1. Number Talks in Middle & High School Classes? A discussion Chris Harris @CharrisMath chharris@eusd.orgchharris@eusd.org TOSA Escondido Union School District California a K-8 school District

2. Me You “The way I teach math ≠ the way I was taught math.” Avery Pickford @woutgeo

3. Why? CCSSM Mathematical Practice Standards 1.Make sense of problems and persevere in solving them. 2.Reason abstractly & quantitatively. 3.Construct viable arguments & critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for & make use of structure. 8.Look for & express regularity in repeated reasoning. CCSSM Fluencies K Add/subtract within 5 1Add/subtract within 10 2Add/subtract within 20 Add/subtract within 100 (pencil & paper) 3Multiply/divide within 100 Add/subtract within 1000 4Add/subtract within 1,000,000 5Multi-digit multiplication 6Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 2X2 systems by inspection Fluent in the Standards means “fast and accurate.” It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. Assessing fluency requires attending to issues of time (and even perhaps rhythm, which could be achieved with technology).

4. Why? CCSSM Mathematical Practice Standards 1.Make sense of problems and persevere in solving them. 2.Reason abstractly & quantitatively. 3.Construct viable arguments & critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for & make use of structure. 8.Look for & express regularity in repeated reasoning. CCSSM Fluencies K Add/subtract within 5 1Add/subtract within 10 2Add/subtract within 20 Add/subtract within 100 (pencil & paper) 3Multiply/divide within 100 Add/subtract within 1000 4Add/subtract within 1,000,000 5Multi-digit multiplication 6Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 2X2 systems by inspection

5. When? Whenever 10-15 minutes whenever you have time. Could be a warm up. Doesn’t have to be what you’re teaching at the moment. Review/reinforce past skills.

6. Who? Everyone!! - language learners - SPED - advanced learners - intervention students - shy students - ‘not so’ shy students!

7. Why Number Talks in Elementary Classes? Where? Anywhere! All you need is some chart paper, markers and students!!

8. How? This is the book & method most commonly used in elementary school “Simply defined, number talks are five- to fifteen-minute classroom conversations around purposefully crafted computation problems that are solved mentally.” Sherry Parrish, Teaching Children Mathematics October 2011

9. This is the book for grades 4 - 10 “Making Number Talks Matter is about helping students take back the authority of their own reasoning through a short fifteen minute daily routine called Number Talks, in which they reason mentally with numbers.”

10. Teach students hand signals Get rid of pencils & paper Present problem Accept all answers, non-judgmentally Have students justify their answers Make a written record (Don’t forget to stop!!) BUT let’s look at dot cards

11. Why Dot Cards? numbers represent quantities you can use dots flexibly (& numbers too) students can be successful almost always guarantees several correct answers useful introduction to Number Talks

12. For the teacher wait time gently probe their thinking (whether it is right or wrong) look for multiple strategies listen – don’t explain a student’s words continue to do Number Talks – it gets better!! expect precision of language record the thinking – in a correct mathematical fashion get students to talk to each other multiple answers are great! students should ‘present’ their answers sometimes you can share your way of thinking nudge students beyond the algorithm

13. Let’s give it a try