October 1, 2009
Dear Parents:
The process for math placement for seventh grade takes the entire sixth grade year and involves several instruments. The purpose of this letter is to acquaint you with these instruments, to provide you with the benchmarks which we use for placement, and to invite you to a meeting to answer any questions you may have regarding the sixth grade curriculum and math placement at CMS. The math department also feels it is important to include a general description of a student in each course. These characteristics are:
Directed: Prealgebra
Students can follow a model given concrete examples and experiences. They demonstrate proficiency with previous topics after considerable review. The course provides explicit instruction in reading the text and in how to use resources. Extensive class time is spent processing homework. The focus is on extensive practice and activities which extend and refine concepts.
Guided: Prealgebra
Students can follow a model and can reach an abstract level of understanding with guidance. They can assimilate and reproduce ideas in variations of problem solving situations already experienced. Students demonstrate consistent facility with computational skills. The course provides students with background information so that they are able to read the text with understanding. Moderate class time is spent processing homework. Students are regularly asked to apply concepts to new situations. A test/quiz average of 70 or better must be maintained.
Independent: Prealgebra
Students readily grasp new concepts and relate those concepts to other situations. Possessing excellent computational skills, they have insights into complex relationships and see patterns beyond expectations. They demonstrate enthusiasm for the subject and are comfortable with an increasing level of abstraction and difficulty. Students are regularly asked to read sections of the text to preview the next class. A minimal amount of class time is spent processing homework. Students are often asked to apply concepts to novel situations in both class exercises and in assessments. A test/quiz average of 80 or better must be maintained.
We use four instruments in determining placement. They are listed in order of importance.
Concord Middle School Prognosis Test: weighted twice
This instrument has been a reliable predictor of prealgebra readiness. As with many prognosis tests, it provides short explanations followed by examples in the areas of number theory, computation, logical thinking, geometry, and problem solving. It then asks multiple choice or short answer questions on the topic that get increasingly more complex and/or abstract. The hour long test is usually given over two days in late March.
Test Average: weighted once
The test averages for each term are considered as well as the overall test average. The reasons for giving modified tests are taken into consideration for placement. (Students taking modified tests are not automatically placed in the directed level.) Modified tests are generally more specific in content and do not refer to the conditions under which a student took a test (extra time, in learning center).
Continental Mathematics League Contests (CML): weighted once
These contests are given monthly from November through March. We participate in the more difficult division, a change from elementary school. Each consists of six nonroutine problems which are to be solved in 30 minutes without the aid of a calculator, ruler, protractor or graph paper. Students may use any method they like and are required only to give an answer. These challenges appeal to students who do the work in their heads and have difficulty explaining their process in writing. All students benefit from the sharing of strategies when the contests are reviewed in class. Contests from previous years routinely used throughout the year.
New England Math League Contest: weighted onehalf
This is a 30 minute, 40 question multiple choice contest given in March. Calculators are allowed. The items cover computation, geometry, interpreting graphs, and problem solving.
In some years, some exemplary sixth grade math students have been asked to take the American Mathematics Competition to be considered for the independent level algebra, an eighth grade course, in the seventh grade. The AMC8 is given every November to seventh and eighth grade students. The test may be given to exemplary sixth graders in May. All other criteria would indicate that these students would be placed in grade 7 independent.
The chart below provides the benchmarks used to place students in the seventh grade. Since no placement instrument is perfect, there are some overlaps in the ranges to allow teachers some flexibility for individual differences and special circumstances.
instrument 
directed 
guided 
independent 
gr8 independent 
CMS Prognosis (raw score) 
up to 16 
16  30 
28  40 
40 or above 
CML (%) 
up to 40% 
35  70% 
above 65% 
80% or above 
NEML (raw score) 
up to 18 
16  25 
23  40 
37 or above 
AMC8 (raw score) 
na 
na 
na 
15  25 
Test average* (%) 




Current math placement: 




Directed 
up to 92 
89 or above 


Guided 
up to 75 
72 to 92 
89 or above 

Independent 

up to 85 
82 or above 
98100 
*Ranges for test average and midyear are based on the student’s current placement.
The purpose of the meeting will be to answer any questions you may have regarding the placement process and/or the sixth grade curriculum. It would be helpful if you could send questions in advance to the office in either building. We may find certain trends or areas of interest which would focus our preliminary remarks.
Respectfully,
Meg McCann Lynne Beattie
Math Dept. Chair Principal 