Countdown to theConnecticut Mastery

Test(Math Component)

Larry Hillman,

Presenter

January 19, 2011

What is the Math CMT?

• The Fourth Generation of the Math CMT assesses student performance on a range of skills and concepts expected to be mastered by students at each grade level.

• The skills and concepts are aligned with the content and performance standards in Connecticut’s Mathematics Curriculum Framework.

• The framework includes mathematics content and instructional processes recommended by the National Council of Teachers of Mathematics (NCTM) and assessed on the National Assessment of Educational Progress (NAEP)

What type of questions are on the Math CMT?

The Math CMT consists of multiple-choice, open-ended and grid-in questions.

How is the Math CMT scored?

• Each multiple choice question is worth 1 point.

• Each grid-in question is worth 1 point.

• A student can earn 0, 1 or 2 points on the open-ended questions. In order to receive 2 points, the student must clearly show his or her work, or explain his or her answer.

Multiple-Choice Question Format(Example)

Alyssa has to read a book for her social studies class. Last night she read ½ of the book. This morning she read ⅓ of the book. If she still has 25 pages left to read, how many pages are in the book?

A. 50 C. 125

B. 75 D. 150

What must a student be able to do to answer this determine the correct answer to this question?

• The student will have to add the fractions, but in order to do so, the fractions must have a common denominator.

• To find the common denominator, the student will have to find the least common multiple (LCM) of 2 and 3. The LCM of 2 and 3 is 6.

• Rewrite the fractions using the common denominator of 6 (3/6 + 2/6).• Add the fractions: 3/6 + 2/6 = 5/6

If Alyssa read 5/6 of the book, that means there remains 1/6 of the book left to read. The question tells us that there are 25 pages left to read,

so 25 pages = 1/6 of the book.

The question being asked is

“How many pages are in the book?”

If 1/6 of the book is 25 pages, to find the total number of pages, multiply 25 x 6 = 150

The correct answer is “D. 150”.

Open-Ended Question Format(Example)

These numbers form a pattern.

100, 99, 97, 94, 90, 85, 79, 72, ____

Which number should come next in this pattern?______

Explain how you arrived at your answer______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

What must a student be able to do to answer this determine the correct answer to this question?

• The student must be able to identify the pattern presented by the sequence of numbers, and then extend the pattern.

• Identifying the pattern: What is happening from one number to the next?

100, 99, 97, 94, 90, 85, 79, 72, ____

• Extending the pattern: If the pattern continues, what will be the next number?

64

Show your work or explain how you determined your answer.

(Sample answer):

Subtract 1 from the first number to get the 2nd number; Subtract 2 from

the second number to get the 3rd number; Subtract 3 from the third number to

get the 4th number, etc. Since 72 is the 8th number in the sequence, subtract 8

from 72 to get the next number, 64.

Grid-In Question Format (Example)

A Blu-Ray DVD player has a regular price of

$245.00. It goes on sale at a 20% discount. What

is the sale price of the player?

There are two ways to find the correct answer to this question.

• A student can calculate 20% of $245.00, then subtract that amount from $245.00 in order to obtain the sale price.

-or-

• A student can subtract 20% from 100% (leaving 80%), then calculate 80% of $245.00.

Using either method, the student should find the correct answer, $196.00. This answer must be entered into a “bubble

grid” like the one shown below.

There are two parts to the bubble grid: *The boxes for students to write the numbers

*The “bubbles” to be filled in

Students are encouraged to use this four-step problem-solving method:

1. Identify the problem“What is the question?”“What am I being asked to find?”“What do I know?“What information am I given”?

2. Create a Plan“How do I use what I know to find what I am being asked to find?”

3. Follow the Plan

4. Check the Answer“Did I answer the question being asked?”“Does my answer make sense?”“Is my answer reasonable?”

Some Problem-Solving Strategies

A. Make an organized list

B. Look for a pattern

C. Make a chart or a graph

D. Draw a picture or a diagram

E. Guess and check

F. Work backward.

More Problem-Solving Strategies

G. Write a formula or equation

H. Use logical thinking

I. Make a model

J. Make a simpler problem by breaking the problem down into small steps

K. Recognize when you have too much or too little information

The problem solving strategy that should be used in a given situation…

is the one that works best

for that particular student.

Logical Thinking Problem

Four musicians, John, Paul, George, and Ringo, are standing in line, one behind the

other. John is not third in line. Paul is immediately behind George. Ringo is

second in line. In what order are the four musicians standing?

What must a student be able to do to answer this determine the correct answer to this question?

• One strategy might be to make a table and record the information in the problem onto the table.

John Paul George Ringo

1

2

3

4

The problem tells us that Ringo is second and John is not third. We can enter that information into the table

John Paul George Ringo

1

2 yes

3 no

4

Since Ringo is second, he can’t be first, third or fourth, so we can eliminate those possibilities. Additionally , nobody else can be second.

John Paul George Ringo

1 no

2 no no no yes

3 no no

4 no

Since Paul is immediately behind George, there needs to be two consecutive open spaces. The only options are third and fourth. By

process of elimination, John has to be first.

John Paul George Ringo

1 yes no no no

2 no no no yes

3 no no yes no

4 no yes no no

Solution

1st John

2nd Ringo

3rd George

4th Paul

What skills are tested on the Math CMT?

The Math CMT is broken down into 25 discrete topics known as “strands”. Each strand is meant to assess student performance on specific skills.

These “Strands” include:

• Identifying place value

• Fractions, decimals and percents

• Computation using whole numbers and decimals

• Solving word problems

• Estimating Solutions to Problems

• Customary and Metric Measures

• Geometric Shapes and Properties

• Tables, Graphs and Charts

• Probability

• Patterns

• Algebraic Concepts

• Logical Reasoning

How is the Math CMT administered?

The Math CMT is broken into 3

sections, taken on 3 separate days.

On one section, the students

are not permitted to use calculators.

On the other two sections,

calculators are permitted.

Will my child be ready for the CMT?

• Throughout the school year, your child’s math teacher has be helping your child master the skills and concepts that will be tested on the CMT.

• Our teachers will spend extra time helping students practice those skills in which prior test results have demonstrated the greatest need for improvement.

What has the staff at West Rocks Middle School been doing to help my child prepare for the Math CMT?

• Administering CMT “Progress Tests”;

• Tracking student performance on the Progress Tests in order to identify those skills for which the teacher needs to devote additional instructional time;

• Introducing students to “Study Island”, an online resource where students can answer CMT-type questions on their own and receive immediate feedback

• Conducting after-school extra-help sessions to improve student performance on selected strands.

Is there anything I can do to help my child prepare for the CMT?

Of course!!!

You can help your child prepare for the Math CMT in several ways:

Have you child memorize the multiplication table

Quiz your child on the meaning of math vocabulary terms

Examples of CMT math vocabulary:

• What is a numerator?

• What is a factor?

• What operation do I do to find the product of 2 numbers?

• What is a pattern?

• What is the place value of a number?

( A complete vocabulary list will be given to you tonight)

Have your child go online and practice with “Study Island”

Ask your child to show you his or her homework

• Your child should routinely have math homework right until the CMT.

• Continue to be involved! Have your child explain the homework to you.

All of the teachers and staff at West Rocks Middle School have the highest expectations of our students

on the upcoming CMT.

GOOD LUCK!!!