# Tasks, Units & Student Work

## Kindergarten Math: Books on Shelves

Books on Shelves is the culminating task in a multi-week unit focused on operations and algebraic thinking. Students demonstrate mastery by completing the Books on Shelves task in one class period.

Suggested Use: Review the task and rubric before looking at the student work. Then, look at the student work and click on the red arrows to see an explanation of the student's performance on the task. Scroll down to the bottom of the student work to see suggested instructional next steps.

### Instructional Implications: Books on Shelves K

Achievement Level: Expert

Note: Student work identified at this level is exceeding grade-level expectations

The following is a list of instructional implications that you may want to consider for students performing at the Expert level. In addition, you may want to consult the suggestions for the Practitioner level:

• Find combinations for numbers greater than ten
• Investigate and prove generalization-total combinations is one less than sum being found .
• Investigate and prove generalization-if zero can be considered the total combinations is one more than sum .
• Solve problem more than one way to verify that answer is correct .
• Relate problem to a similar one completed and discuss how they are mathematically similar .
• Discover and discuss why an even number has a fair share/equal combination but an odd number does not .

### Instructional Implications: Books on Shelves K

Student Achievement Level: Practitioner

The following is a list of instructional implications that you may want to consider for students performing at the Practitioner level. In addition, you may want to consult the suggestions for the Novice and Apprentice levels:

• Include more writing of number sentences to support the possible combinations for any number up to ten in a student's diagram, table, etc.
• Discuss and solve problems where zero would be used in a combination and when it would not be used
• Introduce the language term-commutative property
• Encourage student to make more than one mathematically relevant connection about her/his work
• Investigate where a combination is a fair share
• Introduce another strategy to solve the same problem-model, diagram/key, organized list, table.

### Instructional Implications: Books on Shelves K

Student Achievement Levels: Novice and Apprentice

The following is a list of instructional implications that you may want to consider for students performing at the Novice and Apprentice levels:

• continue to subitize with student to "see" sixness, or any number up to ten using hands and dot cards
• use manipulatives to investigate "fact families"/combinations of six or other numbers up to ten to discover how applying the commutative property in an organized manner can support a correct answer.
• use a ten frame to find combinations of six or other numbers up to ten
• use games such as cup and counters to find combinations of six or other numbers to up ten
• use graph paper and two color crayons to show combinations to six or other numbers up to ten, cut apart to show how the two "staircases" match for commutative property
• use number sentences to represent combinations/commutative property
• review mathematical language-model, number sentence, diagram, key, per, total, equal, add, fair share, combination, more than, less than
• review how to make a model with manipulatives or a diagram with a key
• have centers available for investigation and practice
• Provide leading questions to begin reflection on the solution in order to see regularities, structures, patterns, trends, etc.
• Solve similar problems using four, five, seven, eight, nine, or ten

### Instructional Implications: Books on Shelves K

Student Achievement Levels: Novice and Apprentice

The following is a list of instructional implications that you may want to consider for students performing at the Novice and Apprentice levels:

• continue to subitize with student to "see" sixness, or any number up to ten using hands and dot cards
• use manipulatives to investigate "fact families"/combinations of six or other numbers up to ten to discover how applying the commutative property in an organized manner can support a correct answer.
• use a ten frame to find combinations of six or other numbers up to ten
• use games such as cup and counters to find combinations of six or other numbers to up ten
• use graph paper and two color crayons to show combinations to six or other numbers up to ten, cut apart to show how the two "staircases" match for commutative property
• use number sentences to represent combinations/commutative property
• review mathematical language-model, number sentence, diagram, key, per, total, equal, add, fair share, combination, more than, less than
• review how to make a model with manipulatives or a diagram with a key
• have centers available for investigation and practice
• Provide leading questions to begin reflection on the solution in order to see regularities, structures, patterns, trends, etc.
• Solve similar problems using four, five, seven, eight, nine, or ten