standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Problem 1
Two different students solved the problem
$$1\frac9{10}+5\frac4{10}$$
below. Study their work and determine whether the strategy they used works.
|                          **             Student A            **                          |                          **             Student B            **                          |
|------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1a.png | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1b.png |
Problem 2
Two different students solved the problem
$$4\frac38-3\frac68$$
below. Study their work and determine whether the strategy they used works.
|                           **            Student C           **                           |                           **            Student D           **                           |
|------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2a.png | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2b.png |
Problem 3
Solve.
| $$1+\frac{5}{12}$$                          $$\frac{11}{12} + \frac5{12}$$ | $$8+4\frac36$$                          $$7\frac56+4\frac36$$ | $$1\frac1{10}-\frac1{10}$$                          $$1\frac1{10}-\frac2{10}$$                          $$1\frac1{10}-\frac4{10}$$ | $$6\frac15-5$$                          $$6\frac15-4\frac45$$                          $$6\frac15-4\frac25$$ |
|----------------------------------------------------------------------------|---------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------|


aligns: no