1. Catherine Castillo, Numeracy Coach
Math Groups Now What?
Josh Holt, Principal
Catherine Castillo, Numeracy Coach
Portland Elementary

3. Clear Goal(s)
Participants will locate and explore district resources available to provide interventions for struggling learners in mathematics.
Participants will understand the importance of informal and pre-formal notation in preparing students for conceptual understanding and procedural fluency.

4. Recent Teacher Concern
5th Grade Teacher:
My grade-level partner and I are struggling with teaching factorization. Most of our students do not know their multiplication facts. Do we come to a screeching halt with teaching chapter 2 Factorization or do we continue pushing through? I am not comfortable with pushing through the chapter. I feel like we need to go back and give a refresher course on teaching multiplication. What do you think?
How would you respond to this teacher?

5. Fifth Grade CCSS
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 5.NF.4 Apply and extend previous understand of multiplication to multiply a fraction or whole number by a fraction.

6. Iceberg Model
The Iceberg Model is a visual metaphor, distinguishing the role of informal, pre-formal, and formal representations used by students. The iceberg consists of the “tip of the iceberg” and a much larger area underneath, the “floating capacity.” The tip of the iceberg represents the targeted formal procedure or symbolic representation. In the floating capacity of the iceberg, moving from the bottom layer to the water-line, informal, context-bound representations, transition to pre-formal, strategies and models that can be used across many different problems. (Verbal and quantitative exist here)

7. Addition

8. 3 Aspects of Number Verbal Quantitative Symbolic “Five…six,seven”
OOOOO, 00
Symbolic
“5+2=7”

9. Simultaneous Round Table
In your groups, determine the tip of the iceberg (formal notation) for multiplication.
Then using the iceberg sheet provided, each person writes an idea for the informal and pre-formal notation on his paper.
When the presenter says rotate, everyone passes their paper clockwise and adds their thought to the new paper.
*Use the CCSS by domain to help you.

10. Multiplication
Formal Notation
3 x 4 = 12
Informal Notation

11. AVMR Screener x/÷ Questions
This is an array with 4 in each row and 7 rows. How many dots in all (first row uncovered)
8 x 4 =
32 ÷ 4=
If I have 27 cupcakes and I want to put them in packages of 6, how many packages will I need?

12. What Can They Do?
As we watch the following video clips assessing multiplication, use your graphic organizer to take notes on each child.
Please note what the student can do.
We must first be able to recognize what pre-requisite skills a student has in the domain before we can determine next steps for instruction.

13. A Look at a 5th Grader (BB)
Miracle
Miracle Package Problem
Noah
Landon
Landon Package Problem
Gehrig (3rd)
Brendan
Isaiah (4th)

14. What Do I Do With a Child who…?
Look through the Strategic Intervention Guide for 5th grade.
Think about the activities you saw and the conversations you had about the iceberg.
Where do you start?

15. My Math Resources Assessment Masters Am I Ready Assessment
Am I Ready Review
Grade-level below multiplication lessons
Reteach sheets for small group
Strategic Intervention Guide

16. Next Steps
As you think about your next steps in small groups how might you use our district resources to support struggling students in numeracy?
Thinking about the iceberg activity focusing on formal notation and floating capacity, what shifts have you made that may aid you in future planning for small group numeracy instruction?
Timed Pair Share
1 minute think time, 1 minute share time

18. Sources
Hazekamp, J. (2011). Why before how: Singapore math computation strategies. Peterborough, N.H.: Crystal Springs Books. Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding. Mathematics Teaching in the Middle School, 14(2), Wright, R., & Collins, D. (2012). Developing number knowledge assessment, teaching & intervention with 7-11-year-olds. London: SAGE. Wright, R. (2006). Teaching number in the classroom with 4-8 year olds. London: Paul Chapman Publishing.

19. Links
My Math Solon Schools (AVMR Videos) Kentucky Numeracy Project