4

3

2

1

Prerequisite Knowledge

demonstrates an

excellent understanding of the  pre-requisite knowledge for the key concept and makes clear connections between the knowledge and the key concept

demonstrates an

understanding of the  pre-requisite knowledge for the key concept and makes connections between this knowledge and the key concept

demonstrates some

understanding of the  pre-requisite knowledge for the key concept and makes limited connections between this knowledge and the key concept

demonstrates little

understanding of the  pre-requisite knowledge for the key concept and does not make connections between this knowledge and the key concept

Concrete Materials

demonstrates an excellent ability to use a variety of concrete materials appropriately and correctly, gives clear and detailed  explanations of each manipulative with accompanying models

demonstrates an ability to use a variety of concrete materials appropriately and correctly, gives clear and detailed  explanations of each manipulative with accompanying models

demonstrates some ability to use a  limited variety of concrete materials appropriately and correctly, gives a partially complete  explanation of each manipulative with accompanying models

demonstrates a limited ability to use concrete materials appropriately and correctly, gives partial or no explanations of each manipulative, possibly without accompanying models

Collection  of Activities, Problems, and Investigations

the resources strongly connect to the key concept and direct a range of rich mathematical activity (content and

processes)

the resources connect to the key concept and direct a range of rich mathematical activity (content and

processes)

the resources either connect to the key concept or direct a range of rich mathematical activity, but not both

the connections

between the resources and the key concept is loose, and they do not engage a range of

mathematical

processes

Relational Explanation

Includes more than one clear and detailed relational explanation that demonstrates a deep understanding of the rules behind the reasons

Includes one clear and detailed relational explanation that demonstrates a deep understanding of the rules behind the reasons

Includes one relational explanation that demonstrates some understanding of the rules behind the reasons

Includes one relational explanation that demonstrates little to no understanding of the rules behind the reasons

Algorithms

Presents a wide variety of possible algorithms with clear explanations of each strategy, demonstrating a clear understanding of the values of alternative algorithms

Presents a several possible algorithms with clear explanations of each strategy, demonstrating a good understanding of the values of alternative algorithms

Presents limited possible algorithms with some explanations of each strategy, demonstrating a some understanding of the values of alternative algorithms

Presents no alternative algorithms without explanations, demonstrating little to understanding of the values of alternative algorithms

Depth  and breadth of  exploration

demonstrates an

excellent  understanding of the key concept and demonstrates evidence of extensive research related to the key concept

demonstrates a very

good understanding of the key concept and demonstrates evidence of a good amount of research related to the key concept

demonstrates some

understanding of the key concept and demonstrates minimal evidence of  research related to the key concept

demonstrates a lack of understanding of the key concept and demonstrates little to no evidence of research related to the key concept

Communication of  ideas

engaging and

knowledgeable

presentation of the

key concept and of the

accompanying writing

solid and clear

presentation of the

key concept and of the

accompanying writing

some aspects of the

presentation of the

key concept and the

accompanying writing showed professionalism

the presentation of the key concept and the

accompanying writing lacked professionalism