Fractions and Numerical Fractions and Numerical FluencyFluency

Goals & PurposesGoals & Purposes

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

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

Increase teacher knowledge of rational Increase teacher knowledge of rational numbers.numbers.

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

Solve the Following Problem Think about the strategy/strategies you used

to solve the following problem.

Yesterday I baked my family a 9x13 pan of brownies. I cut the brownies in individual servings. Russell took ½ of the brownies, Chris took 1/3 of what was left, Natalie took ¼ of what was then left in the pan. An hour later Chris came back and took two more brownies, leaving one brownie for me. How many individual pieces did I cut the brownies into to begin with?

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.

How Did You Solve the How Did You Solve the Problem?Problem?

Share your strategies with your neighbor.Share your strategies with your neighbor. Share your strategies with the whole Share your strategies with the whole

group. group.

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.

Development of FractionsDevelopment of Fractions

Where and How Do We See Where and How Do We See Fractions?Fractions?

Importance of the WholeImportance of the Whole

Referents Referents

Reference points of 0, ½, and 1Reference points of 0, ½, and 1 Fraction EstimatorsFraction Estimators How Big Am I?How Big Am I?

Solve the Following Problem Think about the strategy/strategies you

used to solve the following problem.

2/4, 3/6, 4/8, and 5/10 are all equivalent to 1/2. What is the relationship between the numerator and denominator in each fraction? Explain why they are equivalent to 1/2.

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.

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 TEKS teach this concept to the TEKS Refinement Wall.Refinement Wall.

Equivalent FractionsEquivalent Fractions

How Do I Compare? Let Me Count the How Do I Compare? Let Me Count the Ways.Ways.

Equality for AllEquality for All Mixing It UpMixing It Up

Building Foundations for Building Foundations for MathematicsMathematics

Numerical Fluency Defined!Numerical Fluency Defined!

““Mingle to Music”Mingle to Music”

Stand with mind map and a writing utensil.Stand with mind map and a writing utensil. When the music begins, walk around the room with your When the music begins, walk around the room with your

paper.paper. When music stops, freeze and turn to the person closest When music stops, freeze and turn to the person closest

to you.to you. If you do not have a partner, raise your hand and walk to If you do not have a partner, raise your hand and walk to

another person raising his/her hand.another person raising his/her hand. Each partner shares his/her mind map. As you are Each partner shares his/her mind map. As you are

listening, add ideas you did not have on your mind map.listening, add ideas you did not have on your mind map. Tell participants they will have 2 minutes each (total of 4 Tell participants they will have 2 minutes each (total of 4

minutes) to share and add to mind map.minutes) to share and add to mind map. When the music begins again, thank your partner and When the music begins again, thank your partner and

walk around the room again.walk around the room again. Continue this process two more times. Continue this process two more times.

Building Foundations for Building Foundations for MathematicsMathematics

Numerical Fluency Defined!Numerical Fluency Defined!

What Are the Next Steps?What Are the Next Steps?