Number Worlds intervention program from SRA
http://www.sranumberworlds.com/ (The following information is from their website.)
Number Worlds is an intervention math program that focuses on students who are one or more grade levels
behind in mathematics. All the tools teachers need to assess students’ abilities, individualize instruction, build
foundational skills and concepts, and make learning fun are provided in this math remediation program. SRA
Number Worlds includes a prevention program for Grades PreK-1 that builds foundational math skills and
prepares younger children to understand more complex concepts later.
Number Worlds provides instruction for students who are one to two grade levels behind their peers in
mathematics. Lessons are designed to take 45-60 minutes. It is highly recommended that intervention students
spend at least one hour daily using Number Worlds, which can be taught in addition to regular math instruction.
Because of the range of student proficiency, each level in Number Worlds may provide appropriate intervention
for students in different grade levels. Using the Placement Test in Assessment combined with the Number
Knowledge Test will effectively place students in the appropriate level and unit.
Prevention Levels A-C
Number Worlds includes instruction in grades PreK-1 to prevent math failure in later grades. Each level
provides thirty weeks of daily instruction to improve students’ grasp of the world of mathematics. These levels
are appropriate for students who come to school with impoverished math understanding, but other students will
benefit from them as well.
Intervention Levels D-J
For students in grades 1-8 who are one or more grade levels behind in math, Number Worlds builds on students’
current level of understanding with six 4-week intensive units per grade. At these grades, students may have
difficulty with one, two, or many different math concepts. The goal of the Number Worlds units is to develop
foundational understandings in each concept so that students develop on-level mathematical proficiency.
Algebra Readiness
An Algebra Readiness program with the Number Worlds philosophy includes instruction for students who are
not ready for algebra in grade 8 or 9. This course develops foundational concepts to prepare students for onlevel work in algebra.
Prices
Materials for each Level shown above include teacher resources (print and electronic) for all levels plus student
workbooks for Level C-J. Prices for teacher resources and student workbooks for an intervention group of 5
students range from $673 - $719. Additional student workbooks can be purchased separately.
Research (from http://www.sranumberworlds.com/downloads/results/NWResearch.pdf)
Number Worlds is a research- and standards-based intervention math curriculum intended to develop student
math proficiency for all students. The program incorporates the findings of several different types of research:
• Field Tests
• Effectiveness Studies
• Educational Research
• Research on How Children Learn
Different types of research have been used to develop effective curriculum interventions to bring students
struggling in mathematics to mathematical literacy and fluency. Curriculum designed for math intervention
must focus on core concepts and procedures and must address differentiated instruction strategies to meet the
needs of struggling students.
Field Tests
Number Worlds is an elementary math curriculum that has been under continual development for almost twenty
years. Number Worlds has simple objectives.
• Teach foundational math concepts and skills
• Expose children to the major ways number is represented and talked about in modern cultures
• Build the rich set of inter-connected knowledge that underlies number sense
• Lead children’s natural developmental progression
• Provide plenty of opportunity for children to communicate mathematically, both orally and in writing
• Ensure that activities are appropriate for children from a wide range of social and cultural backgrounds
• Emphasize Professional Development
Levels A-D were developed, tested, and refined over a period of 20 years. Levels E-H were built using the
lessons, objectives, and model of levels A-D. These levels are currently being field tested. The results of the
field tests will be used to refine these levels and build the middle school levels I, J, and algebra readiness.
As the figure below shows, the magnet school group began kindergarten with substantially higher scores on the
Number Knowledge test than those children in the Number Worlds and control groups. The gap indicated a
developmental lag that exceeded one year, and for many children in the Number Worlds group,that lag was
closer to two years. By the end of the kindergarten year, however, the Number Worlds children had narrowed
this gap to a small fraction of its initial size. By the end of second grade, the Number Worlds children actually
outperformed the magnet school group. In contrast, the initial gap between the control group and the magnet
school group did not narrow over time. The control group children did make steady progress over the 3 years;
however, they were never able to catch up. (http://www.sranumberworlds.com/results.html)
Longitudinal study showing mean developmental scores
in mathematical knowledge during Grades K–2
Building Blocks is an online software program to strengthen basic number concepts and number sense for
students in pre-kindergarten, kindergarten and 1st grade.
Building Blocks helps you develop students' mathematical knowledge through various activities. The system
embeds mathematical learning into students' daily activities with the goal of helping kids relate their informal
math knowledge to more formal mathematical concepts. These engaging research-based computer activities and
management system guide children through mathematical learning trajectories.
ORIGOmath – a Step-by-Step Approach to Computation
http://www.origoeducation.com/origomath/
Sequenced supplemental program that provides an overall plan and approach for developing and assessing
students' mathematical understanding and computation skills.
Program components:
The program is a comprehensive package with a teacher sourcebook and student journal for every grade. The
teacher sourcebooks provide all the necessary mathematics content and step-by-step methodology to teach and
assess fluency in computation. The student journals consist of in-class and homework pages with related work
printed back-to-back on each perforated page.
Each Grade-level Sourcebook contains:





Introduction including program overview, research base, index, and glossary
Prerequisite skills checklist
Twelve 20-page units of 5 sequenced session plans
7-page post-test with short-answer and multiple-choice questions
Class and individual recording sheets
Each unit contains:








Mathematical background
List of language students will use and develop
Content expectations
Unit-specific assessment options
Intervention options
5 sequenced session plans
Referenced blackline masters
Materials and resources overview
Each session plan includes:








Session focus
Sequenced daily number sense discussion
Step-by-step activity including possible student responses
Whole-class reflection
Materials list
Computation practice activity
Consolidation and/or extension activities
Answers to corresponding student journal pages
Prices:
Each Grade-level Sourcebook (teacher’s guide) is $99.95
Each Grade-level Student Journal is $9.99 (minimum order of 10)
A scope and sequence for the entire program is on the next page. Grade levels are intended to indicate the Grade
Level Content Expectations that are addressed in those units, although they can be used with students in other
grades whose performance places them in an earlier grade level.
Scope and Sequence for OrigoMath
Grade
1
Number
Early number sense: count,
order numbers, read and
write 2-digit numbers, count
forward and back by 10’s,
2’s and 5’s, group by tens
and ones, etc.
2
Read and write hundreds,
use number line to develop
relative position for 2- and
3-digit numbers, use place
value to build numbers, use
number line, read and write
amounts in dollars and
cents, etc.
Read and write 4-digit
numbers, locate on a
number line, use place value
to build numbers, read and
write amounts in dollars and
cents, etc.
3
4
Read and write 4- and 5digit numbers, locate on a
number line, compare, order
and sequence 4-digit
numbers, etc.
5
Read, write, and compare 5& 6-digit numbers; round
numbers to whole number
or tenth; relate common
fractions and decimals using
number lines & area models;
read, write and compare
decimals to thousandths,
etc.
6
Read and write whole
numbers from an everyday
situation; locate decimals on
number lines; read, write
and compare decimals to
thousandths and locate on
number lines; relate
fractions using number lines;
use rules to find equivalent
fractions; relate percentages
to common and decimal
fractions, etc.
Addition & Subtraction
Solve active and static
addition problems, write
number sentences, relate
part-part-whole and missing
addend to subtraction, use
strategies (count-on,
doubling, bridge-to-10), etc.
Write related facts (fact
families), relate operations
in word problems, use
extended strategies, number
lines and place value for 2digit addition & subtraction,
etc.
Multiplication & Division
No content in 1st grade.
Write related facts,
reinforce and extend
strategies, use place value to
add & subtract 2- and 3-digit
numbers, develop mental
strategies, use the algorithm
fluently when needed, etc.
Extend mental strategies
including use of place value,
use the algorithm fluently
with 3-digit numbers,
calculate change and counton from an amount to a
dollar-and-cent amount, etc.
Work with percentages,
relate to fractions; work
with fraction equivalence;
use strategies including
place value to add/subtract
3- and 4-digit numbers and
tenths; add/subtract
decimals to hundredths;
solve problems involving
money; add/subtract
common fractions with
same denominators, etc.
Reinforce addition and
subtraction
Write fact families (2s and 5s
facts), use strategies, relate
the x symbol to equal
groups, an array and sets,
relate division to mult., solve
division problems with
remainders, etc.
Use known facts or factors
to multiply, write fact
families (4s, 6s, 8s, 9s), work
with remainders, use
strategies to divide, record
steps to multiply and divide,
etc.
Use factors and other
strategies to multiply and
divide; multiply by fractions,
etc.
Multiply by 1 and 0,
investigate multiplication
patterns (9s facts), develop
relationship rules for mult. &
division, use equations to
record situations, etc.
Use place value to multiply
2-digit numbers; solve
percentage problems; use
place value strategies to
divide; calculate rates
(speed, price); work with
ratio problems; use models
to multiply and divide
common fractions, etc.
Write equations with 2 or
more operations; work with
unknowns; write rules to
describe relationships
between two sets of data;
apply properties of
operations and use
parentheses, etc.
Use language of equal
groups and arrays, use x and
÷ symbols, skip count, use
strategies for multiplication,
use materials to divide by 2,
4 or 5, write related facts,
etc.
Algebra
Express addition and
subtraction in equation
form, work with “more
than,” “less than,” “not
equal,” use a balance
situation to relate addition
and subtraction, etc.
Use equations to record
addition and subtraction
situations, use a balance
situation to write equations,
use addition to subtract 2digit numbers, etc.
Use equations to record any
of the four operations,
investigate patterns/rules
with 2 operations, use the
inverse operation, apply
commutative, associative,
distributive properties, etc.
Use equations to record any
of the four operations; use
parentheses and apply
properties of operations;
write relationships as rules,
etc.
PALS Math (Peer-Assisted Learning Strategies)
http://kc.vanderbilt.edu/pals/about/AboutMath.html
PALS combines proven instructional principles and practices and peer mediation so that research-based reading
and math activities are effective, feasible, and enjoyable. PALS is a version of classwide peer tutoring. Teachers
identify which children require help on specific skills and who the most appropriate children are to help other
children learn those skills. Using this information, teachers pair students in the class, so that partners work
simultaneously and productively on different activities that address the problems they are experiencing. Pairs
are changed regularly, and over a period of time as students work on a variety of skills, all students have the
opportunity to be "coaches" and "players."
PALS creates pairs in a classroom, each geared to the individual student's needs, instead of a single, teacherdirected activity that may end up addressing the problems of only a few children. The strategy also creates
opportunities for a teacher to circulate in the class, observe students, and provide individual remedial lessons.
PALS is designed to complement, not replace, existing reading and math curriculum. PALS is a 25- to 35minute activity implemented 2 to 4 times a week.
ABOUT PALS Math
PALS Math has two basic coaching procedures: coaching and practice. During coaching, students work on a
sheet of problems in the skill area (e.g., adding, subtracting with regrouping, number concepts, charts, and
graphs) to which they have been assigned. The coach uses a sheet that contains a series of questions, differing
by problem type, designed to guide the player. Coaches also use a correction procedure. Coaching usually lasts
15-20 minutes. Materials are available for kindergarten through grade 6.
During practice, every student receives a mixed-problem worksheet containing the problem type just worked
on, as well as easier types of problems. Students work independently until about two-thirds of class are finished.
Students then exchange papers and score each others' practice sheets. Practice lasts 5-10 minutes.
Students earn points for cooperating and constructing good explanations during coaching and for doing
problems correctly during practice.
Costs
K and 1st grade: Manuals are $40 each. The K DVD is $15.
2nd-6th grade: Manual costs $40. The DVD is $15. Student materials for each grade cost $30 each.