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Math Program Models

 

 

 

Small Group Math Instruction

 

We use either Corrective Math modules or Connecting Math Concepts.  Both math programs are learner verified, and have gone through extensive field testing prior to publishing.

 

We decide which program to use based on testing results of both standardized testing and placement testing that is a part of the curriculum.  We also look at the age of the student.  ALL of our curriculum is aligned with state standards, and has a larger research base and approval for use in intervention models than nearly any curriculum on the market.

Corrective Math Modules

 

Corrective Math is divided into 7 modules:

  1. Addition,
  2. Subtraction,
  3. Multiplication,
  4. Division,
  5. Basic Fractions,
  6. Decimals and Percents and
  7. Ratios and Equations

 

It is geared for students in grade 2 through adult who have difficulty achieving at grade level.  It enables students to accurately translate word problems into numerical statements by paying attention to key words in the problem, determining the correct operation needed for the problem, and then going through a step by step process to correctly solve the problem.  There is daily fact practice complete with timed tests.

There are also mastery tests in facts and problem solving at regular intervals to ensure student mastery.  Because of the various modules, the series is flexible, and allows us to target problem math areas in a systematic way and ensures students will learn to work mathematical problems. accurately and confidently.  In the fractions modules, we emphasize the key concepts behind fractions, and do not just teach the “process” of computing fractions.  We increase ability in mathematical computation, rules, mathematical reasoning, and the core concepts involved for problem solving strategies.     Carefully structured practice develops skills students need to learn efficiently from instructional materials by helping them.

  • Learn and retain facts
  • Understand place value
  • Solve computational problems
  • Discriminate among various types of story problems

Connecting Math Concepts (CMC)

 

CMC is a developmental math program for grades K-8.  CMC is based on the rationale that understanding mathematics requires making connections.  Connections are among concepts within mathematics, across daily instructional activities involving math, and between math and the world around us.  CMC is like no other basal math program on the market.  Lessons are organized in tracks, (with 4-6 tracks per lesson), which is the ongoing development of a particular topic.  These tracks continue for multiple lessons ensuring students receive enough repetition for complete mastery of a topic.  New information is introduced in small steps, allowing for greater and greater complexity of skills being learned.  When students have mastered a track, it is incorporated with other tracks.  This is how greater and greater connections are made.  Application and extension activities are provided in every lesson.  These include problem solving, manipulatives, games, and cooperative-learning activities.  CMC’s design features plus higher-order content equals accelerated cognitive growth.  Mastery tests are given after every tenth lesson to monitor progress and mastery.

This is a direct instruction program designed to introduce basic math concepts for grade levels K-2nd in a highly structured method. There are three levels of instruction each including 120 thirty minute lessons.  Each level also includes periodic summary tests to progress monitor skill growth.  Each level also includes a brief placement test to determine the most appropriate initial placement for each student.

Level A starts around a Kindergarten skill level and addresses the areas of: Counting, Symbol Recognition, Quantity Comparisons, Addition, Subtraction, Place Values, Problem solving, and Basic Applications.

Level B begins near a 1st grade skill level and addresses the areas of: Place Value, Number Families, Facts, Number Relationships, Measurement, Addition, Subtraction, Metal Arithmetic, Money, Basic Multiplication, Shapes, Tables, and Problem Solving.

Level C begins near the 2nd grade skill level and addresses the areas of: Addition, Subtraction, Multiplication, Division, Mental Arithmetic, More Than / Less Than, Number Relations, Place Values, Estimations, Basic Calculator Use, Equation Concepts, Problem solving, Tables, Fractions, Graphs, Time, Money, Area, and Volume.

Level D begins near the 4thgrade skill level and continues into the 8thgrade level.  This section addresses the areas of: Facts, Calculator Skills, Whole Number Operations, Mental Arithmetic, Column Multiplication, Column Subtraction, Division, Equation and Relationship, Place Value, Fractions, Ratios and Proportions, Number Families, Word Problems, Geometry, Functions, Probability, and Projects.

Level E begins near the 5th grade level and overlaps with many of the categories in Level D, providing additional instruction, depth, and practice.

Level F begins near the 6th grade level and similarly overlaps with Levels D and E providing additional instruction, depth and practice.

As with all DI lessons, about 85% of each lesson is repetition of a previously taught skill.  This helps to ensure mastery.  Each lesson is broken into strands and tracks.  Rather than math being taught in a spiral format, where skills are introduced, then omitted for a chapter or two, the strands appear in each lesson, with more and more complexity being added as mastery occurs.  This ensures true learning and the transfer of information into long-term memory in the brain.  Each concept and skill is broken down into the smallest sub-skill in order to accelerate performance of high risk students. In-program mastery tests occur frequently, giving both the student and the teacher immediate feedback.

 

An example of our student’s Math progress, year 2010!

 

 

 

Students

Student Age at Test

Grade Level at Test

 

Initial Test

 

Individual Retest

 

Reading
Grade
Level

Spelling
Grade
Level

Math
Grade
Level

 

Age at Retest

Reading
Grade
Level

Spelling
Grade
Level

Math
Grade
Level

Michael  J

5 yrs 9 mos

K

 

K

K

Pre S

 

6 yrs  6 mos

2

1

*

Jamie S

9 yrs 1 mo

4

 

6

3

3

 

9 yrs 7 mos

 

 

5

Cameron  C

15 yrs 3 mo

9

 

4

5

5

 

15 yrs 6 mos

9

4

*

Jonas C

10 yrs  7 mos

5

 

3

3

4

 

11yrs 2 mos

5

*

*

Sebastian  K

12 yrs 7mos

6

 

5

2

6

 

13 yrs 8 mos

 *

Rosa S

6 yrs  9 mos

1

 

K

K

1

 

7yrs  2 mos

1

*

*

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