# Reading For Thinking 6th Edition Answer Key.rar Fixed

So--understanding the commutative law of multiplication, lets you start to understand that both ways of thinking of division will give you the same answers and you can use them interchangeably. That's really useful, because sometimes you can figure out the answer more quickly by one method than another. On the Children's Mathematics Children's Strategies CD, you can watch how quickly a girl solves a measurement division by skip counting (In the Multiplication & Division tab, watch Counting, Measurement Division). In the next interview (In the Multiplication & Division tab, watch Derived Facts, Partitive Division), the girl solves a partitive division problem with the same numbers. She remembers from the previous problem that 7 groups of 3 is 21, but she doesn't have a commutative law perspective on multiplication yet, she doesn't make the connection that 3 groups of 7 is also 21, and so she goes through some pretty complicated mental arithmetic steps to convert those 7 groups of 3 into 3 groups of 7 (very cool thinking, by the way--you can tell that she has a really good grasp on numbers).

## reading for thinking 6th edition answer key.rar

Rate problems are a more general version of the sort of thinking involved in price problems. Whereas price problems involve a price per item (cost for 1 item), general rate problems can relate a wider variety of things. Miles per hour is the most familar rate for most of us (relating distance--miles, and time--hours), but there are lots of others: words per minute (reading or typing), bushels per acre (corn or other crops), miles per gallon. Rate problems are usually appropriate for children at the age when they are familiar with the things being compared. In these examples, if children had experience (perhaps in science) with measuring distances things moved, and elapsed time with stop watches, these problems would be appropriate.