Welcome to the Make Math MeaningfulAudio-Web Conference

Feb. 4, 2004

Sheryl Beglinger

Comprehensive Center Region VI

smbeglinger@wisc.edu

Internet Sites for Lessons on Number Sense

• Developing Number Sense

• Making Sense of Numbers (gr. 3 – 5)

• Number Sense and Sensibility (gr. 6 – 8)

• SCORE Mathematics Number Sense

Numbers and Operations Standard of the NCTM

Instructional programs from pre-kindergarten through grade 12 should enable all students to-

• understand numbers, ways of representing numbers, relationship among numbers and number systems

• understand operations and how they relate to one another

• compute fluently and make reasonable estimates

(Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pg. 32)

•compute fluently and make reasonable estimates

• “Estimation serves as an important companion to computation.”*– Used to judge the reasonableness of a

computation– Helps to develop number sense

• Students need to share their estimation strategies so that other students can develop a range of estimation strategies

*(Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pg. 155)

Estimation Activity

Numbers to multiply Estimated product Actual product Difference

Estimation Activities on the Internet

• Estimating a Sum by Rounding

• Estimate the Difference between two Numbers

• Glowla’s Estimation Contraption

Emphasis of these Content Standards by Grade Levels

(Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pg. 30)

Algebra

Algebra Standard

Instructional programs from pre-kindergarten through grade 12 should enable all students to:

• Understand patterns, relations, and function• Represent and analyze mathematical situations

and structures using algebraic symbols• Use mathematical models to represent and

understand quantitative relationships• Analyze change in various contexts

(Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pg. 37)

Growing Squares

1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

Investigate numerical and geometric patterns and express them mathematically in words or symbols.

Students should be encouraged to explain these patterns verbally and to make predictions about what will happen if the sequence is continued.

Understand patterns, relations, and function

• Activities– Scholastic Internet Field Trip – Patterns

– Stop That Creature!

– Function Machine

– Mystery Operations

Represent and analyze mathematical situations and structures using

algebraic symbols.

Super Chocolates are arranged in boxes so that a caramel is placed in the center of each array of four chocolates, as shown below. The dimensions of the box tell you how many columns and how many rows of chocolates come in the box. Develop a method to find the number of caramels in any box if you know its dimensions. Explain and justify your method using words, diagrams, or expressions.

C = LW – L – W + 1

-use mathematical models to represent and understand quantitative relationships

• Swimming Pool Problem (Part 1)• (Part 2)

from Ferrini-Mundy, J., Lappan, G., & Phillips, E. (1997). Experiences with patterning. Teaching Children Mathematics, 3(6), 282-289.

Tat Ming is designing square swimming pools. Each pool has a square center that is the area of the water. Tat Ming uses blue tiles to represent the water. Around each pool there is a border of white tiles. Here are pictures of the three smallest square pools that he can design, with blue tiles for the interior and white tiles for the border.

Analyze change in various contexts

• Learning about Rate of Change in Linear Functions Using Interactive Graphs

• Possible or Not? Interpreting Graphs

• NASA Explores National Standards – Analyzing Change in Various Contexts

• Using Graphs to Convey Information

Internet Websites to Explore Algebra

• NASA Explores National Standards – Algebra

• Score Mathematics – Algebra and Functions

Session Wrap Up• Check out our webpage:

Make Math Meaningful

• Questions/Comments???

• For Copy of Power point Sheryl Beglinger’s Staff Page

• Next Week - Geometry