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1. Identify and
generate equivalent forms of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a yard.
2. Use place
value concepts to represent whole numbers and decimals using
numerals, words, expanded notation and physical models. For
example:
a. Recognize
100 means 10 tens as well as a single entity (1 hundred)
through physical models and trading games.
b. Describe
the multiplicative nature of the number system; e.g., the
structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1.
c. Model
the size of 1000 in multiple ways; e.g., packaging 1000 objects
into 10 boxes of 100, modeling a meter with centimeter and
decimeter strips, or gathering 1000 pop-can tabs.
d. Explain
the concept of tenths and hundredths using physical models, such
as metric pieces, base ten blocks, decimal squares or money.
3. Use
mathematical language and symbols to compare and order; e.g., less
than, greater than, at most, at least, <, >, =,
,
.
4. Count money
and make change using coins and paper bills to ten dollars.
5. Represent
fractions and mixed numbers using words, numerals and physical
models.
6. Compare and order commonly used fractions and mixed
numbers using number lines, models (such as fraction circles or
bars), points
of reference (such as more or less than ½ ), and equivalent forms
using physical or visual models.
7. Recognize and
use decimal and fraction concepts and notations as related ways of
representing parts of a whole or a set; e.g., 3 of 10
marbles
are red can also be described as
and 3 tenths are red.
8. Model,
represent and explain multiplication; e.g., repeated addition,
skip counting, rectangular arrays and area model. For example:
a. Use
conventional mathematical symbols to write equations for word
problems involving multiplication.
b. Understand
that, unlike addition and subtraction, the factors in
multiplication and division may have different units; e.g., 3
boxes of 5 cookies each.
9. Model,
represent and explain division; e.g., sharing equally, repeated
subtraction, rectangular arrays and area model. For example:
a. Translate
contextual situations involving division into conventional
mathematical symbols.
b. Explain
how a remainder may impact an answer in a real-world situation;
e.g., 14 cookies being shared by 4 children.
10.
Explain and use relationships between operations, such as:
a. relate
addition and subtraction as inverse operations;
b. relate
multiplication and division as inverse operations;
c. relate
addition to multiplication (repeated addition);
d. relate
subtraction to division (repeated subtraction).
11.
Model and use the commutative and associative properties
for addition and multiplication.
12.
Add and subtract whole numbers with and without regrouping.
13.
Demonstrate fluency in multiplication facts through 10 and
corresponding division facts.
14.
Multiply and divide 2- and 3-digit numbers by a
single-digit number, without remainders for division.
15.
Evaluate the reasonableness of computations based upon
operations and the numbers involved; e.g., considering relative
size, place value and estimates.
Measurement Standard
1.
Identify and select appropriate units for measuring:
a. length
miles, kilometers and other units of measure as appropriate;
b. volume
(capacity) gallons;
c. weight
ounces, pounds, grams, or kilograms;
d. temperature
degrees (Fahrenheit or Celsius).
2. Establish
personal or common referents to include additional units; e.g., a
gallon container of milk; a postage stamp is about a square inch.
3. Tell time to
the nearest minute and find elapsed time using a calendar or a
clock.
4. Read
thermometers in both Fahrenheit and Celsius scales.
5. Estimate and
measure length, weight and volume (capacity), using
metric and U.S. customary units, accurate to the nearest
or
unit as appropriate.
6. Use appropriate measurement tools and techniques to construct
a figure or
approximate an amount
of specified length, weight or volume (capacity); e.g., construct
a rectangle with length 2
inches and width 3 inches, fill a measuring cup to the
cup mark.
7.
Make estimates for perimeter, area and volume using links,
tiles, cubes and other models.
Geometry and Spatial Sense Standard
1. Analyze and
describe properties of two-dimensional shapes and
three-dimensional objects using terms such as vertex, edge, angle,
side and face.
2. Identify and
describe the relative size of angles with respect to right angles
as follows:
a. Use
physical models, like straws, to make different sized angles by
opening and closing the sides, not by changing the side lengths.
b. Identify,
classify and draw right, acute, obtuse and straight angles.
3. Find and name
locations on a labeled grid or coordinate system; e.g., a map or
graph.
4. Draw lines of
symmetry to verify symmetrical two-dimensional shapes.
5. Build a
three-dimensional model of an object composed of cubes; e.g.,
construct a model based on an illustration or actual object.
Patterns, Functions and Algebra Standard
1. Extend
multiplicative and growing patterns, and describe the pattern or
rule in words.
2. Analyze and
replicate arithmetic sequences with and without a calculator.
3. Use patterns
to make predictions, identify relationships, and solve problems.
4.
Model
problem situations using objects, pictures, tables, numbers,
letters and other symbols.
5.
Write, solve and explain simple mathematical statements,
such as 7 + □
> 8 or ∆
+ 8 = 10.
6. Express
mathematical relationships as equations and inequalities.
7. Create tables
to record, organize and analyze data to discover patterns and
rules.
8. Identify and
describe quantitative changes, especially those involving addition
and subtraction; e.g., the height of water in a glass becoming 1
centimeter lower each week due to evaporation.
Data Analysis and Probability Standard
1.
Collect and organize data from an experiment, such as
recording and classifying observations or measurements, in
response to a question posed.
2. Draw and
interpret picture graphs in which a symbol or picture represents
more than one object.
3. Read,
interpret and construct bar graphs with intervals greater than
one.
4. Support a
conclusion or prediction orally and in writing, using information
in a table or graph.
5. Match a set
of data with a graphical representation of the data.
6. Translate
information freely among charts, tables, line plots, picture
graphs and bar graphs; e.g., create a bar graph from the
information in a chart.
7. Analyze and
interpret information represented on a timeline.
8. Identify the
mode of a data set and describe the information it gives about a
data set.
9. Conduct a
simple experiment or simulation of a simple event, record the
results in a chart, table or graph, and use the results to draw
conclusions about the likelihood of possible outcomes.
10.
Use physical models, pictures, diagrams and lists to solve
problems involving possible arrangements or combinations of two to
four objects.
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