Open Ended QuestionsFrom Massachusetts

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Grade 3 2009 MCAS Grade 3 Mathematics Question 14: Number Sense and Operations

• 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.

• 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 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 MathematicsQuestion 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.

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 62009 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 MathematicsQuestion 14: Patterns, Relations, and Algebra

Ms. Gleason is opening a new restaurant. • 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 School2009 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??????

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

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