1. Mathematics Summit
Southern Indiana Deanery: Focus on
Mathematics Instruction

2. Standards for the Day
• Deepen understanding of new Common
Core State Standards for mathematics
• Create understanding of using multiple
representations and approaches to problem
solving
• Apply a variety of strategies to support and
promote the learning of mathematics
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

3. Agenda
DAY II
• Analysis of New Common Core State Standards
• Using Multiple Representations to Develop Deeper
Understanding
• Using Number lines and manipulatives to support
conceptual understanding
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

4. Quick Write
From our time together yesterday,
What ideas, strategies, concepts, routines do
you want to revisit as you plan your
classroom for the upcoming year? Which do
you want to focus on initially? & How do you
plan on accomplishing this?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

5. Reasoning Abstractly and
Quantitatively
• 5.NBT.6: Find whole-number quotients of
whole numbers with up to four-digit
dividends and two-digit divisors, using
strategies based on place value, the
properties of operations, and/or the
relationship between multiplication and
division. Illustrate and explain the
calculation by using equations, rectangular
arrays, and/or area models.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

6. • Working in non-grade level groups (2-3)
Divide 365÷4 (by hand) using three different
methods.
(Keep in mind, we are developing reasoning and
sense-making, and multiple approaches/methods
to use with our students )
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

7. Method 1 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

8. Method 2 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

9. Method 3 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

10. Method 4 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

11. Method 5 of ∞
112/4 = 28
112/4 = 28
112/4 = 28
24/4 = 6 5/4 = 1 R1
365 = 112+112+112+24+5 = 28+28+28+6+1+¼ = 91¼
4 4
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

12. Common Core State Standards for Mathematics
K-8 Mathematics Content
Operations & Number & Number & Ratios &
Counting & Measurement The Number Expressions Statistics &
DOMAINS Algebraic Operations Geometry Operations: Proportional Functions
Cardinality & Data System & Equations Probability
Thinking in Base Ten Fractions Relationships
K X X X X X
1 X X X X
2 X X X X
3 X X X X X
4 X X X X X
5 X X X X X
6 X X X X X
7 X X X X X
8 X X X X X
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

13. 6 7 8
Proportional Understand ratio concepts and use ratio Analyze proportional relationships and use
reasoning to solve problems them to solve real‐world and mathematical
Relationships
problems.
The Number Apply and extend previous understandings Apply and extend previous understandings Know that there are numbers that are not
of multiplication and division to divide of operations with fractions to add, rational, and approximate them by rational
System fractions by fractions. subtract, multiply, and divide rational numbers.
Compute fluently with multi‐digit numbers numbers.
and find common factors and multiples.
Apply and extend previous understandings
of numbers to the system of rational
numbers.
Expressions Apply and extend previous understandings Use properties of operations to generate Work with radicals and integer exponents.
of arithmetic to algebraic expressions. equivalent expressions. Understand the connections between
and Equations Reason about and solve one‐variable Solve real‐life and mathematical problems proportional relationships, lines, and linear
equations and inequalities. using numerical and algebraic expressions equations.
Represent and analyze quantitative and equations.
relationships between dependent and
independent variables.
Functions Define, evaluate, and compare functions.
Use functions to model relationships
between quantities.
Geometry Solve real‐world and mathematical Draw, construct and describe geometrical Understand congruence and similarity using
problems involving area, surface area, and figures and describe the relationships physical models, transparencies, or
volume. between them. geometry software.
Solve real‐life and mathematical problems Understand and apply the Pythagorean
involving angle measure, area, surface area, Theorem.
and volume. Solve real‐world and mathematical
problems involving volume of cylinders,
cones, and spheres.
Statistics and Develop understanding of statistical Use random sampling to draw inferences Investigate patterns of association in
variability. about a population. bivariate data.
Probability Summarize and describe distributions. Draw informal comparative inferences
about two populations.
Investigate chance processes and develop,
use and evaluate probability models.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

14. Content Analysis
In grade level groups:
• Identify new content for your grade level
• Identify different opportunities for using
multiple representations, approaches,
number forms
• Develop a priority list of content &
approaches to be developed during the
transition period.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

15. Content Analysis
In school groups:
• Outline content priorities at each grade level
• Identify both major and minor shifts
• Shift emphases – decide that teachers will
pay more attention to x and y in 2011-2012
and less attention to z
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

16. Quick Write
Based on this morning’s conversations, what
do you want to remember? How have you
added any more thinking to the
routines/processes that you are planning on
implementing this year?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

17. Working with Manipulatives
• Don’t assume that students make the
connections between the different
forms/representations of the problems
You must be intentional in doing this!
• As with any process, students need to
develop understanding of the process prior
to attempting to learn new material.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

18. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

19. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

20. How do we represent in mathematics?
Number
Algebra
Graphical
Sentence
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

21. Grade Level Content
Working in multi-grade groups work through
several of the problems on the page.
What does it look like?
How do the ideas progress across the
grades?
How do I support, develop student skills in
this area?
Collaborative for Teaching andCTL, Mathematical
Learning 21
SID: Focus on Mathematics Instruction
Literacy August 3, 2011

22. Literacy in Mathematics
Reading
Vocabulary
Development
Speaking/
Listening Writing2
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

23. Community Wiki
sidmath.pbworks.com
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011

24. Community Wiki
sidmath.pbworks.com
By the way, what is a Wiki?
rodaniel@ctlonline.org
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011