Take ten cards 0 to 9. Arrange the cards in such a manner that their sum must be 9. There are many ways to do it. In how many ways can you do it?
Cards can be arranged to make sums of 9 in multiple ways:
Pairs that sum to 9: (0, 9), (1, 8), (2, 7), (3, 6), (4, 5), (5, 4), (6, 3), (7, 2), (8, 1), (9, 0)
∴ There are 10 different pairs of cards that add up to 9.
Groups of three cards: (0, 1, 8), (0, 2, 7), etc.
Explanation
The chapter uses card activities to explore addition combinations. This project helps children discover all possible pairs that sum to 9, building understanding of number relationships and addition facts.
Solution Steps
List all pairs of cards from 0 to 9 that sum to 9: (0,9), (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0)
Count the pairs: There are 10 different pairs
Identify groups of three cards that also sum to 9: (0,1,8), (0,2,7), etc.