from Van de Walle Teaching Student Centered Mathematics K-3 and Carpenter, et. al. Children’s Mathematics: Cognitively Guided Instruction

 Three children successfully solved addition and subtraction tasks for two digit numbers.  Fourteen of the twenty-one children used their fingers to count all or count on as they solved such problems as = ___ and = ___.  Three of the children needed cubes to solve such problems and counted all the cubes.  One child had difficulty counting more than seven cubes accurately.

Counting & number relationships are the basis for Problem solving which leads to Fluency with whole numbers

 Number concepts are intimately tied to the world around us. Application of number relationships to the real world marks the beginning of making sense of the world in a mathematical fashion.

 Entering kindergarten children can most always pick the set that is more.  Although the concept of less is logically equivalent to more, the word “less” is often more difficult for children than “more.”  Whenever you ask “Which is more,” also ask “Which is less.”

 Counting tells how many things are in a set. When counting a set of objects, the last word in the counting sequence names the quantity for that set.  Children will learn how to count before they understand that the last count word indicates the amount of the set. (the cardinality principle)  Resource: Illuminations “Let’s Count to 10”

 Frequent short practice drills are recommended for children who have difficulty with this.

 Numbers are related to each other through a variety of number relationships. The number 7, for example, is more than 4, less than 9, composed of 3 and 4 as well as 2 and 5, is three away from 10, and can be quickly recognized in several patterned arrangements of dots.  Number relationships for 7 further extend to an understanding of 17, 57 and 370.

 Simon says, Show six fingers.  Janice, tell us about the way you showed six fingers.  Peter, yours is different. Tell us about yours.  Does anyone have a different way to show six fingers?  Simon says, Show nine fingers.

Graphics are from Van de Walle & Lovin, Teaching Student- Centered Mathematics: Grades K-3

 Manipulatives  Video  How to Teach a Child Math – Part 1  How to Teach a Child Math - Part 2  Packet

 Careful observation during number relationship station activities will tell you a lot about where your children are with number concepts.

 Very important for basic addition fact families.  Kindergarten and early first grade children should be able to see a set of six with a set of 10 and know that the total is 16 – but they should not be asked to state that the 1 in 16 represents “one ten” or that the 6 represents “six ones.” (what’s a one?)

 Given what you’ve seen and read, what’s the best way to help children learn these things?  In whole classrooms  In small groups  One-on-one  Article on using play to teach number sense

 Double 3 is the bug double  Double 4 is the spider double  Double 5 is the hand double  Double 6 is the egg carton double  Double 7 is the two-week double  Double 8 is the crayon double  Double 9 is the 18-wheeler double

 The hundreds chart is an essential tool for every K-3 classroom!

 Estimation and measurement:  Will it be more or less than 10 footprints long? Will the apple weigh more or less than 20 wooden blocks? Are there more or less than 15 unifix cubes in this long bar?  Closer to ______ or to _______? 5 or 20 footprints, 10 or 30 blocks, 10 or 50 cubes?  About _______? … how many footprints? how many blocks? how many unifix cubes?

 Could the teacher be 15 feet tall?  Could your living room be 15 feet wide?  Can a person jump 15 feet high?  Could three children stretch their arms 15 feet?

 When kindergarten and first-grade children are regularly asked to solve problems, not only do they develop a collection of number relationships, but they also learn addition and subtraction facts based on these relationships.