Third Grade Math
|
Standard 1:
The student uses numerical and computational concepts and
procedures in a variety of situations. |
Benchmark
1: NUMBER SENSE - The student
demonstrates number sense for whole numbers, simple fractions, money, and
decimals in a variety of situations.
The student:
1. compares and orders whole numbers to 100,000 and fractions with like denominators involving sixteenths, twelfths, eighths, fourths, thirds, halves, tenths, and hundredths using concrete materials.
2. knows, explains, and uses addition, subtraction, and multiplication to show equivalent representations for whole numbers such as 3x2=4+2.
3. knows, explains, and represents whole numbers to 100,000; decimals to tenths and hundredths; simple fractions; money (making change, mixed coinage for any amount, and money exchanges).
The student:
1. uses appropriate representations of whole numbers to formulate and solve real-world problems.
2. determines reasonableness of numerical values involving whole numbers, simple fractions, and decimals when used as monetary amounts.
Benchmark
2: NUMBER SYSTEMS AND THEIR PROPERTIES -
The student demonstrates an understanding of whole numbers with a special
emphasis on place value, recognizes, uses, and explains their properties, and
extends these properties to simple fractions, mixed numbers, decimals and money.
The student:
1. recognizes the need for whole numbers, simple fractions, and decimals (tenths and hundredths).
2. classifies various types of numbers as whole numbers, mixed numbers, fractions, and decimals.
3. identifies the place value of various digits from hundredths to one-hundred thousands.
4. identifies, models, writes, and reads numbers using numerals, words, and expanded form from hundredths to one hundred thousands such as sixty-four thousand three hundred eighty = 64,380 = 60,000 + 4,000 + 300 + 80 + 0.
5. uses the concepts of the following whole number properties: commutative property of addition and multiplication; additive and multiplicative identity properties (zero property of addition and multiplicative property of one); the distributive property; the symmetric property of addition and multiplication such as 100=20+80 is the same as 20+80=100; and the multiplicative property of zero with two factors such as 9x0=0 or 112x0=0.
6. identifies odd and even whole numbers to 1000.
The student:
1. uses properties of the whole number system and money to explain reasoning, and to formulate and solve real-world problems.
2. uses and explains whole number properties to perform various computational procedures.
Benchmark
3: ESTIMATION - The student
uses numerical estimation with whole numbers, simple fractions, decimals, and
money in a variety of situations.
The student:
1. uses a wide variety of computational methods including mental mathematics, paper and pencil, concrete materials, and technological tools such as calculators to estimate quantities involving whole numbers, simple fractions (halves, thirds, and fourths), decimals (.1 or .01), and money.
2. explains and uses estimation techniques, including rounding to the nearest tens, hundreds, or thousand.
3. recognizes and explains the differences between exact and approximate values.
The student:
1. uses estimation to check reasonableness of results, and makes predictions in situations involving whole numbers, fractions including mixed numbers, decimals and money.
2. adjusts original rational number estimates based on additional information (estimation from a frame of reference).
3. determines if a problem situation calls for an exact or approximate answer and performs the appropriate computation.
4. estimates monetary amounts needed to make purchases.
Benchmark
4: COMPUTATION - The student
explains and performs computation with whole numbers,
addition and subtraction of proper fractions with like denominators, and
money in a variety of situations.
The student:
1. uses a wide variety of computational methods including mental arithmetic (doubles and neighbors), paper and pencil, concrete materials, and technological tools such as calculators.
2. states and uses multiplication facts up through the 5’s plus the 10’s as well as the corresponding division facts with efficiency and accuracy.
3. explains and performs the following computational procedures:
whole number addition and subtraction up to the one hundred thousands place.
multiplication of a two-digit number by a one-digit number, using mathematics facts appropriate for the grade level with and without concrete materials.
addition and subtraction of monetary amounts using dollar and cents notation such as $47.07 + $356.96.
4. explains the relationship between addition and subtraction.
5. knows different ways to read and write the same multiplication expression such as: 6x4 is the same as 6•4.
The student:
1. selects and uses computational procedures to formulate and solve real-world problems involving selected whole numbers and money.
|
Standard
2: The student uses algebraic
concepts and procedures in a variety of situations. |
Benchmark
1: PATTERNS - The student
recognizes, describes, extends, develops, and explains relationships in patterns
from a variety of situations.
Using concrete materials, drawings, or other representations, the student:
1. identifies, states, and continues patterns presented in a variety of formats: numeric, visual, oral, written, kinesthetic, pictorial, tabular, graphical, or listing.
2. recognizes patterns involving two changes.
3. creates a pattern.
A partial list of patterns to help students meet these indicators could
include:
whole number patterns both increasing and decreasing (20, 15, 10).
money and time patterns ($.25, $.50, $.75 or
patterns occurring in life such as seasons, temperature or weather, appropriate for grade level topics across the curriculum.
number theory patterns, such as: odd, evens, and multiples through 5’s.
kinesthetic patterns such as clapping.
visual patterns involving two attributes.
Special Note: Working with various types of patterns is an important precursor to working with functions and sequences in middle school and high school.
The student:
1. generalizes patterns using written descriptions.
2. recognizes the same general pattern presented in different representations.
Benchmark
2: VARIABLES, EQUATIONS, AND
INEQUALITIES - The student uses symbols and whole numbers to solve simple
equations and inequalities in a variety of situations.
Third
Grade Knowledge Base Indicators
The student:
1. explains and uses symbols for unknown quantities.
2. solves equations involving only one operation up to 99.
3. finds missing multiplication facts and corresponding division facts through 5 and 10.
4. solves money equations up to a dollar.
5. compares two whole numbers between 0 and 999 using symbols (>,<, or =) and words (less than, greater than, or equal to).
The student:
1. uses symbols to represent problem situations which involve unknown quantities.
2. formulates and solves problem situations involving one-step equations in one unknown with a whole number solution.
The student:
1. uses a variety of methods to recognize relationships between whole numbers including mental mathematics, paper and pencil, concrete materials, and graphing utilities or other technological tools.
2. generalizes patterns by stating the rule using symbol notation.
3. identifies and graphs ordered pairs in the first quadrant.
4. finds
values and determines rules involving addition and subtraction of whole numbers
using input/output machines or T-tables.
The student:
1. uses concrete items, symbols and equations, tables, graphs, pictures and written descriptions to represent and describe mathematical relationships.
Benchmark
4: MODELS - The student
develops and uses models to represent and justify mathematical relationships
found in a variety of situations.
Third
Grade Knowledge Base Indicators
The student:
1. uses mathematical models to represent and explain mathematical concepts and procedures.
2. creates mathematical models to show the relationship between two or more things.
The student knows, explains, and uses mathematical models such as:
graphs using real objects, representational objects or abstract representations to display data.
place value models to compare, order and represent whole numbers.
process models for whole number operations such as multiplication arrays, division sets, the number line, and the hundreds chart.
money (coins), fraction models (fraction strips), decimal models (base ten blocks, coins) and mixed number models (patterns blocks) to compare, order or represent numerical quantities.
tables and charts to organize data.
Venn Diagrams to sort up to two attributes.
diagrams and pictures to represent problem situations.
The student:
1. recognizes the same situation can be represented in more than one way such as using a Venn diagram, a written description or a frequency table to show how the objects from a given list fall into specific categories.
Special Note: The mathematical modeling process involves:
a) selecting key features and relationships within the real world situation and representing these concepts in mathematical terms through some sort of mathematical model;
b) performing manipulations and mathematical procedures within the mathematical model;
c) interpreting the results of the manipulations within the mathematical model and using these results to make inferences about the original real-world situation.
|
Standard
3: The student uses geometric
concepts and procedures in a variety of situations. |
Benchmark
1: GEOMETRIC FIGURES AND THEIR
PROPERTIES - The student recognizes or investigates properties of simple
geometric figures in a variety of situations.
The student:
1. uses appropriate technology, manipulatives or drawings to recognize and investigate properties of simple geometric figures.
2. recognizes and describes rhombus, octagon, pentagon.
3. recognizes and describes the following geometric figures: cylinder, cone, sphere and cube.
4. determines if a figure contains any lines of symmetry and draws them if they exist.
5. recognizes similar and congruent figures.
The student:
1. formulates and solves real-world problems by applying basic properties of geometric figures.
2. combines several geometric shapes to make a larger shape.
Benchmark
2: MEASUREMENT AND ESTIMATION
- The student estimates and measures using standard and nonstandard units in a
variety of situations.
The student:
1. finds the perimeter of squares, rectangles, and triangles given the measure of all the sides.
2. selects, uses, or explains measurement tools and units of measure appropriate for the situation.
3. states the number of hours in a day and days in a year.
4. understands appropriate uses of length, width, height, and temperature.
5. measures length to the nearest half inch, to the nearest centimeter or nonstandard units of measure to nearest whole unit; volume to the nearest pint, cup, quart, gallon or liter; temperature to the nearest degree.
6. selects, explains the selection of, or uses measurement tools, units of measure, and degrees of accuracy appropriate to a given situation.
7. reads and tells time to the minute on analog and digital clocks.
The student:
1. formulates and solves real-world problems by applying measurements and measurement formulas.
2. uses estimation to check reasonableness of measurements and calculations.
3. adjusts original measurements based on additional information (estimation from a frame of reference).
4. uses map scales to measure distance between locations.
Benchmark
3: TRANSFORMATIONAL GEOMETRY -
The student recognizes up to two transformations of basic geometric figures in a
variety situations.
The student:
1. recognizes or performs one transformation (rotation/turn, reflection/flip, and translation/slide) on basic two-dimensional shapes.
2. knows and uses cardinal directions (north, south, east, west, northeast, southwest, etc.)
The student:
1. describes or draws basic two-dimensional shapes as they would appear after undergoing a specified transformation without actually performing the transformation with concrete objects.
2. recognizes and explains real-life situations where transformations take place.
3. gives or uses directions to move from one location to another on a map.
The student:
1. identifies points in the first quadrant of the coordinate plane.
2. uses two numbers or a letter and a number to identify points on a coordinate grid.
The student:
1. uses coordinate grids to formulate and solve real-world problems, such as identifying locations and giving or following directions to move from one location to another
|
Standard
4: The student uses concepts
and procedures of data analysis in a variety of situations. |
The student:
1. lists some of the possible outcomes of a simple experiment.
2. recognizes whether the outcome of an event is impossible, certain, likely, or unlikely.
The student:
1. conducts experiments and simulations involving a simple event, records the results in a chart, table or graph, and uses the results to draw conclusions about the event.
The student:
1. organizes, displays and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized and accurate manner including correct titles, labels, categories or whole number intervals. Specific graphical displays of whole number, monetary unit, and categorical data include:
frequency tables.
horizontal and vertical bar graphs.
Venn diagrams and other pictorial displays.
charts and tables.
line graphs.
pictographs.
2. knows, explains, and conducts sampling techniques (observations, polls, tally marks, and interviews) for gathering data.
3. ranks the values of a data set containing whole numbers.
4. identifies mode for a data set containing whole numbers.
5. calculates the range for a whole number data set.
The student:
1. uses data analysis to make reasonable inferences, predications, answer questions, and make decisions from data displayed in a variety of formats. (See listing of graphical displays.)
2. recognizes that the same data set can be displayed in a variety of formats. (i.e. Different display formats for the same data set can look different, but still be the same data set.)