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Transparency-5TEXTEAMS Rethinking Middle School Mathematics: Numerical Reasoning

Why Do We Need This Stuff Anyway?Transparency

List examples of how we use numbers in everyday life.


What’s the Point?Transparency

The students in Miss Faith’s math class are divided into

groups. Each group is able to earn points through a variety of

activities. At the end of a certain time period, the points are

divided evenly between the members of the group. What are

the advantages and disadvantages of recording this division

in integer quotient and remainder form? In fraction form? In

decimal form?

11TEXTEAMS Rethinking Middle School Mathematics: Numerical Reasoning

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0.200.600.700.80

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10% 20% 30%

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And Around We Go!Interest Inventory Transparency

Favorite Sport # Ratio

Football

Baseball

Basketball

Other

Favorite Soft Drink # Ratio

Coca Cola

Dr. Pepper

Pepsi

Other

Favorite Music # Ratio

Rock

Country

Rap

Alternative

Other

Favorite Color # Ratio

Green

Blue

Red

Other


Four-Tenths Plus Seven-Tenths Is Eleven-TenthsTransparency 1

Suppose one of your students turned in this work. Whenyou questioned the student about the last problem, the re-sponse was “four tenths plus seven tenths is eleventhtenths.” What approach would you use to help this childcorrect the error?

.2 .38 .91 .5 .7

+.6 +.47 +.43 +.25 +.4

.8 .85 1.34 .75 .11


Four Tenths plus Seven Tenths is Eleven TenthsTransparency 2

We will use the jigsaw approach to rotate through the centersand share information with other group members.

1. Each group member will select a different problem from thechart on Transparency 1.

2. Each participant will rotate through the four centersconsidering how the different model(s) would work with theerror in the problem they selected.

3. When step 2 is completed, participants working with thesame problem will meet to discuss their experience withthe four different types of models.

4. After step 3 is completed, participants will return to theiroriginal groups. Each participant will debrief the othermembers on what they learned from working with the fourmodels and the error in their problem


Does One-and-One Make Two?Transparency

In basketball, Team A is inwhat is known as a one-and-one situation when theopposing team, Team B,has made a total of sevenfouls. Each time Team A goes to thefree throw line, they will get a secondfree throw if they make the first one.

Suppose Michelle makes 50% of thefree throws she attempts. What isthe probability she will make 2 points,1 point, or 0 points?


More or Less?Transparency

1. Three-fifths of the earth’s land was oncecovered in forests. Today half of thoseforests are gone. What fractional partof the earth’s land is now covered inforests?

2. In basketball, Team A is in what isknown as a one-and-one situation whenthe opposing team, Team B, has made atotal of seven fouls. Each time Team Agoes to the free throw line, they will get asecond free throw if they make the firstone.

Suppose Michelle makes half of the free throws sheattempts, what is the probability she will make 2 points,1 point, or 0 points?


Final ReflectionsTransparency 1: Organizing Our Ideas

(from R. Charles and J. Lobato’s Future Basics: Developing Numerical Power,NCSM, 1998, p. 13)

A Numerically Powerful Child1. develops meaning for numbers and operations

a. connects numerals with situations from life experiences

b. knows that numbers have multiple interpretations

c. understands that number size is relative

d. connects addition, subtraction, multiplication, and divisionwith actions arising in real-world situations

e. understands the effects of operating on numbers

f. creates appropriate representations for numbers

g. creates appropriate representations for operations




A Numerically Powerful Child2. makes sense of numerical and quantitative situations

a. expects numerical calculations to make sense

b. connects numbers to the quantities that the numbers areused to measure

c. relates the operations of addition, subtraction,multiplication, and division to a range of quantitativesituations

d. seeks to understand relationships among quantities inreal-world situations

e. relates computations to quantities in real-world situations

f. assesses whether the result of a calculation makessense in the context of the numbers and real-worldquantities involved




A Numerically Powerful Child3. looks for relationships among numbers and operations

a. decomposes or breaks apart numbers in different ways

b. knows how numbers are related to other numbers

c. understands how the operations are connected to eachother




A Numerically Powerful Child4. understands computational strategies and uses them

appropriately and efficiently

a. correctly performs the steps in an algorithm anddiscusses the underlying ideas and importantrelationships used

b. makes a conscious effort to complete calculations usingprior knowledge and simpler calculations

c. often uses a variety of calculation strategies, even whencompleting calculations involving the same operation

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