Mathematics

Essential Resources

Mathematics Item Specifications

In 2014 Missouri legislators passed House Bill 1490, mandating the development of the Missouri Learning Expectations. In April of 2016, these Missouri Learning Expectations were adopted by the State Board of Education. Groups of Missouri educators from across the state collaborated to create the documents necessary to support the implementation of these expectations.

One of the documents developed is the item specification document, which includes all Missouri grade level/course expectations arranged by domains/strands. It defines what could be measured on a variety of assessments. The document serves as the foundation of the assessment development process.

Although teachers may use this document to provide clarity to the expectations, these specifications are intended for summative, benchmark, and large‐scale assessment purposes.

Components of the item specifications include:

• Expectation Unwrapped breaks down a list of clearly delineated content and skills the students are expected to know and be able to do upon mastery of the Expectation.
• Depth of Knowledge (DOK) Ceiling indicates the highest level of cognitive complexity that would typically be assessed on a large scale assessment. The DOK ceiling is not intended to limit the complexity one might reach in classroom instruction.
• Item Format indicates the types of items used in large scale assessment. For each expectation, the item format specifies the type best suited for that particular expectation.
• Content Limits/Assessment Boundaries are parameters that item writers should consider when developing a large scale assessment. For example, some expectations should not be assessed on a large scale assessment but are better suited for local assessment.
• Sample stems are examples that address the specific elements of each expectation and address varying DOK levels. The sample stems provided in this document are in no way intended to limit the depth and breadth of possible item stems. The expectation should be assessed in a variety of ways.
• Calculator Designation indicates whether a calculator will be available for test questions written to a particular expectations on the large-scale assessment.
   

  Kindergarten	Grade 6
  Grade 1	Grade 7
  Grade 2	Grade 8
  Grade 3	Algebra I
  Grade 4	Algebra II
  Grade 5	Geometry

Expanded Version of the Mathematics Grade- and Course-Level Expectations

The following documents, linked below, were created by Missouri educators to provide classroom teachers a more descriptive version of the mathematics Grade- and Course-Level Expectations (GLEs and CLEs).  Much of this work came from the committees that developed the new expectations; however, many other educators have read and contributed to them.  Please remember, these are curriculum development documents and are not designed as an assessment resource.  Additionally, the examples and lists provided are not exhaustive and are not meant to place limits on the work being done in Missouri classrooms or on assessment development.

While all efforts were made by the committees to provide a clear expectation of student learning, at times it may be difficult to ascertain exactly what the committee intended.  These documents will alleviate some of the questions that inevitably arise when new expectations are released.

In the example below, which illustrates how the documents are organized, the left-hand side lists the official GLE or CLE in order.  The right-hand side is the expanded expectation.

The reader will find instances where both the original and expanded versions are the same.  In these cases it was determined the expectation was clear and any additional description could be detrimental or limiting to the original intent of the committee.

These are working documents and the authors encourage the readers to develop their own examples and lists to bring these mathematics expectations to life in their classrooms.  Also note that these curriculum development documents may be updated in the future to include more detail or clarification of the intended student learning.

Performance Level Descriptors (PLD)

Assessed Standards

The Revised standards, approved on April 19, 2016 are for implementation beginning in the 2016-2017 academic year. They will be assessed beginning in the 2017-2018 school year.

Mathematics - K-5: K-5 PDF | K-5 Word
Mathematics - 6-12: 6-12 PDF | 6-12 Word
Mathematics - K-12: K-12 Excel 

Additional Resources

• Math Crosswalks: K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Algebra 1 | Algebra 2 | Geometry
• 2020-2021 Grade-Level Assessment Blueprints 
• 2020-2021 EOC Blueprints

MLS-Math Resources

• Math End-of-Course Reference Sheet 
• Math Reference Sheet 3-5
• Math Reference Sheet 6-8 

Math Practice Forms

Grade 3

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide

Grade 4

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide

Grade 5

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide

Grade 6

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide
• Math Scoring Rubric Guide

Grade 7

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide
• Math Scoring Rubric Guide

Grade 8

• Math Paper/Pencil
• Math Large Print
• Math Scoring Guide
• Math Scoring Rubric Guide 

EOC Practice Forms

• Algebra I
• Geometry 
• Algebra II 

Presentations

Math Content meeting materials and recording at the Math Hub

Updates on the Implementation of the Mathematics Missouri Learning Standards

• Curriculum and Assessment Update January 2019
• Assessment Update September 20, 2018

Professional Learning

Math Content Meetings for 2021 – 2022 will be in September, November, January and March.  This year we are currently planning on virtual sessions.  Here is the link to the Curriculum calendar:  https://dese.mo.gov/college-career-readiness/curriculum#Calendar to register for these meetings.  On each of these months there will be a K – 5, 6 – 12, and an Assessment Update session.

Math Content meeting materials and recording at the Math Hub. 

Please contact Chip Sharp at chip.sharp@dese.mo.gov with questions or for more details.

Enhanced Learning Maps (ELM)

Take advantage of a free professional development opportunity! The Missouri Department of Elementary and Secondary Education is recruiting interested teachers to participate in the Enhanced Learning Maps (ELM) project, an innovative program aimed at developing and implementing research-based instructional resources for English language arts and mathematics taught in grades 2-8. For more information, call the Office of College and Career Readiness/Curriculum and Assessment at 573-751-3545 or click this link:  https://bit.ly/2q6Jy47 

Interface 2022 – Changing the Story

For over thirty years the Interface Conference has been a place where educators collaborate to improve mathematics and science instruction for the children of Missouri. Please consider presenting at one of Missouri’s premier professional learning events.  Feel free to forward this message to other educators that you believe would also be interested in providing high quality presentations.

The 2022 Interface dates are:

• Tuesday, February 22– Thursday, February 24, 2022
  *Interface A and B will held simultaneously due to the virtual nature of this conference.
• 2022 Interface Registration Information – available Fall 2021

Sponsored by the Missouri Department of Elementary and Secondary Education in cooperation with the MU Conference Office  

• Contact Chip Sharp 

​National Council of Teachers of Mathematics 

Professional Mathematics Organizations

It is vital for Missouri mathematics educators to be active life-long learners in the field of improving mathematics instruction.  Two characteristics of being a life-long learner are an active engagement in professional organizations and networking with other professionals in your field.  The following organizations, listed below, are available to support mathematics educators.  Please consider becoming an active member in one or more of these groups.  If you have questions please visit their websites or contact the individual listed for each group.

National Mathematics Organizations

National Council of Teachers of Mathematics (NCTM)

• Website: http://www.nctm.org/ 
   

National Council of Supervisors of Mathematics (NCSM)

• Membership: https://www.mathedleadership.org/join/index.html
• Missouri Team Leader: Marilyn Cannon marilyn.cannon@raytownschools.org

State-Wide Mathematics Organizations

Missouri Council of Teachers of Mathematics (MCTM)

• Website: https://www.moctm.org/
• Contact: Cindy Bryant, mo.mathgal@mchsi.com 

Missouri Council of Supervisors of Mathematics (MoCSM)

• Contact: Sherri Kane, sherri.kane@lsr7.net

American Regions Mathematics League (ARML)

• Website: http://associations.missouristate.edu/moarml/default.htm
• Contact: Sonya Land, sonya@mathisfun.org

Missouri Mathematics Association for the Advancement of Teacher Training (MAT)2

• Website: https://sites.google.com/site/missourimatsquared/
• Contact: Ann McCoy, mccoy@ucmo.edu

Regional Mathematics Organizations

Central Missouri Mathematics Educators (CM2E)

• Website: http://www.ucmo.edu/math-cs/undergrad/mathed/educators.cfm
• Contact: Ann McCoy, mccoy@ucmo.edu

Kansas City Area Teachers of Mathematics (KCATM)

• Website: www.kcatm.net/
• Contact: Rita Barger, bargerr@umkc.edu

Mathematics Educators of Greater St. Louis (MEGSL)

• Website: http://www.megsl.org/
• Contact: Patrick Mooney, pmooney@pkwy.k12.mo.us

Mathematics Educators of South Central Missouri (MESCM)

• Contact: Jerry Trick, jerrytrick@missouristate.edu

Southwest Missouri District Association of Mathematics Teachers (SWMDAMT)

• Website: http://associations.missouristate.edu/swmdamt/default.htm
• Contact: Jesse Hiett, jehiett@spsmail.org

Additional Sample Items

Grade 1

• Number Sense and Operations in Base Ten

  • 1.NBT.A.4 Example 1
  • 1.NBT.B.5 Example 1
  • 1.NBT.B.6 Examples 1 and 2
  • 1.NBT.B.7 Examples 1 and 2

• Number Sense and Operations

  • 1.NS.A.2 Example 1

• Relationships and Algebraic Thinking

  • 1.RA.A.1 Example 1
  • 1.RA.A.1 Examples 2 and 3

Grade 3

• Data and Statistics

  • 3.DS.A.2 Example 1 
  • 3.DS.A.4 Example 1

• Geometry and Measurement

  • 3.GM.A.2 Example 1 
  • 3.GM.A.3 Example 1 
  • 3.GM.B.4 Example 1
  • 3.GM.B.4 Example 2 
  • 3.GM.B.5 Example 1 
  • 3.GM.B.6 Example 1 
  • 3.GM.B.6 Example 2 
  • 3.GM.B.8 Example 1
  • 3.GM.C.9 Example 1 
  • 3.GM.C.10 Example 1
  • 3.GM.C.11 Example 1 
  • 3.GM.C.11 Example 2 
  • 3.GM.C.12 Examples 1, 2, and 3
  • 3.GM.C.12 Example 4 
  • 3.GM.C.13 Examples 1 and 2
  • 3.GM.C.14 Example 1

• Number Sense and Operations in Fractions

  • 3.NF.A.3 Example 1 
  • 3.NF.A.3 Example 2 
  • 3.NF.A.3 Example 3
  • 3.NF.A.6 Example 1
  • 3.NF.A.6 Example 2 
  • 3.NF.A.6 Example 3
  • 3.NF.A.7 Example 1 
  • 3.NF.A.7 Example 2 
  • 3.NF.A.7 Example 3
  • 3.NF.A.7 Example 4 

• Relationships and Algebraic Thinking

  • 3.RA.D.10 Examples 1 and 2 

Grade 4

• Data and Statistics

  • 4.DS.A.1 Example 1
  • 4.DS.A.2 Example 1

• Geometry and Measurement

  • 4.GM.A.1 Example 1
  • 4.GM.A.2 Example 1
  • 4.GM.A.3 Example 1
  • 4.GM.B.4 Example 1
  • 4.GM.C.7 Example 1
  • 4.GM.C.8 Example 1

• Number Sense and Operations in Base Ten

  • 4.NBT.A.1 Example 1
  • 4.NBT.A.1 Example 2
  • 4.NBT.A.2 Example 1
  • 4.NBT.A.2 Example 2
  • 4.NBT.A.3 Example 1
  • 4.NBT.A.5 Example 1
  • 4.NBT.A.5 Example 2
  • 4.NBT.A.6 Example 1
  • 4.NBT.A.6 Example 2
  • 4.NBT.A.7 Examples 1 and 2

• Number Sense and Operations in Fractions

  • 4.NF.A.1 Example 1
  • 4.NF.A.1 Example 2
  • 4.NF.A.1 Example 3
  • 4.NF.A.1 Examples 4 and 5
  • 4.NF.A.1 Example 6
  • 4.NF.A.1 Examples 7 and 8
  • 4.NF.A.2 Example 1
  • 4.NF.A.2 Example 2
  • 4.NF.A.2 Examples 3 and 4
  • 4.NF.A.2 Example 5
  • 4.NF.A.2 Example 6
  • 4.NF.A.3 Example 1
  • 4.NF.A.3 Example 2
  • 4.NF.B.5 Example 1
  • 4.NF.B.5 Example 2
  • 4.NF.B.6 Example 1
  • 4.NF.B.6 Example 2
  • 4.NF.B.7 Examples 1 and 2
  • 4.NF.B.8 Example 1
  • 4.NF.C.9 Example 1
  • 4.NF.C.9 Example 2
  • 4.NF.C.10 Example 1
  • 4.NF.C.10 Example 2
  • 4.NF.C.10 Example 3
  • 4.NF.C.11 Example 1
  • 4.NF.C.11 Example 2
  • 4.NF.C.11 Example 3
  • 4.NF.C.11 Example 4
  • 4.NF.C.12 Example 1
  • 4.NF.C.12 Example 2
  • 4.NF.C.12 Example 3
  • 4.NF.C.12 Example 4
  • 4.NF.C.12 Example 5

• Relationships and Algebraic Thinking

  • 4.RA.B.4 Example 1
  • 4.RA.C.6 Example 1
  • 4.RA.C.7 Example 1 

Grade 5

• Geometry and Measurement

  • 5.GM.A.3 Example 1

• Number Sense and Operations in Base Ten

  • 5.NBT.A.1 Examples 1 and 2
  • 5.NBT.A.3 Example 1
  • 5.NBT.A.3 Example 2
  • 5.NBT.A.4 Examples 1 and 2
  • 5.NBT.A.7 Example 1
  • 5.NBT.A.8 Example 1
  • 5.NBT.A.8 Example 2

• Number Sense and Operations in Fractions

  • 5.NF.A.2 Example 1
  • 5.NF.A.2 Example 2
  • 5.NF.A.2 Example 3
  • 5.NF.A.3 Examples 1 and 2
  • 5.NF.A.3 Example 3
  • 5.NF.A.3 Examples 4 and 5
  • 5.NF.A.3 Example 6
  • 5.NF.B.4 Examples 1 and 2
  • 5.NF.B.4 Examples 3, 4, and 5
  • 5.NF.B.4 Example 6
  • 5.NF.B.5a Example 1
  • 5.NF.B.5b Examples 1 and 2
  • 5.NF.B.5b Example 3
  • 5.NF.B.5b Example 4
  • 5.NF.B.5c Example 1
  • 5.NF.B.5c Example 2
  • 5.NF.B.5c Examples 3 and 4
  • 5.NF.B.5c Example 5
  • 5.NF.B.5d Examples 1 and 2
  • 5.NF.B.5d Examples 3 and 4
  • 5.NF.B.5d Example 5
  • 5.NF.B.5d Example 6
  • 5.NF.B.6 Example 1
  • 5.NF.B.6 Example 2
  • 5.NF.B.7b Examples 1 and 2

• Relationships and Algebraic Thinking

  • 5.RA.A.1 Example 1
  • 5.RA.C.5 Examples 1, 2, and 3

Grade 6

• Data Analysis, Statistics and Probability

  • 6.DSP.A.1 Example 1

• Expressions, Equations and Inequalities

  • 6.EEI.A.1 Example 1
  • 6.EEI.A.1 Example 2
  • 6.EEI.A.2a Example 1
  • 6.EEI.A.2a Example 2
  • 6.EEI.A.2b Example 1
  • 6.EEI.A.2b Example 2
  • 6.EEI.A.2c Example 1
  • 6.EEI.A.2c Example 2
  • 6.EEI.A.2c Example 3
  • 6.EEI.A.2e Example 1
  • 6.EEI.A.3 Example 1
  • 6.EEI.A.3 Example 2
  • 6.EEI.A.3 Example 3
  • 6.EEI.B.4 Examples 1, 2, and 3
  • 6.EEI.B.4 Example 4
  • 6.EEI.B.4 Example 5
  • 6.EEI.B.4 Example 6
  • 6.EEI.B.4 Example 7
  • 6.EEI.B.5 Examples 1 and 2
  • 6.EEI.B.5 Example 3
  • 6.EEI.B.5 Example 4
  • 6.EEI.B.5 Example 5
  • 6.EEI.B.6 Example 1
  • 6.EEI.B.6 Example 2
  • 6.EEI.B.7 Example 1
  • 6.EEI.B.7 Example 2
  • 6.EEI.B.8a Example 1
  • 6.EEI.B.8b Example 1
  • 6.EEI.C.9a Example 1
  • 6.EEI.C.9a Example 2
  • 6.EEI.C.9a Example 3
  • 6.EEI.C.9b Example 1
  • 6.EEI.C.9b Example 2

• Geometry and Measurement

  • 6.GM.A.1 Example 1
  • 6.GM.A.2a Example 1
  • 6.GM.A.3c Example 1
  • 6.GM.A.4b Examples 1 and 2

• Number Sense and Operations

  • 6.NS.C.6c Examples 1, 2, and 3

• Ratios and Proportional Relationship

  • 6.RP.A.1 Example 1
  • 6.RP.A.2 Example 2
  • 6.RP.A.3a Example 1
  • 6.RP.A.3a Example 2
  • 6.RP.A.3c Example 1
  • 6.RP.A.3d Example 1

Grade 7

• Data Analysis, Statistics and Probability

  • 7.DSP.C.5b Example 1
  • 7.DSP.C.8a Example 1
  • 7.DSP.C.8b Example 1

• Expressions, Equations and Inequalities

  • 7.EEI.A.1 Example 1
  • 7.EEI.A.2 Example 1
  • 7.EEI.B.4b Example 1
  • 7.EEI.B.4c Example 1

• Geometry and Measurement

  • 7.GM.A.1 Example 1
  • 7.GM.A.2a Examples 1 and 2
  • 7.GM.A.2b Examples 1 and 2
  • 7.GM.A.3 Example 1
  • 7.GM.A.4a Example 1

• Number Sense and Operations

  • 7.NS.A.2f Example 1
  • 7.NS.A.2f Examples 2, 3, and 4
  • 7.NS.A.3 Example 1

• Ratios and Proportional Relationship

  • 7.RP.A.1 Example 1 
  • 7.RP.A.1 Example 2
  • 7.RP.A.1 Example 3
  • 7.RP.A.2c Example 1
  • 7.RP.A.2d Example 1
  • 7.RP.A.3 Example 1

Grade 8

• Data Analysis, Statistics and Probability

  • 8.DSP.A.1 Example 1
  • 8.DSP.A.2 Example 1

• Expressions, Equations and Inequalities

  • 8.EEI.A.1 Example 1
  • 8.EEI.A.1 Example 2
  • 8.EEI.A.2a Example 1
  • 8.EEI.A.2b Example 1
  • 8.EEI.A.2c Example 1
  • 8.EEI.A.4b Example 1
  • 8.EEI.B.5a Example 1
  • 8.EEI.B.5a Example 2
  • 8.EEI.B.5a Example 3
  • 8.EEI.B.5b Example 1
  • 8.EEI.B.5b Example 2
  • 8.EEI.C.7a Examples 1 and 2
  • 8.EEI.C.7b Examples 1, 2, and 3
  • 8.EEI.C.8c Example 1
  • 8.EEI.C.8d Example 1

• Functions

  • 8.F.B.4a Example 1
  • 8.F.B.4b Example 1
  • 8.F.B.4c Example 1

• Geometry and Measurement

  • 8.GM.A.1b Example 1
  • 8.GM.A.3 Example 1
  • 8.GM.A.4a Example 1
  • 8.GM.B.6 Example 1
  • 8.GM.B.7 Example 1
  • 8.GM.B.8 Example 1

• Number Sense and Operations

  • 8.NS.A.1a Example 1
  • 8.NS.A.1b Example 1
  • 8.NS.A.1c Example 1
  • 8.NS.A.1d Example 1
  • 8.NS.A.2 Example 1

Algebra 1

• Building Functions

  • A1.BF.A.1 Example 1
  • A1.BF.A.1 Example 2
  • A1.BF.A.1 Examples 3 and 4

• Creating Equations And Inequalities

  • A1.CED.A.1 Example 1
  • A1.CED.A.1 Example 2
  • A1.CED.A.2 Example 1
  • A1.CED.A.2 Example 2
  • A1.CED.A.3 Example 1
  • A1.CED.A.3 Example 2
  • A1.CED.A.3 Example 3
  • A1.CED.A.3 Example 4
  • A1.CED.A.4 Examples 1 and 2
  • A1.CED.A.4 Example 3
  • A1.CED.A.4 Example 4
  • A1.CED.A.4 Example 5
  • A1.CED.A.4 Example 6

• Data And Statistics

  • A1.DS.A.1 Examples 1 and 2
  • A1.DS.A.2 Example 1
  • A1.DS.A.3 Example 1
  • A1.DS.A.5b Example 1
  • A1.DS.A.6 Example 1

• Interpreting Functions

  • A1.IF.C.7 Example 1

• Linear, Quadratic And Exponential Models

  • A1.LQE.A.1a Example 1
  • A1.LQE.A.1a Example 2
  • A1.LQE.A.2 Example 1
  • A1.LQE.A.2 Example 2
  • A1.LQE.A.3 Example 1
  • A1.LQE.B.4 Example 1
  • A1.LQE.B.6 Example 1

• Number And Quantity

  • A1.NQ.A.1 Example 1
  • A1.NQ.B.3a Example 1
  • A1.NQ.B.3d Example 1
  • A1.NQ.B.4 Example 1
  • A1.NQ.B.5 Example 1

• Seeing Structure In Expressions

  • A1.SSE.A.1 Example 1
  • A1.SSE.A.3a Example 1
  • A1.SSE.A.3b Example 1
  • A1.SSE.A.3b Example 2
  • A1.SSE.A.3b Example 3

Geometry

• Congruence

  • G.CO.A.1 Example 1
  • G.CO.A.2 Example 1
  • G.CO.C.8 Example 1
  • G.CO.C.9 Example 1
  • G.CO.C.9 Example 2
  • G.CO.C.9 Example 3
  • G.CO.C.10 Example 1

• Similarity, Right Triangles And Trigonometry

  • G.SRT.A.3 Example 1

Algebra 2

• Arithmetic With Polynomials And Rational Expressions

  • A2.APR.A.2 Example 1
  • A2.APR.A.2 Example 2
  • A2.APR.A.3 Example 1
  • A2.APR.A.4 Example 1

• Building Functions

  • A2.BF.A.1 Example 1
  • A2.BF.A.1 Example 2
  • A2.BF.A.2. Example 1
  • A2.BF.A.2 Example 2

• Modeling With Functions, Or Functions And Modeling

  • A2.FM.A.1 Example 1
  • A2.FM.A.1 Example 2

• Interpreting Functions

  • A2.IF.A.2 Example 1

• Number And Quantity

  • A2.NQ.B.5 Example 1
  • A2.NQ.B.6 Example 1

• Reasoning With Equations And Inequalities

  • A2.REI.A.2 Example 1
  • A2.REI.A.2 Example 2
  • A2.REI.B.3 Example 1

• Seeing Structure In Expressions Functions

  • A2.SSE.A.3 Example 1
  • A2.SSE.A.3 Example 2
  • A2.SSE.A.4 Example 1

Released Scored Performance Events