Please do the following exercises from chapter (12.1). You should follow the instructions carefully!!!
12. Use an array, a rectangular area, a number line, or base-ten blocks to model each of these properties for a particular instance.
a. distributive property of multiplication over addition: 7 × (44 + 6) = 7 × 44 + 7 × 6
b. associative property of addition: 96 + 21 = 96 + (4 + 17) = (96 + 4) + 17
c. commutative property of multiplication: 17.4 × 3.5 = 3.5 × 17.4
d. associative property of multiplication: (4 × 3) × 6 = 4 × (3 × 6)
e. commutative property of addition: 314+838=838+314
15. Following is a child’s description of his or her computation of 21 × 15.
▶ To find twenty-one times fifteen, I multiply 20 × 15 because that is easy. Two times fifteen is thirty, so for twenty I add a zero and get three hundred. But I need one more than twenty. Three hundred and one! ◀
a. If the child is using correct logic, discuss what property he or she may be recognizing and describing. If the child is making an error, describe what property he or she appears not to understand.
b.Model the child’s correct thinking or use the model to show the correct thinking.
Name of the Textbook in case you need it: Reconceptualizing Mathematics for Elementary School Teachers, 3rd Edition by Sowder, Sowder & Nickerson (2017). You should be able to find it online.
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