3B · Chapter 9 · exam
Chapter practice examination
Original untimed practice examination. Not a secure or official placement test.
Original untimed practice examination. Not a secure or official placement test. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.
Assessment · 24 questions
Questions
Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.
- A1
A student answers the following question with “>”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compare 4/10 and 5/10. Write > or <. (3 points)
Reveal explanation
Answer: <
The suggested answer is not correct. Both fractions use pieces of size 1/10, so compare 4 pieces with 5 pieces: 4/10 < 5/10.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A2
A same-sized whole is split into 8 equal parts and 2 parts are shaded. What fraction is shaded? (2 points)
Reveal explanation
Answer: 1/4
The denominator counts all 8 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 1/4.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A3
Compare 7/8 and 5/8. Write > or <. (2 points)
Reveal explanation
Answer: >
Both fractions use pieces of size 1/8, so compare 7 pieces with 5 pieces: 7/8 > 5/8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A4
Compare 1/4 and 1/8. Write > or <. (2 points)
Reveal explanation
Answer: >
There are 1 pieces in each fraction, but 1/4 is a larger piece than 1/8 when the whole is identical.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A5
A student answers the following question with “2/2”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Between 0 and 1, a line is split into 4 equal intervals. What fraction is at the 2nd tick after 0? (3 points)
Reveal explanation
Answer: 1/2
The suggested answer is not correct. Each interval represents 1/4. Moving 2 intervals from zero reaches 2/4, or 1/2 in simplest form.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
An interval from zero to one divided into equal segments. - A6
A same-sized whole is split into 6 equal parts and 2 parts are shaded. What fraction is shaded? (2 points)
Reveal explanation
Answer: 1/3
The denominator counts all 6 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 1/3.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A7
Compare 8/12 and 7/12. Write > or <. (2 points)
Reveal explanation
Answer: >
Both fractions use pieces of size 1/12, so compare 8 pieces with 7 pieces: 8/12 > 7/12.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A8
Compare 5/8 and 1/8. Write > or <. (2 points)
Reveal explanation
Answer: >
Both fractions use pieces of size 1/8, so compare 5 pieces with 1 pieces: 5/8 > 1/8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A9
A student answers the following question with “4/5”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Between 0 and 1, a line is split into 10 equal intervals. What fraction is at the 6th tick after 0? (3 points)
Reveal explanation
Answer: 3/5
The suggested answer is not correct. Each interval represents 1/10. Moving 6 intervals from zero reaches 6/10, or 3/5 in simplest form.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
An interval from zero to one divided into equal segments. - A10
Between 0 and 1, a line is split into 12 equal intervals. What fraction is at the 6th tick after 0? (2 points)
Reveal explanation
Answer: 1/2
Each interval represents 1/12. Moving 6 intervals from zero reaches 6/12, or 1/2 in simplest form.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
An interval from zero to one divided into equal segments. - A11
A same-sized whole is split into 8 equal parts and 5 parts are shaded. What fraction is shaded? (2 points)
Reveal explanation
Answer: 5/8
The denominator counts all 8 equal parts; the numerator counts the 5 shaded parts. In simplest form this is 5/8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A12
Compare 4/12 and 4/8. Write > or <. (2 points)
Reveal explanation
Answer: <
There are 4 pieces in each fraction, but 1/8 is a larger piece than 1/12 when the whole is identical.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A13
A student answers the following question with “>”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compare 3/8 and 7/8. Write > or <. (3 points)
Reveal explanation
Answer: <
The suggested answer is not correct. Both fractions use pieces of size 1/8, so compare 3 pieces with 7 pieces: 3/8 < 7/8.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A14
Compare 2/10 and 2/6. Write > or <. (2 points)
Reveal explanation
Answer: <
There are 2 pieces in each fraction, but 1/6 is a larger piece than 1/10 when the whole is identical.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A15
Compare 1/6 and 1/8. Write > or <. (2 points)
Reveal explanation
Answer: >
There are 1 pieces in each fraction, but 1/6 is a larger piece than 1/8 when the whole is identical.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A16
A same-sized whole is split into 12 equal parts and 11 parts are shaded. What fraction is shaded? (2 points)
Reveal explanation
Answer: 11/12
The denominator counts all 12 equal parts; the numerator counts the 11 shaded parts. In simplest form this is 11/12.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A17
A student answers the following question with “>”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compare 5/10 and 5/6. Write > or <. (3 points)
Reveal explanation
Answer: <
The suggested answer is not correct. There are 5 pieces in each fraction, but 1/6 is a larger piece than 1/10 when the whole is identical.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A18
A same-sized whole is split into 8 equal parts and 6 parts are shaded. What fraction is shaded? (2 points)
Reveal explanation
Answer: 3/4
The denominator counts all 8 equal parts; the numerator counts the 6 shaded parts. In simplest form this is 3/4.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A19
Between 0 and 1, a line is split into 6 equal intervals. What fraction is at the 5th tick after 0? (2 points)
Reveal explanation
Answer: 5/6
Each interval represents 1/6. Moving 5 intervals from zero reaches 5/6, or 5/6 in simplest form.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
An interval from zero to one divided into equal segments. - A20
Compare 3/6 and 3/10. Write > or <. (2 points)
Reveal explanation
Answer: >
There are 3 pieces in each fraction, but 1/6 is a larger piece than 1/10 when the whole is identical.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A21
A student answers the following question with “4/4”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Between 0 and 1, a line is split into 4 equal intervals. What fraction is at the 3rd tick after 0? (3 points)
Reveal explanation
Answer: 3/4
The suggested answer is not correct. Each interval represents 1/4. Moving 3 intervals from zero reaches 3/4, or 3/4 in simplest form.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
An interval from zero to one divided into equal segments. - A22
Between 0 and 1, a line is split into 10 equal intervals. What fraction is at the 7th tick after 0? (2 points)
Reveal explanation
Answer: 7/10
Each interval represents 1/10. Moving 7 intervals from zero reaches 7/10, or 7/10 in simplest form.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
An interval from zero to one divided into equal segments. - A23
A student marks 1/8 at the first tick on a 0-to-1 line but drew only 7 equal intervals. Explain and correct the model. (3 points)
Reveal explanation
Answer: 8 equal intervals
To show 1/8, the full unit length must be divided into 8 equal intervals, not 7.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.
- A24
A ribbon is split into 8 equal pieces; 6 are colored. Another ribbon is twice as long but also has 6 colored of 8 equal pieces. Are the colored lengths equal? (3 points)
Reveal explanation
Answer: No
Equal fractions of differently sized wholes need not represent equal physical lengths.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.