# Drawing Animal Pictures

Ryan is drawing ten pictures of animals to put on his bedroom door. Ryan has finished drawing five animal pictures. How many more animal pictures does Ryan have to draw? Show and tell how you know.

## Plan

#### Underlying Mathematical Concepts

#### Possible Problem-Solving Strategies

#### Formal Mathematical Language and Symbolic Notation

A student may independently select a printed number line, number chart, ten frame, graph paper, etc. as they work on a task.

### Suggested materials

Engagement Image:

Teachers may project the image below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving.

### Possible Solutions

## Solutions tabs

### Assess

### Anchor Papers

#### Novice 1

### Scoring Rationale

#### Problem Solving

#### Apprentice

The student's strategy of diagramming the five pictures needed to be completed works to solve the first part of the task. The student's answer, "He has 5 on the door," is not correct.

#### Reasoning & Proof

#### Apprentice

The student shows correct reasoning of the underlying concept of five completed pictures. The student does not diagram the pictures that need to be completed.

#### Communication

#### Novice

The student does not use any mathematical language.

#### Connections

#### Novice

The student does not make any mathematically relevant observation about their solution.

#### Representation

#### Apprentice

The student's diagram of the five completed pictures is appropriate and accurate to the first part of the task. The student defines the five pictures and the drawing on the first picture in the scribing. The student does not diagram the pictures that need to be completed.

#### Overall Achievement Level:

#### Novice

#### Apprentice 1

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of diagramming the five complete pictures and the five pictures needed to be completed on the door works to solve the task. The student's answer, "5 more," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student diagrams the completed pictures, the pictures needed to be completed, and compares the two totals to determine that five pictures need to be completed.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *more*.

#### Connections

#### Novice

The student does not make a mathematically relevant observation about their solution.

#### Representation

#### Practitioner

The student's diagram of the five completed pictures and the five pictures needed to be completed on a door is appropriate and accurate to the task. The student's scribing defines the door, finished pictures and pictures needed to be drawn.

#### Overall Achievement Level:

#### Apprentice

The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in "Connections," the student may still receive an achievement level score of Apprentice. To learn more about Exemplars scoring, please refer to the section of your dashboard called "Tools for Success" and click on the link for “Using the Assessment Rubric.”

#### Apprentice 2

### Scoring Rationale

#### Problem Solving

#### Apprentice

The student's strategy of diagramming pictures would work to solve the task, but the student omits the 10th picture. The student's answer, "4," is not correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student diagrams the completed pictures, the pictures needed to be completed, and compares the two totals to determine that four pictures need to be completed. The student makes an error in leaving out picture number 10. This is not considered a lack of reasoning but a careless counting error.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms *diagram*, *key*.

#### Connections

#### Novice

The student does not make any mathematically relevant observation about their solution.

#### Representation

#### Apprentice

The student's diagram of the five completed pictures and four pictures needed to be completed is appropriate to the task but is not accurate. The 10th picture is not indicated. The student's key and scribing defines the finished pictures and pictures needed to be drawn.

#### Overall Achievement Level:

#### Apprentice

The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in "Connections," the student may still receive an achievement level score of Apprentice. To learn more about Exemplars scoring, please refer to the section of your dashboard called "Tools for Success" and click on the link for “Using the Assessment Rubric.”

#### Apprentice 3

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of diagramming the five completed pictures on the door and diagramming all 10 pictures with five crossed out works to solve the task. The student's answer, "5," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student diagrams the completed pictures, the pictures needed to be completed and compares the two totals to determine that five pictures need to be completed.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *diagram*.

#### Connections

#### Novice

The student does not make any mathematically relevant observation about their solution.

#### Representation

#### Practitioner

The student's diagram of the five completed pictures on a door and the 10 pictures with five crossed out is appropriate and accurate to the task. The student's scribing defines the door, finished pictures and pictures needed to be drawn.

#### Overall Achievement Level:

#### Apprentice

The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in "Connections," the student may still receive an achievement level score of Apprentice. To learn more about Exemplars scoring, please refer to the section of your dashboard called "Tools for Success" and click on the link for “Using the Assessment Rubric.”

#### Practitioner 1

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of diagramming the five completed pictures and the five pictures needed to be drawn works to solve the task. The student's answer, "5," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student diagrams the completed pictures, the pictures needed to be completed and compares the two totals to determine that five pictures need to be completed.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms *diagram*, *key*.

#### Connections

#### Practitioner

The student makes the mathematically relevant observation, "It is the same, 5 done, 5 to do, That is what I see."

#### Representation

#### Practitioner

The student's diagram of the five completed pictures and the five pictures needed to be drawn is appropriate to the task and accurate. The student's key and scribing defines the drawn pictures and the pictures not drawn.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 2

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a tally chart to show the five completed pictures and the five pictures needed to be drawn works to solve the task. The student's answer, "5 more," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student tallies the completed pictures, the pictures needed to be completed, and compares the two totals to determine that five pictures need to be completed.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms "tallys," *(tally chart)*, *more*, *amount*.

#### Connections

#### Practitioner

The student makes the mathematically relevant observation, "I see Ryan has the same amount of pictures finished and to draw." The student also describes how a tally works, "You go 1, 2, 3, 4 then the sideways tally for 5."

#### Representation

#### Practitioner

The student's tally chart of the five finished pictures and the five unfinished pictures needed to be drawn is appropriate to the task and accurate.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 3

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a number line to show the five completed pictures and the five pictures that still need to be drawn works to solve the task. The student's answer, "5 more," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student jumps the five completed pictures. The student understands that they need to count on from five to find that there are five more pictures to draw.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms *number line*, *more*, *diagram*.

#### Connections

#### Practitioner

The student uses a new strategy of a diagram to show the five finished drawings and states, "He has to do those 5 more for 6, 7, 8, 9, 10 pictures. Then he will be all done." The student does not earn the Expert level because they did not compare the two strategies to confirm that the answer is correct.

#### Representation

#### Practitioner

The student's number line is appropriate to the task. The numbers are labeled and the "jumps" are accurate. The student's diagram is appropriate to the task. The scribing provides the necessary labels for the completed pictures.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 4

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a ten frame to show the five completed pictures and the five pictures needed to be drawn works to solve the task. The student's answer, "5," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student uses circles for the five finished pictures. The student understands that five and five more is ten.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms *ten frame*, *more*, *number*.

#### Connections

#### Practitioner

The student makes a mathematically relevant observation about their solution. The student states, "Look, Ryan has the same picture number done and to draw. That is 5 and 5 for 10 pictures."

#### Representation

#### Practitioner

The student's ten frame is appropriate to the task. The student defines the circles as pictures in their scribing.

#### Overall Achievement Level:

#### Practitioner

#### Expert 1

### Scoring Rationale

#### Problem Solving

#### Expert

The student's strategy of using a diagram to show the number of completed pictures on the door and the number of pictures needed to be completed works to solve the task. The student's answer, "5 more to Do," is correct. The student also verifies that their answer is correct.

#### Reasoning & Proof

#### Expert

The student shows correct reasoning of the underlying concepts of the task. The student diagrams the completed pictures, the pictures needed to be completed and compares the two totals to determine that five pictures need to be completed. The student also uses a tally to compare the completed and need to be completed pictures. The student also brings the concepts of odd, even, and one-half to the task.

#### Communication

#### Expert

The student correctly uses the mathematical terms *diagram*, *key*, *even*, *odd*, *tally*, *equals*, *more*. The student also uses the mathematical notation, "1/2."

#### Connections

#### Expert

The student makes mathematically relevant Expert observations: "10-even, ten pictures is even number," "5-odd, 5 pictures is odd number," "1/2 of the pictures are done but 1/2 are not done." The student uses a tally to verify that their diagram is correct and states, "5 + 5 = 10, five are done, five more to do equals ten in all for pictures," "5 more to Do," "You always got to do five more pictures."

#### Representation

#### Expert

The student's diagram of the five completed pictures on the door and the five pictures needed to be drawn is appropriate to the task and accurate. The student's key and scribing defines the paper, animal pictures and door. The student creates an accurate tally using their key to verify that five more pictures need to be drawn.