Operation ActionOperation ActionOperation ActionOperation Action

Multiplication and DivisionMultiplication and Division

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

Equal GroupsTotal Objects UnknownIt 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 Grps.

No of objs. per grp.

Total No. of Objs.

7 lawns

8gal/lawn

?

Equal GroupsNo. of Grps. Unknown

It takes 8 gallons of 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 Grps.

No. of Objs. Per grp.

Total no. of objs.

? 8 gal/lawn

56 gal

Equal GroupsNo. of Objs./Grp.

UnknownIf 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 Grps.

No. of Objs. per grp.

Total no. of Objs.

7 lawns

? 56 gal

Area/ArraysArea 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/ArraysDimension 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 ComparisonsRatio

UnknownThe 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 One

Comparison

Set Two

8 sq. yds

56 sq. yds

Relative ComparisonOne 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 One

Comparison

Set Two

8 sq. yds

7 ?

Relative ComparisonOne 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 One

Comparison

Set 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.

ExampleA 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/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?