Assessment
Best Practices
Learning Activities and Games
Lesson Planning
Teacher Support
Assessment—Tools to assist in the evaluation of student readiness, ability, and achievement:
- Tests
- Rubrics
- Benchmarks
- Checklists
Best Practices in Mathematics Instruction—Current educational research for professional development:
- Instructional strategies
- Professional resources
- Periodical and journal articles
Learning Activities and Games—Instructional games, worksheets, and activities:
- Enhancing instruction
- Enrichment
- Remediation
- Reteaching
- Individualized assistance
- ESL
Lesson Planning—Tools for planning and development of mathematics instruction:
- State content standards
- Teaching tips
- Lesson plan ideas
Teacher Support—Ideas and resources to assist teachers:
- Ask a Question or Share an Idea
- FAQs
- Instructional Ideas
Measurement Handouts:
Number Lines
Quadrant Grid
Square Centimeter Grid
Square Inch Grid
ACSI/Purposeful Design Publications does not endorse these resources and recommends that each one be evaluated for usefulness and appropriateness prior to use in the classroom. ACSI does not guarantee the functionality of the resource links, since each link is maintained by each individual website developer.
Assessment—Tools to assist in the evaluation of student readiness, ability, and achievement.
Campus Rubric Studio and Gallery: This website provides both the tools to build your own rubrics and a repository of public rubrics organized by subject.
The Math Forum at Drexel: From the homepage, select “About The Math Forum” to locate the site map. From this quick reference sheet you will be able to navigate to many different math resources including assessment ideas in the math education category. Be sure to check out the vast array of materials available for team problem solving, research, puzzles, and problem solving.
Response to Intervention: Response to Intervention (RTI) is a tiered approach to help struggling students. The need for further instruction is determined by carefully monitoring the student at each tier of intervention. There is specific content about using this approach in mathematics instruction.
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Best Practices in Mathematics Instruction—Current educational research for professional development.
National Center for Learning Disabilities: The classroom strategies section for Grades K–8 includes an extensive discussion of accommodations for students with learning disabilities, assistive technology, and techniques to aid learning. Some are specifically for math and others are more general. The introduction also provides a checklist of signs and symptoms of learning disabilities.
Access Center: The Access Center is a national technical assistance (TA) center funded by the U.S. Department of Education’s Office of Special Education Programs. Their mission is to improve educational outcomes for grade K–8 students with disabilities. This is an excellent source for professional development modules to support the training of teachers as well as short discussions on mathematics instruction for students with learning disabilities including strategies such as of concrete-representational-abstract and computer-assisted instruction. Many of these techniques can be used for a wide variety of learners.
The Math Forum at Drexel: The Math Forum is dedicated to helping teachers to improve math education and students to learn math by utilizing the power of the Web. Explore this website for a vast array of resources for all grade levels.
National Library of Virtual Manipulatives: Organized by grade level and math strand, virtual manipulatives activities for a wide range of concepts are available for all grade levels. They can be selected by type of manipulative and are related to the National Council of Teachers of Mathematics (NCTM) standards. Also available in Spanish and French.
Response to Intervention: Response to Intervention (RTI) is a tiered approach to help struggling students. The need for further instruction is determined by carefully monitoring the student at each tier of intervention. There is specific content about using this approach in mathematics instruction.
Digital Media: Using public media to engage students with mathematics is made easier by using this site. Provides access to printable worksheets, assessments, project ideas, standards-based resources, program schedules, and lesson plans.
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Learning Activities and Games—Instructional games, worksheets, and activities.
Set: The game of Set & Trilogy is an attribute game that can help students age 6 and up in developing their mathematical reasoning. A daily puzzle is available. A discussion of the mathematics, including set theory and number squares, behind the game is available for older students. A section for teachers includes ideas for using the game in the classroom and references to other materials using the game to teach mathematics. You may also purchase the game from this site.
Illuminations: Interactive lessons to make math come alive in your classroom are organized by grade level band and by topic—everything from counting to probability to geometry. Clear instructions make these useable for both individual use and classroom demonstrations.
United States Mint: This H.I.P. Pocket Change kids’ page includes a games section that provides interactive activities for elementary students. Check the teachers and parents link at the bottom of the page for grade-level information and games-related resources.
Free Math Drills: Hundreds of math worksheets are provided for a variety of math subjects at all levels including arithmetic, money, fractions, order of operations as well as special holiday-themed versions and blank graph paper. Use these for practice, review, assessment, or with manipulatives for a wide variety of activities. Also included are interactive games and flashcards. This site is available in several different languages.
Free Math Worksheets: Generate your own customized worksheets for your classroom. Includes basic facts, pre-algebra, Sudoku, and many others. Choose your title and directions, difficulty level, and number of problems. It also generates an answer key.
Texas Instruments: A large bank of innovative classroom activities using TI calculators. Each activity is aligned with curriculum standards. Browse by subject and then select the grade level and model of calculator to narrow your search.
Math Homework Help: For middle school students the free math workbooks listed under more resources can be used as an online tutor. The step-by-step approach allows students to attempt problems themselves but have immediate help if needed. There are also interactive math games under learning activities.
Worksheets: SuperKids® provides user reviews of educational software and free educational tools such as a make-your-own math worksheet creator and online logic games.
Activity-based Learning: Students study science and engineering subjects using math-related exercises and literature. Search the site by typing math in the “find it” box.
Digital Media: Using public media to engage students with mathematics is made easier by using this site. Provides access to printable worksheets, assessments, project ideas, standards-based resources, program schedules, and lesson plans.
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Lesson Planning—Tools for planning and development of mathematics instruction.
United States Mint: This H.I.P. Pocket Change kids’ page includes a teacher section providing lesson plans for grades K–8. Be sure to check the additional materials at the end of the lesson plan section and click on Math (for coin-related lesson plans by grade level), Teacher Features (classroom ideas related to other features on this site), and Unit Plans (grouped by curricular objectives).
Illuminations: Complete lesson plans for individual topics are provided for Grades K–12 math teachers. You can search by grade level band, math standard category, or a descriptive word. Each lesson has a learning objective, materials list, and an instructional plan. Some include assessment options and ideas for extensions. You can learn more about the National Council of Teachers of Mathematics standards or check out hundreds of exemplary online resources.
Access Center: The Access Center is a national technical assistance (TA) center funded by the U.S. Department of Education’s Office of Special Education Programs. Their mission is to improve educational outcomes for grade K–8 students with disabilities. This is an excellent source for professional development modules to support the training of teachers as well as short discussions on mathematics instruction for students with learning disabilities including strategies such as of concrete-representational-abstract and computer-assisted instruction. Many of these techniques can be used for a wide variety of learners.
Council of Chief State School Offices: This organization is a no partisan, nonprofit organization of public officials from departments of education in the various states. This website provides links to the fifty states content standards. You can access this by looking under Projects and then the Assessment and Standards heading.
Teachers Network: From the homepage of this nationwide, nonprofit organization you can go to the “Lesson Plans” page. Here you can search the library of teacher-generated lesson plans by topic for various subjects by grade level (K–12).
Kuyers Math Curriculum: These materials are available for download free of charge. They are designed to supplement existing high school and middle school math curricula. They are based on a Christian framework that “teaches that mathematics can inspire delight and awe, pointing beyond itself to God.”
Digital Media: Using public media to engage students with mathematics is made easier by using this site. Provides access to printable worksheets, assessments, project ideas, standards-based resources, program schedules, and lesson plans.
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Teacher Support:
Ask a Question or Share an Idea
Do you have a question to ask or an idea to share about the Purposeful Design Mathematics series? Email your question or idea directly to the Math Consultant.
FAQs—a listing of the questions asked of the Math Consultant and the responses:
What are the distinctives of the ACSI Purposeful Design Math series?
The approach to math education used in our math series emphasizes the development of math concepts and the ability to solve application problems. Concept development includes the use of manipulatives, investigations, and hands-on activities. Students learn basic addition, subtraction, multiplication, and division skills with understanding. Current research in math education shows that concept development and application are essential for a quality education. Algebra and geometry strands begin at the kindergarten level, leading students to be successful in high school mathematics. While you may see fewer problems on the page, as compared to some other books, those problems have been designed to provide a reasonable balance of practice and application.
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How should our school go about developing a high-quality mathematics curriculum that meets the current standards?
The following information is summarized from a National Council of Teachers of Mathematics publication available in the ACSI catalog. I would encourage you to purchase this Administrator’s Guide to assist you in developing a high-quality mathematics curriculum. The National Council of Teachers of Mathematics has identified the following six principles as the foundation of a high-quality mathematics program. (Administrator’s guide: How to support and improve mathematics education in your school, 2003, NCTM).
Equity—A quality mathematics program requires high expectations and appropriate support for all students.
Curriculum—A series of math textbooks must be more than a book for each grade level. Each book must be focused on grade-level appropriate material that is built upon the previous grade-level text and prepares the student for the next. Appropriate vocabulary should be presented at each grade level and supported with activities that strengthen knowledge and use of proper terms.
Teaching—Good teaching requires understanding what students know and need to learn, then supporting them in a variety of ways to learn it well. Manipulatives are one of the tools in the teacher’s tool box.
Learning—When students build new knowledge from experience, using prior knowledge as a foundation, they can learn mathematics with understanding.
Assessment—Assessing the progress of students should be a learning experience for the student, as well as a tool to help the teacher determine instructional plans.
Technology—Technology influences the mathematics that is presented to the students and should support and enhance students’ learning.
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What does ACSI provide to help me become a better math teacher?
Be sure to take advantage of the mathematics seminars available at your ACSI convention. Our office also provides in-service training at selected schools.
Math by Design: Teaching for Understanding is a quarterly online publication designed to provide periodic updates on the Purposeful Design Mathematics series and to give teachers practical advice and current information on the best methods for math instruction at all grade levels.
You can receive Math by Design: Teaching for Understanding by giving your email address through this email connection. View the current issue and all previous issues on the ACSI website. Some of the topics include manipulatives, math journals, literature, and technology.
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The kindergarten level of Purposeful Design Mathematics is too hard (too easy) and too long (too short) for my class. What should I do?
The text is designed to provide more than enough material for a typical kindergarten class. Kindergarten schedules vary from 4-day to 5-day, as well as half-day to all-day programs, and the number of minutes per day spent on math varies greatly; it is necessary for the kindergarten teacher to determine what parts of the text to use. If the school has a scope and sequence for kindergarten math, it should be an easy task to select the appropriate lessons.
The complement of skills presented in kindergarten will help prepare the student for first grade, but it is not a prerequisite for beginning the first grade text. Recognizing the abilities of your students, you may want to adapt or expand some of the suggested activities.
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I am a home school parent. Do I need to purchase the Teacher Edition or can I get by with just the Student Edition of Purposeful Design mathematics?
A home school parent (teacher) absolutely needs the Teacher Edition! A large part of the instructional material that the student needs to receive is in the Teacher Edition. The student will miss a significant part of the program if they do not receive the teacher-directed, hands-on portion of each lesson. The Teacher Edition includes all the tests, blackline masters (for review, practice, and enrichment), answer keys, and reproducible copies of manipulative tools. It is a complete package.
You may want to “co-op” with some other home school parents and trade Teacher Editions when you are done with a particular grade level. Check online for Teacher Editions that may be available from previous users.
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How does the Purposeful Design Mathematics series provide the necessary review of skills and concepts?
In addition to cumulative reviews and formal assessments, the student text contains appropriately placed review sections at the end of many of the lessons. There are noticeably fewer of these review sections in the higher grades. As new material is presented, the previous skills are still being used to solve the problems, so a formal review section is not always necessary. The last lesson of each chapter is a review, complete with games and activities in the Teacher Edition. Some grade levels contain a review section halfway through each chapter. The warm-up exercises and/or introductory activities at the beginning lesson are part of the review necessary for the concepts presented in that particular lesson. Most grade levels contain more than 200 blackline masters, many of which can be used as review exercises if needed.
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How do I challenge my more advanced students?
Research supports the idea that providing more challenging problems and hands on activities in an area of study is better than moving ahead to new concepts. Just giving advanced students more problems to do often gives them a negative feeling towards math. Providing fun and challenging activities fosters a better spirit and may encourage the other students to work towards proficiency in math so that they may do more of the “fun” things. Use the cross-curricular connections provided in your Teacher Edition as well as the enrichment blacklines. These activities can strengthen problem-solving skills and logic reasoning. Using the links provided on the ACSI Mathematics Resources webpages gives you an almost limitless number of possible enrichment activities.
Be sure to check out ACSI's quarterly publication, Math by Design for more ideas using literature, games, and manipulatives to keep your students engaged in math.
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How can I help students who are struggling in math?
The Teacher Edition of Purposeful Design Mathematics includes activities and blackline masters designed specifically for remediation and review. Making sure that a student has mastered the basic math facts is essential. Have the student use flashcards, drill sheets, and games to assist in memorizing the facts. Use more frequent, informal assessment to track the progress of these students. Having them use manipulatives to show you their reasoning can open a window into how they think. This in turn will help you adjust your teaching to accommodate them.
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