11/05/2025
CPA Approach in Building Your Child’s Mathematical Foundation
A little backstory:�One of my former clients from my wedding organizing side gig—who later became a good friend—reached out to ask if I offered math tutoring to help prepare her child for the next grade level. Her child, then a first grader, was performing so well, so I focused on deepening her mastery of Grade 1 competencies and gradually introduced Grade 2 concepts through advanced sessions.
I later learned that she previously attended a Montessori school, which I believe played a key role in helping her develop a solid concrete understanding of mathematical ideas.
As someone who's into the CPA approach, I used concrete models, pictorial worksheets, and interactive tasks during our sessions. Toward the end of the program, aside from a post-test, I designed a simple “performance task” to assess how she could apply what she had learned in a real-life context.
Since it was her grandpa's birthday, I asked if she’d like to plan a birthday dinner—from shopping to setting up the party. She excitedly said yes and decided to prepare dinner for 20 people.
She came up with a food list, and I gave her ₱7,000 in play money (cut-out bills and coins) to go shopping. I set up a mock supermarket with labeled prices for the items she needed.
While shopping, she:
* Checked that she had enough money for her selected items.
* Counted her change correctly.
* Adjusted her choices when she realized ₱7000 wasn’t enough to buy everything.�Despite the budget constraint, she cleverly ensured that she still had a viand, drink, dessert, and a cake—prioritizing what mattered most to her. When I told her we didn’t have enough money left, she replied, “Oh well, at least we have a cake!” 😁
Next, I gave her one piece of construction paper and told her we needed to make 20 paper plates. She divided the paper evenly—an application of division and fractions. Then, she arranged them on a square table and decided, “Let’s make 4 groups of 5 plates each since the table has 4 sides.” This led into multiplication and spatial reasoning.
Then came the candy: she had to divide 100 candies among the 20 plates. I asked, “How can we make sure each person gets the same number of candies?”
Though we hadn’t focused much on division, we had explored multiplication. I was curious to see what she’d do. After a few minutes of thinking, she said:�"What if we half the 100—that’s two 50s. Then we half 50 again… that’s 25 for each group so we now have 4 groups of 25?”�So I replied with a question, I asked how she’d divide those 25 among the people in each group. She grabbed her multiplication board and said,�“5 x 5 is 25! So, 5 in each plate!”�My heart was quietly clapping with joy.
She even applied what she learned to slicing the leche flan and the (crumpled) chocolate crumble cake!
One more thing I noticed: when children are asked to “act as the teacher” and explain their thinking, they tend to process ideas more deeply. Letting her teach me was an effective way to boost her confidence and understanding.
Key Takeaways:
* Concrete materials engage children in learning math concepts in a fun, meaningful, and digestible way.
* Pictorial representations build a bridge between hands-on materials and abstract thinking.
* Relatable, story-based scenarios increase curiosity and motivation, making learning more connected to real life.
This is just the beginning, but she's off to a strong start.�And I just want to say—kudos to her awesome mom for providing such intentional and thoughtful support for her daughter’s learning! 💛
14/03/2024