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1. 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.,
,
, “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.
2. Use place
value structure of the base-ten number system to read, write,
represent and compare whole numbers through millions and decimals
through thousandths.
3. Round whole
numbers to a given place value.
4. Identify and represent factors and multiples of whole
numbers through 100, and classify numbers as prime or composite.
5. Use models
and points of reference to compare commonly used fractions.
6. 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 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235.
7. 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.
8. Solve
problems involving counting money & making change, using both
coins & paper bills.
9. Estimate the
results of computations involving whole numbers, fractions and
decimals, using a variety of strategies.
10.
Use physical models, visual representations, and paper and
pencil to add and subtract decimals and commonly used fractions
with like denominators.
11.
Develop and explain strategies for performing computations
mentally.
12.
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.
13.
Use a variety of methods and appropriate tools for
computing with whole numbers; e.g., mental math, paper and pencil,
and calculator.
14.
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 Standard
1. 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.
2. Demonstrate
and describe perimeter as surrounding and area as covering a
two-dimensional shape, and volume as filling a three-dimensional
object.
3. 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).
4. 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.
5. Make simple
unit conversions within a measurement system; e.g., inches to
feet, kilograms to grams, quarts to gallons.
6. Write, solve
and verify solutions to multi-step problems involving measurement.
Geometry and Spatial Sense Standard
1. Identify,
describe and model intersecting, parallel and perpendicular lines
and line segments; e.g., use straws or other material to model
lines.
2. Describe,
classify, compare and model two- and three-dimensional objects
using their attributes.
3.
Identify similarities and differences of quadrilaterals;
e.g., squares, rectangles, parallelograms and trapezoids.
4.
Identify and define triangles based on angle measures
(equiangular, right, acute and obtuse triangles) and side lengths
(isosceles, equilateral and scalene triangles).
5.
Describe points, lines and planes, and identify models in
the environment.
6.
Specify
locations and plot ordered pairs on a coordinate plane, using
first quadrant points.
7.
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.
8.
Use geometric models to solve problems in other
areas of mathematics, such as number (multiplication/division)
and measurement (area, perimeter, border).
Patterns, Functions and Algebra Standard
1. Use models
and words to describe, extend and make generalizations of patterns
and relationships occurring in computation, numerical patterns,
geometry, graphs and other applications.
2. Represent and
analyze patterns and functions using words, tables and graphs.
3. Construct a
table of values to solve problems associated with a mathematical
relationship.
4. Use rules and
variables to describe patterns and other relationships.
5. Represent
mathematical relationships with equations or inequalities.
6. Describe how
a change in one variable affects the value of a related variable;
e.g., as one increases the other increases or as one increases the
other decreases.
Data Analysis and Probability Standard
1.
Create a plan for collecting data for a specific purpose.
2.
Represent and interpret data using tables, bar graphs, line
plots and line graphs.
3.
Interpret and construct Venn diagrams to sort and describe
data.
4.
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.
5.
Propose
and explain interpretations and predictions based on data
displayed in tables, charts and graphs.
6.
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.
7.
Identify
the median of a set of data and describe what it indicates about
the data.
8. Use range, median
and mode to make comparisons among related sets of data.
9. Conduct simple
probability experiments and draw conclusions from the results;
e.g., rolling number cubes or drawing marbles from a bag.
10.
Represent the likelihood of possible outcomes for chance
situations; e.g., probability of selecting a red marble from a bag
containing 3 red and 5 white marbles.
11.
Relate the concepts of impossible and certain-to-happen
events to the numerical values of 0 (impossible) and 1 (certain).
12.
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.
13.
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 pairs
of shoes.
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