Assessment/Accountability
Massachusetts Comprehensive Assessment System

Grade 4

Mathematics

Content and Skills to be Assessed by MCAS

January 1998

Massachusetts Department of Elementary and Secondary Education

Number Sense

Number Sense and Numeration

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• construct number meaning by using manipulatives and other physical materials to represent concepts of numbers in the real world.
• demonstrate an understanding of our numeration system by relating counting, grouping, and place value concepts.
• interpret the multiple uses of numbers by taking real-world situations and translating them into numerical statements.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• model number order through hundred thousands in different ways, e.g., 2,400 as 2 thousand and 4 hundred base ten blocks or as 24 hundred base ten blocks; represent a number value on a number line. [see Question 1]
• identify the magnitude of numbers through hundred thousands, e.g., 100 is the same as 4 twenty-fives, it is twice as big as fifty, it is half of two hundred, it is one tenth of one thousand.
• apply counting and grouping strategies, e.g., count by tens beginning with any given number. [see Question 2]
• apply number theory concepts, e.g., odd/even, factors, multiples, number sequences. [see Question 4]
• read, write, and interpret different place value representations through hundred thousands, e.g., number sentences, expanded notation. [see Question 3]
• use numbers to identify and quantify, e.g., ordinal numbers, calendar and time intervals, measurements.
• translate pictures and/or verbal (written) descriptions to numerical statements.

For details and samples of student learning related to these learning standards, see page 34 of the Massachusetts Mathematics Curriculum Framework.

Sample Questions

Multiple-choice Questions:

1.

On the number line above, to which number does the arrow point?

A. 7

B. 12

*C. 15

D. 17

2. Maria counts aloud by fours. George counts aloud by sevens. If they both count correctly, which number below will BOTH say aloud?

A. 14

B. 21

*C. 28

D. 32

3. By how much would the value of 5,647 be decreased if the 5 were replaced by a 2?

A. 3

B. 300

*C. 3,000

D. 30,000

Open-response Question:

4. Corey worked these problems.

When Corey finished, he said,

"I think that the sum of ANY two numbers is always an even number."

a. Is Corey correct? Explain the reasons for your answer using pictures, numbers, or words.

Maya looked at Corey's work. She thought a bit and said,

"I think that the sum of any two ODD numbers is always an odd number."

b. Is Maya correct? Explain the reasons for your answer using pictures, numbers, or words.

Number Sense

Concepts of Whole Number Operations

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• model and discuss a variety of problem situations to help students move from the concrete to the abstract.
• relate the mathematical language and symbolism of operations to problem situations.
• identify a variety of problem structures that can be represented by a single operation.
• know when to use the operations of addition, subtraction, multiplication, and division; and describe their relationships.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• use a variety of models to show understanding of the four basic operations, e.g., charts, arrays, diagrams, physical models. [see Question 7]
• use mathematical language and symbols of operations in describing problem situations. [see Question 5]
• create word problems using each of the four basic operations.
• relate each of the four basic operations to a variety of problem structures, e.g., subtraction as comparison (how much less/more), equalizing (how many more are needed to make these equal), separation (how many remaining); multiplication as arrays, times as many, combining equal groups. [see Question 5]
• recognize and use the relationships between operations, e.g., inverse operations, multiplication as repeated addition. [see Question 8]
• identify the appropriate operation(s) to use in single- and multi-step problems. [see Questions 6, 8]

For details and samples of student learning related to these learning standards, see page 35 of the Massachusetts Mathematics Curriculum Framework.

Multiple choice Questions:

5. Which of the following problems CANNOT be solved using the number sentence below?

A. Siu Ping had 15 trading cards. She gave 8 to Jim. How many does she have now?

*B. Siu Ping needs 15 more trading cards than Jim has. Jim has 8. How many does Siu Ping need?

C. Siu Ping has 15 trading cards. Jim has 8. How many more does Siu Ping have than Jim?

D. Siu Ping needs 15 trading cards. She has 8. How many more does she need?

6. Suman made 32 cupcakes for a bake sale. He is putting his cupcakes into boxes, with 4 cupcakes in each box. Which of the following will tell him how many boxes he needs?

A. Multiply 32 by 4.

B. Add 4 and 32.

*C. Divide 32 by 4.

D. Subtract 4 from 32.

Short-answer Question:

7. Shannon is adding two numbers using the base ten blocks shown below. Write a number sentence for the problem Shannon is doing. Be sure to include the answer.

Correct response: 1,343 + 265 = 1,608 (or equivalent equation)

Open-response Question:

8. Show or explain TWO different ways Tamika can solve the problem below.

There are 14 members in the reading club. What is the fewest number of books the club will need if each member borrows 5 books at the same time?

Number Sense

Fractions and Decimals

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• demonstrate an understanding of the basic concepts of fractions, mixed numbers, and decimals.
• use models to relate fractions to decimals, find equivalent fractions, and explore operations on fractions and decimals.
• apply fractions and decimals to problem situations.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• identify models (regions or sets) of fractions, mixed numbers, and decimals.
• describe the meaning of fractions in terms of equal parts of a whole. [see Questions 9, 14]
• model, compare, and order fractions through twelfths. [see Question 14]
• represent place value for decimals in a variety of ways, e.g., number lines, base ten blocks. [see Question 11]
• model, compare, and order decimals up to hundredths, e.g., relate decimals to money concepts. [see Question 13]
• model, compare, and order mixed numbers. [see Question 12]
• relate decimals to fractions in tenths and hundredths, e.g., 0.2 is the same as 2/10.
• identify and find equivalent fractions, e.g., 1/2 = 2/4.
• model addition and subtraction of fractions and decimals with manipulatives, e.g., Cuisinaire rods, base ten blocks, pattern blocks. [see Question 10]
• solve problems involving fractions, decimals, and mixed numbers.

For details and samples of student learning related to these learning standards, see page 36 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

9. Cherie divided her candy bar into thirds. She gave one-third to her sister and one-third to her brother. How much of her candy bar does she have left?

*A. 1/3

B. 1/2

C. 1/4

D. 1/6

10.

Margarita brought a sheet of nine stickers to school. At recess, she shared some with her friends, so that she has only2/9 of the stickers left. How many stickers did she give to her friends?

A. 2

B. 3

C. 6

*D. 7

11. Use the two bars below to answer the question.

Which number is shown by the shaded parts of the bars?

*A. 1.3

B. 1.7

C. 1 1/3

D. 1 3/7

12. Use the numbers in the box below to answer the question.

2 3/8

1 3/4

16/8

5/4

Which list shows the numbers in order from LEAST to GREATEST?

A. 1 3/4

5/4

16/8

2 3/8

*B. 5/4

1 3/4

16/8

2 3/8

C. 2 3/8

16/8

1 3/4

5/4

D. 16/8

2 3/8

5/4

1 3/4

13. Which number below is GREATEST?

A. 0.07

*B. 0.6

C. 0.56

D. 0.18

Open-response Question:

14.

Marcus ordered a submarine sandwich for lunch. Marcus is going to share the sandwich with his brother, Luis. This is what they say:

Marcus: Would you rather have 1/3 or 1/6 of the sandwich?

Luis: I'm really hungry, so I want 1/6 because that's more than1/3.

Marcus: Wait! That doesn't make sense.

Luis: Yes, it does! Anybody knows that 6 is more than 3, so 1/6 of a sandwich has to be more than 1/3 of it .

Tell who is correct and explain why.

Number Sense

Estimation

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• describe the strategies used in exploring estimation.
• determine when an estimate is appropriate.
• apply estimation when working with quantities, measurement, and computation.
• use estimation to check solutions to determine if the results of computational problems make sense.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• use and describe a variety of strategies for estimation, e.g., sampling, front-end, grouping, rounding. [see Questions 15, 16, 17]
• round numbers to the nearest ten, hundred, thousand, and ten thousand.
• round fractions and decimals to the nearest whole number.
• verify the reasonableness of solutions in addition, subtraction, multiplication, and division problems by using estimation.

For details and samples of student learning related to these learning standards, see page 37 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

15.

The picture above shows birds flying south for the winter. About how many birds are in the picture? Use ESTIMATION to determine your answer.

A. fewer than 100

*B. between 100 and 1,000

C. between 1,000 and 5,000

D. more than 5,000

16. Alex read his new book for 1 hour and then used a bookmark to mark his place. About how much longer will it take Alex to finish reading his book if he continues at this pace?

A. 1/2 hour

*B. 2 hours

C. 5 hours

D. 10 hours

Open-response Question:

17. Lee goes shopping with only $20 to spend. He sees the four items below and decides to estimate to see if he has enough money to buy all of them.

a. Estimate to decide if Lee has enough money. Does he have enough?

b. Explain how you estimated so that you are sure your answer is correct.

Number Sense

Whole Number Computation

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• model, explain, and develop proficiency with basic facts and algorithms.
• use calculators in appropriate computational situations.Ý

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• use basic facts (addition, subtraction, multiplication, and division tables) to compute.
• compute using whole numbers, e.g., addition and subtraction with four-digit numbers, multiplication with three-digit numbers by two-digit numbers, dividing by single-digit numbers with remainders. [see Questions 18, 20, 21, 22, 23]
• explain computational procedures, including routine and non-routine algorithms. [see Question 19]

For details and samples of student learning related to these learning standards, see page 38 of the Massachusetts Mathematics Curriculum Framework.

Ý See page 13 for more information about calculator use.

Multiple-choice Question:

18. Kim's uncle is a truck driver. On his last trip, he drove from Boston to Chicago, then to Denver, and back to Boston. Kim found the following information in an atlas.

Based on this information, how many miles did Kim's uncle travel?

A. 2,845 miles

B. 3,945 miles

C. 2,855 miles

*D. 3,955 miles

19.

A student completed the subtraction problem above. The changes to the top number

show that 245 is the same as

*A. 2 hundreds, 3 tens, 15 ones.

B. 2 hundreds, 31 tens, 5 ones.

C. 2 hundreds, 315 ones.

D. 2 thousands, 3 hundreds, 1 ten, 5 ones.

Short-answer Questions:

20. What digit should be put in the boxes to give the answer shown?

Correct response: 2

21. Compute:

397

x 54

_____

Correct response: 21,438

22. Compute:

_______

3)896

Correct response: 298 R2

Open-response Question:

23. Use information in the box below to answer the question.

Bristol Garden Center

Sale on marigold plants!!!

Buy each plant for only 23¢.

Save more money -- Buy a tray of 6 plants for only $1.25.

Save even more money -- Buy a box of 24 plants for only $3.69.

Ms. Edwards, Mr. Rossi, and Dr. Bernard are the first customers at the sale.

a. Ms. Edwards is buying 5 plants. How much will she pay?

b. Mr. Rossi is buying 15 boxes, with 24 plants in each box. How much will he pay?

c. Dr. Bernard wants to buy EXACTLY 55 plants. She wants to save as much money as possible.

• How many boxes of 24 plants, trays of 6 plants, and single plants should she buy?
• How much will her plants cost?

Patterns, Relations, and Functions

Patterns and Relationships

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• identify, describe, extend, and create a wide variety of patterns.
• represent and describe mathematical relationships.
• explore the use of variables and open sentences to express relationships.
• use patterns and relationships to analyze mathematical situations.

To assess these standards, students will be expected to solve problems, use appropriate mathematical communication skills, use mathematical reasoning, and make connections in questions that require them to:

• sort, categorize, and classify objects or data.
• sequence events.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• identify, describe, extend, and create numerical and geometric patterns in many forms, e.g., repeating and growing patterns, sequencing. [see Question 24]
• analyze and apply number patterns, formulate rules and generalizations, make predictions, draw conclusions, and organize information. [see Questions 25, 26, 28]
• represent and explain mathematical relationships using pictures, models, tables, graphs, words, number sentences, and mathematical notations (symbols), e.g., >, <, = .
• solve problems using numeric and geometric patterns and relationships.
• identify and locate points on a coordinate grid. [see Question 27]

For details and samples of student learning related to these learning standards, see page 57 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Question:

24. In the following set of 40 numbers, some numbers have been circled according to a number pattern. Study the pattern. Which numbers should be circled in the FOURTH row?

A. 32, 35, 38

B. 31, 33, 35, 37, 39

C. 31, 34, 37, 40

*D. 33, 36, 39

Short-answer Questions:

25. How many of the SMALLEST squares will be in Figure 5 if this pattern continues?

Correct response: 25

26. Study the pattern below. Write the rule to find the next number in the pattern.

25, 21, 17, 13, ________

Correct response: subtract 4

27.

On the map above, which ordered pair gives the location of the house?

A. (A,1)

B. (D,1)

*C. (A,3)

D. (D,4)

Open-response Question:

28. Each number machine has a rule. When a number is put into a number machine, the number that comes out depends on the rule.

If you can figure out the rule for a machine, then you will know what number will come out for any number that is put in.

MACHINE X

When a 3 goes in, a 5 comes out.

When a 4 goes in, a 6 comes out.
When a 5 goes in, a 7 comes out.

a. When an 8 goes in, what number comes out?

b. Explain in words what Machine X does to numbers.

c. Choose another number. What other number will come out when you put your number into the machine?

MACHINE Y is a new machine.

When a 3 goes in, a 5 comes out.
When a 4 goes in, a 7 comes out.
When a 5 goes in, a 9 comes out.

d. When an 8 goes in, what number comes out?

e. Explain in words what Machine Y does to numbers.

f. Choose another number. What other number will come out when you put your number into the machine?

Patterns, Relations, and Functions

Algebra/Mathematical Structure

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• discover how to form, then write, number sentences for real problems.
• investigate and describe ways to find missing components in number sentences.
• demonstrate through hands-on activities, an understanding of maintaining balances in number sentences.
• explain the use of variables in number sentences.
• explore and demonstrate an understanding of commutative properties for addition and multiplication.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• identify and write number sentences with variable(s) to describe real-world situations. [see Question 29]
• identify a missing part in a mathematical sentence, e.g., missing addend. [see Questions 31, 32]
• model equivalence in number sentences, e.g., (8 + 2) + 1 = 10 + 1, 2 x 6 = 3 x 4. [see Question 33]
• find replacements for variables that make number sentences true, e.g., a + b = 10,
  [] - () = 6. [see Question 32]
• explain and apply the order property, e.g., 2 + 3 = 3 + 2, 2 x 3 = 3 x 2. [see Questions 30, 32]

For details and samples of student learning related to these learning standards, see pages 58 and 59 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

29. Which number sentence could be used to solve the problem in the box below?

There are 48 people who signed up to go on a covered wagon ride. Each wagon can hold 6 people. If all the people go at the same time, how many wagons are needed to carry everyone on the ride?

A. 48 + 6 = []

B. 48 ­ 6 = []

C. 48 x 6 = []

*D. 48 / 6 = []

30. Jerry took a long time to compute 2 x 17 x 5. Megan said, "The answer is simple. It's 10 times 17, or 170."

Megan recognized that

*A. 2 x 17 x 5 = 2 x 5 x 17.

B. 5 x 17 = 85.

C. 2 x 17 x 5 = 2 x 17 + 2 x 5.

D. 2 x 17 = 17 x 2.

Short-answer Questions:

31. What number belongs in the [] to make the second number sentence true?

Correct response: 54

32. What number belongs in the boxes (*) to make BOTH number sentences true?

Correct response: 12

Open-Response Question:

33. Use the picture below to answer the question.

a. How many stars will balance ONE square?

b. How many stars will balance TWO squares?

c. Three stars and six hearts are on one side of the scale. How many SQUARES must be on the other side to balance the scale?
Show or explain how you know.

Geometry and Measurement

Geometry and Spatial Sense

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• describe, model, draw, and classify shapes.
• investigate and predict the results of combining, subdividing, and changing shapes.
• develop spatial sense.
• use geometric ideas to develop numerical ideas.
• recognize and appreciate geometry in the world.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• use many types of shapes, (e.g., squares, cubes, rectangles, prisms, rhombi, parallelograms, polygons, pyramids, circles, spheres) and identify the figures by their properties (e.g., number of right angles, symmetry, number of faces, two or three dimensions). [see Question 35]
• draw two-dimensional shapes.
• classify lines as parallel, perpendicular, or
  intersecting. [see Question 38]
• identify angles as right, acute, or obtuse. [see Question 38]
• determine new shapes that can be made from combining, subdividing, or folding shapes, e.g., shapes made from three given shapes.
• apply transformations, e.g., flips, slides, turns. [see Question 34]
• identify symmetric figures and lines of symmetry. [see Question 37]
• identify shapes and figures from different perspectives. [see Question 36]
• identify geometric shapes that appear in both natural and human-made objects.

For details and samples of student learning related to these learning standards, see page 72 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

34. Figure 1 Figure 2

The letter in Figure 1 was moved as shown in Figure 2. How was it moved?

A. It was slid.

*B. It was flipped.

C. It was turned.

D. It was measured.

35. All of these are hoogles:

None of these is a hoogle:

Which of the following is a hoogle?

*A. B.

C. D.

36. Use the figure below to answer the question.

Which of the following shows a view of the figure from the FRONT?

*A.

B.

C.

D.

Short-answer Question:

37. Use the shapes below to answer the question.

How many of these shapes have AT LEAST TWO lines of symmetry?

Correct response: 3 shapes

Open-response Question:

38. Complete the map shown below.

Obtuse angle--
an angle greater than a right angle

Acute angle--
an angle less than a right angle

a. Draw Broadway Street PARALLEL to Main Street. Write the name BROADWAY on this street.

b. Draw Birch Street PERPENDICULAR to Main Street. Write the name BIRCH on this street.

c. Draw Walnut Street so that it INTERSECTS Main Street but is NOT perpendicular to Main Street. Write the name WALNUT on this street.

d. Mark one OBTUSE angle on your drawing with the letter O.

e. Mark one ACUTE angle on your drawing with the letter A.

Geometry and Measurement

Measurement

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• demonstrate the attributes of length, capacity, weight, area, volume, time, temperature, and angle.
• use the process of measuring and the concepts related to units of measurement.
• make and use estimates of measurement.
• measure in everyday problem situations.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• find the perimeter, area, and volume of shapes using diagrams, models, and manipulatives, e.g., fitting smaller congruent boxes into a larger box (volume). [see Questions 39, 43, 45]
• tell time to the nearest minute using analog and digital clocks, and determine elapsed time. [see Question 40]
• select and use non-standard units of measurement. [see Question 41]
• select and use customary (English) units to measure capacity, length, weight, and temperature. [see Question 44]
• select and use metric units to measure capacity, length, weight, and temperature.
• estimate measurements. [see Question 42]
• solve measurement problems. [see Questions 44, 45]

For details and samples of student learning related to these learning standards, see page 73 of The Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

39. Use the picture below to answer the question.

How many more SMALL cubes are needed to complete the LARGE cube above?

*A. 6

B. 5

C. 4

D. 7

40. The fourth grade class is going to the Boston Museum of Science. This is how they will spend their time:

• 1 hour and 15 minutes at the Hayden Planetarium
• 45 minutes for a lunch break
• 1 hour and 45 minutes at the Wildlife Exhibit
• 1 hour and 15 minutes at the Omni Theater

If the class arrives at the museum at 9:00 a.m., what is the EARLIEST time they will leave?

A. 1:00 p.m.

B. 1:15 p.m.

*C. 2:00 p.m.

D. 2:45 p.m.

41. Use the table below to answer the question.

Terry, Karen, and Roberto each correctly measured the width of the same room. Each of them used a measuring stick of a different length.

Whose measuring stick was the LONGEST?

A. Terry's measuring stick

*B. Karen's measuring stick

C. Roberto's measuring stick

D. There is not enough information to tell.

42.

The MOST REASONABLE estimate for the weight of an adult's rocking chair is

A. 12 grams.

*B. 12 kilograms.

C. 120 kilograms.

D. 1200 grams.

43. Evan used centimeter cubes to make a building 6 cm long, 2 cm wide, and 2 cm tall. He uses the same cubes to make a building 2 cm long and 2 cm wide. How tall will his new building be?

A. 2 cm

B. 4 cm

*C. 6 cm

D. 8 cm

Open-response Questions:

44. Use the design below and the inch ruler from your tool kit to answer the question.

Your class has designed a school "patch" for students to wear on their jackets. Its actual size and shape are shown above. The students have volunteered to glue yarn around the edge of each patch.

a. Measure each side of the patch to the nearest 1/2 inch and put your measurement on the line by each letter.

b. How much yarn will be needed for EACH patch? Show or explain your work.

45. The city is building a small park downtown. The park is 40 meters long and 30 meters wide.

There will be a rectangular garden in the park 25 meters long by 20 meters wide. The rest of the park will be paved.

a. Decide where to put the garden area. Shade the garden area on the park grid shown above.

b. What is the area of the garden space in the park? Explain or show how you found your answer.

c. What is the area of the paved space in the park? Explain or show how you found your answer.

40 meters

Statistics and Probability

Curriculum Framework Learning Standards

Students engage in problem solving, communicating, reasoning, and connecting to:

• collect, organize, and describe data.
• construct, read, and interpret displays of data.
• formulate and solve problems that involve collecting and analyzing data.
• explore and describe the concepts of chance.

Assessment Expectations

On the Mathematics section of MCAS, students will be expected to:

• read, describe, analyze, and interpret data presented in charts, tables, bar graphs, circle graphs, line graphs, pictographs, line plots, and tallies.
• draw conclusions and make predictions based on data. [see Question 48]
• identify appropriate ways to display different types of data, e.g., choose the best way to represent a given set of data based on its purpose.
• organize data and construct displays, e.g., tables, charts, tallies, graphs. [see Question 48]
• identify a graph to represent a given set of data. [see Question 46]
• determine the number of possible combinations, e.g., how many combinations of one shirt and one pair of jeans can be made from three shirts and two pairs of jeans?
• determine the chance that a given event will occur, e.g., what are the chances of rolling 3, using a cube with the numbers 1­6? [see Questions 47, 49]

For details and samples of student learning related to these learning standards, see page 88 of the Massachusetts Mathematics Curriculum Framework.

Multiple-choice Questions:

46. Which graph MOST LIKELY shows the average weight of students in three different grades?

A.

*B.

C.

D.

47. Box X has 20 tiles numbered 1 to 20.

Box Y has 50 tiles numbered 1 to 50.

Box Z has 100 tiles numbered 1 to 100.

Mark is going to choose a numbered tile from one of the boxes without looking into the box.
From which box would he have the BEST chance of choosing a tile numbered 15?

*A. Box X

B. Box Y

C. Box Z

D. It doesn't matter which box.

Open-response Questions:

48. The fourth graders in Ms. Chung's class bought some candies that come in small bags. Each student in the class reported how many candies were in his or her bag. Here are the numbers the students reported.

a. Make a table or an organized list that shows the data above.

b. Ms. Chung also bought a small bag of candies from the same place. Based on the numbers of candies in the students' bags, how many candies do you think are in her bag? Explain the reasons for your answer.

49. Barbara made a spinner using each letter in her name. It looked like this:

a. Barbara spins her spinner. Is there an equal chance of the spinner landing on the letters B, A, and R? Explain your thinking.

Debby also made a spinner for her name that looked like this:

b. Debby and Barbara are going to spin their spinners to try to land on a B. Does Debby have a GREATER, LESSER, or EQUAL chance to spin a B than Barbara? Explain how you know.

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