Using manipulatives to teach abstract math concepts

Teach solving algebraic equations using manipulatives. Concept: Solving '2x + 3 = 11'. Manipulatives: Use cups to represent the variable 'x' and two-color counters for integers. Process (Concrete-Representational-Abstract): 1. Concrete: Students model the equation on a mat. They place 2 cups and 3 positive counters on one side, and 11 positive counters on the other. To solve, they remove 3 counters from each side, then divide the remaining 8 counters equally between the 2 cups. They find each cup (x) equals 4. 2. Representational: Students draw pictures of the cups and counters to solve similar problems. 3. Abstract: Students transition to solving the equation using only symbols and numbers. This progression builds conceptual understanding before procedural fluency.