MATH first page

Meaningful Activities that Help

A Workshop for Number Sense  

(Recommended length: two, two and one half hour sessions)

Rationale:

Number sense was described by Howden (1989) as "good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms" (p. 11) Most adults who exhibit "math anxiety" have not fully developed their number sense. Therefore, before tackling any specific topic in mathematics we advise reviewing the elements of number sense.

The NCTM Standards defines number sense as involving five components:

• 1. Well-understood number meanings
• 2. Multiple relationships among numbers
• 3. Recognition of the relative magnitude of numbers
• 4. Knowledge of the effect of operations on numbers
• 5. Referents to measure of things in the real world.

A full understanding of number sense begins with whole numbers. An understanding of numbers includes counting, numerical recognition, more and less relationships, part-part-whole ideas, anchoring to special numbers such as 5 and 10, connections with the "real" world of work and home.

Workshop Goal:

This workshop is designed to provide adult educators with practical instructional activities which help adult literacy students make the connections between math concepts and math operations through the investigation of  whole number operations, the discovery of patterns, and the value of estimation in solving mathematical problems in school , as well as in daily life.  Activities encourage participants, through the use of manipulatives, calculators, whole body movements and personal experience, to review (and in some cases to become aware of, or to develop) the "number sense" which is essential to successful learning in mathematics .

Workshop Objectives:

• a. Understand a sensible order and sequence of topics related to number sense.
• b. Develop specific strategies that will facilitate numeracy learning for a variety of learners.
• c. Explore the use of tools for teaching number sense, including calculators and manipulatives.
• d. Review basic concepts of number operations as a basis for helping teachers "Link new math learning to previous learning. Teach concepts before rules."

(Refer to "Framework for Adult Numeracy Standards")

Agenda

A. Welcome, Introductions and Opening Activity

     Ice Breaker Activity

B. Session Overview and Negotiation

• a. Review SCANS, ANPN Standards, New York State Standards ( Brief information lecture by presenter/s)
• b. Participant needs and interests. In small groups, using one or two words on individual "post its" participants list adult students' major problem areas in mathematics. -Post on board or flip chart. Prioritize by categorizing and ordering.  Plan to address major areas of concern as they relate to and number sense.
• c. Brainstorm definition of "Number Sense" (Large group exercise)  (Desired response summarize as "comfort with numbers-relieving anxiety, ability to observe patterns in order to predict outcomes, make judgment, build algorithms, etc.) Refer to NCTM definition above
• d. ( Optional Activity ) Relate importance of "Number Sense" to successful completion of GED test.   -In small groups, using problems from "Practice GED (ACE) and using only number sense and no pencil/pen or               paper, choose  correct answers   -Discover how much of the test may be completed using this strategy.

C. Order and Sequence

React to the statement  "It is/is not it necessary to teach: Addition, subtraction, multiplication, division, first for whole numbers, then fractions, decimals, followed by per cent."  

     -Divide participants into two groups, pro and con.

     -Feedback: Post & compare results, draw conclusion- the usual order and sequence may not be a hard and fast rule in  teaching adults.

D. Activities  

Chose from the following list of activities those which best fit the needs of participants, the time frame of workshop and materials available.  Check the Activity Page for more detailed information about the activities.

Looking at Numbers

• Visual Pictures of Numbers
• Anchor Numbers  
• Odd and Even Numbers  
• Greater Than, Less Than:
• Closer To, Farther From:

Looking at Number Operations  

• Defining Number Operations "Different Ways of 'Seeing': Basic Mathematics Operations ".

Looking at Number Facts

Learning Strategies for Memorizing Number Facts

• Constructing an Addition Table
• Looking at the Completed Addition Table

Multiplication Strategies

• Constructing a Multiplication Table
• Finding Patterns  The 5, 9, and 10, Times Table. Other Tables
• Memorizing Multiplication Facts
• Drawing Numbers  

Review, Reflections, and "Next Step"

End of first session

Agenda

Day Two

Welcome and Review of First Session

Feedback from "Next Step" Assignment

Looking at Subtraction:

• Review of definitions of subtraction,
• Part part whole
• Addition /subtraction relation
• Non commutability of subtraction,
• Absolute numbers

Looking at Division:

• Review of definitions of division
• Part part whole
• Multiplication/division relation
• Non commutability
• Identity factor

Place Value and our Number System:

• Movement to the left and to the right
• Adding like things by placement in columns
• Personal algorithms for addition, subtraction, multiplication, division
• Multiplying  and dividing by powers of ten
• The magnitude of numbers,

Math in Everyday Life:  It's Situational!

• Exact Answers (Tests and the "Real World)
• Rounding up or down, (Ages, Budgets, Miles, Business)

Closure and Next Steps

Workshop Evaluation:

Meaningful Activities That Help

Number Sense

Workshop Evaluation

Workshop Goal:

This workshop is designed to provide adult educators with practical instructional activities which help adult literacy students make the connections between math concepts and math operations through the investigation of  whole number operations, the discovery of patterns, and the value of estimation in solving mathematical problems in school , as well as in daily life.  Activities encourage participants, through the use of manipulatives, calculators, whole body movements and personal experience, to review (and in some cases to become aware of, or to develop) the "number sense" which is essential to successful learning in mathematics .

1. In your opinion, has the goal of this workshop been met?          Yes          No.

Comment:

2. Do you feel the information and strategies presented in this workshop will be of help to you as you

plan for teaching mathematics?        Yes        No.

Comment:

3. Do you feel the activities presented in this workshop will be of help to you as you plan for teaching

mathematics?          Yes        No.

Comment:

4. Do you feel the handouts supplied in this workshop will be of help to you as you plan for teaching

mathematics?          Yes        No.

Comment:

5. Have you any suggestions for additional information, strategies, and/or activities that you think would

be particularly helpful to participants in future math workshops? If so please list them below.

Suggestions:

Thank you for your input.