Standards Academy

Grades 3 and 4Day 3

Welcome BackReflection on yesterday:

• 4 Point Evaluation

• Parking Lot

Objectives• Build a Solid Understanding of the

Fractions Progression Document• Examine Essential Fraction Strategies

• Modeling Fractions on a number line• Equivalent Fractions• Addition and Subtraction of Fractions• Multiplication of Fractions

• Study Core Standards Related to Fractions

Context and ModelsRegion or Area Models

• Helps students visualize parts of the whole.

Length Models• Helps students visualize iteration, counting

and measurement.

Set Models• Helps build understanding of division and

ratio concepts.

Various Models

Fraction Brainstorm1. Fold a paper into three columns.2. Title each column after a different

fraction model.3. With a partner, generate some

question types or activities that work well with that model.

4. See how many you can list that have nothing to do with pizza or food.

Early fractions instruction generally focuses on the idea that fractions represent parts of a whole. Although the part-whole interpretation of fractions is important, too often instruction does not convey another simple but critical idea: fractions are numbers with magnitudes (values) that can be either ordered or considered equivalent.

Many common misconceptions—such as that two fractions should be added by adding the numerators and then adding the denominators—stem from not understanding that fractions are numbers with magnitudes. Not understanding this can even lead to confusion regarding whether fractions are numbers. For example, many students believe that four-thirds is not a number, advancing explanations such as, “You cannot have four parts of an object that is divided into three parts.”

Further, many students do not understand that fractions provide a unit of measure that allows more precise measurement than whole numbers; these students fail to realize that an infinite range of numbers exists between successive whole numbers or between any two fractions. Reliance on part-whole instruction alone also leaves unclear how fractions are related to whole numbers.

So Why the Number line?

After reading this excerpt from the IES practice guide take a moment to:

• Think: Why emphasize instruction on the

number line?

• Pair: Turn to a partner and discuss why.

• Share: With the class discuss what you and

your partner think.

Block Party1. Read the Progression Document.

2. Take 3 min to read your card and think about its meaning.

3. When signaled, find the person who has the same card as

you, share your thinking and clarify each other's

understanding.

4. When signaled, mingle around the room finding a new

partner. Share, explain and discuss your quote cards.

5. Repeat as many mingles as time allows.

Ah-ha!“Unit fractions are the basic building blocks of fractions in the same sense

the number 1 is the basic building block of whole numbers; just as every

whole number is obtained by combining a sufficient number of 1’s,

every fraction is obtained by combining a sufficient number of unit

fractions.”http://www.illustrativemathematics.org/fractions_progression

Fraction Strategies

D

B

C

A

Concrete Representational Abstract

     

Core Connection   Progression Connection

   Key Terms

 Prerequisite/Corequisite Skills

 DOK 1 DOK 2 DOK 3

     

Fraction Equivalence Snow Ball Fight!

1. Skim the progression document for information about fraction equivalence.

2. Find one statement or model to write down, and one question both pertaining to fraction equivalence.

3. Crumble your notes and toss them across the room.

4. Pick up one note and it take back to your partner or triads to discuss.

Ah-ha!“Fraction equivalence is founded in reasoning and experimentation with number lines and tape diagrams.

Students will need numerous exposures and opportunities to

discover and explore equivalence in order to form a solid conceptual

understanding.”

http://www.illustrativemathematics.org/fractions_progression

Equivalency Strategies

A

B

Reasonaboutthis..

Addition and Subtraction1. Solve and review your task individually. Think

about the following questions:• Can this be modeled with a number line? Is there a better model?• How could a student use their understanding of unit fractions to

solve this?• Can this be seen as composed of unit fractions or decomposed to

unit fractions?• Does the student need to convert to common units?

2. As a table discuss your various tasks. • Have each member describe their task.• Address the questions from step one.

3. Extend your discussion• What’s the math? How could it be improved? What is the relation

to addition and subtraction of fractions? What is the core connection? What support/vocabulary/background would your students need?

Addition and Subtraction

 

http://www.illustrativemathematics.org/fractions_progression

AB

C

E

Concrete Representational Abstract

     

Core Connection   Progression Connection

   Key Terms

 Prerequisite/Corequisite Skills

 DOK 1 DOK 2 DOK 3

     

If only…….Let’s check out this oldie but

goody

Multiplication1. Read article individually. 2. Form groups to discuss the following

questions:a) What assumptions does the author of the text

hold?b) What do you agree with?c) What do you want to argue?d) What do you want to aspire to?

3. Take turns making sure each person at your table has an opportunity to respond to each of the 4 A’s.

Multiplication

http://www.illustrativemathematics.org/fractions_progression

A B

C D

Wrap Up & ReflectQuestions or Concerns……..

Complete a 4 point evaluation:• What went well today?• What could be improved?• What do you need more support in?• What did you master?