Grade 9 Assessment of Mathematics

2015, Academic

Released Item-Specific Rubrics and Sample Student Responses with Annotations

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Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

More Snacks, Please!

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Application of knowledge and skills to determine the mass of raisins in a 250g package using ratios, rates or proportions shows limited effectiveness due to

� misunderstanding of concepts;

� incorrect selection or misuse of procedures.

20

Application of knowledge and skills to determine the mass of raisins in a 250g package using ratios, rates or proportions shows some effectiveness due to

� partial understanding of the concepts;

� errors and/or omissions in the application of the procedures.

30

Application of knowledge and skills to determine the mass of raisins in a 250g package using ratios, rates or proportions shows considerable effectiveness due to

� an understanding of most of the concepts;

� minor errors and/or omissions in the application of the procedures.

40

Application of knowledge and skills to determine the mass of raisins in a 250g package using ratios, rates or proportions shows a high degree of effectiveness due to

� a thorough understanding of the concepts;

� an accurate application of the procedures (any minor errors and/or omissions do not detract from the demonstration of a thorough understanding).

Anchor - Code 10

Academic (Question 12) Item: More Snacks, Please!

Annotation:Response demonstrates a misunderstanding of concepts; number of parts (8) and portion of raisins not determined, and only divides by 3 and/or 5 with no multiplying.

Anchor - Code 20

Academic (Question 12) Item: More Snacks, Please!

Annotation:Response demonstrates a partial understanding of the concepts; number of parts not determined (8), but uses a proportion of raisins (3/5) and correctly determines the mass of raisins based on this ratio (multiplies and divides to determine 150 g).

Anchor - Code 30

Academic (Question 12) Item: More Snacks, Please!

Annotation:Response demonstrates an omission in the application of the procedures; correctly determined number of parts (8) and divided by 8 to determine the mass per part (31.25 g), but total mass of raisins not determined (no multiplying by 3).

Anchor - Code 40

Academic (Question 12) Item: More Snacks, Please!

Annotation:Response demonstrates an accurate application of the procedures; correctly determined number of parts (8), portion of raisins (3/8) and mass of raisins (95 g). Rounding 37.5% to 38% does not detract from a thorough understanding.

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

Getting Fit

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Application of knowledge and skills to determine the sign-up fee and the type of variation with justication shows limited effectiveness due to

� misunderstanding of concepts;

� incorrect selection or misuse of procedures.

20

Application of knowledge and skills to determine the sign-up fee and the type of variation with justication shows some effectiveness due to

� partial understanding of the concepts;

� errors and/or omissions in the application of the procedures.

30

Application of knowledge and skills to determine the sign-up fee and the type of variation with justication shows considerable effectiveness due to

� an understanding of most of the concepts;

� minor errors and/or omissions in the application of the procedures.

40

Application of knowledge and skills to determine the sign-up fee and the type of variation with justication shows a high degree of effectiveness due to

� a thorough understanding of the concepts;

� an accurate application of the procedures (any minor errors and/or omissions do not detract from the demonstration of a thorough understanding).

Anchor - Code 10

Academic (Question 13) Item: Getting Fit

Annotation:Response demonstrates a misunderstanding of concepts; a difference of 7 is calculated and used to calculate the rate per class but initial value not determined and direct variation circled incorrectly with justification that does not reference sign-up fee/origin.

Anchor - Code 20

Academic (Question 13) Item: Getting Fit

Annotation:Response demonstrates errors in the application of the procedures; sign-up fee determined incorrectly as treated as direct variation but partial variation circled correctly and justification references sign-up fee (start fee). Note: difference (7) calculated but not used to determine rate or sign-up fee.

Anchor - Code 30

Academic (Question 13) Item: Getting Fit

Annotation:Response demonstrates a minor omission in the application of the procedures; a difference calculated (7) and used to determine the rate per class (3.50) but sign-up fee not determined correctly. Partial variation circled correctly and justification references sign-up fee (fixed cost of $3.50 and $3.50 identified as sign-up fee).

Anchor - Code 40

Academic (Question 13) Item: Getting Fit

Annotation:Response demonstrates a thorough understanding of the concepts; a difference calculated (7) and used to determine sign-up fee correctly. Partial variation circled and justification references sign-up fee/origin.

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

Kenny’s Big Adventure

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Problem-solving process used to describe the 3 segments of Kenny’s ride including distance travelled, time, direction and speed in km/min shows limited effectiveness due to

� minimal evidence of a solution process;

� limited identification of important elements of the problem;

� too much emphasis on unimportant elements of the problem;

� no conclusions presented or conclusion presented without supporting evidence.

20

Problem-solving process used to describe the 3 segments of Kenny’s ride including distance travelled, time, direction and speed in km/min shows some effectiveness due to

� an incomplete solution process;

� identification of some of the important elements of the problem;

� some understanding of the relationships between important elements of the problem;

� simple conclusions with little supporting evidence.

30

Problem-solving process used to describe the 3 segments of Kenny’s ride including distance travelled, time, direction and speed in km/min shows considerable effectiveness due to

� a solution process that is nearly complete;

� identification of most of the important elements of the problem;

� a considerable understanding of the relationships between important elements of the problem;

� appropriate conclusions with supporting evidence.

40

Problem-solving process used to describe the 3 segments of Kenny’s ride including distance travelled, time, direction and speed in km/min shows a high degree of effectiveness due to

� a complete solution process;

� identification of all important elements of the problem;

� a thorough understanding of the relationships between all of the important elements of the problem;

� appropriate conclusions with thorough and insightful supporting evidence.

Anchor - Code 10

Academic (Question 14) Item: Kenny’s Big Adventure

Annotation:Response demonstrates a limited identification of important elements of the problem; less than 6 correct as distance for a and times for all correct only.

Anchor - Code 20

Academic (Question 14) Item: Kenny’s Big Adventure

Annotation:Response demonstrates an identification of some of the important elements of the problem; at least 6 of all the distances, times, directions and/or speeds correct (incorrect time for b and incorrect speeds for a and c and not based on distance/time as calculated time/distance).

Anchor - Code 30

Academic (Question 14) Item: Kenny’s Big Adventure

Annotation:Response demonstrates an identification of most of the important elements of the problem; up to 2 errors (speeds not in km per 1 min for segment a and c), but all the rest of the distances, times, directions and speed (speed for b is acceptable as 0 km in 15 min) are correct.

Anchor - Code 40

Academic (Question 14) Item: Kenny’s Big Adventure

Annotation:Response demonstrates a thorough understanding of the relationships between all of the important elements of the problem; all distances, times, directions and speeds correct for all segments.

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

Comparing Relationships

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Application of knowledge and skills to determine which of three linear relationships have equivalent rates of change with justification shows limited effectiveness due to

� misunderstanding of concepts;

� incorrect selection or misuse of procedures.

20

Application of knowledge and skills to determine which of three linear relationships have equivalent rates of change with justification shows some effectiveness due to

� partial understanding of the concepts;

� errors and/or omissions in the application of the procedures.

30

Application of knowledge and skills to determine which of three linear relationships have equivalent rates of change with justification shows considerable effectiveness due to

� an understanding of most of the concepts;

� minor errors and/or omissions in the application of the procedures.

40

Application of knowledge and skills to determine which of three linear relationships have equivalent rates of change with justification shows a high degree of effectiveness due to

� a thorough understanding of the concepts;

� an accurate application of the procedures (any minor errors and/or omissions do not detract from the demonstration of a thorough understanding).

Anchor - Code 10

Academic (Question 15) Item: Comparing Relationships

Annotation:Response demonstrates a misunderstanding of the concepts; rates not determined correctly for any of the relationships and insufficient support for relationships circled as rates missing and incorrectly states rates of change are negative for Relationships 1 and 3.

Anchor - Code 20

Academic (Question 15) Item: Comparing Relationships

Annotation:Response demonstrates an error and omission in the application of the procedures; rate determined correctly for one (or none) of the relationships (Relationship 2 is incorrect and 3 is omitted), and Relationships 1 and 2 stated as equal based on errors.

Anchor - Code 30

Academic (Question 15) Item: Comparing Relationships

Annotation:Reponse demonstrates a minor omission in the application of the procedures; rates determined correctly for at least two relationships (rate for Relationship 2 is omitted), and Relationship 1 and 3 circled correctly.

Anchor - Code 40

Academic (Question 15) Item: Comparing Relationships

Annotation:Response demonstrates an accurate application of the procedures; rates determined correctly for all three relationships and Relationship 1 and 3 circled correctly. Rate for Relationship 2 is not in lowest terms and does not detract from a thorough understanding.

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

Making Equations!

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Problem-solving process used to determine the equation of the line with the same y-intercept as a given line and perpendicular to the line shown on the grid shows limited effectiveness due to

� minimal evidence of a solution process;

� limited identification of important elements of the problem;

� too much emphasis on unimportant elements of the problem;

� no conclusions presented or conclusion presented without supporting evidence.

20

Problem-solving process used to determine the equation of the line with the same y-intercept as a given line and perpendicular to the line shown on the grid shows some effectiveness due to

� an incomplete solution process;

� identification of some of the important elements of the problem;

� some understanding of the relationships between important elements of the problem;

� simple conclusions with little supporting evidence.

30

Problem-solving process used to determine the equation of the line with the same y-intercept as a given line and perpendicular to the line shown on the grid shows considerable effectiveness due to

� a solution process that is nearly complete;

� identification of most of the important elements of the problem;

� a considerable understanding of the relationships between important elements of the problem;

� appropriate conclusions with supporting evidence.

40

Problem-solving process used to determine the equation of the line with the same y-intercept as a given line and perpendicular to the line shown on the grid shows a high degree of effectiveness due to

� a complete solution process;

� identification of all important elements of the problem;

� a thorough understanding of the relationships between all of the important elements of the problem;

� appropriate conclusions with thorough and insightful supporting evidence.

Anchor - Code 10

Academic (Question 16) Item: Making Equations!

Annotation:Response demonstrates a limited identification of important elements of the problem; correctly determined y-intercept (-6), but no evidence of determining slope of given line (2/3 not on page) or attempting to change slope (negative or reciprocal).

Anchor - Code 20

Academic (Question 16) Item: Making Equations!

Annotation:Response demonstrates some understanding of the relationships between important elements of the problem; one step missing as no evidence of determining slope of perpendicular line, but correctly determined slope of given line (2/3) and y-intercept (-6) determined, with or without equation of line.

Anchor - Code 30

Academic (Question 16) Item: Making Equations!

Annotation:Response demonstrates an identification of most of the important elements of the problem; one error in process as correctly determined slope of given line (2/3), correct y-intercept determined (-6), attempts to determine slope of perpendicular line (reciprocal and/or negative determined) with minor error (only reciprocal OR only negative) and equation of line determined based on error.

Anchor - Code 40

Academic (Question 16) Item: Making Equations!

Annotation:Response demonstrates an identification of all important elements of the problem; correctly determined slope of given line (2/3), slope of perpendicular line (-3/2), y-intercept (-6) and equation of perpendicular line. Note: slope of -6/4 equivalent to -3/2.

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

Skate On!

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Problem-solving process used to determine the perimeter of the composite shape and the total cost of fencing shows limited effectiveness due to

� minimal evidence of a solution process;

� limited identification of important elements of the problem;

� too much emphasis on unimportant elements of the problem;

� no conclusions presented or conclusion presented without supporting evidence.

20

Problem-solving process used to determine the perimeter of the composite shape and the total cost of fencing shows some effectiveness due to

� an incomplete solution process;

� identification of some of the important elements of the problem;

� some understanding of the relationships between important elements of the problem;

� simple conclusions with little supporting evidence.

30

Problem-solving process used to determine the perimeter of the composite shape and the total cost of fencing shows considerable effectiveness due to

� a solution process that is nearly complete;

� identification of most of the important elements of the problem;

� a considerable understanding of the relationships between important elements of the problem;

� appropriate conclusions with supporting evidence.

40

Problem-solving process used to determine the perimeter of the composite shape and the total cost of fencing shows a high degree of effectiveness due to

� a complete solution process;

� identification of all important elements of the problem;

� a thorough understanding of the relationships between all of the important elements of the problem;

� appropriate conclusions with thorough and insightful supporting evidence.

Anchor - Code 10

Academic (Question 17) Item: Skate On!

Annotation:Response demonstrates a limited identification of important elements of the problem; perimeter of only one part (semicircle or any rectangle) determined correctly (area determined incorrectly for rectangle with incorrect width) but values not added and cost not determined (no multiplying by 6.20).

Anchor - Code 20

Academic (Question 17) Item: Skate On!

Annotation:Response demonstrates an identification of some of the important elements of the problem; errors in determining perimeter (extra side (26) added, length of unknown side (48) not determined and circumference not divided by 2) but circumference of circle and sides of rectangle added. Cost not determined.

Anchor - Code 30

Academic (Question 17) Item: Skate On!

Annotation:Response demonstrates a considerable understanding of the relationship between important elements of the problem; errors determining perimeter (extra side (26) added and length of unknown side (48) not determined as used 61) but correctly determined circumference of semicircle and added sides of rectangle. Cost determined correctly based on these errors (multiplied by 6.20).

Anchor - Code 40

Academic (Question 17) Item: Skate On!

Annotation:Response demonstrates an identification of all important elements of the problem; perimeter determined correctly (circumference of semicircle (41) and 3 sides of rectangle (48, 48, 26) determined correctly and added). Cost determined correctly (multiplied by 6.20).

Assessment of Mathematics

Grade 9 Academic Program

Specific Open-Response Scoring Guide

A Schoolyard

Code Descriptor

B Blank: nothing written or drawn in response to the question

I

- Illegible: cannot be read; completely crossed out/erased; not written in English;- Irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings, “?”, “!”, “I don’t know”);- Off topic: no relationship of written work to the question.

10

Application of knowledge and skills used to determine the values of x and y with justification using geometric properties including the interior/exterior angles of a polygon shows limited effectiveness due to

� misunderstanding of concepts;

� incorrect selection or misuse of procedures.

20

Application of knowledge and skills used to determine the values of x and y with justification using geometric properties including the interior/exterior angles of a polygon shows some effectiveness due to

� partial understanding of the concepts;

� errors and/or omissions in the application of the procedures.

30

Application of knowledge and skills used to determine the values of x and y with justification using geometric properties including the interior/exterior angles of a polygon shows considerable effectiveness due to

� an understanding of most of the concepts;

� minor errors and/or omissions in the application of the procedures.

40

Application of knowledge and skills used to determine the values of x and y with justification using geometric properties including the interior/exterior angles of a polygon shows a high degree of effectiveness due to

� a thorough understanding of the concepts;

� an accurate application of the procedures (any minor errors and/or omissions do not detract from the demonstration of a thorough understanding).

Anchor - Code 10

Academic (Question 18) Item: A Schoolyard

Annotation:Response demonstrates a misunderstanding of concepts; values of x and y are incorrect and value of x is incorrect based on the value of y. Justification shows incorrect sum used for decagon and process incomplete for determining x.

Anchor - Code 20

Academic (Question 18) Item: A Schoolyard

Annotation:Response demonstrates a partial understanding of the concepts; value of y is correct with justification (sum of angles in decagon and dividing by 10), but value of x is incorrect and justification does not connect value of y to x.

Anchor - Code 30

Academic (Question 18) Item: A Schoolyard

Annotation:Response demonstrates an omission in the application of the procedures; value of y is correct with justification (sum of angles in decagon or divided by 10) and value of x is incorrect but supplement of y determined. Omitted sum of angles in triangle.

Anchor - Code 40

Academic (Question 18) Item: A Schoolyard

Annotation:Response demonstrates a thorough understanding of the concepts; values of x and y are correct with justification (sum of angles in decagon 1440 and/or dividing by 10, supplementary angles and sum of angles in triangle).