Operations and Numerical FluencyOperations and Numerical Fluency

25 + 25 =10 + 10 + 5 + 10 + 10 + 5 =

10, 20, 25, 35, 45, 5020 + 20 + 5 + 5 = 40 + 10 =

50 I just thought of it as 2 quarters

and 2 quarters is 50 cents. So, 25 + 25 = 50

Goals & PurposesGoals & Purposes

Increase teacher knowledge regarding the Increase teacher knowledge regarding the refinements of the TEKS relating to numerical refinements of the TEKS relating to numerical fluency.fluency.

Increase teacher knowledge of composing and Increase teacher knowledge of composing and decomposing numbers.decomposing numbers.

Increase teacher knowledge of the use of Increase teacher knowledge of the use of strategies to teach numerical fluency for strategies to teach numerical fluency for operations of whole numbers.operations of whole numbers.

Develop an understanding of the use of Develop an understanding of the use of metacognition in problem solving.metacognition in problem solving.

Defining Addition, Subtraction, Defining Addition, Subtraction, Multiplication, and Division of Whole Multiplication, and Division of Whole

NumbersNumbers

At your table, develop a definition of At your table, develop a definition of addition, subtraction, multiplication, and addition, subtraction, multiplication, and division based on the TEKS for your division based on the TEKS for your particular grade level.particular grade level.

Small groups share their answer with the Small groups share their answer with the large group.large group.

Solve the Following Problem

Mrs. Parks is buying ice-cream bars for the 17 dozen students at her school. The ice cream bars are packaged 10 to a box. What is an estimate of the number of boxes she has to buy so that each student gets at least 1 ice cream bar?

What am I supposed to What am I supposed to find?find?

PicturePicture

Table/Chart/ListTable/Chart/List Number SentenceNumber Sentence

Explain how you derived your answer(s)?

Write down your thought processes as you solve the following problem.

Let us come back together and Let us come back together and share solutions and strategies share solutions and strategies with groups.with groups.

TEKSTEKS

Each group will be assigned a grade level.Each group will be assigned a grade level. Identify the TEKS in your grade level (K-5) Identify the TEKS in your grade level (K-5)

that students must master in order to have that students must master in order to have success in solving this 5success in solving this 5thth grade problem. grade problem.

Are there any refinements that need to be Are there any refinements that need to be identified? Add refined TEKS needed to identified? Add refined TEKS needed to teach this concept to the poster board.teach this concept to the poster board.

EstimationEstimation

Measurement estimationMeasurement estimation Quantity estimationQuantity estimation Computational estimationComputational estimation

Computational EstimationComputational Estimation

Computational estimation is the ability to Computational estimation is the ability to quickly produce an approximate result for quickly produce an approximate result for a computation that will be adequate for the a computation that will be adequate for the situation.situation.

Computational EstimationComputational Estimation

Front-end ApproachFront-end Approach Rounding MethodsRounding Methods Compatible NumbersCompatible Numbers

BREAKBREAK

Addition and Subtraction of Addition and Subtraction of Whole NumbersWhole Numbers

Amy is 8 years old. She was assigned a Amy is 8 years old. She was assigned a school project regarding her family. She school project regarding her family. She did not know the year that her did not know the year that her grandmother was born, but did know that grandmother was born, but did know that she just celebrated her 86she just celebrated her 86thth birthday. How birthday. How could Amy determine the year her could Amy determine the year her grandmother was born? grandmother was born?

Double Digit Addition and Double Digit Addition and Subtraction Through the Use of Subtraction Through the Use of

StrategiesStrategies Reflect on how you have solved previous Reflect on how you have solved previous

problems. Have you always used a problems. Have you always used a traditional algorithm to solve the problem?traditional algorithm to solve the problem?

Think about how children use inventive Think about how children use inventive strategies to solve problems.strategies to solve problems.

How important is students’ metacognition How important is students’ metacognition of solving mathematical problems?of solving mathematical problems?

Relationships in Multiplication and Relationships in Multiplication and DivisionDivision

12

1x12

2x6

3x412x1

6x24x3

Relationships of OperationsRelationships of Operations Brainstorm at your table all the relationships Brainstorm at your table all the relationships

between the operations of whole numbers.between the operations of whole numbers.

Walk 7 steps from where you are now and share Walk 7 steps from where you are now and share relationships with someone near you.relationships with someone near you.

Take 7 more steps and repeat this procedure.Take 7 more steps and repeat this procedure.

Share with the whole group relationships that Share with the whole group relationships that were found. were found.

When to Develop AutomaticityWhen to Develop Automaticity

Once you have taught two strategies, drill Once you have taught two strategies, drill based on those strategies.based on those strategies.

Teach more strategies.Teach more strategies. Automaticity is needed ONLY after Automaticity is needed ONLY after

students have developed a meaningful students have developed a meaningful concept of addition, subtraction, concept of addition, subtraction, multiplication, or division and they have multiplication, or division and they have also developed flexible and useful also developed flexible and useful strategies for those operations. strategies for those operations.

How to Develop AutomaticityHow to Develop Automaticity

The competition is to be developed from The competition is to be developed from within the child (intrinsic motivation), not within the child (intrinsic motivation), not against other children.against other children.

Using time as the goal.Using time as the goal. Using number of problems as the goal.Using number of problems as the goal.

BREAKBREAK