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Operation Action Multiplication and Division Operation Action Multiplication and Division

Overview • • Equal Groups Area/Arrays Combinations Relative Comparison Overview • • Equal Groups Area/Arrays Combinations Relative Comparison

Equal Groups Total Objects Unknown It takes 8 gallons of gasoline to mow the 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. 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 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. 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 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. 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 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 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 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 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 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 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 Absolute Comparison • How does the cost of the toy compare to the money Gary has?