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90 Cards in this Set
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What are 3 types of Fraction models?

region or area
length set 

This model emphasizes the partwhole concept and the meaning of the relative size of a part to the whole.

Region


Name some examples of a region or area model.

circular pie pieces
rectangular regions fourths on a geoboard paper folding pattern blocks drawings on grids or dot paper 

Pattern blocks and rectangular regions are classified as what kind of model?

region or area


Fourths on a geoboard and drawings on grids or dot paper are classified as what kind of model?

region or area


Circular pie pieces and pattern blocks are classified as what kind of model?

region or area


________ fraction piece models are the most commonly used area model.

circular


____________ can help students clarify ideas where fractions are concerned.

models


Area and length models are continuous. What are set models?

discreet


Construction paper strips can be used to show what?

equivalent fractions


What activity can be used to compare fractions?

construction paper strips


What activity can be used for adding fractions?

construction paper strips


What three things can you show by using construction paper strips?

adding fractions
equivalent fractions comparing fractions 

1/3 of a garden is an example that can be shown using which model?

region or area


3/4 of an inch is an example that can be shown using which model?

length


1/2 of the class is an example that can be shown using which model?

set


In this model, lengths or measurements are compared instead of areas.

length


Name some examples of length models.

Cuisenaire rods
Strips of paper Number line (emphasize when teaching fractions) Linear models (measurement tools) 

Cuisenaire rods and strips of paper are example of what kind of model?

length


Number line and linear models are examples of what kind of model?

length


The whole is understood to be a set of objects, and subsets of the whole make up fractional parts is what kind of model?

set model


Name an example of a set model.

Counters in two colors on opposite sides (can be flipped to change their color to model various fractional parts of a whole set)


It is important to remember that students must be able to ______ fractions across models.

explore


If students never see fractions represented as a _________, they will struggle to solve any problem or context that is linear.

length


What are the three benchmark fractions?

0, 1/2,1


For fractions less than 1, comparing them what will give a lot of information to students?

the three benchmark fractions


3/20 is close to which benchmark?

0


¾ is between ½ and 1. This is an example of using what?

a fraction benchmark


Can you use the fraction benchmarks for numbers like 3 3/7?

Yes because 3/7 is close to 1/2


What are the 2 requirements for fractional parts?

Must be same size
Correct number of parts 

When using fractional parts, emphasizing the number of parts that make up a whole determines what?

the name of the fractional parts or shares


The number of fractional parts determines the what?

fractional amount


Partitioning into 4 parts, means each part is __________ of the unit.

1/4


The fractional parts must be the same ______, though not necessarily the same ______.

size
shape 

A unit fractions is a fraction with ____ as the numerator.

1 (1/2)


The reciprocal of a unit fraction is a what?

positive number (2)


The top number in a fraction is the _______ number.

counting


The top number in a fraction tells how many what?

parts or shares we have


The top number in a fraction tells how many shares have been what?

counted


The bottom number in a fraction tells how big what is?

the part


The bottom number in a fraction tells what?

Tells what is being counted
Tells how big the part is If it is a 4, it means we are counting fourths; 6 we are counting sixths, etc 

What order should you teach fractions?

simplifying
equivalent comparing 

When teaching ____________ you have students use contexts and models to find different names for a fraction.

equivalent fractions


When teaching __________ you use a traditional algorithm: find the common denominator.

comparing fractions


What activities could you use when teaching equivalent fractions?

dot paper equivalencies


When teaching to put a fraction in simplest form, do not say what?

reducing fractions


What conceptual thought pattern would you use to compare 3/8 and 5/8?

more of the same size parts (same denominator)


What conceptual thought pattern would you use to compare 3/4 and 3/7?

Same number of parts, but parts of different sizes (same numerator)


What conceptual thought pattern would you use to compare 3/7 and 5/8 5/4 and 7/8?

More and less than onehalf or onewhole.


What conceptual thought patter would you use to tell why 9/10 is greater than ¾?

closeness to onehalf or onewhole (each is one fractional part away from one whole)


Addition using fraction tiles. On Monday, Bully ate 1/8 of a pepperoni pizza and 5/8 of a cheese pizza. How much pizza did Bully eat on Monday?

1/8
+1/8, 1/8, 1/8, 1/8, 1/8 __________________ 1/8, 1/8, 1/8, 1/8, 1/8, 1/8 (6/8) 

Multiplication using fraction tiles. There was 4/5 of a gallon of maroon paint in Bully's bucket. Bully used 3/4 of that to paint his house. What part of the original gallon did Bully use?

1. Make the 5ths in bucket horizontally.
2. Make the 4ths in bucket vertically. 3. Circle 3/4ths 

Division using fraction tiles. Bully has 3 yards of material. He is making costumes for the home football games. If each patter requires 1 1/6 yards of material, how many patterns will he be able to make?

Make 3 yards visual.
Divide the last yard into 6ths. 1 1/6 = 1 costume 1 1/6 = 1 costume 2 costumes can be made 

Bully has 12/15 of a bag of bones. If he eats 3/15 of a bag per serving, how many servings does he have?

1. Draw the 12 bones
2. divide them into equal groups of three 3. count the number of groups made 

_________ is a comparison of an attribute of an item or situation with a unit that has the same attribute.

measurement


Lengths are compared to units of _________.

length


Areas are compared to units of _________,

area


Time is compared to units of _______.

time


What are the steps to measuring?

1. Decide on the attribute to be measured
2. Select a unit that has that attribute 3. Compare the units, by filling, covering, matching, or using some other method, with the attribute of the object being measured. The number of units required to match the object is the measure. 

What are the four attributes in measurement?

weight, volume/capacity, length, and area


What are the 5 units of measure?

volume/capacity
weight/mass time money angle measurement 

Area is a measure of what?

covering


What is step one of measuring?

decide on an attribute (weight, length, etc) to be measured


What is step two of measuring?

Select a unit that has that attribute.(length=rods, string, or paper clips)


__________________ make it easier to focus directly on the attribute being measured.

nonstandard units


___________ can avoid conflicting objectives in the same beginning lesson

nonstandard units


___________ can be motivating when learning how to measure.

nonstandard units


_______________ are essential objectives of a measurement program.

standard units


Once a measuring concept is fairly well developed, ___________ can be effectively introduced

standard units


Name some informal units to teach length with.

foot prints
ropes straws toothpicks paper clips 

Name some informal units to teach area with.

Plastic chips
Color tiles Squares from cardboard Newspaper sheets 

Name some informal units to teach volume and capacity with.

Plastic cups and medicine cups
Plastic jars and containers Styrofoam packing peanuts Sugar cubes 

What the levels of the van Hiele Model?

0. Visualization
1. Analysis 2. Informal Deduction 3. Deduction 4. Rigor 

What is an example activity for the Visualization level?

Sorting yellow shapes in class (Shapes, shapes, shapes)


What is an example activity for the Analysis level?

Geoboard shapes


What is an example activity for the Informal Deduction level?

Shape Riddle (property lists with definitions)


The deduction level occurs when?

High school geometry


The rigor level occurs when?

with a college math major


What level do they think about shapes and what they “look like”?

visualization


What level do they produce classes or groupings of shapes that seem to be “alike”?

visualization


What level do they think about classes of shapes rather than individual shapes?

Analysis


What level do they able to produce properties of the shapes?

Analysis


What level do they think about properties of shapes?

informal deduction


What level do they produce relationships among properties of geometric objects?

informal deduction


An activity you could use to move students from Level 0 to Level 1 is what?

choose shape and match it to one in the room


Why is choosing a shape and matching it to one in the room a good activity/

attends to a variety of characteristics of shapes in sorting and building activities


Instruction at Level 1 should focus on what?

properties of the shapes


In what level should you encourage students to make conjectures and test them?

Level 1 or 2


__________ is an intuition about shapes and the relationships among shapes.

spatial sense


___________ includes the ability to visualize objects and relationships mentally.

spatial
