1. Math Alliance Teaching All Learners Summer 2011 Beth Schefelker Melissa Hedges Chris Guthrie

2.  3. Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback and frequent cumulative review.  5. Intervention materials should include opportunities for students to work with representations of mathematical ideas and interventionists should be proficient in the use of representations of mathematical ideas  6. Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.

3. We are learning to  Deepen our understanding of fluency and the role of explicit instruction We will be successful when  Articulate a common understanding of fluency the role of explicit instruction plays in supporting the development of fluency in students.

4.  What does it mean to be fluent with single digit addition and subtraction?  What is your definition of explicit instruction?

5. When thinking about student understanding what are the milestones we need to look for in order to provide “focused” interventions? Some ideas:  Cardinality identifies it’s quantity.  Value – as notated by it’s place in the base ten system  Magnitude of number

6.  Use the least amount of cards to build this number.  As you work, monitor your thinking by recording your moves on a sticky note.  Keep in mind the changes made to the number and how you would verbalize the move you made.  Retrace those moves on the 100’s chart. How does this representation deepen your understanding about the number?

7.  Use the cubes to make a number from 1-9.  Change the number by 30 more  Change the number by 10 less  Change the number by change both 10’s and ones?  Debrief: What ideas of number understanding did this activity address?

10.  Fluency at each grade level involves a mixture of knowing some answers, knowing some answers from patterns and knowing some answers from the use of strategies.  K-5 Operations and Algebraic Thinking Progressions Document p. 18

11. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on making ten decomposing a number leading to a ten using the relationship between addition & subtraction creating equivalent but easier or known sums

12. Ten frames show relationships of small numbers to five and ten, in particular, drawing attention to the role of 10.

13.  Counting on.  Make a ten.  Use an easier “equivalent” problem. Transform the problem in some way Use fives Use a helping fact Use doubles

14. Strategies:  Make a ten.  Use a double.  Use fives.  Use some other equivalent problem. Put 8 counters on your first frame & 6 counters on your second frame.

15.  How does the teacher try to make the mathematics of the lesson explicit?  What questions does he ask?  Use a sticky note to take notes – use slide on CRA and multiple representations

16. Practice with basic facts  6 + 7  8 + 7  9+ 8  8+5  9 + 4

17.  The word “fluency” appears in the CCSSM from kindergarten through sixth grade. ◦ single-digit, multi-digit, and rational number computation  The word “strategy” or “strategies” appears in the CCSSM 23 times - 1 st grade through 7 th grade.

18.  Look at your definition of fluency that you wrote at the beginning of the session. How has your thinking changed? ◦ Fluency at each grade level involves a mixture of knowing some answers, knowing some answers from patterns and knowing some answers from the use of strategies.  K-5 Operations and Algebraic Thinking Progressions Document p. 18