a random assortment of items through the day…
What are people doing from last time that is working
- I notice, I wonder…
- Problem solving
- Using models
- Students talking
- Slowly opening up problems
Big ideas of mathematics: language of quantity, change, shape, dimension, chance
Goal: build students depth of understanding and comfort in these areas through discourse
Through: multiple representations
The 10% perspective
Pedagogical decision – when a student provides a response, how much do you want to push? How far will you continue to going along the path of their thoughts?
Book Title: The Problem with Math is English
Number Talks: 2 + 2 + 2 + 10 + 10 +10
- How did you work with the 10s? Did you add or group? Then, what did you do with the 2s?
Domain: Operations & Algebraic Thinking
Cluster: Understanding addition and subtraction
?How does this relate to number sense?
**Progression is by age, not grade.
What are the representations? How are we putting together and taking apart?
- preK – exploring addition and subtraction with fingers and objects. Decomposing quantity (less than or equal to 5, then to 10) into pairs in more than one way (using objects / drawings)
- Grade 1 – using objects, drawings and equations with a symbol for the unknown number
- add to / take from / put together
Focus on word problems – explaining! Use the practices.
1.OA.6 First Grade!
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).
Progresses to 2.OA.2
Fluently add and subtract within 20 using mental strategies (what’s the picture that you see?). By end of Grade 2, know from memory all sums of two one-digit numbers.
Where has the math been? fragmented, skill-driven, incoherent
Where are we going? fewer, deeper, examples & specificity (focus, rigor & clarity)
Why would I subtract when I can add-on?
Take home quote of the day – don’t stop pushing for student thought.
“If a student answers in the way that you were thinking, it should not keep you from asking did anyone do it differently?”