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Sample MTEL65 Middle School Math Open Response

May 14th, 2021 | Comments Off on Sample MTEL65 Middle School Math Open Response | Certification Prep, Math Certification, Teacher's Lounge Blog, Teaching Licenses

MA DESE is updating many MTEL exams over the coming year.  As of the end of May, the MTEL 47 Middle School Math exam will be replaced by the MTEL 65 Middle School Math exam.  This is a welcome change for many as many of the more difficult concepts, including calculus and discrete math, were removed for this new exam.  There will still be two open response questions on this MTEL exam and one is quite different than the previous exam. Here is a quick sample problem with a response.  For more information on preparing for this exam, please check out our full-length, MTEL prep comprehensive course with unlimited expert instructor support. (www.prepforward.com/mtel-massachusetts)

The following is a sample problem for Objective 14 on the new MTEL 65 exam. 

Standard: The Massachusetts Mathematics Curriculum Framework for grade 7 provides the following content standard:
Expressions and Equations (7.EE)
1. Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.


1. Solve for x:  3x – 7 = 2/3
2. Factor  x2 + 4x + 4
3. Simplify  6(-x + 0.5) 

Analyze standard 7.EE.1.  Identify related prerequisite concepts and skills.  Critique whether the problems listed above are aligned with the content standard. Provide your own problem with different representations to teach the standard. Explain your reasoning.


Here is a sample response for the above problem. 

The 7th grade standard under Expressions and Equations involves an application of the properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. Therefore, a student must understand associative, commutative, and distributive properties as a prerequisite. Furthermore, as the coefficients are rational, a student must be comfortable with all the operations with rational numbers, including negatives, fractions, and decimals. Finally, students must understand how to identify if two expressions are equivalent. 

Given Problems:

1. Solve for x:  3x – 7 = 2/3
2. Factor  x2 + 4x + 4
3. Simplify  6(-x + 0.5) 

There were three sample problems given for teaching this standard. Unfortunately, the first sample problem does not fit under this standard as the problem asks the student to solve an equation, which is a concept that is taught later as this standard only deals with expressions. The second sample problem also does not fit under this standard as it is not a linear expression, but a quadratic expression. The third sample problem is an appropriate question to ask students under this standard. 

In addition to problems similar to the third sample problem, one part of this standard is teaching students to use the distributive property to find equivalent expressions.  An area model will help students visualize this.  A sample is included below.

In this problem, a student would be asked to simplify 3(2x + 5).  Using the area model, they would be asked to find the area of each rectangle and then add them together to find the total area of both rectangles. 



MA DESE’s Only Preferred MTEL Course Vendor

April 1st, 2020 | Comments Off on MA DESE’s Only Preferred MTEL Course Vendor | Certification Prep, Literacy Certification, Math Certification, Reading Certification, Remote Learning, Teacher's Lounge Blog, Teaching Licenses, Writing Certification

MTEL prep

No one disputes the fact that there is more and more pressure on public school educators to make a difference in the lives of the children they teach, no matter what level of professional experience they have. This applies to both elementary and secondary school students and first year and experienced teachers.

New teachers are most often targeted for improving their skills to ensure that they are as ready as they can be for their experience in the classroom. PrepForward is pleased to be a part of that preparation process. As one of the premier vendors for MTEL courses, PrepForward offers courses for educators to enhance and excel in their skills for educating students in classrooms across Massachusetts. PrepForward was chosen as MA Department of Elementary and Secondary Education’s only preferred vendor for MTEL preparation courses. One important aspect of our work with MA DESE is to increase diversity in the teacher workforce.

We are committed to providing teacher preparation courses that aid educators in boosting their teaching skills before they even enter the classroom. This has the added benefit of equipping teachers to help students grow academically and to achieve student success in the classroom for those who may not be on the average spectrum. Students benefit from teachers who have a greater skill set and teachers benefit from increased knowledge to reach all types of learners.

The online classes we offer are designed so that, upon completion, educators can pass the MTEL exams. All courses introduce detailed lessons, full-length practice tests, question explanations, instructor support, 24-hour access, and interactive applications. Courses include general curriculum classes for general and middle-school mathematics, reading, and communication and literacy skills in reading and writing.

Since our program is an approved provider for the MA Department of Education, our courses are available for professional development points, as well. We are pleased to have helped thousands of educators across Massachusetts pass their MTEL exams.