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

 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.

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.

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

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

 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?

 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?

 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

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

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

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

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.

 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

Practice with basic facts    9+ 8  8+5  9 + 4

 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.

 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