Transcript Open Ended Questions

Open Ended Questions
From Massachusetts
What does a complete
solution look like?
Grade 3
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2009 MCAS Grade 3 Mathematics
Question 14: Number Sense and Operations
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Tom, Nuno, and Paul each made a pizza. All the pizzas were the same size and
shape.
Tom cut his pizza into 2 equal pieces.
Nuno cut his pizza into 3 equal pieces.
Paul cut his pizza into 4 equal pieces.
a.
Which boy has the smallest size pieces of pizza? Show or explain how you
got your answer.
b.
Each boy ate some of the pizza he made.
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Tom ate 1 piece of his pizza.
Nuno ate 1 piece of his pizza.
Paul ate 2 pieces of his pizza.
Which boys ate the same amount of pizza? Show or explain how you got
your answer.
Grade 4
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2009 MCAS Grade 4 Mathematics
Question 4: Measurement Christina’s schedule for Tuesday afternoon is
shown in the chart below.
Christina’s Schedule
Time
Activity
3:00 p.m.
Get out of school
3:30 p.m.
Dance class begins
4:15 p.m.
Dance class ends
5:00 p.m.
Do homework
5:45 p.m.
Eat dinner
How many minutes does Christina have between when she gets out of
school and when her dance class begins?
How many minutes is Christina’s dance class? Show or explain how you got
your answer.
It takes Christina’s family 1 hour 15 minutes to eat dinner. At what time will
her family finish eating dinner? Show or explain how you got your answer.
Grade 5
2009 MCAS Grade 5 Mathematics
Question 13: Number Sense and Operations
Ms. Hendricks asked her students how they get to school
each day. She collected their answers and determined the
following results.
• Half of her students take the bus.
• 15 of her students walk.
• The rest of her students ride with their parents.
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What percent of the students take the bus?
What percent of the students walk? Explain how you know
that your answer is correct.
What percent of the students ride with their parents? Show
or explain how you got your answer.
Grade 6
2009 MCAS Grade 6 Mathematics
Question 7: Number Sense and Operations
The table below shows the distance, in
kilometers, Lisa ran each day for 5 days.
a)
Write the five distances in order from greatest
to least.
b) Estimate the average distance, in kilometers,
Lisa ran each day for the 5 days. Explain your
estimation strategy.
c) To prepare for a race, Lisa plans to run
100 kilometers over a number of days.
d) Based on your answer to part (b), estimate the
number of days it will take Lisa to run
100 kilometers. Explain your estimation
strategy.
Grade 7
Grade 8
2009 MCAS Grade 8 Mathematics
Question 14: Patterns, Relations, and Algebra
Ms. Gleason is opening a new restaurant.
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She has enough booths to seat up to 40 people.
She is ordering tables to fill the rest of the seating space.
Each table can seat up to 6 people.
a) If t represents the number of tables Ms. Gleason orders, write an
expression to show the total number of people that can be seated at
booths and tables.
b) Write an inequality that could be used to determine t, the number of tables
Ms. Gleason needs to order so that she has enough seating at booths and
tables for at least 125 people.
c) Solve the inequality from part (b) to determine the number of tables Ms.
Gleason needs to order. Show or explain how you got your answer.
High School
2009 MCAS Grade 10 Mathematics
Question 20: Number Sense and Operations
Thomas plays a number game using a spinner with four
congruent sections. The sections are labeled W, X, Y,
and Z, as shown below.
In the game, a player receives the number of points
represented by the expression in the section where the
arrow stops. The first player to get 20 points or more
wins.
a) During one game, Thomas needed 10 or more points to
win. On his next spin the arrow stopped on section Z.
Did he receive enough points to win? Show your work to
justify your answer.
b) Which is worth more points, section X or section Z?
Show your work to justify your answer.
c) Thomas believes section W and section Y are worth an
equal number of points. Is Thomas correct? Explain your
reasoning.
What does a complete solution
look like??????
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Check out the following slides
Grade 3 complete solution
Grade 3 complete solution
Grade 4 complete solution
Grade 4 complete solution
Grade 5 complete solution
Grade 5 complete solution
Grade 6 complete solution
Grade 6 complete solution
Grade 7 complete solution
Grade 7 complete solution
Grade 8 complete solution
High School complete solution
High School complete solution
Links
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http://www.doe.mass.edu/mcas/student/
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