Foundations and learning approach
What does CPA mean in Singapore Math?
CPA stands for Concrete, Pictorial and Abstract. It is an important approach in Singapore primary mathematics. Learners explore an idea with objects, represent relationships in pictures and connect them to mathematical symbols. The essential step is explaining how the three forms represent the same idea.
A model should connect to the objects
Counters, ten frames, number bonds and bar models can make quantities, parts, wholes and equal groups visible. Choose a representation for the relationship in the problem, then ask learners what each part represents.
Move 2 from the group of 5 to complete ten with 8. Three remain, so the total is still 13.
View larger image ↗Return to objects and pictures when useful
Even after writing an equation, learners can revisit objects or pictures to explain and check it. There is no need to rush away from useful representations. Change the numbers and discuss how the same idea applies. These original examples explain the approach; they are not placement tests.
ONE IDEA · THREE REPRESENTATIONS
Explore one problem through CPA
Explore with objects
Arrange 8 counters and 5 more. Move 2 from the second group to make ten, leaving 3.
Represent the relationship
Draw 8 dots in a ten frame, add 2, and draw the remaining 3 outside. The picture still represents all 13 counters.
Connect to mathematical symbols
8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. Explain that 2 and 3 are the two parts of 5.
Ask your child to identify how the objects, picture and numbers represent the same quantities. Return to objects or pictures when the connection is unclear.
Read more: NIE · Singapore Primary Mathematics: CPA ↗
Keep exploring together
Choose activities that match the learner’s knowledge and readiness, and discuss what you notice. Explore the curriculum or parent guide below.