Consider Eva’s work and verbal explanation of the standard a…

Consider Eva’s work and verbal explanation of the standard algorithm for computing 389 + 475. a)  What does each “carried 1” in Eva’s work represent? b)  Eva’s teacher said “I agree with you that we start with 9 + 5. But are we adding 1 + 8 + 7 ones? What do you think Eva’s teacher is trying to help Eva understand? c)  Educators suggest using the language of “carried” in addition computations may confuse students. Why? What term should be used that is more descriptive of the mathematical ideas? d)  Add 159 + 76 using the US standard algorithm like Eva did, and write an accompanying explanation of the steps that avoids the term “carried” and more clearly addresses what is being added each time.

Consider the following word problem: Rachael has 14 puppi…

Consider the following word problem: Rachael has 14 puppies. Donna has 8 puppies. How many more puppies does Rachael have than Donna? a)  Grace and Hannah disagree on how to solve this problem. Grace writes 14 – 8 = ☐as her number equation, but Hannah claims that 8 + ☐= 14 is the correct equation to use. Whose number equation better directly models the situation? b)  Consider the following problem: Petra has 14 carrot sticks in her lunch box. She eats 8 carrot sticks for lunch. How many carrot sticks does Petra have left to eat? Whose number equation from part (a) better directly models the situation presented in this problem? Explain your choice.