Sunday, July 20, 2008

Singapore Math model drawing

Another problem that I would have had a hard time with before learning about model drawing this past week:

Johnny bought 6 hotdogs and 10 hamburgers for the baseball team for $36.00. Each hamburger cost $.40 more than each hotdog. How much did Johnny spend on hamburgers?

First things first, read the problem sentence by sentence underlining the who and what

Johnny bought 6 hotdogs and 10 hamburgers for the baseball team for $36.00. Each hamburger cost $.40 more than each hotdog. How much did Johnny spend on hamburgers?

Step two: List the varibles:


Johnny's Hotdogs

Johnny's Hamburgers

Step three: draw a unit bar to model each varible, make these all the same size


Johnny's Hotdogs [][][][][][]

Johnny's Hamburgers [][][][][][][][][][]

Step four: determine what each unit bar represents and where you need to place a question mark.

In this problem that is what we are not sure of. We know that our total is $36 and we know that each hamburger cost $0.40 more than each hot dog. So we can add these to our problem.

Johnny's Hotdogs [][][][][][]
TOTAL COST $36
Johnny's Hamburgers [][][][][][][][][][]
+ 0.40+ 0.40 +0.40 + 0.40 + 0.40 + 0.40 + 0.40 + 0.40 + 0.40 + 0.40

Now we know that the hot dogs added $0.40 time 10 to our cost more than the equal cost of the hot dogs to hamburgers so we know that the hamburgers added $4.00.

So we need to subtract $4.00 from $36 giving us $32.

From here we can look that we have 16 parts that make up the $32.00.

So we can divide the $32 by 16 to give us $2.00

Which means each hot dog cost $2.00, and each hamburger cost $2.40.

So our answer to the question would be:

Johnny paid $24.00 for the hamburgers.



Another example of this:
Stacy bought 3 chocolate cakes and 2 vanilla cakes for $18.20. If each chocolate cake cost $1.20 more than each vanilla cake, what was the total cost of the cakes?


First things first, read the problem sentence by sentence underlining the who and what

Stacy bought 3 vanilla cakes and 2 chocolate cakes for $18.20. If each chocolate cake cost $1.20 more than each vanilla cake, what was the total cost of the cakes?

Step two: List the varibles:

Vanilla cake

Chocolate cake


Step three: draw a unit bar to model each varible, make these all the same size


Vanilla cake [][][]

Chocolate cake [][]

Step four: determine what each unit bar represents and where you need to place a question mark.

In this problem that is what we are not sure of. We know that our total is $18.20 and we know that each chocolate cake cost $1.20 more than each vanilla cake. So we can add these to our problem.

Vanilla cake [][][]
TOTAL $18.20
Chocolate cake [][]
+ $1.20 + $1.20


Now we know that the choclate cakes added $1.20 times 2 to our cost more than the equal cost of the chocolate cakes and the vanilla cakes, so the chocolate cakes added $2.40 to our cost

So we need to subtract $2.40 from $18.20 giving us $15.80.

From here we can look that we have 5 parts that make up the $15.80.

So we can divide the $15.80 by 5 to give us $3.16

Which means each Vanilla cake cost $3.16, and each chocolate cake cost $4.36

All of the vanilla cakes would cost $3.16 x 3 = $9.48
So our answer to the question would be:

Stacy paid $9.48 for the vanilla cakes.

I am telling you before this training I would have been lost when I read "each chocolate cake cost $1.20 more than each vanilla cake"!
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