Solving Equations: An Algebra Intervention »

The author team of Brad Witzel, PhD, and Paul Riccomini, PhD, are professors whose research emphases are mathematics education and students with exceptional learning needs. Simple Equations is their third intervention for struggling students in mathematics with Pearson. Teachers have been using their interventions around the globe and have found wonderful and unique success. They have also written a textbook on Computations of Fractions: Math Intervention for Elementary and Middle Grades Students, which came out in 2009, and Computation of Integers: Math Intervention for Elementary and Middle Grades Students, coming out in 2010.

This timely new book is filled with essential research-based information that teachers and pre-service teachers alike need in order to help more students achieve mathematical standards by employing the concrete to representational to abstract (CRA) sequence of instruction with forms of algebraic equations. Proven to help students of all levels acquire and retain knowledge of mathematical concepts better than repeated abstract instruction alone, the CRA sequence of instruction employs: the use of hands-on manipulatives, learning to draw pictures of the steps, and finally transitioning from the pictorial representations to true abstract instruction expected by most state standards. Features placement test and fluency probes to help inform instruction and improve student proficiency. The research for CRA is powerful. However, there are few models out there that guide teachers in their delivery. All practicing teachers of mathematics, especially those who teach math to students who struggle or who have a disability, will benefit greatly from the techniques, content, and research of Witzel and Riccomini’s new book, a research-based, hands-on, applicable guide for mathematics educators everywhere.

Introduction……………….

Overview……………….

Description of Manipulatives……………….

Organization of Materials……………….

Who Can Use this intervention? ……………….

How to Use this Intervention……………….

Pretest Assessments……………….

Posttest Assessment……………….

Instructional Lessons……………….

Lesson 1–Simplifying Expressions –concrete level learning sheet……………….

Lesson 1– Simplifying Expressions–concrete level lesson plan……………….

Lesson 2 — Simplifying Expressions – representational level learning sheet ……………….

Lesson 2 — Simplifying Expressions – representational level lesson plan ……………….

Lesson 3 — Simplifying Expressions — abstract level learning sheet ……………….

Lesson 3 — Simplifying Expressions — abstract level lesson plan ……………….

Lesson 4 — Simplifying Expressions — abstract level learning sheet……………….

Lesson 4 — Simplifying Expressions — abstract level lesson plan……………….

Lesson 5 — abstract level fluency sheet……………….

Lesson 5 — abstract level fluency sheet lesson plan……………….

Lesson 6 — One step inverse operations — concrete level learning sheet……………….

Lesson 6 — One step inverse operations — concrete level lesson plan……………….

Lesson 7 — One step inverse operations —representational level learning sheet……………….

Lesson 7 — One step inverse operations —representational level lesson plan……………….

Lesson 8 — One step inverse operations — abstract level learning sheet……………….

Lesson 8 — One step inverse operations — abstract level lesson plan……………….

Lesson 9 — One step inverse operations — abstract level learning sheet……………….

Lesson 9 — One step inverse operations — abstract level lesson plan……………….

Lesson 10 — abstract level fluency cumulative practice sheet……………….

Lesson 10 — abstract level fluency cumulative lesson plan……………….

Lesson 11 — Two+ step inverse operations — concrete level learning sheet……………….

Lesson 11 — Two+ step inverse operations — concrete level lesson plan……………….

Lesson 12 — Two+ step inverse operations — representational level learning sheet……………….

Lesson 12 — Two+ step inverse operations — representational level lesson plan……………….

Lesson 13 — Two+ step inverse operations — abstract level learning sheet……………….

Lesson 13 — Two+ step inverse operations — abstract level lesson plan……………….

Lesson 14 — Two+ step inverse operations — abstract level fluency practice……………….

Lesson 14 — Two+ step inverse operations — abstract level lesson plan……………….

Lesson 15 — abstract level cumulative fluency practice sheet……………….

Lesson 15 — advanced abstract level cumulative fluency practice sheet…………………

Lesson 16 — Simplifying and solving equations — concrete level learning sheet……………….

Lesson 16 — Simplifying and solving equations — concrete level lesson plan……………….

Lesson 17 — Simplifying and solving equations — representational level learning sheet……………….

Lesson 17 — Simplifying and solving equations — representational level lesson plan……………….

Lesson 18 — Simplifying and solving equations — abstract level learning sheet……………….

Lesson 18 — Simplifying and solving equations — abstract level lesson plan……………….

Lesson 19 — Simplifying and solving equations — abstract level fluency learning sheet……………….

Lesson 19 — Simplifying and solving equations — abstract level fluency lesson plan……………….

Lesson 20 — abstract level cumulative fluency practice sheet……………….

Lesson 20 — abstract level cumulative fluency lesson plan……………….

Lesson 21 — Transformational equations — concrete level learning sheet……………….

Lesson 21 — Transformational equations — concrete level lesson plan……………….

Lesson 22 — Transformational equations — representational level learning sheet……………….

Lesson 22 — Transformational equations — representational level lesson plan……………….

Lesson 23 — Transformational equations — abstract level learning sheet……………….

Lesson 23 — Transformational equations — abstract level lesson plan……………….

Lesson 24 — Transformational equations — abstract level fluency cumulative learning sheet……………….

Lesson 24 — Transformational equations — abstract level fluency cumulative lesson plan……………….

Lesson 25 — Transformational equations — abstract level fluency cumulative learning sheet……………….

Lesson 25 — Transformational equations — abstract level fluency cumulative lesson plan……………….

Lesson 26 — Graphing transition

Lesson 26 — Graphing transition lesson outline

Answer Key……………….

References……………….

Appendix of Learning Sheets………………

Appendix of Materials……………….