Concepts • Skills • Problem Solving

What is Vertical Alignment?

Vertical alignment is a process that provides learners with an articulated, coherent sequence of content. It ensures that content standards and units of study are introduced, reinforced, and assessed and that instruction is targeted on student needs and California Mathematics Standards.

Why is Vertical Alignment Important?

Strong vertical alignment accommodates a wide variety of developmental levels. It allows teachers increased precision in their teaching because they are not teaching content that is covered elsewhere or that students have previously mastered.

5 Keys to Success

1. Back-Mapping

   According to The College Board, about 80% of students who successfully complete Algebra I and Geometry by 10th grade attend and succeed in college. That 80% is nearly constant regardless of race. (Changing the Odds:Factors Increasing Access to College, 1990)

   California Mathematics: Concepts, Skills, and Problem Solving  was conceived and developed with the final result in mind - student success in Algebra I and beyond. The authors, using the California Mathematics Standards as their guide, developed this brand-new series by "back-mapping" from the desired result of student success in Algebra I, Geometry, and beyond.

2. Balanced, In-Depth Content

   California Mathematics: Concepts, Skills, and Problem Solving  was developed to specifically target the skills and topics that give students the most difficulty.

      

   

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6

Teacher Resources

• Facts Practice
  Select a Fact Practice Addition Sums to 10 (horizontal).rtf Addition Sums to 10 (horizontal).tst Addition Sums to 10 (vertical).rtf Addition Sums to 10 (vertical).tst Addition Sums to 20 (horizontal).rtf Addition Sums to 20 (horizontal).tst Addition Sums to 20 (vertical).rtf Addition Sums to 20 (vertical).tst Division Up to 10 (horizontal).rtf Division Up to 10 (horizontal).tst Division Up to 10 (vertical).rtf Division Up to 10 (vertical).tst Division Up to 20 (horizontal).rtf Division Up to 20 (horizontal).tst Division Up to 20 (vertical).rtf Division Up to 20 (vertical).tst Multiplication Up to 10 (horizontal).rtf Multiplication Up to 10 (horizontal).tst Multiplication Up to 10 (vertical).rtf Multiplication Up to 10 (vertical).tst Multiplication Up to 20 (horizontal).rtf Multiplication Up to 20 (horizontal).tst Multiplication Up to 20 (vertical).rtf Multiplication Up to 20 (vertical).tst Subtraction Up to 10 (horizontal).rtf Subtraction Up to 10 (horizontal).tst Subtraction Up to 10 (vertical).rtf Subtraction Up to 10 (vertical).tst Subtraction Up to 20 (horizontal).rtf Subtraction Up to 20 (horizontal).tst Subtraction Up to 20 (vertical).rtf Subtraction Up to 20 (vertical).tst
• Technology Training
  • ExamView Assessment Suite
  • Interactive Classroom
  • TeacherWorks Plus

• Mathematical Proofs
• Visual Vocabulary Card
  Choose a Grade Grade K - Answers Grade 1 - Answers Grade 2 - Answers Grade 3 - Answers Grade 4 - Answers Grade 5 - Answers
• Mathematics Literature Books
• Math Songs Lesson Plans
  Choose a Grade Grades K - 1 Grades 2 - 3 Grades 4 - 5

• Multiply by Nine

• Additional Divide Whole Number Resources
  • Divide Whole Number Student Material
  • Divide Whole Number Teacher Material

• Additional Money Resources
  • Money Student Material
  • Money Teacher Material

• Professional Development
  Video Library
  • Grade K
  • Grade 1
  • Grade 2
  • Grade 3
  • Grade 4
  • Grade 5
• Teach, Use and Succeed
  • Macmillan Math Connects
    Pre-Kindergarten Program
    Walkthrough
  • Grades K-2
  • Grades 3-5
• California Math and English Learners Standards Alignment

• Meet the Author
  • Mary Behr Altieri
  • Don S. Balka
  • Roger Day, Ph.D.
  • Philip D. Gonsalves
  • Ellen C. Grace
  • Stephen Krulik
  • Carol E. Malloy, Ph.D.
  • Rhonda J. Molix-Bailey
  • Lois Gordon Moseley
  • Brian Mowry
  • Christina L Myren
  • Jack Price, Ed.D.
  • Mary Esther Reynosa
  • Rafaela M. Santa Cruz
  • Robyn Silbey
  • Kathleen Vielhaber

• Math Adventures with Dot and Ray User Guide

• Family Letters

2. Ongoing Assessment

   California Mathematics: Concepts, Skills, and Problem Solving  includes diagnostic, formative, and summative assessment; data-driven instruction; intervention options; and performance tracking, as well as remediation, acceleration, and enrichment tools throughout the program

3. Intervention and Differentiated Instruction

   In order for students to overcome difficulties with mathematics learning, attention is paid to their backgrounds, the nature of their previous instruction, and underlying learning differences. California Mathematics: Concepts, Skills, and Problem Solving includes a two pronged approach to intervention.

   Strategic Teachers can use the myriad of intervention tips and ancillary materials to address the needs of students who need strategic intervention.

   Intensive For students who are two or more years below grade level, California Math Triumphs provides step-by-step instruction, vocabulary support, and data-driven decision making to help students succeed.

   For students not ready for Algebra I in Grade 8, California Algebra Readiness provides highly focused instructional materials to help students rebuild foundational skills and concepts and prepare for algebra success.

4. Professional Development

   California Mathematics: Concepts, Skills, and Problem Solving includes many opportunities for teacher professional development. Additional learning opportunities in various formats-video, online, and on-site instruction-are fully aligned and articulated from grade K through Algebra II.