NORTH SCHOOL MATH TRAIL
Miss Lesak's fourth grade accelerated math students studied many concepts this year. As a grade level, fourth graders worked especially hard to become better problem solvers. Students followed a problem solving analysis that broke down a word problem for them into more approachable steps. First, students had to be sure they could understand what was being asked. Then, students had to follow a plan to solve the problem. Third, students would solve the problem. Finally, the students worked the problem backwards as a way to look back and check heir work. As an end of the year project, students worked in cooperative groups of four to develop their own word problems. They then broke them down into the four problem solving analysis steps so others can solve their problems using these steps.
Problem 1:
By:
Alex L., Joe K., Savanna B., David M.
The length of Miss Lesak’s classroom is 1,010 cm. The width of Miss Lesak’s classroom is 913 cm. What is the area of Miss Lesak’s classroom?
Problem Solving Analysis:
Understand:
Q: What do you know?
A: The length of Miss Lesak’s classroom is 1,010 cm. and the width is 913 cm.
Q: What do you need to find out?
A: What is the area of Miss Lesak’s classroom?
Plan:
Q: What is your plan for solving the problem?
A: Multiply length by width, or 1,010 cm. X 913 cm.
Solve:
Q: Use the facts you know to make the equation and solve.
A: 1010
X 913
3030
10100
+ 909000
922130
Q: Write the answer in a complete sentence.
A: The area of Miss Lesak’s classroom is 922,130 cm²
Look Back:
Q: Check to see if your answer makes sense.
A: Take the area and divide it by the width. You should get the height. You could also take the area and divide it by the height. You should get the width.
Pictured: Savanna B. & David M.
Not pictured: Alex L., Joe K.
Problem 2:
By: Hayley N., Mark V., Taylor R., Donnie P.
Taylor, Hayley, Mark and Donnie are standing on each other to see how tall they all are together. If Taylor is 62 in., Mark is 58 in., Hayley is 62 in., and Donnie is 58 in., how tall are we all together? Give the answer in feet and inches.
Problem Solving Analysis:
Understand:
Q: What do you know?
A: We know that Taylor and Hayley are 62 in. each and Mark and Donnie are 58 in. each.
Q: What do you need to find out?
A: How tall are we all together in feet and inches?
Plan:
Q: What is your plan for solving the problem?
A: Add all our heights together in inches and then convert it into feet and inches.
Solve:
Q: Use the facts you know to make the equation and solve.
A: 62 in. + 62 in. = 124 in. 124 in. 2 0_ft._
58 in. + 58 in. = 116 in. +116 in. 12 in) 2 4 0 in.
240 in.
- 2 4
0 0
-
0
0
Q: Write the answer in a complete sentence.
A: The height of all four of us together is 20 feet exactly.
Look Back:
Q: Check to see if your answer makes sense.
A: Multiply 20 ft. X 12 in. to see if you get 240 in. Then subtract 124 in. from 240 in. to see if you get 116 in. (You could also subtract 116 in. from 240 in. to see if you get 124 in.) Then subtract 62 in. from 124 in. to see if you get 62 in. Subtract 58 in. from 116 in. to see if you get 58 in.
Pictured: Taylor R. and Hayley N.
Not pictured: Mark V. and Donnie P.
Problem 3:
By: Jamie F., Garrett A., Danny J., Horacio G.
There
are two chalkboards and one bulletin board.
One chalkboard’s area is 88,572 sq. cm. and one bulletin board’s area
is 50,180 sq. cm. What is the area of two chalkboards and one bulletin board?
(The two chalkboards are the same size.)
Problem
Solving Analysis:
Understand:
Q:
What do you know?
A:
We know that there are two chalkboards and one bulletin board.
One chalkboard’s area is 88,572 sq. cm. and the bulletin board’s area
is 50,180 sq. cm.
Q:
What do you need to find out?
A:
What is the area of two chalkboards and one bulletin board?
Plan:
Q:
What is your plan for solving the problem?
A:
Multiply 88,572 sq. cm. X 2 and then add this number to 50,180 sq. cm.
Solve:
Q:
Use the facts you know to make the equation and solve.
A:
88,572 sq. cm.
177,144 sq. cm.
+ 50,180 sq. cm.
227,324 sq. cm.
Q:
Write the answer in a complete sentence.
A:
The area of two chalkboards and one bulletin board is 227,324 sq. cm.
Look
Back:
Q:
Check to see if your answer makes sense.
A:
Subtract 50,180 sq. cm. from 227,324 sq. cm. and make sure it is 177,144
sq. cm.
Then divide 177,144 sq. cm. by two and make sure it is 88,572 sq. cm.
Pictured:Garrett
A., Horacio G. & Jamie F.
Not
pictured: Danny J.
Problem 4:
By: Bridget O., Carla S., Chris S., Tyler A.
North School’s 4th
grade hall is 23 meters and 16 inches long.
The width is 72 inches. The
meter stick is 39 inches long. What
is the area of the North School’s 4th grade hall in inches?
Problem Solving
Analysis:
Understand:
Q: What do you know?
A: The length of the hall is 23 meters and 16 inches and the
width is 72 inches. The meter stick
is 39 in. long.
Q: What do you need to find
out?
A: What is the area of
North School’s 4th grade hallway in inches?
Plan:
Q: What is your plan for
solving the problem?
A: Multiply 23 meters X 39
in. Then add this number to 16 in.
This is the length in inches. To
find the area, multiply the length by the width, or 72 inches.
Solve:
Q: Use the facts you know
to make the equation and solve.
A: 23 m.
897 in.
913 in.
X39
in.
+ 16
in. X 72 in.
117
913 in.
1826
+780
+63910
897
in.
65,736
sq. in.
Q: Write the answer in a
complete sentence.
A: The area of the 4th
grade hallway is 65,736 sq. in.
Look Back:
Q: Check to see if your
answer makes sense.
A: Divide 65,736 sq. in. by 72 in. (the width) to make sure you
get 913 in. (the length.) Then
subtract 16 in. from 913 in. to make sure you get 897 in. (the part of the
length that was measured in meters.) Then
divide 897 in. by 39 in. to make sure you get 23 meters.
Pictured:
Chris S., & Bridget O.
Not
pictured: Carla S., & Tyler A.
Problem 5:
By: Steven P., John D., Lucas F., Daniel M.
There are 15 female brine
shrimp in the tank in Miss Lesak’s class.
If each shrimp laid 1,456 eggs, how many baby shrimp will there be when
they hatch?
Problem Solving Analysis:
Understand:
Q: What do you know?
A: There are 15 shrimp eggs in the tank and they each will lay 1,456 eggs.
Q: What do you need to find out?
A: How many baby shrimp will there be when all the eggs hatch?
Plan:
Q: What is your plan for solving the problem?
A: Multiply 1,456 eggs by 15 shrimp.
Solve:
Q: Use the facts you know to make the equation and solve.
A: 1,456 eggs
X 15 females
7,280
+4,560
21,840 new baby brine shrimp
Q: Write the answer in a complete sentence.
A: There are 21,840 new baby brine shrimp.
Look Back:
Q: Check to see if your answer makes sense.
A: Divide 21,840 new baby brine shrimp by 15 females to make sure you get 1,456 babies for each female.
Pictured: John D., Steven P., Lucas F.
Not pictured: Daniel M.
Problem 6:
By: Jessika N., Ashley J., Kevin R., Gurpreet H.
If a book was 7 cm. long
and our kickball field is perfectly square (1500 cm. on each side,) how many
books would it take to go around the perimeter?
Problem Solving
Analysis:
Understand:
Q: What do you know?
A: We know the book is 7 cm. long.
We know that one side of the field 1500 cm. long and there are four equal
sides.
Q: What do you need to find
out?
A: How many books would it
take to go around the perimeter?
Plan:
Q: What is your plan for
solving the problem?
A: Find the perimeter of
the field by multiplying 1500 cm X 4 sides.
Then divide this number by 7 cm., the length of the book.
Solve:
Q: Use the facts you know
to make the equation and solve.
A: 1500 cm.
857
X
4 sides
7)6000 cm
6,000 cm.
- 56
40
-35
50
- 49
1
Q: Write the answer
in a complete sentence.
A: The book goes around the field about 857 times (with a
remainder of 1.)
Look Back:
Q: Check to see if your
answer makes sense.
A: Multiply 857 times around X 7 cm. to make sure you get 5,999. Then add the remainder of 1 to make sure you get 6,000 cm. as the perimeter of the field. Then divide 6,000 cm. by 4 sides to make sure you get 1500 cm. for each side of the field.
Pictured: Kevin R.
Not pictured: Jessika N., Ashley J., Gurpreet H.