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90 Cards in this Set
- Front
- Back
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what is a ratio |
comparison of two numbers or quantities |
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Rate
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ratio when the measuring units describing two quantities being compared are different
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what type of comparisons does the idea of ratio involve |
multiplicative comparison |
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what is a porportion |
a statement that two ratios are equal |
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what should the beginning experiences for equal ratios included |
number patterns and repeated addition |
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what procedure should children use for generating equal ratios |
multiply both terms by the same number |
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what is a scale drawing |
smaller or larger representation of an object |
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what does percent mean |
parts per hundred |
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what should children use at the concrete level to understand percent |
base ten blocks |
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what are the percent benchmarks |
1,10,25,50,100 |
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what can a rational number be expressed as |
decimal, percent, fraction |
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what is an excellent real worl context for practicing percents |
shopping |
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what are examples of everyday situations involving finding a percent of a number |
computing sales tax, discount, commission, and interest |
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what are three approaches to solving percent problems |
proportion method, equation method, unitary analysis method |
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What are the three skills needed for Unitary Analysis?
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Number sense, Operation sense, Estimation skills
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What is included as the geometry components of the math program at the elementary level
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Study of two and three dimensional shapes and objects
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What are the five levels of van hiele
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Visualization, analysis, informal deduction, formal deduction, rigid level
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What is visualization level
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Think about shapes in terms of what they resemble
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What is the analysis level
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Think in terms of properties but don't see relationship between any of the properties
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What is the informal deduction level
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Notice the relationship between and within figures
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What is the formal deduction level
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Relationships between properties of shapes but also relationships of axioms, definitions, theorems
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What is visualization level
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Think about shapes in terms of what they resemble
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What is informal deduction level
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Notice the relationship between and working figures and formulate meaningful defintions
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What is prerecognition
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Can't distinguish three sided from four sided
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What are most elementary children at
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Visualization and analysis
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What order does level go
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Sequential but not age dependent
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What language should be used at elementary level
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Informal terms and expressions; formal language will develop over time
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What is topology
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The study of properties of figures that's stay the same even under distortions
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What are the ways distortion can be achieved
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Bending, stretching, twisting, shrinking
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What is polyhedra
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3deminisonal shapes with faces consisting of polygons
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What are polygons
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Two dimensional Plane figures with straight line segments (with three or more straight sides)
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What are regular polygons
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Plane figures with sides that are all same length and angles
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What is regular poluhedron
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One whose faces consist of same kind of regular congruent polygons, with the same number of edges meeting at each vertex of the figure.
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What is stellating
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Building into solids to form different solids
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What is truncating
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Modify solids by cutting off sections in systematic way
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What is a prism
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Polyhedron with two congruent parallel bases that are polygons and all the remaining faces are parallelograms
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What are pyramids
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Whose base is a polygon and all rest of faces are triangles
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What are cylinders
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Surface generated by a family of lines parallel to a given line and passing through a curve in a plane
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What is eulers rule
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Faces +Vertices- edges= 2
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What can polygons be
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Convex or concave
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What are concave polygons
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When not all line segments roam inside the figure
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What is symmetry
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Every point of bisected shapes has a reflective point in the other side
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What is rotational symmetry
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When a figure is rotated about a point for an amount less than 360 degrees and the rotated shape matches the original shape.
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What are congruent figures
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Those that have the same size and shape
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What are similar figures
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Those that have the same shape but not always the same size
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What's a translation
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Movement along a straight line
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What are rigid transformations
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Translations, reflections, rotations
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What are rotation
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Movement of a figure around a point
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What is tessellation
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Filling a plane figure with the same plane shape with no gaps or overlaps
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What is spatial sense
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Involves both visualization and orientation
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Visualization
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The ability to mentally picture how objects appear under some rigid motion or other transformation
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Orientation
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The ability to note positions of objects and to maintain an accurate perception of objects
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Tangram
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Seven piece puzzle consisting of five triangles, one square, and one parallelogram cut from a square
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Dissection motion operation
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The operation of partitioning and then dissecting a figure for the purpose of rearranging the pieces
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What is a measurement attribute
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Characteristic that can be quantified by comparing to a unit
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Measurement
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a comparison of a standard unit for measuring a certain attribute with the attribute possessed by a given object.
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What is the instructional sequence for measurement
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Perception and direct comparison, nonstandard measurement, standard measurement
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What is the first stage of instructional sequence refferred to ss
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Premeasurement
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It does not require a unit nor assigning a number to the object being measured
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Premeasurement
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Task involving ordering three or more objects according to a particular attribute
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Seriation
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What is the criterion for selecting the appropriate unit to measure with
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Has the same attribute as that to be measured, size of unit relative to object measured
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What are standard units
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Units that have been agreed on and accepted by a group of people
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What is length of a object
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The distance between two end points
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What is area
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Amount of surface enclosed by a curve in the plane
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What is volume
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Amount of space inside a closed three dimensional region
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What is capacity
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The amount a container will hold
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What is mass
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Amount of matter in an object
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What is weight |
The force of gravity acting on the mass |
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What is time
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When an event occurred or will occur and how long an event lasted
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What is temperature
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Measure of how hot or cold an object is
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What is commonly used for recording temperature in metric system
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Celsius scale
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What is angle
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The Union of two rays that have the same end point
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What is a percent
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Part to whole ratio that has 100 as it second term
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What is the best way to teach concepts of ratios
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Begin with real world problems, act them out with proportional manipulative, draw meaningful pictures, work toward symbolic mode
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What is a unit rate
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When the second term is 1, the rate is called unit rate
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What would you use to distinguish the difference between polyhedron and regular polyhedra |
Informal deduction |
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What is measurment
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Comparison of an attribute of an object to standarized unit
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How many regular polyhedra are there
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5
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How many semi regular polyhedra are there
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13
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What are pyramids
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Polyhedron whose base is a polygon and all the rest of the faces are triangles that meet at a vertex
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What are cones |
Surface generated with a family of all likes through a given point and adding through a curve in a plane |
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Irregular polyhedra
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not all of the faces are congruent
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Plane symmetry
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a three dimensional shape has plane symmetry if a plan passing through the figure bisects it such that every point of the figure on one side of the plane has a reflection image on the other side of the plane
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What are the 9 different translations, reflections, and rotations.
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horizontal slide, vertical slide, oblique slide,
Reflection about a line on a figure, reflection about a line not on the figure, reflection line intersects with a vertex, turning point inside a figure, turning point on the figure, turning point outside the figure |
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What are the two systems of standard units that are used in the united states?
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Customary system and metric system
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strategies used by good estimators include:
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Referents, chunking, and unitizing
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perimeter
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the distance around a closed figure
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Iteration of the unit
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to reuse the same unit.All things used to measure an object must be the same size.The next unit begins at the precise point that the previous unit ends.
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Proportional Reasoning
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Ability to understand ratiosInvolves both qualitative and quantitative thinkingConcerns prediction and multiple comparisons
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Reflection
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Movement of a figure about a line; outside the figure, on a side of the figure, or intersecting with a vertex
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