**Developing Fractions Sense**

**Developing Fractions Sense Student Workbook A (Grade 3)**

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**Developing Fractions Sense Student Workbook B (Grade 4)**

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**Developing Fractions Sense Student Workbook C (Grade 5)**

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**Hands-On Equations Level 1 and verbal Problems Level 1 **

**Hands-On Equations teaching points by lessons: Levels I, II, and III**

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**Common Core Math Standards**

The Common Core Math Standards for Mathematical Practices seeks to have students conceptualize mathematics, rather than do mathematics by rote. Students are expected to observe mathematical structure and to reason and communicate mathematics.

More than twenty years before the Common Core Math Standards appeared on the scene, Dr. Henry Borenson, the inventor of Hands-On Equations, was already using “common core mathematical practices” in his work with students. With peer-reviewed published articles such as, “Teaching the Process of Mathematical Investigation,” “Teaching Student to Think in Mathematics and to Make Conjectures,” and “Promoting Mathematical Creativity in the Classroom,” Dr. Borenson emphasized the importance of students being able to understand and communicate mathematics.

Since algebra deals with abstract symbols many students have difficulty conceptualizing mathematics. The visual and kinesthetic approach of Hands-On Equations enables students to literally grasp algebraic concepts concretely, pictorially and then abstractly.

The Making Algebra Child's Play and the Demystifying Verbal Problems workshops enable teachers to experience a classroom situation where the standards of mathematical practices are modeled by the instructor.

**Common Core State Standards **

**Mathematical Content**

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Borenson, Henry (2012). " Are the common core state standards for mathematics in grades three and four reasonable? Rethinking word problems using a letter for the unknown.__"__ Newsletter of the National Council of Supervisors of Mathematics (NCSM), Volume 42, Number 4, 24-25.

As early as the third grade the Common Core Math Standards requires students to be able to solve verbal problems and to express the problem as an abstract equation using a letter for the unknown. Hands-On Equations enables students to experience sucess by first representing the problem concretely or pictorially, and only then by an abstract equation using a letter for the unknown.

Our two-day training will provide your teachers with the skills to help their students **meet **the following Common Core Mathematical Content standards:

- Solve two-step word problems and represent those problems using equations with a letter standing for the unknown. (3.OA.8). Click here for video demo.
- Solve multistep word problems using drawing and equations with a symbol for the unknown (4.OA.2). Click here for video demo.
- Apply the property of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+x) to produce the equivalent expression 6+3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y) (6EE.3)
- Understand that positive and negative numbers have opposite values (6.NS.5)
- Solve mathematical problems using algebraic expressions and equations (7.EE.4). Click here for video demo.
- Recognize linear equations which have no solutions, one solution, and infinitely many solutions (8.EE.7)
- Strategically choose process for solving equations in one variable (grade 8)