# These are just different ways of expressing 8 3 t

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Lesson 10NYS COMMON CORE MATHEMATICS CURRICULUM54S:(Write18the sum of 6 and 14= (6 + 14)÷8.)T:What do you notice about the diagrams?S:They are drawn exactly the same way.We don’t even need to evaluate the expressions tocompare them.You can see that they will simplify to the same quantity.I knew it would be thesame before I drew it because finding 1 eighth of something and dividing by 8 are the same thing.T:Look at the next pair of expressions.Work with your partner to compare them without calculating.S:(Work and write 4 ×83>4 times the quotient of 3 and 8.)T:How did you compare these expressions without calculating?S:They both multiply something by 4.Since 8 thirds is greater than 3 eighths, the expression on theleft is larger.Since both expressions multiply with a factor of 4, the fraction that shows thesmaller amount results in a product that is also less.T:Compare the final pair of expressions independently without calculating.Be prepared to share yourthoughts.S:(Work and write subtract 2 from12of 9<(11÷2) – 2.)T:How did you know which expression was greater?Turn and talk.S:11 divided by 2 is 11 halves, and 11 halves is greater than 9 halves.Half of 9 is less than half of11, and since we’re subtracting 2 from both of them, the expression on the right is greater.Problem Set(10 minutes)Students should do their personal best to complete the Problem Set within the allotted 10 minutes.For someclasses, it may be appropriate to modify the assignment by specifying which problems they work on first.

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