Multifaceted Number Concepts 197Rigorous Problem Solving with the Concept of
Commutative and Associative Properties 1
Sandy decided to collect shiny dimes. She found 3 dimes each
day for 1 week. She doubled her collection the second week.
Part A
Which equations use the associative property to represent the
number of dimes Sandy found?
o (3 x 1) x 2 = 3 x (1 x 2)
o (7 x 3) + 2 = 7 x (3 + 2)
o (7 x 7) + 2 = 7 x (7 + 2)
o (7 x 3) x 2 = 7 x (3 x 2)
o (7 + 3) x 2 = 7 x (3 + 2)
o (3 x 7) x 2 = 3 x (7 x 2)
Part B
By the next month, Sandy had 100 dimes. She gave Kayla
half of her dimes. She gave Kass 23 of her dimes. Does the
associative property represent how many dimes Sandy
has left?
(100 ÷ 2) – 23 = 100 ÷ (2 – 23)
Yes or no?
Explain your answer.
© 2016, Math Intervention: Grades 3–5, Jennifer Taylor-Cox, Routledge