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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 part-whole 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 one-half or one-whole.
What conceptual thought patter would you use to tell why 9/10 is greater than ¾?
closeness to one-half or one-whole (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