meter stick.
Find dates on a calendar. (“If today is Tuesday,
November 7, what date will next Tuesday be?”)
COLLECTING AND GRAPHING DATA
Plot data on a bar graph—the number of
books read in one week by students, for
example, or the height and weight of every
student in the class.
Compare bar graphs—the number of books
read during the first week of October, for
example, compared to the number of books
read during the third week of January.
SAMPLE OF STUDENT WORK AND RUBRIC (SCORING GUIDE)
CREATING SHAPES OF A GIVEN AREA
Assignment: Using a template (a tracing/
measuring tool), draw five shapes that are
different, but that have the same area.
Rubric:
Secure (able to apply the concept or skill on
their own): There are five different shapes.
Each shape has the same area. Each shape
is labeled with the correct area. The shapes
are drawn using a template. The student
can explain verbally how he or she found
the area of the shapes and can explain different attributes of the shapes.
Developing (in the process of developing understanding): There are four to five shapes, but
they have only small differences. Most or
all shapes have the same area and are
labeled with the correct area. The student
can explain verbally how he or she found the area of the shapes and can explain different
attributes of the shapes, with some prompting.
Beginning (just starting to explore a concept or skill): There are four to five shapes, but they
aren’t different or the shapes don’t have the same area. Shapes are labeled with the area
with one to two mistakes. Most shapes are drawn with a free hand instead of a template
(lines aren’t straight). The student needs help in thinking about how he or she found the
area of the shapes and how to explain different attributes of the shapes.
SAMPLE GAME
“NAME THAT NUMBER”
Tools: Deck of cards with the Queens
labeled as zero, the Aces labeled as 1,
and the other face cards removed
Number of players: 3 or 4
Rules: Players try to find different
ways of expressing a number on a
drawn card by adding or subtracting
the numbers on other randomly
drawn cards.
Example: Ashley shuffles the cards and
places five cards face up on the table.
She places the rest of the deck face
down on the table and turns over the
top card. This card, the number 8, is
the “number to be named.” Tawnya
tries to find a different way to display
the number 8 using the five cards on
the table. She chooses a 9 and a 1 and
tells the others that “9 minus 1 equals
8.” She takes all three cards and
replaces them with three new cards
from the deck. Ben tries to name the
next card using the cards on the table.
If he can’t create a problem to match
the number, he loses his turn and the
cards are set aside. The children take
turns playing until there are not
enough cards left in the deck.
9
10 What your child should be learning:
THIRD GRADE GOALS
T H I R D
G R A D E
G R A D U A T E S
NUMBERS
Count forward and backward by 10s, 100s,
and 1,000s from any four-digit number.
Identify “place value” in three- and four-digit
numbers. For example, in 1458, 1 is in the
1000s place, 4 is in the 100s place, 5 is in the
10s place and 8 is in the 1s place:
1458=1000+400+50+8.
them equally between five people. How many
books will each person get?”)
S H O U L D . . .
example, enter 5+5= and continue to press =
to make the calculator count by 5s.) Use a
calculator to add and subtract multi-digit
numbers (674-157).
Divide a number by 1. Know that a number
divided by itself equals 1.
Know addition and subtraction facts by memory. Recognize that if 5+1=6, then 50+10=60
and 500+100=600 (“fact extension”).
Write multiplication facts for square numbers
(52=5x5, or 25).
Write five- and six-digit whole numbers when
they are read out loud. (“Fifteen thousand
eight hundred forty two” = 15,842.)
2
1
11 12
21 22
31 32
41 42
51 52
61 62
71 72
81 82
91 92
101 102
Understand fractions as equal parts of a whole.
4
14
24
34
44
54
64
74
84
94
104
3
13
23
33
43
53
63
73
83
93
103
6
5
15 16
25 26
35 36
45 46
55 56
65 66
75 76
85 86
95 96
105 106
8
7
18
17
28
27
38
37
48
47
58
57
68
67
78
77
88
87
98
97
107 108
9
19
29
39
49
59
69
79
89
99
109
0
10
20
30
40
50
60
70
80
90
100
110
Number Chart
Begin to understand decimals.
Write dollar and cent notation ($.30, $1.25).
ADDING, SUBTRACTING,
MULTIPLYING, DIVIDING
Understand that there are many ways to show
a number. (Ways to show 100: 50+50, 50x2,
1243-1143, 200 divided by 2, 1/2 of 200, four
quarters, 10x20 divided by 2…)
Solve multi-digit addition and subtraction
“number stories” (word problems). Have
successful strategies (methods that work) for
adding and subtracting.*
Understand the relationship between addition
and multiplication (2x5 is the same as adding
5+5; 3x6 is the same as 6+6+6). Understand
multiplication as “array totals” (an
arrangement of objects or symbols laid out
in rows).
Example of an array for 3x4:
Use a calculator for “skip” counts. (For
▲ ▲ ▲ ▲
SAMPLE HOMEWORK
▲ ▲ ▲ ▲
Find examples of multiples (more than
one of the same item) around your
home or neighborhood. For example, 4
legs on a chair, 12 eggs in a carton.
Write two “number stories” (word
problems) about your groups of items.
▲ ▲ ▲ ▲
Understand dividing whole numbers in terms
of making equal groups, with or without a
remainder. (“I have 50 books. I want to divide
* For more information, ask a teacher to explain strategies your child may be using.
Begin to memorize basic multiplication facts
through the 10 times table.
Use a memory key on a calculator to help in
solving multi-step problems.
PROBLEM-SOLVING
Solve addition, subtraction and simple multiplication number stories.
Make up addition, subtraction and simple
multiplication number stories for given equations. (“Write a number story for 9x8=72.”)
Solve simple division number stories using
objects, pictures or diagrams.
Solve problems with more than one step
using familiar strategies such as guessing and
checking, drawing a picture, creating a model,
making a table, or looking for a pattern. (“The
daycare center down the street uses about 5
quarts of milk every day. If each child drinks
Third Grade 11
MATHEMATICS
about a half pint of milk each day, how many
children are in the daycare center?”)
PATTERNS, SEQUENCES AND
MATHEMATICAL REASONING
Use knowledge of addition, subtraction and
“fact extension” (if 3+2=5, then 30+20=50) to
solve problems.
Use a calculator to count by 1000s, 100s, and
10s to review patterns in place value
(4567+1000=5567, 5567+3000=8567).
Use a number chart to find differences
between pairs of numbers.
MEASURING
GEOMETRY
SAMPLE GAME
Identify similarities and differences among 3dimensional shapes.
“BROKEN CALCULATOR”
Recognize right angles.
Tools: Calculator
Using straws and twist ties, create and name
some polygons (2-dimensional figures made
up of line segments).
Number of players: 2
EXPLORING DATA AND CHANCE
Understand simple data analysis. For example,
the class counts the letters in everyone’s first
names and looks for the range (the difference
between the greatest number of letters and the
smallest number of letters) and the median (the
number of letters that falls in the middle).
Tell time to five-minute intervals and oneminute intervals.
Show familiarity with the metric units
centimeter, decimeter, meter, and kilometer.
Show familiarity with the U.S. units inch, foot,
yard, and mile.
Use a ruler to measure inches and
centimeters.
Know some equivalent measures, such as the
number of inches in a foot and the number of
centimeters in a meter.
Show familiarity with different types of scales
for measuring weight, such as balance scales
and bathroom scales.
Identify basic units of weight measure in the
U.S. and the metric systems: ounce, pound,
gram, kilogram, and liter.
Example: Kyle chooses the number 9 as
the broken number. Jasmine enters 3x3
into the calculator.
SAMPLE OF STUDENT WORK
“FUNCTION MACHINE”
Assignment: Figure out the rule, write the rule in the “function machine” and complete
the “in/out box.”
Explanation: The “rule” describes what the student does to find the number. In this case,
the student is given “8” and “28:” the rule is “+20.” The “function machine” is a fun way
for children to understand the relationship between addition and subtraction—you put
“+20” into the function machine and the answer comes out the other end. Or, if the function machine shows what comes out, the student determines what must have been put
in. The “in/out box” is a diagram showing the results of using the function machine.
Completed Assignment
Uncompleted
Assignment
8
28
50
Read negative numbers on a Celsius
thermometer.
Compare pairs of temperatures, including
temperatures below zero, and identify which
is warmer or colder. (“Yesterday the temperature
was -2°. Today it is -3°. Yesterday was warmer
than today.”)
Rules: Player One picks a number to be
the “broken” number. Both players pretend this number key is broken and
Player Two must find a different way to
display the number on the calculator.
Players take turns using the calculator.
40
95
150
12 What your child should be learning:
FOURTH GRADE GOALS
F O U R T H
G R A D E
G R A D U A T E S
NUMBERS
Know equivalent names for numbers
(535=500+35, 60=6x10).
S H O U L D . . .
Identify fractional parts of collections of objects,
such as the orange sections illustrated below.
Read and write numbers to millions. Identify
“place value” to millions.
Identify fractional parts of geometric shapes.
Have a successful strategy (a method that works)
for adding and subtracting multi-digit numbers.*
Have a successful strategy for solving multidigit multiplication problems.*
“Shade in” a percent of a geometric shape.
PROBLEM-SOLVING
Use and explain strategies for solving
multiplication and division “number stories”
(word problems).
SAMPLE HOMEWORK
Make a list of all the people in your
family. Include all the people living at
home now and any brothers or sisters
living elsewhere. The people who live at
home do not have to be related to you.
Write your own name on the list too.
You will need this information to learn
about the sizes of families in your class.
Note: This homework assignment contributes to a class activity on family
sizes. The class makes a graph showing
the “Number of People in Our Families”
and answers questions about the largest
number of people in a family, the smallest number of people in a family, the
mode (the number that occurs most
often), and the median (the number that
would fall in the middle if all the
numbers in the set were laid out in
order).
Create multiplication and division number stories.
ADDING, SUBTRACTING,
MULTIPLYING, DIVIDING
Know basic addition and subtraction facts
from memory.
Identify and use square numbers (52=5x5).
Solve problems with more than one step
using one or more familiar strategies, such as
creating a model, making a table, looking for
a pattern, or drawing pictures. (“Your job is to
paint a large circle on a basketball court. How
will you do it? You don’t have a compass that
is big enough!”)
PATTERNS, SEQUENCES, AND
MATHEMATICAL REASONING
Explain the relationship between multiplication and division.
Use tables of data to solve problems.
Know basic multiplication facts from memory.
Know “extended” multiplication facts (if
2x3=6, then 20x30=600).
Use rate tables to solve problems. (“Jen
received an allowance of $8 in 4 weeks. At
this rate, how much allowance did she receive
per week?”)
Use a calculator to rename any fraction as a
decimal or a percent ( 3/4=.75, or 75%).
Jen’s Allowance
Estimate the magnitude (greatness in size) of
answers to multiplication problems. (“A blue
whale weighs as much as about 425,000 kittens. About how many kittens weigh as much
as 4 blue whales? Estimate if the answer is in
the 10s, 100s, 1000s, 10,000s, 100,000s, or
1,000,000s.”)
Week
Amount
1
2
3
4
$8.00
One example of a rate table
* For more information, ask a teacher to explain strategies your child may be using.
Fourth Grade 13
MATHEMATICS
GEOMETRY
MEASURING
Name, draw, and label lines, “line segments”
(lines between two given points) and “rays”
(lines that start at a defined point and continue to infinity).
Use coordinates to identify points on a grid.
triangle
angle
2
1
x axis
0
parallel lines
“NAME THAT NUMBER”
data point (3,2)
y axis
Name and draw angles, triangles and quadrangles (any shape with 4 angles).
SAMPLE GAME
1
2
3
4
5
Solve elapsed time problems. (“The bus
arrives at 3:20 p.m. It is now 2:57 p.m. The
bus will arrive in how many minutes?”)
Use personal references, such as a foot, hand,
finger, or arm, to estimate lengths.
quadrangle
right angle
Identify and describe right angles and parallel lines.
Identify lines of symmetry (the line or lines
that can divide a shape into mirror images).
line of symmetry
Use a map scale to estimate distances.
Find locations using longitude and latitude,
and find the longitude and the latitude for
given locations.
Measure in feet, inches, centimeters, meters
and decimeters.
area
EXPLORING DATA AND CHANCE
Use and understand the terms “maximum”
and “minimum” in reference to a set of data.
Find the area of a shape by counting squares
and parts of squares.
Describe the properties of a parallelogram (a
4-sided figure with 2 pairs of parallel sides).
Find the median of a set of data (the number
that would fall in the middle if all the numbers
in the set were laid out in order) and the
mode (the number that occurs most often).
TRAIL MIX (FROM THE FOURTH GRADE NEW STANDARDS REFERENCE EXAM)
Assignment: Tran and Jenna are members of a hiking club. They are using this recipe to
make trail mix for their club to take on a hike.
Raisins
Peanuts
Shredded Coconut
1 cup
2 cups
1/2 cup
Number of players: 2 or 3
Rules: Players try to find different
ways of expressing a number on a
drawn card by adding, subtracting,
multiplying or dividing the numbers
on the cards they have been dealt.
16
7
5
8
2
10
Example: Rob shuffles the cards and
deals 5 cards to himself and 5 to
Brittany, the other player. From the
remaining deck, he turns over the top
card, a 16. This is the “target number.”
Brittany tries to find a different way to
display the number 16 using as many
of her cards as possible. She has the
cards 7, 5, 8, 2 and 10. Using four of
her cards, she displays
7x2=14; 14+10=24 ; 24-8=16
SAMPLE OF STUDENT WORK
Trail Mix Recipe (Enough for 1 bag):
Tools: Deck of cards with the Queens
labeled as zero, the Aces labeled as 1,
and the eight other face cards (4
Kings, 4 Jacks) labeled as 11 through
18. The 2s through 10s have their own
values.
They bought:
3 pounds of raisins—enough for 12 cups
5 pounds of peanuts—enough for 18 cups
16 ounces of shredded coconut—enough
for 5 cups
(continued on page 16)
She records her solution on a sheet of
paper and sets aside the cards she
used. After Rob takes his turn at displaying the number 16 with his cards,
both draw new cards from the deck to
replace the ones used. The 16 goes to
the bottom of the deck and the top
card becomes the new target number.
The player who sets aside the most
cards wins.
14 What your child should be learning:
FIFTH GRADE GOALS
F I F T H
G R A D E
G R A D U A T E S
NUMBERS
Determine whether a number is prime (a
number greater than 1 with exactly 2 factors: 1
and itself, such as the number 7) or composite
(a number with more than one factor, such as
the number 14). (Factors are numbers that are
multiplied to equal a given number.)
Find equivalents for whole numbers (40, 20x2,
37+3…).
Find equivalent fractions (2/3 is the same as
4/6) and rename fractions in their simplest
forms (8/16 is 1/2).
Rename familiar fractions (such as 1/2, 2/3, 3/4…)
as decimals and percents (3/4= .75, or 75%).
Identify place value to trillions.
Identify place value of decimals to the
thousandths place (.008).
“Shade in” a fractional part of a whole and
identify the part that is shaded-in as a fraction,
a decimal, and a percent of the whole.
25%, .25, 1/4
S H O U L D . . .
• Adding and subtracting multi-digit whole
numbers and decimals
• Multiplying multi-digit whole numbers
• Dividing whole numbers
• Adding and subtracting fractions with like
denominators (1/8 + 3/8) and unlike
denominators (1/3 + 3/8)
he can use. How many different groups of
stamps could Julio use on his package?”)
PATTERNS, SEQUENCES, AND
MATHEMATICAL REASONING
Explain the relationship between multiplication
and division.
• Adding and subtracting mixed numbers
(3/4 + 1 1/3)
Use parentheses in “number sentences”
(sentences made up of numbers and a symbol
that shows their relationship) to show the order
of operations—for example, (4+8)x9÷3=36, but
4+8x9÷3=28.
• Converting between mixed numbers and
fractions (1 2/3 = 5/3)
Determine whether number sentences
containing parentheses are true or false.
Add signed numbers—for example, 3+(-8)= -5.
PROBLEM-SOLVING
Use and explain strategies for solving multiplication and division “number stories” (word
problems).
Create multiplication and division number
stories.
Solve problems with more than one step
using one or more familiar strategies, such as
creating a model, making a table, looking for
a pattern, or drawing pictures. (“Julio is
mailing a small package to Tony, who lives in
another city. Julio has to put 18 cents worth of
stamps on the package. Julio has 10-cent
stamps, 4-cent stamps, and 2-cent stamps that
Use negative numbers in context—on a
thermometer, for example.
Compare and order fractions and positive and
negative numbers (1/3 is less than 1/2, -2 is
greater than -10).
Solve basic and “extended” multiplication and
division facts (if 11x5=55, then 11x50=550; if
10÷5=2, then 100÷50=2).
Identify “factors” of a number (numbers that
are multiplied to equal a given number). For
example, 7 and 3 are factors of 21.
Identify a fractional part of a defined shape or
set, such as the orange sections below.
SAMPLE HOMEWORK
Add:
Add or subtract:
30 + (-21)
5/8 + 9/4
-24 + (-24)
7 3/4 + 3/16
ADDING, SUBTRACTING, MULTIPLYING,
DIVIDING, AND USING PROCEDURES
-41 + 24
5 3/8 - 2 1/4
-7 + (-19)
3 7/8 + 4 5/8
Have successful strategies* (methods that
work) for:
-55 + 55
* For more information, ask a teacher to explain strategies your child may be using.
MENTAL ARITHMETIC AND NUMBER
SYSTEMS
Use and understand the terms “numerator”
(the number above the line in a fraction) and
“denominator” (the number below the line in
a fraction).
Fifth Grade 15
MATHEMATICS
Use a calculator to rename any fraction as a
decimal or a percent.
Mentally convert a simple fraction into a
decimal or a percent, and vice versa.
Use fractions to represent ratios (5 out of 10
students eat breakfast every morning—5/10
or 5:10).
Write numbers in different ways, including:
• “Standard” notation (3,445)
expressing a number as the product of its prime
factors (12=2x2x3). (Prime factors are factors that
can’t be divided into smaller whole numbers.)
MEASURING
Find the perimeter (the sum of the lengths of
the sides) of polygons (2-dimensional figures
made up of “line segments”—lines between
two given points).
SAMPLE GAME
“FACTOR CAPTOR”
Tools: 48 “counters” (coins, buttons,
checkers…), scratch paper, calculator,
Factor Captor number grid
2
• “Expanded” notation (3000 + 400 + 40 + 5)
• “Exponential” notation (3 x 103 + 4 x 102 +
4 x 101 + 5 x 10)
3
3
perimeter = 14
6
Find the “prime factorization” of a number—
(continued on page 16)
SAMPLE OF STUDENT WORK
JUMP ROPE CONTEST (FROM THE FIFTH GRADE PSSA—THE PENNSYLVANIA STATE TEST)
Four students competed in a 2-day Jump Rope Contest. On the first day of the contest,
they completed the following numbers of jumps:
Lori—41 jumps
Jim—45 jumps
Peg—33 jumps
The graph shows how many jumps the 4
students completed on Day 2 of the contest.
A) After 2 days, who had the most total jumps?
B) By how many jumps did this student
win the contest?
C) To prove your answer, show each step of
your math work for all 4 students and
explain why you solved the problem as you
did. If you used mental math or a calculator
you must write an explanation describing
what you did and also why you solved the
problem as you did. Then, write your
answer in the boxes below.
Will—39 jumps
Factor Captor Number Grid
Number of Players: 2
Rules: One player chooses a two-digit
number on the grid. The other player
covers that number’s factors (the numbers that can be multiplied to equal the
chosen number) with counters, using
each factor only once. Players record the
sums of the factors they have covered as
their scores for the round. If a player
misses any factors, the other player can
cover them and add them to his or her
total score. They take turns until all
numbers on the grid have been covered.
Using a calculator, they add their total
scores to determine the winner.
Example: Shannon covers 27 and writes
down “27” as her score for the round.
Tiffany covers 1, 3 and 9 with counters
(3x9=27; 1x27=27). Her score is 13:
1+3+9. For round two, Tiffany covers 18.
Shannon covers 2, 3 and 6. Tiffany then
covers 9, because 9 is also a factor of 18,
and adds “9” to her score of “18.”
16 What your child should be learning:
MATHEMATICS
FIFTH GRADE, CONTINUED
Draw and measure angles using a protractor.
Draw and measure line segments to the
nearest 1/16 inch.
Measure lengths in both the U.S. (inches, feet,
yards) and the metric systems (centimeters,
decimeters, meters).
GEOMETRY
Define “radius” and “diameter” and solve
problems using radius and diameter.
(greater than 90°), straight (180°), reflex
(greater than 180°), and right (90°).
Sort polygons according to their properties.
Which polygons have right angles, for example?
Which polygons have parallel sides?
Identify and compare the properties of “geometric
solids” (3-dimensional shapes with surfaces,
such as cylinders, cones, spheres, rectangular
prisms and square pyramids).
On a coordinate grid, plot and read “ordered
number pairs” (a point on the X axis matched
to a point on the Y axis) in the positive quadrant.
gles, parallelograms and the base of a prism by
counting units and by using formulas. (Example:
Area of a rectangle = length x width.)
area = 8
EXPLORING DATA AND CHANCE
Collect, organize and interpret data.
data point (3,2)
diameter
positive quadrant
1
radius
y axis
negative quadrant
0
Identify and describe parallel lines.
Identify angles: acute (less than 90°), obtuse
Make and interpret bar graphs.
2
negative quadrant
x axis
1
2
3
negative quadrant
Explain and measure the area of triangles, rectan-
SAMPLE OF STUDENT WORK, GRADE FOUR (continued)
Tran and Jenna follow the recipe exactly. They make as many bags of
trail mix as possible.
Answer these questions. Show all of your work or explain how you figured it out.
How many bags of trail
mix can they make?
Which ingredient do they
run out of first?
How many of the other
two ingredients are left
over when they are done?
In a set of data, find the maximum, the minimum,
the median (the middle number of the set), the
mode (the number that occurs most often), the
range (the difference between the maximum and
minimum), and the mean (the average).
Use terms that describe the probability of
chance events (“It’s likely that it will rain
again today”…“It’s unlikely that no student
will be absent this year”).
17
Why has math instruction changed?
In 1995, the United States and 41 countries
around the world participated in the Third
International Math and Science Study
(TIMSS). Along with testing students at
grades four, eight and 12 on their knowledge
of math and science topics and their ability to
solve problems, TIMSS involved surveying
students, teachers and administrators, reviewing
the content of curriculum programs and textbooks, and videotaping classroom interactions
between teachers and students.
When the test results and analyses of data
were released, American fourth graders had
scores slightly above the international
average. Eighth graders’ scores were lower
than the international average. Twelfth
graders were near the bottom, outscoring only
Cyprus and South Africa. We were the only
industrialized country to show this decline
in performance.
TIMSS researchers who studied the data
about textbook content, the sequence of
courses, and classroom interactions have
offered possible explanations for the U.S.
results. American schools, they said,
approach the teaching of math very
differently from many of our international
counterparts. For example:
• The typical U.S. math curriculum has been
called “a mile wide and an inch deep.” In
other words, it includes so many topics that
few can be covered in depth.
• Educators do not agree on what should be
taught when, so American students may be
taught the same material year after year. For
example, basic fraction and decimal facts
and operations (adding, subtracting, and so
on) are taught from fourth through eighth
grade in this country.
• As documented in TIMSS videos, some
students in American math classrooms are
more likely to sit and watch their teachers
explain procedures than they are to struggle
with math concepts and problem-solving
strategies themselves.
Everyday Mathematics, which was developed
with support from the National Science
Foundation and meets the Department of
Education’s standards for quality, research-
based programs, addresses the challenges
posed by TIMSS by providing:
• A coherent structure, with math topics
introduced in a specific sequence
• An emphasis on problem-solving skills, as
opposed to asking students to perform
essentially the same task over and over
• Early introduction of a range of important,
higher-level math concepts for all students
Note: Southwestern Pennsylvania participated
in a similar study in 1999 called the TIMSS-R,
or “Repeat.” For information about the
results, which are available for the region as a
whole but not by individual school or district,
go to: www.msc.collaboratives.org. For general
information about TIMSS and TIMSS-R, go to:
http://isc.bc.edu/index.html.
For more information about the research base
for Everyday Math, go to:
www.sra4kids.com/everydaylearning/em/
origins.html.
18
GLOSSARY
algebraic expression: A way of expressing a quantity that
uses a “variable.” For example, Tiffany has five more cookies
than Samira. If Samira has c cookies, then Tiffany has c + 5.
algorithm: A set of steps that can be used to carry out a procedure—a way of solving a problem. For example, one
algorithm for adding 14 plus 23 is to write one number
above the other, draw a line underneath, add 4 and 3 which
gives you 7, add 10 and 20 which gives you 30, and then
add 30 and 7 to get 37.
Note: Everyday Math students are encouraged to invent
their own algorithms and find strategies that are successful.
Teachers also show students “alternative” algorithms,
which are additional strategies for performing calculations.
For example, K-2 students may add or subtract using a
number line or a number chart, by thinking of the
quantities as coins, or by using objects. Ask your child’s
teacher to show you some of the invented or alternative
algorithms being used by the class.
area: The measurement of the inside of a given shape.
array: An arrangement of real objects or drawn symbols laid
out in rows to help children visualize multiplication. For
example, to understand three times four, a child might lay
out pattern blocks like this:
▲
▲
▲
▲
▲
▲
▲
▲
▲
▲
▲
▲
attribute: A feature or characteristic of a group or set of things.
For example, a right angle is an “attribute” of squares.
fact family: A group of numbers that are “related” like family
members by being added together, subtracted, multiplied, or
divided. For example, an addition and subtraction “fact family”
for 4, 3, 7 would be 3+4=7, 4+3=7, 7-4=3, 7-3=4.
frames-and-arrows diagram where the frames are all filled
in, but the rule is missing, to discover what rule was used
(“What’s My Rule?” problems). In other problems, there are
two rules to use, represented by different kinds of arrows,
and children are asked to fill in the correct numbers.
2946
Function Machine: A diagram of an imaginary machine that
is programmed to process numbers according to a certain
rule. The student puts a number into the machine and
changes it into a second number by applying the rule.
Sometimes the numbers are given and the student must figure out the rule that was applied. See the sample of student
work on page 11 for an example.
Home Link: The name for the kinds of homework that involve
home activities in kindergarten through third grades.
Math Box: A box on a worksheet containing a math task.
Everyday Math worksheets usually include boxes with different tasks for practicing a variety of skills, rather than one
sheet with problems requiring only one skill.
Math Message: A brief warm-up activity to begin a lesson.
One Math Message: “Take 5 straws and 6 twist-ties. Try to
make two triangles with them.”
Minute Math: Quick math problems for Kindergarten
through third grade that help children develop problemsolving strategies.
5-Minute Math: Fourth and fifth grade math problems, usually given at the beginning of the lesson, that help children
develop mental math skills.
Name-collection Box: Children use a box diagram to write
different names for a number. A “Name-collection Box” for
125 might look like this:
(Answer: The rule is +6.)
One example of a Frames-and-Arrows diagram
2976
2978
number model: A statement showing that two quantities are
equal—an equation. For example, 3+5=6+2. Used in a
“number story,” a number model shows how the parts of
the story are related.
number sentence: A sentence made up of numbers,
operations, and a symbol that shows their relationship. For
example, 2+2=4, or 327>326, or 5+7=15-3.
number story: A word problem made up by children,
teachers or parents that describes a situation that can be
solved numerically. “Jesse had two pairs of clean socks.
After he did his laundry, he had three new clean pairs. How
many pairs of clean socks does he have now?”
operation: A process or action for combining numbers to
produce another number. Addition, subtraction,
multiplication, and division are all examples of operations.
polygon: A 2-dimensional figure. All the sides are line
segments connected end to end.
reference frame: Certain kinds of systems for measuring
quantities, including number lines, clocks, calendars,
thermometers and maps.
100 + 25
$125.00
175 - 50
25 x 5
50 + 50 + 25
fact power: Knowing certain number facts by memory, such as
which pairs of numbers add up to 10, or multiplication facts.
Frames-and-Arrows: A math diagram that children complete
in class or for homework that asks them to complete the
“frames”—which may be squares or circles—using a given
rule, such as “add five.” The arrows represent the rule used
each time. Sometimes children are asked to look at a
number grid puzzle: Part of a number grid in which some
numbers are missing. Number grid puzzles are used for
practicing place value concepts and counting skills.
relation symbol: A symbol that shows the relationship
between two quantities, such as = (equal to), < (less than),
or > (greater than).
square number: A number that is the product of a whole
number multiplied by itself. For example, 5 “squared,” or
52, is the same as 5x5.
number chart or grid: A table in which consecutive numbers
are arranged in rows of ten.
2
1
11 12
21 22
31 32
41 42
51 52
61 62
71 72
81 82
91 92
101 102
3
13
23
33
43
53
63
73
83
93
103
4
14
24
34
44
54
64
74
84
94
104
6
5
15 16
25 26
35 36
45 46
55 56
65 66
75 76
85 86
95 96
105 106
Number chart or grid
8
7
18
17
28
27
38
37
48
47
58
57
68
67
78
77
88
87
98
97
107 108
9
19
29
39
49
59
69
79
89
99
109
0
10
20
30
40
50
60
70
80
90
100
110
Study Link: The name for some kinds of homework in fourth
and fifth grades.
tally mark: A vertical mark used to keep track of the number
of items in a group. Typically they are grouped by fives, to
make it easy to determine the final amount. The fifth line is
a cross-stroke. |||| ||
unit and unit box: The item or object being counted or
measured is the unit. (In the problem, “Twelve cows in a
field walked into another field where two cows were
grazing. How many cows in all?” the unit is cows.) Children
may be asked to write or draw in a “unit box” to show the
unit being used. Using a unit with a number reinforces the
idea that numbers refer to something.
Thanks to our funders
and partners
ALCOA FOUNDATION
Wor king to improve t h e qua l i t y o f l i f e i n Al c o a c o mm u n i t i es w orl d w i d e
MATH AND SCIENCE COLLABORATIVE
PENNSYLVANIA ECONOMY LEAGUE, INC.,
WESTERN DIVISION
PITTSBURGH PUBLIC SCHOOLS
PITTSBURGH COUNCIL ON
PUBLIC EDUCATION
Community Champions for Children’s Achievement
13 Pride Street
Pittsburgh, PA 15219
www.Ed4AllKids.org
Phone 412/434-0851
Fax 412-281-6683
E-mail [email protected]