| Number and Number
Systems |
- Identify
and generate
equivalent forms of fractions and decimals. For example:
a. Connect physical, verbal and symbolic representations of
fractions, decimals and whole numbers (e.g., 1/2, 5/10,
"five-tenths", 0.5 shaded rectangles with half, and five tenths.
b. Understand and explain that ten tenths is the same as one whole
in both fraction and decimal form.
- Use place value structure of the
base-ten number system to read, write, represent and compare whole numbers
through millions and decimals through thousandths.
- Round whole numbers to a given
place value.
- Identify and represent factors and
multiples of whole numbers through 100, and classify numbers as prime or
composite.
- Use models and points of reference
to compare commonly used fractions.
|
| Meaning of Operations |
- Use associative and
distributive properties to simplify and perform computations (e.g., use
left to right multiplication and the distributive property to find an
exact answer without paper and pencil, such as 5X47 = 5X40 + 5X7 = 200+35
= 235.
- Recognize that division may be used
to solve different types of problem situations and interpret the meaning
of remainders (e.g., situations involving measurement, money).
|
| Computation and
Estimation |
- Solve
problems involving
counting money and making change, using both coins and paper bills.
- Estimate the results of
computations involving whole numbers, fractions and decimals, using a
variety of strategies.
- Use physical
models, visual
representations, and paper and pencil to add and subtract decimals and
commonly used fractions with like denominators.
- Develop and explain strategies for
performing computations mentally.
- Analyze and solve multi-step
problems involving addition, subtraction, multiplication and division
using an organized approach, and verify and interpret results with respect
to the original problem.
- Use a variety of methods and
appropriate tools for computing with whole numbers (e.g., mental math,
paper and pencil and calculator.
- Demonstrate fluency in adding and
subtracting whole numbers and in multiplying and dividing whole numbers by
1- and 2-digit numbers and multiples of ten.
|
| Measurement Units |
- Relate the number of
units to the size of the units used to measure an object (e.g., compare
the number of cups to fill a pitcher to the number of quarts to fill the
same pitcher.
- Demonstrate and describe perimeter
as surrounding and area as covering a two-dimensional shape, and volume as
filling a three-dimensional object.
- Identify and select appropriate
units to measure:
a. perimeter - string or links (inches or centimeters).
b. area - tiles (square inches or square centimeters.
c. volume - cubes (cubic inches or cubic centimeters).
|
| Use Measurement
Techniques & Tools |
- Develop and use
strategies to find perimeter using string or links, area using tiles or a
grid, and volume using cubes (e.g., count squares to find area of regular
or irregular shapes on a grid, layer cubes in a box to find its volume.)
- Make simple unit conversions within
a measurement system (e.g., inches to feet, kilograms to grams, quarts to
gallons.)
- Write, solve and verify solutions
to multi-step problems involving measurement.
|
| Characteristics &
Properties |
- Identify, describe and
model intersecting, parallel and perpendicular lines and line segments
(e.g., use straws or other material to model lines.
- Describe, classify, compare and
model two- and three-dimensional objects using their attributes.
- Identify similarities and
differences of quadrilaterals (e.g., squares, rectangles, parallelograms
and trapezoids).
- Identify and define triangles based
on angle measures (equiangular, right, acute and obtuse triangles) and
side lengths (isosceles, equilateral and scalene triangles).
|
| Spatial Relationships |
- Describe points, lines
and planes, and identify models in the environment.
- Specify locations and plot ordered
pairs on a coordinate plane, using first quadrant points.
|
| Transformations &
Symmetry |
Identify, describe and
use reflections (flips), rotations (turns), and translations (slides) in
solving geometric problems (e.g., use transformations to determine if 2
shapes are congruent.
|
| Visualization &
Geometric Models |
Use geometric models to
solve problems in other areas of mathematics, such as number
(multiplication/division) and measurement (area, perimeter, border).
|
| Use Patterns, Relations
& Functions |
- Use models and words to
describe, extend and make generalizations of patterns and relationships
occurring in computation, numerical patterns, geometry, graphs and other
applications.
- Represent and analyze patterns and
functions using words, tables and graphs.
|
| Use Algebraic
Representations |
- Construct a table of
values to solve problems associated with a mathematical relationship.
- Use rules and variables to describe
patterns and other relationships.
- Represent mathematical
relationships with equations and inequalities.
|
| Analyze Change |
Describe how a change in
one variable affects the value of a related variable (e.g., as one
increases the other increases or an one increases the other decreases. |
| Data Collection |
- Create a plan for
collecting data for a specific purpose.
- Represent and interpret data using
tables, bar graphs, line plots and line graphs.
- Interpret and construct Venn
diagrams to sort and describe data.
- Compare different representations
of the same data to evaluate how well each representation shows important
aspects of the data, and identify appropriate ways to display the data.
|
| Statistical Methods |
- Propose and explain
interpretations and predictions based on data displayed in tables, charts
and graphs.
- Describe the characteristics of a
set of data based on a graphical representation, such as range of the
data, clumps of data, and holes in the data.
- Identify the median of a set of
data and describe what it indicates about the data.
- Use range, median and mode to make
comparisons among related sets of data.
|
| Probability |
- Conduct simple
probability experiments and draw conclusions from the results (e.g.,
rolling number cubes or drawing marbles from a bag.
- Represent the likelihood of
possible outcomes for change situations (e.g., probability of selecting a
red marble from a bag containing 3 red and 5 white marbles.
- Relate the concepts of impossible
and certain-to-happen events to the numerical values of 0 (impossible) and
1 (certain).
- Place events in order of likelihood
and use a diagram or appropriate language to compare the chance of each
event occurring (e.g., impossible, unlikely, equal, likely, certain.)
- List and count all possible
combinations using one member from each of several sets, each containing 2
or 3 members, (e.g., the number of possible outfits from 3 shirts, 2
shorts and 2 pair of shoes.
|