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The Next Generation Mathematics Assessments:

Smarter BalancedImplications for Instruction

http://bit.ly/MCTM-SBAC

Danielle Seabold, Kalamazoo RESARuth Anne Hodges, MDE

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2 sets of standards: Practice and ContentCCSS-M present two sets of standardsStandards for Mathematical Practice: How• Carry across all grade levels, K-12• Describe how students interact with & use math• Embody 21st century skillsStandards for Mathematical Content: What• K-8 standards presented by grade level• 9-12 high school standards presented by

conceptual categories (not by course)

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What makes a good problem solver?• 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

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Fundamental change

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.

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A school year at a glance: SBAC

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Assessment Claims for Mathematics

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

Concepts and Procedures

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

Problem Solving

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

Communicating Reasoning

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

Data Analysis and Modeling

Round 3 – released 3/20/12

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Proposed Reporting Categories

• 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.

Total Mathematics Composite Score (for Federal Accountability)

Claim #1: Concepts and Procedures Score~40%

Claim #2: Problem Solving Score~20%

Claim #3: Communicating Reasoning Score~20%

Claim #4: Modeling & Data Analysis Score ~20%

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Six Item Types

• Selected Response

• Constructed Response

• Extended Response

• Performance Tasks

• Technology-Enabled

• Technology-Enhanced

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Selected Response: Single Response – Multiple Choice

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Selected Response: 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

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Constructed Response

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.

Students in Third-Grade

Class Number of Students

Mrs. Roy 24

Mr. Grant 21

Mr. Harrison 22

Ms. Mack 25

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Extended ResponseMs. 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.

Part ADraw 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.

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.]

Pen 1: Length: (feet, square feet) Width: (feet, square feet) Area: (feet, square feet)

Part BMs. 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.

Pen 2: Length: (feet, square feet) Width: (feet, square feet) Area: (feet, square feet)

Pen 3: Length: (feet, square feet) Width: (feet, square feet) Area: (feet, square feet)

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)

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Performance TaskStudent 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.

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Technology-Enabled vs. Technology-Enhanced• 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.).

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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.

Technology-EnhancedCollects Evidence through a Non-Traditional Response

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Cognitive Rigor MatrixThis 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.