1. By Kathy Richardson Assessment #5 Combination Trains Overview & Description of Strategies

2. Learning Number Combinations Children need to see the basic facts as a set of interrelated concepts. Children need to be able to look for relationships between the facts they know and other larger, more complex numbers or problems. Emphasis needs to be on learning number composition and decomposition and number relationships – not just on getting the right answers.

3. What are we trying to determine with this assessment? To determine what number combinations the student knows and to find out if they can use the answer to a combination they know to figure out one they don't know. Does student know the parts of numbers to 10? Can student use efficient strategies to solve problems to 20.

4. Common Core Alignment Kindergarten Operations & Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.5. Fluently add and subtract within 5 Grade 1 Operations & Algebraic Thinking Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.3. Apply properties of operations as strategies to add and subtract. 2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

5. Common Core Alignment continued Grade 1 Operations & Algebraic Thinking Add and subtract within 20. 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

6. What will my students be asked to do during the Combination Train assessment? Students will be presented with connecting cube trains of different lengths – they will be asked to add a variety of number combinations. Will assess their fluency with numbers to 6, to 10, and to 20.

7. Where can I learn more about the mathematics behind this assessment? The Assessing Math Concept series by Kathy Richardson contains important information for educators. It is recommended that teachers read the following information from Combination Trains Concept 5. Learning to Count Example of Student Interview Grade Level Expectations Assessing Children at Work Linking Assessment to Instruction

8. Tips for “Number Combinations” Knows without counting: Student quickly knows the number combinations. Related Combinations: Student is beginning to make connections; knows 3+3 =6, so knows 3+4=7. Counts on or back: Student is able to see one part of the number, but counts on the remaining parts. Counts All: Student isn’t able to combine numbers, and counts all cubes. Guess/No answer: Student not able to answer and has no strategy for figuring it out. “How many cubes? Strategy Unknown: Prompts teacher to ask “How did you think about that?”

9. Assessment Results Summarized at end of assessment as: A – Ready to Apply P – Needs Practice I – Needs Instruction Complete descriptions included in assessment guide.

10. Use AMC Anywhere reporting to view student results. Interpreting & Using Assessment Results Select Reports Select from a variety of reports.

11. Use “Linking Assessment to Instruction” guides for instructional support from Developing Number Concepts Select Downloads Select Linking Assessment