Mathematics

A mathematics curriculum is more than a collection of activities; instead it is a coherent sequencing of core mathematical ideas that are well articulated within and across grades and courses. Such curricula pose problems that promote conceptual understanding, problem solving, and reasoning and are drawn from contexts in everyday life and other subjects. (NCTM, 2014, p. 72).

Math standards progression across grade levels guide our framework for curriculum development.

Numbers

• Counting and Cardinality - Kindergarten
• Numbers and Operations in Base Ten - Grades K-5
• Number and Operations-Fractions - Grades 3-5
• Ratios and Proportional Relationships - Grades 6-7
• The Number System - Grades 6-8
• Number and Quantity - Grades 9-12

Algebra

• Operations and Algebraic Thinking - Grades K-5
• Expressions and Equations - Grades 6-8
• Functions - Grades 8-12
• Algebra - Grades 9-12

Geometry

• Geometry - Grades K-12

Data Collection and Measurement

• Measurement and Data - Grades K-5
• Statistics and Probability - Grades 6-12

Math Curriculum Development Resources

Common Core State Standards site provides parents, educators, policy makers, journalists, and others easy access to the Common Core State Standards, as well as supporting information and resources.

Standards for Mathematical Practices 

Achieve the Core Coherence Map is an interactive website that illustrates the coherent structure of the Common Core State Standards for Mathematics K – High School. Standards relate to one another, both within and across grades.

Focus by Grade Level documents identify where students should spend the large majority of their time on the major work of the grade.  Supporting work and, where appropriate, additional work is also identified that can engage students in the major work of the grade.

Model Competencies in Mathematics This document is a model that a district might choose to use as tool for focusing lessons, resources, and supports so that students are provided the opportunity to deeply engage in the important content of each discipline. Districts and educators can also use these models to guide the development of local assessments and competency-based grading and reporting systems.

MAISA K-12 Mathematics Units is a model math curriculum produced by consultants and local district educators of the Oakland intermediate school district based upon their knowledge of the state and national curriculum standards, their curriculum design experience with local school districts, and their study of professional literature in the field of curriculum. The Michigan School Code requires every school district to establish a local core curriculum and an aligned instructional program, which takes into account the Michigan academic standards and content expectations for English language arts, health, mathematics, science, social studies and world languages. Oakland Schools provides this model to assist school districts in establishing a local core curriculum. 

Posters

Math Practices Poster

Math Practices Competency Poster

Venn Diagram of ELA, Science, and Math Practices Poster

NCTM has identified eight Mathematics Teaching Practices that research indicates are consistent components of every mathematics lesson. Learners should have experiences that enable them to engage with challenging tasks. . . connect new learning with prior knowledge and informal reasoning. . . acquire conceptual as well as procedural knowledge. . . construct knowledge through discourse, activity, and interaction with meaningful problems. . . receive descriptive and timely feedback. . . develop meta-cognitive awareness of themselves as learners, thinkers, and problem solvers” (NCTM, 2014, p. 9).

Instructional Framework

Instructional frameworks provide districts, schools, and classrooms with a clear and cohesive focus on instruction by combining specific expectations for student learning with specific strategies that guide teaching and assessment. The instructional framework selected can serve as a powerful guide for aligning curriculum, teaching, assessment and the learning environment with principles of effective mathematics instruction. Ultimately, an effective instructional framework can move mathematics teachers beyond the mechanical aspects of planning lessons and units to a deeper consideration of how to advance students’ mathematical understanding throughout.

Example: Wayne RESA’s Framework for Ambitious Instruction

Aspects of Rigor

According to the standards, achieving rigor requires us to teach math in a way that balances students' conceptual understanding, their procedural skill and fluency, and their ability to apply what they know and are able to do to real-world, problem-solving situations.

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.

Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures. 

Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Instructional Approaches for Math Rigor

Thinking Through a Lesson Plan Protocol

The Thinking Through a Lesson Plan Protocol (TTLP) provides a framework for developing lessons that use students’ mathematic thinking as the focus in developing their understanding of key ideas.  It helps teachers anticipate what students will do and generate questions they can ask that will promote student learning.  The TTLP is divided into three parts:

Part 1: Selecting and setting up a mathematical task

Part 2: Support students’ exploration of the task

Part 3: Sharing and discussing the task

Essential Instructional Practices in Early Mathematics

The Essential Instructional Practices in Early Mathematics document is a tool intended to support educators across Michigan as we work to enhance the ways in which children learn to use, understand, and do mathematics using a strengths-based approach.  The long-term goal is that these Essential Instructional Practices in Early Mathematics: Prekindergarten to Grade 3 will prompt shifts in systems, learning, teaching, and assessment so that each and every child develops strong early mathematical understanding, skills, and dispositions.

This document was developed by the MAISA Early Task Force, a subcommittee of the Michigan Association of Intermediate School Administrators (MAISA) General Education Leadership Network (GELN), which represents Michigan’s 56 Intermediate School Districts.

Family Math Night

EUPISD Created Family Math Night Toolkit

Promote Fluency and Concepts

Bedtime Math (K-5) Aims to engage parents and children in short math activities with the goal of reducing math anxiety for both parents and kids. The activities can be printed.

Math Fact Fluency (K-5) provides basic fact games and assessment tools found in the book, Math Fact Fluency.  Many of the games have Jamboards for the students to play the games online.

Splat (K-8) guess how many dots are under the splat and explain why.

Which One Doesn't Belong (K-10) is a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Same or Different (K-12) is a routine that provides students opportunities to construct arguments when comparing objects, such as numbers or shapes. 

Number Talk (K-12) A Number Talk develops fluency. The website contains dot images that can be printed along with number problem examples. For a dot image, flash the image for 3 seconds and ask, "How many dots? How did you see it?" Then show them the image to have students check. See the video to further understand dot images. For a number problem, pose a number problem aligned to the child's grade level. Have the child solve it mentally and have them explain their thinking. See the video of a first grader solving 16+12 mentally.

Khan Academy (K-12) offers exercises, quizzes, and tests so student can practice and master skills.  This resource will help students focus on ACT ans SAT prep.  It includes tutorials and practice questions.

NCTM Illuminations (Interactives) (K-12) Interactive games, played online, used to support a wide variety of mathematics content. In the search box, check off "interactives" and appropriate grade band. Then click "search".

Math Communities Blog (2-8) Each week, Math Communities updates the blog with a detailed look into a math activity as well as an article showing a unique look into math education and online learning.

Yummy Math (2-12) is for teachers to use to supplement their existing math curriculum. This a great place to go when students say, “When will I ever use this?” Activities can be as a single lesson filled with rich discussion or a quick class opener. If your state has adopted Common Core, Yummy Math is filled with examples, where students can both create and interpret mathematical models from real data.

Estimation 180 (4-8) is an activity curated by Andrew Stadel, a teacher and Mathematics Coach in California. He created 180 different estimation challenges for his students and published his site, Estimation 180 in 2012. Since then, teachers around the world have been using his lessons to develop students' number sense and reasoning.
This routine engages students in number concepts, including relative size, comparing and ordering numbers, and benchmarks. Some students will use mental math when determining quantities. Similarly, some student may apply spatial reasoning when estimating. 

Turner's Graph of the Week (5-12) Improving math literacy in the classroom with a graph a week.  Students use the same prompt every week to analyze graphs and write a reflection on what they think. Students will become sharper, analytical thinkers in today's world. Students are given the opportunity to communicate their critical thinking and analysis through writing and classroom discussion.

Graphing Stories (6-12) has short video stories that help students learn to graph on a plane. (6-12)

Building Conceptual Understanding and Fluency Through Games from North Carolina (K) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Building Conceptual Understanding and Fluency Through Games from North Carolina (1) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Building Conceptual Understanding and Fluency Through Games from North Carolina (2) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Building Conceptual Understanding and Fluency Through Games from North Carolina (3) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Building Conceptual Understanding and Fluency Through Games from North Carolina (4) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Building Conceptual Understanding and Fluency Through Games from North Carolina (5) Games provide students with opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. The activities can be printed and require minimal tools.

Promote Problem Solving

Would You Rather Math (K-12) provides a quick, fun, visual way to engage students in math-based conversations and have students use math to justify their ideas.

YouCubed (K-12) provides an assortment of tasks, lessons, and videos. The mission of the organization is to inspire, educate and empower teachers of mathematics, transforming the latest research on math into accessible and practical forms.

Open Middle (K-12) problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding.   They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

Desmos Activities (3-5) Includes problem solving and practice opportunities. An account needs to be created; however, it is free. Click the desired activity and hit "Student Preview".

Illustrative Mathematics Tasks (K-12) Higher-order thinking math tasks for each math standard from Kindergarten to High School.

Desmos Geometry Activities (6-8) Includes problem solving and practice opportunities aligned to the geometry standards. An account needs to be created; however, it is free. Click the desired activity and hit "Student Preview".

Desmos Statistics Activities (6-8) Includes problem solving and practice opportunities aligned to the statistics standards. An account needs to be created; however, it is free. Click the desired activity and hit "Student Preview".

Desmos Early Algebra Activities (6-8) Includes problem solving and practice opportunities aligned to the early algebra standards. An account needs to be created; however, it is free. Click the desired activity and hit "Student Preview".

Mathematics Assessment Project (6-12) aims to bring the Common Core State Standards to life in a way that helps teachers, and their students turn their aspirations for achieving them into classroom realities.  The Project provide summative tests or tasks, classroom challenges, and professional development modules.

Math Recovery® in Michigan (K-8) identifies Math Recovery® trained consultants in Michigan and resources developed for the implementation of the Math Recovery® professional development to enhance the instruction of the Michigan math standards. 

The KNP Intervention Database (K-5) contains proven numeracy-developed activities that can be searched by standard, grade level, fluency benchmark, task group or setting. These resources are free, but registration is required. 

Virtual Manipulatives

• Glencoe Virtual Manipulatives
• National Library of Virtual Manipulatives
• Dreambox Learning Manipulatives
• The Math Learning Center - Free Math Apps