Developing Number Concepts in Early Childhood Sponsored by Central Maine Inclusive Schools September 13, 2007 Facilitated by Jim Cook

Major Ideas to develop:  Counting  Part-Whole Relationships  Addition and Subtraction  Place Value

Counting  FNWS  BNWS  1-1 Tagging  Cardinality  Ordinal Numbers Ducks in a Line

Part-Whole Relationships Research says: Children who use the part-whole approach scored significantly higher on number concepts, problem solving, and place value than children who just counted by ones. Research Ideas for the Classroom, Early Childhood Mathematics

Seeing Quantities without Counting  Subitizing  Five Frames  Ten Frames

Activities to Support Part-Whole Relationships  Five—Hide Some  Red and Black  Ten Mice in a Cage

Addition and Subtraction  Strategies to look for: Count all Count on  Count on from the first number  Count on from the greater number Reasoning Strategy Known Fact

Activities to Support Addition and Subtraction  Turn Over Ten  First Off the Bridge  Problem Solving Frumps Fashions Problem Types Grid  X-Ray Vision  Close to 20

Addition and Subtraction Facts Students should be encouraged to use reasoning strategies in order to learn addition and subtraction facts. Reasoning strategies are more powerful and efficient than counting by ones. Students who learn facts through reasoning strategies retain the knowledge better than students who simply memorize.

Addition Facts Strategies  Doubles  Doubles plus or minus one  Make a ten  Near Doubles

Subtraction Facts Strategies  Take away zero  Take away all  Count down  Doubles  How close?  Use ten Take away from the ten Find the total distance of each number from ten  Use related addition facts

Remember:  Solving word problems helps students learn their facts.  Students do not need to know their facts before they are introduced to problem solving.

Place Value  Goals for students Understand the relationship between numbers and groups of tens and ones Understand the significance of the position digits in numbers Make the connection between place value and addition/subtraction

Place Value Ideas to Remember  Students need to relate symbolic numbers to the word form and also to their base-10 representation  Ask students about numbers: “How many groups of ten can be made? How many extras?” “If there are six groups of ten and four extras, how many are there?”

Place Value Activities  Count in more than one way Count beans in more than one way Read The King’s Commissioners  Count using tens and ones Count dots on two-color counters Count using base-10 blocks or tens frames  Connect tens and ones with addition and subtraction The Game of Tens and Ones Plus, Minus, Stay the Same

Mini-lessons to Support Addition  Making Jumps of ten  Using ten  Moving to the next friendly number