# Gingerbread Men

Gina is making six gingerbread men. Gina needs raisins for each gingerbread man's eyes. How many raisins does Gina need to make six gingerbread men? 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, five frames, ten frames, place value strips, 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

#### Novice

The student's strategy of drawing only one gingerbread man and themselves does not work to solve the task.

#### Reasoning & Proof

#### Novice

The student's solution does not demonstrate understanding of the underlying mathematics of the task. The student does not indicate Gina's six gingerbread men and a total of 12 raisins for eyes.

#### Communication

#### Novice

The student is not given credit for the mathematical term *diagram*. The student is drawing a picture of his gingerbread man and themselves. The scribing supports that the student is not addressing Gina's six gingerbread men.

#### Connections

#### Novice

The student does not include a connection in their solution.

#### Representation

#### Novice

The student does not provide any representation to support the underlying mathematics in the task.

#### Overall Achievement Level:

#### Novice

#### Novice 2

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of making a diagram of six gingerbread men with 12 raisin eyes works to solve the task. The student indicates a correct answer, "12," and states, "This is my answer, 12 raisins." A student will often use the letter "A" to represent the word *answer*.

#### Reasoning & Proof

#### Practitioner

The student's diagram is adequate and systematic to support their reasoning and proof.

#### Communication

#### Novice

The student does not use any mathematical language in their solution.

#### Connections

#### Novice

The student does not include a connection in their solution.

#### Representation

#### Practitioner

The student's diagram is appropriate and accurate. Necessary labels for gingerbread man and raisins are provided in the scribing.

#### Overall Achievement Level:

#### Novice

#### Apprentice 1

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of making a diagram of six gingerbread men and using 12 raisins for eyes works to solve the task. The student states a correct answer,"Gina has 12 raisins."

#### Reasoning & Proof

#### Practitioner

The student's diagram is adequate and systematic to support their reasoning and proof.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *diagram*.

#### Connections

#### Novice

The student does not include a connection in their solution. The comment, "I do not like raisins," is not mathematically relevant and cannot be considered an attempt at a mathematical connection.

#### Representation

#### Practitioner

The student's diagram is appropriate and accurate. Necessary labels for gingerbread "people" and raisins are provided in the scribing.

#### 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

#### Practitioner

The student's strategy of making a diagram of six gingerbread men with 12 raisin eyes works to solve the task. The student states a correct answer, "12 raisins." Students often put a circle around an "A" to indicate the word *answer*.

#### Reasoning & Proof

#### Practitioner

The student's diagram is adequate and systematic to support their reasoning and proof. A key and scribing is provided to define the gingerbread men and the raisins.

#### Communication

#### Practitioner

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

#### Connections

#### Novice

The student does not include a connection in their solution.

#### Representation

#### Practitioner

The student's diagram is appropriate and accurate. A key is provided for the gingerbread men, and the raisins for eyes are provided in the scribing.

#### 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 using ten frames to show six pairs of eyes works to solve the task. The student's answer, "12 •" is correct. The student also states, "This says 12 raisins."

#### Reasoning & Proof

#### Practitioner

The student's ten frames support correct reasoning. They indicate two raisins for the eyes of six gingerbread men for a total of 12 raisins.

#### Communication

#### Apprentice

The student correctly uses the mathematical term *ten frame*.

#### Connections

#### Novice

The student solves the task without making a mathematically relevant connection about their solution.

#### Representation

#### Practitioner

The student's ten frames are appropriate and accurate. The student labels each ten frame "raisins." The student provides additional support in the scribing to define the gingerbread men and the raisins for the eyes.

#### 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 making a diagram of six gingerbread men faces and 12 raisin eyes works to solve the task. The student indicates a correct answer, "dozen, 12," and states, "I got 12 raisins."

#### Reasoning & Proof

#### Practitioner

The student has a systematic approach and the diagram supports their thinking.

#### Communication

#### Practitioner

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

#### Connections

#### Practitioner

The student makes the relevant observations, "It's a dozen," and, "This says pair. They have a pair of eyes. We do too."

#### Representation

#### Practitioner

The student's diagram is appropriate and accurate. Necessary labels for the gingerbread men and the raisins for eyes are provided in the scribing.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 2

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of gluing paper "gingerbread men," on their paper and adding the raisin eyes works to solve this task. The student states a correct answer, "My answer is 12 raisins."

#### Reasoning & Proof

#### Practitioner

The student has a systematic approach and the diagram supports their thinking.

#### Communication

#### Practitioner

The student correctly uses two mathematical terms *diagram*, *more*.

#### Connections

#### Practitioner

The student makes the mathematical relevant observation, "She gots more raisins than gingerbread mans."

#### Representation

#### Practitioner

The student's diagram is appropriate and accurate. A key is provided for the raisins and the gingerbread men in the scribing.

#### Overall Achievement Level:

#### Practitioner

#### Practitioner 3

### Scoring Rationale

#### Problem Solving

#### Practitioner

The student's strategy of using a rekenrek to show six pairs of raisins/eyes for six gingerbread men works to solve the task. The student's answer, "Lisa needs 12 raisins," is correct.

#### Reasoning & Proof

#### Practitioner

The student uses correct reasoning by understanding that the task requires using two raisins/eyes per gingerbread man and then finding a total of 12 raisins.

#### Communication

#### Practitioner

The student correctly uses the mathematical terms *rekenrek*, *diagram*, *pair*.

#### Connections

#### Practitioner

The student uses a second strategy, a diagram, to determine Gina needs 12 raisins for six gingerbread men. The student makes the mathematically relevant observation, "Two eyes is a pair."

#### Representation

#### Practitioner

The student correctly moves the beads on the rekenrek to show six groups of two. The scribing defines the six groups as gingerbread men and each bead as a raisin. The student's diagram is accurate and appropriate. The scribing defines the gingerbread men and the raisins/eyes. The student does not compare the two representations to determine that their answer is correct for the Expert level.

#### Overall Achievement Level:

#### Practitioner

#### Expert 1

### Scoring Rationale

#### Problem Solving

#### Expert

The student's strategy of making a diagram of six gingerbread men and 12 raisins for eyes works to solve the task. The student indicates a correct answer, "12." The student then uses an alternative strategy of a table to show the six gingerbread men and 12 raisins for eyes. The student relates this task to a previous, completed problem.

#### Reasoning & Proof

#### Expert

The student creates a table to verify their answer of twelve raisins. The student also relates the problem to a previous, completed task and links the mathematical similarities.

#### Communication

#### Expert

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

#### Connections

#### Expert

The student makes the mathematically relevant Practitioner observations, "Pair of eyes," "Dozen is 12." The student states "2 raisins is a pair," and "I did the add 2 pattern." The student also recreates the task by adding their own gingerbread man for a total of "14," and states, "I did one for me. Now it is 14 raisins." The student makes an Expert connection by verifying their own answer by creating a table and stating, "This is called correct because I got 12 again." The student makes an additional Expert connection by relating the Gingerbread Man task to a task done in the past that involved counting dog legs. "We did that when we counted 3 dogs legs. That table was hard because I did 4, 8, 12 on it."

#### Representation

#### Expert

The student's diagram is appropriate and accurate. The key and the scribings provide all necessary labels. The student's table is appropriate and accurate with all necessary labels included.