1. Concrete: Start by using physical objects, such as actual pencils or counters, to represent the situation. Give both Jane and Mark the same number of pencils. Let's say they each have 10 pencils. Then, physically give two pencils from Jane to Mark.
2. Representational: Use visual representations to support understanding. Draw two separate bars representing Jane's and Mark's pencils. Label each bar with the number of pencils they have. Initially, both bars have the same length (representing the same number of pencils). Then, show visually that Jane gives two pencils to Mark by shortening her bar by two units.
Jane: |______| (10 pencils)
Mark: |______| (10 pencils)
Jane: |____| (8 pencils)
Mark: |________| (12 pencils)
3. Abstract: Use symbols and mathematical notation to represent the scenario. Translate the visual representation into an equation or expression. Let's say x represents the original number of pencils they both had.
Jane: x - I apologize, but it seems like my previous response got cut off. Here is the complete response:
3. Abstract: Use symbols and mathematical notation to represent the scenario. Translate the visual representation into an equation or expression. Let's say x represents the original number of pencils they both had.
Jane: x - 2
Mark: x + 2
According to Jane's claim, Mark has two more pencils than she has. So, we can set up the equation:
x + 2 = x - 2
Simplifying this equation, we can see that the x terms on both sides cancel out:
2 = -2
This equation is not true, and it indicates that there may be an error or misunderstanding in Jane's claim. By using the concrete-representational-abstract approach, students can visualize and understand the situation, and then translate it into abstract mathematical notation to identify any inconsistencies or errors.