The Next Generation Mathematics Assessments: Smarter Balanced
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The Next Generation Mathematics Assessments: Smarter Balanced Implications for Instruction http://bit.ly/MCTM-SBAC Danielle Seabold, Kalamazoo RESA Ruth Anne Hodges, MDE. 2 sets of standards: Practice and Content. CCSS-M present two sets of standards

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The Next Generation Mathematics Assessments: Smarter Balanced

Implications for Instruction

http://bit.ly/MCTM-SBAC

Danielle Seabold, Kalamazoo RESA

Ruth Anne Hodges, MDE


2 sets of standards practice and content
2 sets of standards: Practice and Content Balanced

CCSS-M present two sets of standards

Standards for Mathematical Practice: How

  • Carry across all grade levels, K-12

  • Describe how students interact with & use math

  • Embody 21st century skills

    Standards for Mathematical Content: What

  • K-8 standards presented by grade level

  • 9-12 high school standards presented by conceptual categories (not by course)


What makes a good problem solver
What makes a good problem solver? Balanced

  • What characteristics do good problem solvers share?

  • Develop a ‘top 5 characteristics’ list with your table partner(s). Be prepared to share out.

  • Examine the 8 Standards for Mathematical Practice.

  • Highlight, circle, or underline each of the characteristics of good problem solver you see in the Practice Standards


Fundamental change
Fundamental change Balanced

The CCSS-M require a fundamental shift in instruction; a shift from the procedural to a balance between conceptual and procedural.

The bottom line

  • Teachers can’t “tell” their students how to understand.

  • Teachers must guide their students through problem solving to develop understanding and skill.



Assessment claims for mathematics

Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

Assessment Claims for Mathematics

Problem Solving

Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

Round 3 – released 3/20/12

Concepts and Procedures

Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

Data Analysis and Modeling

Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

Communicating Reasoning


Proposed reporting categories
Proposed Reporting Categories interpret and carry out mathematical procedures with precision and fluency.

  • 5 scores have been proposed

  • There will be a Total Mathematics score, which will be a weighted composite based on the student‘s performance across the four claims.

  • The Total mathematics scores will be vertically scaled across grades.


Six item types
Six Item Types interpret and carry out mathematical procedures with precision and fluency.

  • Selected Response

  • Constructed Response

  • Extended Response

  • Performance Tasks

  • Technology-Enabled

  • Technology-Enhanced


Selected response single response multiple choice
Selected Response: interpret and carry out mathematical procedures with precision and fluency. Single Response – Multiple Choice


Selected response multiple correct options
Selected Response: interpret and carry out mathematical procedures with precision and fluency. Multiple Correct Options

Which of the following statements is a property of a rectangle? Select all that apply.

☐ Contains three sides

☐ Contains four sides

☐ Contains eight sides

☐ Contains two sets of parallel lines

☐ Contains at least one interior angle that is acute

☐ Contains at least one interior angle that is obtuse

☐ All interior angles are right angles

☐ All sides have the same length

☐ All sides are of different length


Constructed response
Constructed Response interpret and carry out mathematical procedures with precision and fluency.

The table below shows the number of students in each third-grade class at Lincoln School.

There are 105 fourth-grade students at Lincoln School. How many more fourth-grade students than third-grade students are at Lincoln School? Show or explain how you found your answer.


Extended response
Extended Response interpret and carry out mathematical procedures with precision and fluency.

Pen 1:

Length: (feet, square feet)

Width: (feet, square feet)

Area: (feet, square feet)

Pen 2:

Length: (feet, square feet)

Width: (feet, square feet)

Area: (feet, square feet)

  • Ms. McCrary wants to make a rabbit pen in a section of her lawn. Her plan for the rabbit pen includes the following:

  • It will be in the shape of a rectangle.

  • It will take 24 feet of fence material to make.

  • Each side will be longer than 1 foot.

  • The length and width will measure whole feet.

Pen 3:

Length: (feet, square feet)

Width: (feet, square feet)

Area: (feet, square feet)

Part A

Draw 3 different rectangles that can each represent Ms. McCrary’s rabbit pen. Be sure to use all 24 feet of fence material for each pen.

Use the grid below. Click the places where you want the corners of your rectangle to be. Draw one rectangle at a time. If you make a mistake, click on your rectangle to delete it. Continue as many times as necessary.

  • Part B

  • Ms. McCrary wants her rabbit to have more than 60 square feet of ground area inside the pen. She finds that if she uses the side of her house as one of the sides of the rabbit pen, she can make the rabbit pen larger.

  • Draw another rectangular rabbit pen.

  • Use all 24 feet of fencing for 3 sides of the pen.

  • Use one side of the house for the other side of the pen.

  • Make sure the ground area inside the pen is greater than 60 square feet.

  • Use the grid below. Click the places where you want the corners of your rectangle to be. If you make a mistake, click on your rectangle to delete it.

Use your keyboard to type the length and width of each rabbit pen you draw. Then type the area of each rabbit pen. Be sure to select the correct unit for each answer.

[Students will input length, width, and area for each rabbit pen. Students will choose unit from drop down menu.]

Use your keyboard to type the length and width of each rabbit pen you draw. Then type the area of each rabbit pen. Be sure to select the correct unit for each answer.

Length: (feet, square feet)

Width: (feet, square feet)

Area: (feet, square feet)


Performance task
Performance Task interpret and carry out mathematical procedures with precision and fluency.

  • Student Directions:

  • Geocaching is an indoor or outdoor treasure-

  • seeking game. You can use different tools to find “treasure.” A treasure seeker attempts to find the hidden treasure, or “geocache,” by calculating the location using clues.

  • In this activity, a geocache is the hidden treasure

  • that you must find using a set of clues. These clues will help you to determine the location of the geocache. To complete this activity, you will:

  • • decipher the clues.

  • • create a map on a grid of where the geocache can be found.

  • • use the map to locate the geocache.

  • • locate new geocaches.

  • • create clues for a new geocaching task.

  • Session 1

  • Deciphering the Clues

  • To begin geocaching, you will need to decipher clues to make your map. The map you will use for geocaching will be a coordinate grid. You will start at the origin and apply the clues to determine the location of the first treasure. You will then apply the same clues, starting at the previous location, to determine the location of the next treasure. Part A On a coordinate grid, what are the coordinates for the origin?

  • Use the Geocaching Clues to answer the following questions. How many geocache treasures are you to find using the clues? Explain how you got your answer. What number of units should you move along the x-axis to find each geocache? Explain how you got your answer. What number of units should you move along the y-axis to find each geocache? Explain how you got your answer.


Technology enabled vs technology enhanced
Technology-Enabled vs. Technology-Enhanced interpret and carry out mathematical procedures with precision and fluency.

  • Technology Enabled Items

    • Constructed-Response, Selected-Response or TEI items that use digital media as the stimulus (sound, video, or interactive widget),

    • Do not require specialized interactions for response and/or accompanying response data.

  • Technology Enhanced Items (TEI):

    • Items that include specialized interactions for response and/or accompanying response data; collects evidence through non-traditional response

    • TEI may include digital media as the stimulus (e.g., sound, video, interactive widget, etc.).


Technology enhanced
Technology-Enhanced interpret and carry out mathematical procedures with precision and fluency.

Collects Evidence through a Non-Traditional Response

The value of y is proportional the the value of x. The constant of proportionality for this relationship is 1. On the grid below, graph this proportional relationship.


Cognitive rigor matrix
Cognitive Rigor Matrix interpret and carry out mathematical procedures with precision and fluency.

This matrix from the Smarter Balanced Content Specifications for Mathematics draws from both Bloom’s (revised) Taxonomy of Educational Objectives and Webb’s Depth-of-Knowledge Levels below.


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