Intervention Name: Concrete-Representational-Abstract Common Core State Standards Domain Areas: (check all that apply) (HS) Data Equations Algebraic and Operations Operations Cardinality Probability Quantity System and and Proportional and and and and and Ten and Number Base Fractions Measurement Modeling Operations Numbers Numbers Number Geometry Ratios Relationships Algebra Counting Thinking – The Expressions Statistics Functions (K) (K-5) (K-5) (3-5) (K-5) (K-HS) (6-7) (6-8) (6-8) (6-HS) (8-HS) (HS) (HS) in X X X X X X X X X X X X X X Setting: (check all that apply) Focus Area: (check all that apply) Whole-class Small-group Individual Acquisition Fluency Generalization X X X X X X Function of Intervention: Concrete-Representational-Abstract (CRA) is an approach to teaching mathematics. Almost all topics in mathematics can be taught using CRA. Students do not have to progress through the concrete to get to the representational and abstract phases. Students often work at the concrete and abstract or representational and abstract phases simultaneously. Brief Description: With CRA, students work with hands-on materials that represent mathematics problems (concrete), pictorial representations of mathematics problems (representational), and mathematics problems with numbers and symbols (abstract). The teacher explicitly bridges the connection between the concrete, representational, and abstract representations of the mathematics problems. Addition example: Concrete: Students work with plastic bears to understand addition of 2 and 4. Representational: Students count pictorial representations of bears to understand addition of 2 and 4. OR Abstract: Students add 2 and 4. 2 + 4 = __ Division with fractional answers examples (adapted from Witzel & Riccomini, 2009): Concrete: Students use manipulatives (i.e., craft sticks and paper cups) to divide 9 sticks into 3 cups divide nine sticks into three cups. How many sticks do we have per cup?” “Let’s Representational: Students draw a picture that represents 9 tallies being divided into 3 groups divide nine tallies into three groups. How many tallies do we have per group?” “Let’s
Intervention Name: Concrete-Representational-Abstract Common Core State Standards Domain Areas: (check all that apply) Counting and Cardinality (K) Operations and Algebraic Thinking (K-5) Numbers and Operations in Base Ten (K-5) Numbers and Operations – Fractions (3-5) Measurement and Data (K-5) Geometry (K-HS) Ratios and Proportional Relationships (6-7) The Number System (6-8) Expressions and Equations (6-8) Statistics and Probability (6-HS) Functions (8-HS) Number and Quantity (HS) Algebra (HS) Modeling (HS) X X X X X X X X X X X X X X Setting: (check all that apply) Focus Area: (check all that apply) Whole-class Small-group Individual Acquisition Fluency Generalization X X X X X X Function of Intervention: Concrete-Representational-Abstract (CRA) is an approach to teaching mathematics. Almost all topics in mathematics can be taught using CRA. Students do not have to progress through the concrete to get to the representational and abstract phases. Students often work at the concrete and abstract or representational and abstract phases simultaneously. Brief Description: With CRA, students work with hands-on materials that represent mathematics problems (concrete), pictorial representations of mathematics problems (representational), and mathematics problems with numbers and symbols (abstract). The teacher explicitly bridges the connection between the concrete, representational, and abstract representations of the mathematics problems. Addition example: Concrete: Students work with plastic bears to understand addition of 2 and 4. Representational: Students count pictorial representations of bears to understand addition of 2 and 4. OR Abstract: Students add 2 and 4. 2 + 4 = __ Division with fractional answers examples (adapted from Witzel & Riccomini, 2009): Concrete: Students use manipulatives (i.e., craft sticks and paper cups) to divide 9 sticks into 3 cups “Let’s divide nine sticks into three cups. How many sticks do we have per cup?” Representational: Students draw a picture that represents 9 tallies being divided into 3 groups “Let’s divide nine tallies into three groups. How many tallies do we have per group?”
EBI-Brief-Template-Concrete-Representational-Abstract.docx