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STANDARDS
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BENCHMARKS
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| Demonstrate
knowledge and use of numbers and their representations
in a broad range of theoretical and practical settings. |
6.A.1a Identify
whole numbers and compare them using the symbols <,>,
or = and the words "less than", "greater
than", or "equal to", applying counting,
grouping and place value concepts. |
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6.A.1b Identify
and model fractions using concrete materials and pictorial
representations. |
| Investigate,
represent and solve problems using number facts, operations
(addition, subtraction, multiplication, division) and
their properties, algorithms and relationships. |
6.B.1 Solve
one- and two-step problems with whole numbers using
addition, subtraction, multiplication and division. |
| Compute and
estimate using mental mathematics, paper-and-pencil
methods, calculators and computers. |
6.C.1a Select
and perform computational procedures to solve problems
with whole numbers. |
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6.C.1b Show
evidence that whole number computational results are
correct and/or that estimates are reasonable. |
| Solve problems
using comparison of quantities, ratios, proportions
and percents. |
6.D.1 Compare
the numbers of objects in groups. |
| Measure and
compare quantities using appropriate units, instruments
and methods. |
7.A.1a Measure
length, volume and weight/mass using rulers, scales
andother appropriate measuring instruments in the customary
and metric systems. |
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7.A.1b Measure
units of time using appropriate instruments (e.g.,
calendars, clocks, watches - both analog and digital). |
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7.A.1c Identify
and describe the relative values and relationships
among coins and solve addition and subtraction problems
using currency. |
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7.A.1d Read
temperatures to the nearest degree from Celsius and
Fahrenheit thermometers. |
| Estimate measurements
and determine acceptable levels of accuracy. |
7.B.1a Given
a problem, describe possible methods for estimating
a given measure. |
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7.B.1b Compare
estimated measures to actual measures taken with appropriate
measuring instruments. |
| Select and
use appropriate technology, instruments and formulas
to solve problems, interpret results and communicate
findings. |
7.C.1 Determine
perimeter and area using concrete materials (e.g.,
geoboards, square tiles, grids, measurement instruments). |
| Describe numerical
relationships using variables and patterns. |
8.A.1a Identify,
describe and extend simple geometric and numeric patterns. |
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8.A.1b Solve
simple number sentences (e.g., 2+?=5). |
| Interpret and
describe numerical relationships using tables, graphs
and symbols. |
8.B.1 Solve
problems involving pattern identification and completion
of patterns. |
| Solve problems
using systems of numbers and their properties. |
8.C.1 Describe
the basic arithmetic operations (addition, subtraction,
multiplication, division) orally, in writing and using
concrete materials and drawings. |
| Use algebraic
concepts and procedures to represent and solve problems. |
8.D.1 Find
the unknown numbers in whole-number addition, subtraction,
multiplication, division situations. |
| Demonstrate
and apply geometric concepts involving points, lines,
planes and space. |
9.A.1a Identify
related two- and three- dimensional shapes including
circle-sphere, square-cube, triangle-pyramid, rectangle-rectangular
prism and their basic properties. |
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9.A.1b Draw
two-dimensional shapes. |
| Identify, describe,
classify and compare relationships using points, lines,
planes and solids. |
9.B.1a Identify
and describe characteristics, similarities and differences
of geometric shapes. |
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9.B.1b Sort,
classify and compare familiar shapes. |
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9.B.1c Identify
lines of symmetry in simple figures and construct symmetrical
figures using various concrete materials. |
| Construct convincing
arguments and proofs to solve problems. |
9.C.1 Draw
logical conclusions and communicate reasoning about
simple geometric figures and patterns using concrete
materials, diagrams and contemporary technology. |
| Use trigonometric
ratios and circular functions to solve problems. |
n/a |
| Organize, describe
and make predictions from existing data. |
10.A.1a Organize
and display data using pictures, tallies, tables, charts
or bar graphs. |
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10.A.1b Answer
questions and make predictions based on given data. |
| Formulate questions,
design data collection methods, gather and analyze
data and communicate findings. |
10.B.1a Formulate
questions of interest and design surveys or experiments
to gather data. |
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10.B.1b Collect,
organize and describe data using pictures, tallies,
tables, charts or bar graphs. |
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10.B.1c Analyze
data, draw conclusions and communicate the results. |
| Determine, describe
and apply the probabilities of events. |
10.C.1a Describe
the concept of probability in relationship to likelihood
and chance. |
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10.C.1b Systematically
list all possible outcomes of a simple one-stage experiment
(e.g., the flip of one coin, the toss of one die, the
spin of a spinner). |
