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Assessment as a Tool for
Learning
Copyright, 1996 © Dale Carnegie & Associates, Inc.
Advantages of Using
Alternative Assessments
– Increase instructional time
– Create more learning opportunities
– Motivate students
– Accommodate differences in learning styles
– Improve problem solving ability
The Take-Home Test
• Uses no class time
• Lengthens time on-task
• Relieves test taking anxiety
• Promotes collaboration and inquiry
• Aids the auditory learner
• Provides real world and complex problem
solving opportunities
Take-Home Test
Example 1: Write and solve a
percentage word problem where the tip
for a meal at a restaurant is $26.15.
Possible solution:
Mrs. Shotsberger and Juan go to dinner at Café Rich. Mrs.
Shotsberger, always diligently watching her figure, orders a
seafood salad. Juan has a prime rib dinner. They share a
bottle of wine. Their bill comes to $130.75 and they leave a
tip for $26.15. What percentage of the bill was the tip?(20%)
Alternative solution:
Mrs. Shotsberger and Juan go to dinner at Café Rich. They
both order salads and several bottles of wine. Confused by
too much wine they leave a 35% tip of $26.15. How much
was the bill?($74.71)
Take-Home Test
Example 2: List the order of operations.
Write and simplify one expression that
includes all four steps.
Order of Operations
1. Work within grouping symbols (),[],{}
2. Simplify exponents
3. Multiply and divide, left to right
4. Add and subtract, left to right
12 ÷ 4 x 7 + 62 - (7 - 3 + 2) =
12 ÷ 4 x 7 + 62 - (4 + 2) =
12 ÷ 4 x 7 + 62 - 6 =
12 ÷ 4 x 7 + 36 - 6 =
3 x 7 + 36 - 6 =
21 + 36 - 6 =
57 - 6 = 51
Collaborative Learning
• Promotes cooperation
• Encourages active participation
• Aids the tactile and auditory learners
Collaborative Learning Evaluation
M&M Candy Worksheet
Do not eat any M&M’s until the lesson is completed.
1. All M&M’s in the package
Total________
2. Number of blue M&M’s
Total________
3. Number of green M&M’s
Total________
4. Number of brown M&M’s
Total________
5. Number of orange M&M’s
Total________
6. Number of yellow M&M’s
Total________
7. Number of red M&M’s
Total________
Complete the following table using the data collected above.
Blue
Green Brown Orange Yellow Red
Fraction
Decimal
Percent
Degrees
Collaborative Learning Evaluation
M&M Candy Worksheet
Do not eat any M&M’s until the lesson is completed.
1. All M&M’s in the package
Total__55____
2. Number of blue M&M’s
Total__13____
3. Number of green M&M’s
Total__12____
4. Number of brown M&M’s
Total__10____
5. Number of orange M&M’s
Total___8____
6. Number of yellow M&M’s
Total___5____
7. Number of red M&M’s
Total___7____
Complete the following table using the data collected above.
Blue
Green Brown Orange Yellow Red
Fraction 13/55
12/55 10/55=2/11 8/55 5/55=1/11 7/55
Decimal .23636… .21818… .1818… .14545… .0909… .12727...
Percent 24%
22%
18%
14%
9%
13%
Degrees 86.4° 79.2°
64.8°
50.4° 32.4° 46.8°
Mini-Projects
• Uses no class time
• Promotes creativity
• Simulates real-world problem solving
End of Unit Project
General Mathematics
Perimeter & Area Unit Project
Using the scale drawing of your room and the two advertisements
you collected, complete the following:
1. Find the perimeter of the room in linear feet.
2. Use your ad for a chair rail, baseboard or wallpaper border to find the
cost for purchasing this material for your room.
Include an extra 10% of the material in the cost.
3. Find the area of the room in square feet or square yards.
4. Use your ad for flooring, carpeting or tiling, to find the cost for
purchasing this material for your room. Include an extra 10% of the
material in the cost.
Possible Solutions:
1. The perimeter is 37 ft. (10+8 1/2+3 1/6+2 +6 5/6+6 1/2)
2. The cost for a wallpaper border @ $13.25/15 feet per roll
10% of 37 = 3.7 So 40.7 feet are needed. 3 rolls = 45 ft.
3 x $13.25 = $39.75 (plus any tax)
3. The area is 71 1/3 square feet or about 8 square yards.
4. The cost for carpeting @ 31.25/square yard, padding included
10% of 8 = .8, almost 1 yd, 8 + 1 = 9, 9 x 31.25 = $281.25
10’
6’ 6”
8’ 6”
6’ 10”
2’
3’ 2”
Short Answer Tests
• Gives insight into student comprehension
• Provides opportunities to revisit problems
and correct errors
• Allows students to solve more meaningful
problems
SHORT ANSWER TEST QUESTION
EXAMPLE 1: You took a number and rounded
it to the hundreds place getting 400. What
would be the largest number you could have
rounded to 400? And the smallest?
Solution: At first I thought 399 was closest to 400 and the largest
but then I realized that 405 would be rounded to 400 also. Anything
above 5 in the tens place would move the 4 to 5, so 449 is the
largest because 450 would round to 500.
Thinking the same way for the smallest possible number - in order to
raise the hundred’s place from 3 to 4 I need a 5 in the tens place, so
350 would be the smallest possible number because 349 would
round to 300.
SHORT ANSWER TEST QUESTION
Example 2: Can you find 5 numbers that
have a mean of 15.6? Are there other
possibilities? Explain.
Possible Solution:
To find the arithmetic mean you add the 5 numbers and
divide by 5. So, 5 numbers/5 = 15.6.
Working backwards: 15.6 x 5 = 78
I need to find any 5 numbers that have a sum of 78.
Example: 10 + 20 + 15 + 20 + 13
There are infinite possibilities.
Test Reflection
• Gives insight into student comprehension
• Relieves test taking anxiety
• Promotes problem solving
TEST REFLECTION
Example 1: Simplify the expression.
3 + 4(2 + 7)
Response on test: 3 + 4(2 +7) = 3 + 8 + 7 = 18
Test Correction: 3 + 4(2 + 7) = 3 + 4(9) = 3 + 36 = 39
I shouldn’t have used the distributive property, just add 2 + 7
This would not receive any credit. I would respond:
3 + 4(2 + 7) = 3 + 4(2) + 4(7) = 3 + 8 + 28 = 39
is the correct use of the distributive property. You could either
distribute OR add within the parentheses first. You distributed
incorrectly.
TEST REFLECTION
Example 2: Compare 2/5 and 7/10.
Test Response: 2/5 > 7/10
Test Correction: 2/5 < 7/10 because 7 and 10 are larger numbers
than 2 and 5.
This would not receive any credit even though 2/5 < 7/10 is true.
I would respond: 2/5 = 4/10 If you multiply both 2 and 5 by 2 you
have an equivalent fraction to 2/5, SO 2/5 < 7/10.
Counter Example: 5/8 < 3/4 even though 5 and 8 are larger than 3
and 4 because 5/8 = 15/24, 3/4 = 18/24 and 15/24 < 18/24
REVIEW
-
Increase instructional time
Create more learning opportunities
Motivate students
Improve problem solving ability
Accommodate differences in learning styles
•Take Home Tests
•Collaborative Learning Evaluations
•Unit/Chapter Mini-Projects
•Short Answer Response Tests
•Test Reflection