This series of nine research-based assessments goes beyond "getting the right answers" to reveal students' true understanding of key math concepts. Kathy Richardson identifies the "Critical Learning Phases" that students move through as they develop an understanding of the foundational mathematical ideas they need to know. The assessments follow the stages of students' growth through these phases as they learn the core concepts for numbers up to 100. Each of the assessment guides includes complete information for understanding the concept being assessed, instructions for administering the assessment, and specific suggestions for instruction.

The assessments are conducted through short, one-on-one student/teacher interviews. Student responses can be captured using paper and pencil forms or with the technology component of the program AMC Anywhere. Assessment results are directly linked to instructional activities in Richardson's Developing Number Concepts series.

Used together, AMC and DNC can support the implementation of K—2 math RTI initiatives. The assessments can be used to screen and then diagnose and progress monitor Tier 2 and 3 students. Instructional activities from Developing Number Concepts can provide small group or individual instruction.

Click on a title below to learn more about the specific goals of each assessment:

To combine single digit numbers by reorganizing them into a 10 and leftovers. To use their knowledge of the parts of numbers to 10 to subtract from numbers up to 20.

Critical Learning Phases:

Describes a 10 as a single entity even though it is composed of 10 single objects

Organizes numbers into groups of one 10 and leftovers

Knows 10 plus any number from 1 to 10

Tells how many needed to make 10

Tells how many leftovers when removing 10 for numbers from 11 to 20

Combines quantities by reorganizing into one 10 and leftovers

Subtracts quantities by breaking numbers apart and recombining whatever is left

Student Interview Forms

Assessment forms to accompany Assessing Math Concepts - Ten Frames by Kathy Richardson. Set of 50.

To determine if the child can tell "how many" in a quantity if the number of tens and ones is known, and to determine if the child can add ten and take away ten without counting. To also determine if the child knows that the total number does not change when counted in a different way, what it means to count by 2's or 5's, how well the child can do this.

Critical Learning Phases:

Organizes quantities into tens and ones

Instantly knows total quantity when number of tens and ones is known

Knows 10 more for any two-digit number

Knows 10 less for any two-digit number

Student Interview Forms

Assessment forms to accompany Assessing Math Concepts - Grouping Tens by Kathy Richardson. Set of 50.

To determine if a child can add and subtract from two-digit numbers by mentally breaking numbers apart and reorganizing them into tens and leftovers, and to determine how the child solves problems presented symbolically.

Critical Learning Phases:

Tells how many needed to make the next 10

Combines numbers by reorganizing them into tens and leftovers when necessary

Breaks apart tens when necessary and reorganizes what is left into tens and leftovers

Student Interview Forms

Assessment forms to accompany Assessing Math Concepts - Two-Digit Addition & Subtraction by Kathy Richardson. Set of 50.