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Operation Action Multiplication and Division

Overview • • Equal Groups Area/Arrays Combinations Relative Comparison

Equal Groups Total Objects Unknown It takes 8 gallons of gasoline to mow the lawn one time. How much gasoline will it take to mow the lawn 7 times. No. of No of Total Grps. objs. No. of per grp. Objs. 7 lawns 8 gal/la wn ?

Equal Groups No. of Grps. Unknown No. of It takes 8 gallons of Grps. gasoline to mow the lawn one time. If 56 gallons of gasoline have been used this season, ? how many times has the lawn been mowed? No. of Total Objs. no. of Per objs. grp. 8 56 gal/la wn

Equal Groups No. of Objs. /Grp. Unknown If 56 gallons of gasoline have been used to mow the lawn 7 times, how much gasoline will it take to mow the lawn one time? No. of Total Grps. Objs. no. of per Objs. grp. 7 lawns ? 56 gal

Area/Arrays Area Unknown A rectangular lawn is 8 yards long and 7 yards wide. What is the area of the lawn? Length Width area 8 yds 7 yds ?

Area/Arrays Dimension Unknown A rectangular lawn has an area of 56 square yards. If it is 7 yards wide, how long is the lawn? Length Width Area ? 7 yds 56 yd. 2

Relative Comparisons Ratio Unknown The front lawn has an area of 8 square yards. The back lawn has an area of 56 square yards. How many times larger is the back lawn than the front lawn? Set Comparison Set One Two 8 sq. 56 yds sq. yds

Relative Comparison One value unknown The front lawn has an area of 8 square yards. The area of the back lawn is 7 times the area of the front lawn. What is the area of the back lawn? Set Comparison Set One Two 8 sq. 7 yds ?

Relative Comparison One value unknown The back lawn has an area of 56 square yards. The area of the back lawn is 7 times the area of the front lawn. What is the area of the front lawn? Set Comparison Set One Two ? 7 56 sq yds

Cautions • Not everyone sees problems the same way, it is not the classification itself that matters it is that teachers provide problems in all categories.

Example A toy sells for \$15. Gary has \$9. How much more money does he need to buy the toy?

Start/Change/End • Gary has \$9 how much more money will he have to get to make \$15?

Part/Whole • Gary has \$9, what can be put with the \$9 to make \$15.

Absolute Comparison • How does the cost of the toy compare to the money Gary has?