# Making Lemonade

Mary wants to make a small glass of lemonade and a large glass of lemonade. Mary needs the juice of four lemons to make a small glass of lemonade. Mary needs the juice of eight lemons to make a large glass of lemonade. Mary has fourteen lemons. Does Mary have enough lemons to make the two glasses of lemonade? Show all your mathematical thinking.

## 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 frames, graph paper, etc. as they work on a task.

### Possible Solutions

## Solutions tabs

### Assess

### Anchor Papers

#### Novice 1

### Scoring Rationale

#### Problem Solving

#### Novice

The student's strategy of using a diagram to represent four, eight, and fourteen lemons, and adding all the lemons, does not work to solve the task. The student's answer, "26 lemons," is not correct.

#### Reasoning & Proof

#### Apprentice

The student shows some correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass. The student does not understand that the sum of four and eight lemons should be compared to fourteen lemons.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *diagram*.

#### Connections

#### Novice

The student does not make a mathematically relevant observation.

#### Representation

#### Apprentice

The student's diagram is appropriate to part of the task but is not accurate. The student diagrams an additional fourteen lemons, which does not support a correct answer. The student defines the lemons in the scribing.

#### Overall Achievement Level:

#### Novice

#### Apprentice 1

### Scoring Rationale

#### Problem Solving

#### Apprentice

The student's strategy of using a diagram to record how many lemons are needed to make a small and a large glass of lemonade, finding a total of lemons and comparing that total to Mary's fourteen lemons, would work to solve the task. But, the student diagrams an extra lemon in the large glass of lemonade. The student's answer, "Yes," is not correct because it is based on incorrect data.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass, finding the total number of lemons needed, and comparing that total to fourteen lemons. The student diagrams nine lemons in the large glass which leads to an incorrect total of thirteen lemons to compare to Mary's total of fourteen lemons. This is considered a careless error and not a flaw in the student's reasoning.

#### Communication

#### Practitioner

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

#### Connections

#### Apprentice

The student attempts to make a mathematically relevant observation, but it is based on an incorrect diagram. The student states, "Mary has one extra lemon because fourteen comes after thirteen." The correct connection is two extra lemons.

#### Representation

#### Apprentice

The student's diagram is appropriate to the task, but is not accurate. The student diagrams an extra lemon in the large glass. A key defines the lemons and glasses.

#### Overall Achievement Level:

#### Apprentice

#### Apprentice 2

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a diagram to record how many lemons are needed to make a small and a large glass of lemonade, computing a total of twelve lemons, and comparing that total to fourteen lemons works to solve the task. The student's answer, "Yes," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass, addition to find the total number of lemons needed, and comparing that total to fourteen lemons.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *diagram*.

#### Connections

#### Novice

The student does not make a mathematically relevant observation about her/his solution.

#### Representation

#### Practitioner

The student's diagram is appropriate to the task and accurate. The student's text and scribing defines the lemons.

#### 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 using a diagram to record how many lemons are needed to make a small and large glass of lemonade, and if Mary has enough lemons works to solve the task. The student's answer, "so Yes," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass, using addition to find the total number of lemons needed, and comparing that total to fourteen lemons.

#### Communication

#### Practitioner

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

#### Connections

#### Practitioner

The student makes the mathematically relevant observations, "2 lemons left over," and, "12 is a dozen."

#### Representation

#### Practitioner

The student's diagram is appropriate to the task and accurate. A key defines the lemons and glasses.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 2

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a tally chart to record how many lemons are needed to make a small and large glass of lemonade, and comparing that total to Mary's fourteen lemons works to solve the task. The student's answer, "Yes," is correct.

#### Reasoning & Proof

#### Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass, using addition to find the total number of lemons needed, and comparing that total to fourteen lemons.

#### Communication

#### Practitioner

The student correctly uses the mathematical term *small* from the task. The student also correctly uses the terms *tally chart*, *dozen*, *tally mark*.

#### Connections

#### Practitioner

The student makes the mathematically relevant observations, "12 is a dozen," and, "2 lemons left."

#### Representation

#### Practitioner

The student's tally chart is appropriate to the task and accurate. All labels are provided and the data is correct.

Note: A key is not necessary if a tally mark represents one.

#### Overall Achievement Level:

#### Practitioner

#### Expert 1

### Scoring Rationale

#### Problem Solving

#### Expert

The student's strategy of using a diagram of four lemons for a small glass and eight lemons for a large glass to find a total of twelve lemons to compare to fourteen lemons works to solve the task. The student's answer, "Yes," is correct. The student verifies her/his answer by using more strategies. The student also brings the concept of half to the problem.

#### Reasoning & Proof

#### Expert

The student shows correct reasoning of the underlying concepts of the task. The student demonstrates understanding of four lemons to one glass, eight lemons to one glass, finding the total number of lemons needed using addition, and comparing that total to fourteen lemons. The student uses conceptual understanding of subtraction and less than to verify her/his answer is correct.

#### Communication

#### Expert

The student correctly uses the mathematical terms *diagram*, *key*, *half*, *dozen*, *pair*, *more*, *less*, *number line*. The student correctly uses the mathematical notation "<".

#### Connections

#### Expert

The student makes the mathematically relevant Practitioner observations, "dozen is 12," "pair is 2 [lemons]," "4-more," "8-less," and, "2 [lemons] left." The student makes the Expert observations, "half 8 [lemons] is 4 [lemons]," and, "12 < 14." The student verifies her/his answer by using a second diagram to count back four and eight lemons, subtraction equations to show the two remaining lemons, a number line using an addition jump of four lemons and then eight individual lemons for a total of twelve lemons. The student states, "I found my answer lots of times. I got yes for enough lemons all the time." The student writes, "I am right."

#### Representation

#### Expert

The student's first and second diagrams are appropriate to the task and accurate. All labels are provided and a key defines the lemons. The student's number line is also appropriate and accurate with all labels included. The student links the representation to verify that her is answer is correct.