1. Effective use of classroom instruction,
meeting the individual needs of
students in mathematics

2.  T F 1. A number with three digits is always
bigger than on with two
 T F 2. To multiply 10, just add zero.
 T F 3. Scales identify intervals of one unit.
 T F 4. „Diamond‟ is a mathematical term
used in learning shape geometry.
 T F 5. When you multiply two numbers
together, the answer is always bigger
than both of the original numbers.
 BONUS : If you draw a square, right-triangle,
rhombus, trapezoid, and hexagon. Will your
shapes look exactly like your neighbor‟s shapes?
Try it!
*Questions taken from TIMMS report of top 4th grade misconceptions

3.  Guided Math is a structured, practical way of
matching math instruction to the diverse
individual learners in the classroom
 Assist students in using reasoning and logic, as
well as basic skills necessary to solve problems
independently
 Differentiated, meeting the needs of all learners
 Fluid groupings
 Target instruction/interventions

5.  Problem Solving
 Reasoning and Proof
 Communication
 Connections
 Representation

6.  conceptual understanding—comprehension of
mathematical concepts, operations, and relations
 procedural fluency—skill in carrying out
procedures flexibly, accurately, efficiently, and
appropriately
 strategic competence—ability to formulate,
represent, and solve mathematical problems
 adaptive reasoning—capacity for logical thought,
reflection, explanation, and justification
 productive disposition—habitual inclination to see
mathematics as sensible, useful, and worthwhile,
coupled with a belief in diligence and one‟s own
efficacy.

8.  These strands are not independent; they
represent different aspects of a complex whole.
 The most important is that the five strands are
interwoven and interdependent in the
development of proficiency in mathematics

9.  1. Make sense of problems and persevere in
solving them.
 2. Reason abstractly and quantitatively.
 3. Construct viable arguments and critique
the reasoning of others.
 4. Model with mathematics.
 6. Attend to precision.
 7. Look for and make use of structure.

10.  Before:
 3-6 students per grouping
 Teacher decides on the focus of the session based on
assessments
 Teacher chooses math activity or problem that will
support selected learning target (“I CAN”)/ Big Idea
 Genuine questions are used to prompt student thinking
 Focus Free Write
 KWHL Chart
 Concept Check
 Arrange a functional room
 You may sit at one table or you may travel from group to
group
 Stations are clearly labeled

11.  During
 Introduce problem/activity
 Question:
 What do you notice?”
 What do you know about today‟s ______________?
 What does the problem tell us?
 What words are tricky? (Anticipate vocabulary
challenges)
 What do you predict will happen next?
 What connections to other ideas do you see in today‟s
activity?
 Students solve problem/begin activity
independently
 Teacher observes the group and coaches individuals as
needed.
Teacher observes and takes anecdotal notes.

12.  After
 Teacher and student discuss the problem as a group to
explore strategies and understandings of the problem
solving process. EMPHASIS ON PROCESS.
 Students share strategies, partial thinking, and solutions.
 Teacher may clarify, re-teach, review skills or vocabulary
used in the session.
 Teacher records observations and evaluates student
problem solving/basic skills
 Based on performance, teacher plans next
session
 Students may be involved in self evaluation
 Rubrics
 Exit Tickets (Assessments)
 Likert/ Feeling of Knowing Scale

13.  The focus is on skills and strategies that students
construct and communicate through the activity
 Session is based on one or two problem-solving
opportunities
 Flexible math groups change based on teacher‟s
ongoing assessments, therefore students are
provided with immediate or next day (exit tickets)
feedback
 Students gain knowledge of vocabulary in context
 Instruction is based on student needs
 Students solve problems independently with
strategies that make sense to them
 Selection of math activity/problem is
differentiated based on student needs

14. Review of Math Fact Math Games Problem-Solving
Component
Previously Mastered Automaticity Practice
Concepts
•Ensure retention of •Increases •Reinforces math •Requires the use
understandings computational standards previously of strategies or
Objectives
previously achieved proficiency of and currently taught, related to concepts
students through prior to Math previously
math fact fluency Workshop modeled, taught,
and practiced.
•A.M. Math •Math Add+ Vantage •Investigation games •Problem of the
•Entrance Slips Games for each Unit day
•Pre-Assessments •Rocket Math to •Teacher Created •10- minute Math
•Hands on Activities assess Games •Problem of the
•Problems to solve •Computational •Commercially Week
•Games Fluency Games prepared games •“Good Question”
Examples
•Activity sheets •First in Math of the Day
•Computer Activities •Greg Tang Math •Menus
•Differentiated
Learning Tasks

15. Investigations Math Journals Computer Use Math Related to
Component
Other Subject
Areas
•Similar to problem- •Enhance •Supports the •Help students
solving practice, but mathematical process understanding of realize the
requires the gathering skills math concepts interrelatedness of
of data or other •Resource for the disciplines
Objectives
information by investigation and for •Focus on the real-
students creation of life applications of
presentation of math
findings
•Real-life, relevant •Mathematical •Math games •math activities
investigations observations •Math fluency tied to current
provided by the •Definitions of math- practice (First in events
teacher or generated specific vocab Math) •Science projects
by students •Recording of •Compass Learning •Math connections
•Test out conjectures conjectures •Smart Tech from social studies,
•Discovery Questions •Log of prob. Solving •Blogs language arts, and
Examples
•I have, who has steps or strategies •Wikis science text books
•Concept Maps •Explanation of
•Matrix mathematical
understandings

16.  Define the Heart of Your Lesson (Content and Task
Decisions)
 Determine the Mathematics
 Think in terms of mathematical concepts not skills
 Describe mathematics, not student behavior
 The best tasks will get at skills through concepts.
 Think about what your student bring to the mathematics
 What do you students know or understand about the concept?
 Are there background ideas they have not developed?
 Is the scaffolding of the learning appropriate for your students?
 Deign or select tasks
 Keep it simple! Good tasks often come from the text you are using
 Children’s Literature can impose great tasks
 Resources should be problem centered and rich mathematically
 Predict student’s approaches to a solution
 Use what you know about your students to predict responses
 Can all engage at some level in the problem solving
 Plan for modifications, adjust tasks accordingly

17.  Articulate student responsibilities
 Discuss and define expectations of dialogue,
writing “S.E.W.” box, and journaling about
thinking
 Students should be able to tell you:
 What they did to get the answer
 Why they did it that way
 Why they think the solution is correct
 Plan the BEFORE activities
 Plan the DURING activities
 Plan the AFTER dialogues (MOST important)

18.  Write out the plan
 Goals/ Big Ideas/ Target Skills/ “I CAN”
 Task and Expectations
 Before Activities
 During Hints and Extensions
 After-Lesson discussion format (Be sure to have
ample time for this)
 Assessments (I enjoy exit tickets as quick
formative/summative checks to best prepare for the
following session)

19.  7 (6 + 1 Computer ) stations are ideal for a K-6
Classroom
 I chose the term stations for the 5th grade setting, however the
term centers could be used.
 Stations activities should be introduced first, then placed in
rotation
 Some stations may stay all year to refresh skills
 Rotations do not need to change all at once
 It is best to change out one station at a time

20.  Concept Games
• Depending on Unit of study example may include:
• Close to 100, Close to 1,000, Close to 7,500, Close to 0 ot 1
• Decimal Duel
• Capture 5
• War with equivalent fractions, decimals, and percents
• Order of Operations Game
 Math Add+Vantage Games
 Number Battle (addition and subtraction)
 Rolling Groups (multiplication)
 Speed (multiplication)
 Treasure Chest
 Marcy Cook
 Thinking Tiles

21.  Critical Thinking/Logic Games to encourage
Conjectures
• Number Puzzles, Tantrix, Rubrics cube
• Qwirkle, Yatzee, and Mancalla
• Math Analagies
 Fluency and Graphing Mosaics
 Computer Station
 Number Sense
 Today‟s Magic Number (TMN, I created for 3rd grade)
 Target Number (Similar to TMN) Math Dice Game
 Multiplication (Juniper Green)
 Leap Frog (Math Add+Vantage)
 Student created Problems

22.  Listen to others and respect their thinking
 Ask thoughtful questions
 Disagree with others in a respectful way
 Volunteer your ideas in group discussion
 Take risks with challenging ideas and problems
 It‟s ok to be wrong, no one is perfect, this is
how we think and learn. Confusion leads to
new learning!
 Enjoy discovering new things about math

23.  Heterogeneous groups lead to higher quality
experiences for all children
 Groups should not be based on overall math
ability, they should be based on content of
point in time
 Groups should be fluid and flexibile

24. Center Visited Date Comments/Reflections
about this center
(station)
• I staple a copy of this on the outside of student math journal
•I keep all student journal in a colored crate in number order.
•Folder up, ready to check or grade
•Folder down, graded

25. Teacher Facilitated/Student Directed 30-40 minutes
Whole Group
Math Learning Centers 20-30 minutes
Closure/Sharing 10 minutes
OR
Whole Group Lesson 4 days a week 45-60 minutes
Math Learning Center 1 day a week 45-60 minutes

26. Time
Activity
Math Fluency Practice 5-10 minutes
Problem Solving Review and Focus (A.M. Math) 5-10 minutes
Sm. Group Instruction & Problem Solving 30-45 minutes
Learning Centers
Independent Practice and Assessments (Exit Tickets, 10-20 minutes
common formative and summative assessments)
Discussion 10-20 minutes
This schedule is flexible, whole group instruction takes place as needed.
Introduction to new content may lead to a day of more discovery and activation
of prior knowledge.

27.  Good Questions or Story Problems given 1-2x
per week.
 Students are provided with a 4 point rubric
 I try to give prompts Tue and Thur. to support
mathematical comprehension
 Should incorporate process standards
 On current content topic
 Released question from state assessments
 Open ended questions
 How to questions
 Evaluation questions
 R.A.F.T.S.

28.  Adding it Up: Helping Children Learn Mathematics. Strands of Mathematical
Proficiency. http://www.nap.edu/openbook.php?record_id=9822&page=115
 Blanke, B. (2010) Guided Math Seminar , Cleveland, Oh.
 Common Core State Standards Initiative. Common core state standards:
Mathematics. Http://www.corestandards.org/the-standards/mathematics
 Linden, T. (n.d.) Teacher created A.M. Math Problem Solving Questions.
 NCTM. NCTM process standards:
http://www.nctm.org/standards/content.aspx?id=322
 Sammons, L. (2009) Guided math ; A framework for mathematics instruction.
Huntington Beach, CA: Shell Education.
 Sammons, L. (2011) Building Mathematical Comprehension. Huntington Beach, CA:
Shell Education
 Small, M. (2009) Good Questions; Great Ways to Differentiate Mathematics Instruction.
Teachers College, Columbia University, New York.
 Stoyle, K. (n.d.) Teacher created materials
 Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching Number in the
Classroom with 4-8 year olds. Thousand Oaks, CA: Sage Publications.
 Wright, R ., Martland, J. Stafford, A., Stranger, G. (2011) Teaching Number;
Advancing Children’s Skills and Strategies. Thousand Oaks, CA: Sage Publications.
 Wright, R.,Ellemor-Collins, D., Tabor, P.(2012) Developing Number Knowledge;
Assessment, Teaching & Intervention with 7-11 year-olds. Thousand Oaks, CA: Sage
Publications.