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Investigations Math Poll Results  Math Program Comparison
Below you will find a sidebyside comparison of Investigations Math and Saxon
Math's philosophy and curriculum. I am thoroughly satisfied that Investigations
Math is an inferior product when compared to other programs. The
school district touts studies used to show how great this program is, but
if you examine
the articles on the prior page you'll find those studies torn apart as works
of people that didn't follow the scientific method in their research. Read
what the Harvard professor had to say about the program and you'll wonder what
kind of research our school board did or if the allegation of kickbacks (Q10
page) might be true.
Traditional math is the type
of math
most of
us
grew up with and it's been sufficient in the past to produce good math students.
Traditional math focuses on a topic
or chapter
of
study,
has the students learn and practice it, then moves on. It is sometimes
up to the individual
to gleen what relationships that unit of study has with other units of study,
unless they have a good teacher that guides them in their comprehension of
such things. There is nothing wrong with the traditional method, but newer
methods have been developed to see if there is a better way to teach.
Saxon math operates more along
the lines of traditional math by focusing on math facts and "how to" do
it, rather than an exploration at early ages in understanding numbers. The
difference between Saxon and "traditional" is that Saxon takes
a study topic and never leaves it alone. In other words, when you move on
to
a new
topic,
the old topics are incorporated directly into the new topic so retention
is greatly improved and math facts are taken in incremental chunks. Please
read the brief
overview below for additional information on this.
The information I have put below comes from websites and information provided
to me by the head of the school district's Investigations Math program.
One topic in particular settled the whole debate for
me: Saxon math's 2nd grade curriculum says students will master multiplication
facts to 5 and the
3rd
grade curriculum says, "master all basic addition, subtraction,
multiplication, and division facts." Investigations NEVER has students
master these facts. In addition to this side by side comparison, check out
Singapore
Math's curriculum which has students starting the basics of multiplication
in 1st grade!
Investigations Math (from
site ) 

Brief Overview 
The Investigations curriculum embodies a different approach from the traditional
textbookbased curriculum. It is designed to invite all students into mathematicsgirls
and boys, diverse cultural, ethnic, and language groups, and students with
different strengths and interests. Problem contexts often call on students
to share experiences from their families, culture, or community. The following
aspects of the curriculum ensure that all students are included in significant
mathematical learning.
Students:
 spend more time exploring problems in depth
 find more than one solution
to many problems they work on
 invent
their own strategies and approaches, rather than relying
on memorized procedures
 choose from a variety of concrete materials
and appropriate technology, including calculators as a natural
part of their
everyday mathematical
work
 express their mathematical thinking through drawing, writing,
and talking
 work in a variety of groupings such as a whole
class, individually, in pairs, and in small groups
 move around
in the classroom as they explore the mathematics in their environment
and talk with their peers
Investigations in Number, Data and Space looks and feels quite different
from a traditional mathematics program. The curriculum at each grade level
is organized into units. Each unit offers two to eight weeks of mathematics
work on topics in number, data analysis, and geometry and consists of a
series of investigations that involve students in the exploration of major
mathematical ideas. Because of the many interconnections among mathematical
ideas, units may revolve around two or three related areas—for example,
addition and subtraction or geometry and fractions.

The Saxon Difference: Our Approach to Math Instruction
Saxon Math is the only major math program on the market today that systematically
distributes instruction and practice and assessment throughout the academic
year as opposed to concentrating, or massing, the instruction, practice
and assessment of related concepts into a short period of time  usually
within a unit or chapter. Saxon Math 's unique approach to math instruction
ensures that students not only gain but also retain essential math skills.
The pedagogy used in Saxon Math is unique, effective and researchbased.
The authors of Saxon Math began developing the series by first breaking
complex concepts into related increments, recognizing that smaller pieces
of information are easier to teach and easier to learn. Then they systematically
distributed the instruction, practice and assessment of those increments
across a grade level. Wellestablished research has shown that this spaced
(distributed) approach has produced significantly higher levels of student
learning than massed presentations such as those found in programs with
a chapterbased approach (Dempster & Farris, 1990).
Incremental Instruction Distributed Across the Level
In Saxon Math , each increment builds on the foundation of earlier increments,
leading students to a deeper understanding of mathematical concepts. The
instruction of related increments is carefully distributed throughout the
grade level, ensuring that students have the opportunity to master each
increment before being introduced to the next related one. Foundational
research has shown that instruction that presents material to be learned
over several intervals (distributed instruction) results in greater student
achievement than instruction that is not distributed (English, Wellburn & Killian,
1934). Further studies have confirmed that distributed instruction is more
effective in a variety of subjects including mathematics (Dempster, 1988;
Hintzman, 1974; Reynolds & Glasser, 1964).
Continual Practice Distributed Across the Level
Practice of an increment is distributed continually across each grade
level. Continual, distributed practice ensures that concepts are committed
to students' longterm memory and that students achieve automaticity of
basic math skills. Several research studies show that students who are
taught with a mathematics curriculum that uses continual practice and review
show greater skill acquisition and math achievement (Good & Grouws,
1979; MacDonald, 1984; Hardesty, 1986; Mayfield & Chase, 2002; Usnick,
1991; Ornstein, 1990). Additional studies have concluded that spaced (distributed)
practice results in higher performance than massed practice (Dhaliwal,
1987; Proctor, 1980).
Cumulative Assessment Distributed Across the Level
The frequent, cumulative assessments in Saxon Math assess both the acquisition
and maintenance of concepts. Assessments are built into each fifth lesson
to help teachers frequently gauge students' progress. And, since each of
the assessments is cumulative, teachers can also monitor students' retention
of skills. The Saxon Math assessment strategies are based on foundational
research showing that effective assessment is frequent and cumulative rather
than infrequent or related only to content covered since the last test
(Dempster, 1991). 
Kindergarten 
 Mathematical thinking
 Collecting, counting, measuring
 How many in all?
 Pattern Trains and hopscotch paths (exploring patterns)
 Building Blocksexploring geometry
 Counting Ourselves and others (exploring data)

 count forward and backward orally and on a
 number line
 count with onetoone correspondence
 count by 1's, 2's, 5's and 10's
 compare and order numbers and objects
 identify, match, and divide sets
 identify ordinal position to fifth
 act out and draw pictures for addition
and
 subtraction stories
 identify a missing number in a sentence and a
 missing
shape in a matrix
 know a symbol can stand for a missing number
 in a sentence
 identify and count pennies, nickels, and dimes
 identify quarters and onedollar
bills
 write money amounts using cent symbol (¢)
 select coins for given
amount
 write numerals to 30
 identify one half and one fourth
 identify right and left and use other
positional
 words and phrases
 identify, sort, and compare geometric
shapes
 and solids
 identify line of symmetry
and create symmetrical
 designs
 sort and identify sorting
rule
 identify and
extend patterns and geometric
 designs
 graph real objects
and pictures
 determine
questions
for a survey
 tell and
show
time to the hour
 use a calendar
and
identify its parts
 identify
which
of
two
events takes
more
or
less
 time
 compare,
order, and
measure using standard
 and nonstandard
units
 describe
likelihood
of an
event

1st Grade 
 Mathematical thinking (introduction of routines and comparing and combining)
 Building number sense (understanding numbers and number relationships)
 Number games and story problems (addition and subtraction)
 Building number sense (exploring patterns in numbers)
 Bigger, taller, heavier, smaller (measuring)
 Quilt Squares and block towns (2D and 3D geometry)
 Survey questions and secret rules (collecting and sorting data)

 skip count by 1's, 2's, 5's, and 10's
 compare and order numbers
 identify place value to 100
 identify ordinal position to tenth
 identify a sorting rule
 identify and extend patterns
 solve routine and nonroutine problems
 master all basic addition facts
and most of the basic subtraction facts
 add and subtract twodigit numbers without regrouping
 use comparison symbols
 picture and name fractions
 identify a fractional part of a set
 measure using inches, feet, and centimeters
 compare volume, mass, and
area
 tell time to the half hour
 order events by time
 count pennies, nickels, dimes, and quarters
 identify and draw polygons
 identify geometric solids
 tally
 identify events as certain, likely, or impossible
 create, read, and write
observations from real graphs, pictographs, and bar graphs

2nd Grade 
 Mathematical thinking (introduction of routines with counting and categorizing)
 Coins, coupons, and combinations (addition combinations)
 Putting together and taking apart (addition and subtraction)
 Shapes, halves, and symmetry (geometry and fractions)
 Timelines and rhythm patterns (representing time and patterns in rhythms)
 How long? How far? (measuring)
 Survey questions and secret rules (collecting and sorting data)
 Does it walk, crawl, or swim (sorting, classifying data)
 How many pockets? How many teeth? (collecting and representing data)

 skip count by 1's, 2's, 3's, 4's, 5's, 10's, 25's, and 100's
 compare and
order numbers
 identify ordinal position to tenth
 identify sorting and patterning rules
 solve routine and nonroutine problems
 master all basic addition and subtraction
facts
 identify commutative and associative properties of addition
 identify place
value in a threedigit number
 master multiplication facts to 5
 add and subtract twodigit numbers
 picture and name fractions
 measure to the nearest half inch, centimeter,
and foot
 compare volume
 compare and measure mass
 measure perimeter and area
 tell time to fiveminute intervals
 count pennies, nickels, dimes, and
quarters
 show change from $1.00
 multiply by 0
 identify geometric solids
 identify lines of symmetry
 identify angles
 tally
 create, read, and write observations from real graphs, pictographs,
bar graphs, Venn
diagrams, and line graphs

3rd Grade 
 Mathematical Thinking (introduction of routines and materials)
 Landmarks in the hundreds (practice with base ten system to 100)
 Combining and comparing (addition and subtraction)
 Things that come in groups (multiplication and division)
 Fair Shares (exploring fractions)
 Up and down the number line (positive and negative changes on the number
line)
 Paces to feet (measuring)
 Flips, turns, and area (2D geometry)
 Turtle paths (2D geometry)
 Exploring solids and boxes (3D geometry)

 skip count by whole numbers
 compare and order numbers
 identify place value
 identify ordinal position to twentieth
 identify and complete patterns
 solve routine and nonroutine problems
 master all basic addition, subtraction,
multiplication, and division facts
 add/subtract multidigit numbers
 multiply a multidigit number by a singledigit
number
 divide by singledigit divisors
 add positive and negative numbers
 picture, name, and order fractions
 add and subtract fractions with common
denominators
 measure to the nearest quarter inch, millimeter, foot,
and yard
 identify the volume of standard
containers
 compare and measure mass
 measure perimeter and area
 tell time to the minute
 determine elapsed time
 count money
 make change for a dollar
 identify angles
 identify lines of symmetry
 identify function rules
 graph ordered pairs on a coordinate graph
tally
 write addition, subtraction, multiplication, and division
fact families
 write story problems for addition/subtraction
number sentences
 create, read, and write observations
from real graphs, pictographs, bar graphs, Venn diagrams,
and line graphs

4th Grade 
 Mathematical thinking (introduction to routines with thinking, reasoning,
and communication)
 Landmarks in the thousands (practice with number system to 1000)
 Money, miles, and large numbers (addition and subtraction)
 Arrays and shares (multiplication and division)
 Packages and groups (multiplication and division)
 Different shapes and equal pieces (fractions and measurement)
 3 out of 4 like spaghetti (fractions and data)
 Changes and over time (exploring and representing changes)
 Sunken ships and grid patterns (coordinate grids and ordered pairs)
 Sunken ships and grid patterns (2D geometry)
 Different shapes and equal pieces (geometry and fractions)
 Seeing solids and silhouettes
 The shape of the data (statistics)

 read, write, compare, and order large numbers
 write numbers in expanded
form and identify place value
 identify prime and composite numbers
 identify perfect squares and cubes,
square roots, and cube roots
 approximate square roots
 identify the approximate value of pi
 represent numbers using Roman numerals
 identify a function rule
 simplify expressions containing exponents
 label number lines using fractions,
decimals, and positive and negative numbers
 master basic addition,
subtraction, and division facts
 add, subtract, and multiply using
mental computation
 add, subtract, and multiply multidigit numbers
using algorithms
 divide a multidigit number
by a singledigit number
 represent division remainders as fractions
 represent mixed numbers as
improper
 fractions and improper fractions as mixed numbers
 add and subtract decimals
 write fractions as percents and percents
as fractions
 name and draw polygons
and geometric solids
 identify and draw parallel and
perpendicular lines
 draw lines
of symmetry and reflections
 identify congruent and similar polygons
 draw circles using a compass
 measure and draw angles using a protractor
 identify and draw right, acute,
and obtuse triangles
 measure to the nearest millimeter or sixteenth
of an inch
 estimate and measure distance using feet, yards, and
meters
 use a scale on a map
 estimate and compare the mass of objects
 find the volume of a rectangular
prism
 estimate and measure perimeter, circumference, and area
 read a thermometer
 use a perpetual calendar
 tell time to the second
 find elapsed time
 locate information on a table or chart
 create and read bar graphs, pictographs,
and line graphs
 create and read a Venn diagram
 conduct a survey and represent the results
 find the mean
 identify the probability of an event

5th Grade 
 Mathematical thinking (introduction to routines and extending understanding
of baseten number system)
 Building on numbers you know (addition, subtraction, multiplication and
division as well as estimation)
 Name that portion (fractions, percents and decimals)
 Patterns of change (exploring and working with tables/graph for changes
over time)
 Measurement benchmarks (estimating and measuring)
 Picturing polygons (2D geometry)
 Containers and cubes (3D geometry/volume)
 Data, cats, kids, and ads (statistics)
 Between never and always (probability)

 wholenumber concepts and computation
 estimation
 patterns and sequences
 fractions, decimals, and mixed numbers
 percent
 wordproblems
 properties of operations
 integers
 divisibility concepts
 prime and composite numbers
 ratios
 square roots
 scale drawings
 measurement and unit conversion
 statistics
 probability
 data display and analysis
 perimeter and area
 volume
 symmetry
 tessellations
 transformations
 realworld connections

6th Grade 
 Prime time (factors and multiples)
 Bits and pieces I, II, III (understanding and using rational numbers)
 Formalizing patterns into equations and rules (solving simple equations)
 Shapes and designs (2D geometry)
 Covering and surrounding (2D measurement)
 How likely is it? (probability)
 Data about us (statistics)

 simplifying expressions containing
 parentheses
 operations with signed numbers
 graphing functions
 wordproblems
 powers and roots
 ratios and proportions
 percents
 fractions, decimals, and mixed numbers
 divisibility concepts
 prime factorization
 estimation
 realworld connections
 integers
 functions
 unit multipliers
 statistics and probability
 frequency tables
 data collection, display, and analysis
 formulas
 geometric constructions
 scale factor
 capacity and volume
 complementary and supplementary angles

Investigations Math Menu
** Most important pages to read (all have value but if you will only read
a few pages make it these)
* Very important
