Math CAMPPP 2012
Balancing Assessment
K-4 Breakout Five
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Participant Learning Goals:
Participants will:
• investigate portfolio assessment
• deepen their understanding of Balanced
Assessment
• become aware of important understandings and
misconceptions and how to assess for
understanding in the learning of fractions.
Minds on:
Inside/Outside Circle
4 Discussions:
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Discussion #1
• Describe any experience you have had
with portfolio assessment?
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Discussion #2
• What is one thing from Chris’ presentation
that you don’t think would work in K-4?
How could this be tweaked for K-4?
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Discussion #3
• Describe one criterion that you would like
to see represented in a student portfolio?
Explain.
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Discussion #4
• Describe an idea about assessment that
you would like to learn more about?
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Sharing Our Stories
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The Fruity Set Problem
• In groups of 4 (mixed grade), work
together to solve the following problem.
(you may use materials/manipulatives)
• Record your solution on chart paper.
• Post your solution.
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The Fruity Set Problem
A basket of fruit, containing mangos, blueberries, apples and
cherries was delivered to the palace.
The king took one sixth of all the fruit.
From what was left, the queen took one fifth of the fruit.
From what was left, the princess took one fourth of the fruit.
From what was left, the prince took one third of the fruit..
From what was left, the duchess took one half of the fruit..
This left only 2 blueberries and 1 mango in the bowl for the
servant.
How many pieces of fruit were originally in the basket?
Gallery Walk
• What are the big ideas and
misconceptions about fractions that this
problem may address/expose?
• Write these on stickies and post them on
the learning wall.
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Guess and Check
Pick a multiple of 6 - let’s say 60.
One sixth of 60 is 10 which leaves 50.
One fifth of 50 is 10
One fourth of 40 is 10
One third of 30 is 10
One half of 20 is 10
10 left over is too high
Try a lower multiple of 6.
Finding a Pattern
Start with 24
One sixth of 24 equals 4
One fifth of 20 equals 4
One fourth of 16 equals 4
Choose a lower number
One sixth of 18 equals 3
One fifth of 15 equals 3
3 blueberries is what was left so
6 people times 3 equals 18 pieces of fruit.
Draw a Diagram
King removes
one sixth of
fruit
Queen removes
one fifth of
remainder
Princess
removes one
fourth of
remainder
Prince
removes one
third of
remainder
Duchess
removes one
half of
remainder
2 blueberries
and a mango left
Another Diagram
King
3
Queen
3
Princess
Prince
3
3
3 + 3 + 3 + 3 + 3 + 3 = 18
Duchess
3
Servant
3
Working Backwards
Servant receives 3 pieces.
Duchess (took one half) so 3 is half of 6
Prince
(took one third) so 6 is two thirds of 9
Princess (took one fourth) so 9 is three fourths of 12
Queen
(took one fifth) so 12 is four fifths of 15
King
(took one sixth) so 1 is five sixths of 18
Algebraic
Solution
Myth: fractional parts of an area need to
look exactly the same (size and
shape)
• Re-organize into homogeneous
grade groups of 4 to 6.
• Consider the following problem.
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Is one fourth of the square in the
picture shaded?
(P61 A Focus on Fractions)
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Maria’s Response p62
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William’s Response p63
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Placemat
• What do you know about each student‘s
understanding?”
• “What are you unsure of?”
• “What would you ask each next?”
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Group Placemat
What I would ask Maria next:
Informed
Practice:
What I am sure about William`s understanding:
What I would ask William next:
What I am sure about Maria`s understanding:
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William`s Follow-up p63
William took 4 marbles out of his desk . He said that
even though the marbles were not the same size, one
of the marbles was one fourth of his set of four marbles
– the shaded portion of the square is one piece out of
four pieces , so it is one fourth of the square
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Maria`s Follow-up pg 64
Mrs. Armstrong asked Maria if each of the figures below
showed one fourth of the figure shaded.
“No, one fourth is not shaded because Square 1 is not divided into 4 equal parts and
Square 2 is divided into 2 unequal parts not 4 parts.”
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Placemat Part 2
• Add to your group’s placemat any new
information you have about Maria or
William’s understanding.
• Complete the circle in middle: How can
this follow-up student work inform
teaching/practice?
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Reflection – Your Choice
• What is your A-HA
moment from today?
• Record for your
treasure box.
• Comment on the
following quote:
• “A fine glass vase goes
from treasure to trash,
the moment it is broken.
Fortunately, something
else happens to you and
me. Pick up your pieces.
Then, help me gather
mine.” ― Vera Nazarian,
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Home Activity
Problem:
• Find as many different ways to show
one half a geoboard and record each
way on the grid square handout.
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