MATHEMATICS

OBJECTIVES FOR GRADE 1

By the end of grade 1, students will be able to:

1. Demonstrate an understanding of the concept of place value

using various proportional and nonproportional models.

2. Read and write numerals through 100.

3. Order any set of numbers between 1 and 100.

4. Count up to 100 by ones and skip count by twos, fives, and

tens.

5. Use proportional and nonproportional models to model addition

and subtraction.

6. Write an addition or subtraction sentence that describes a

modeled situation.

7. Demonstrate the commutative, the associative, and the identity

properties for addition.

8. Find the sum of three one-digit numbers.

9. Work two-digit addition and subtraction problems.

10. Use a calculator to make mathematical discoveries and to do

two-digit addition and subtraction problems.

11. Make estimates before making measurements, performing

computations, and solving word problems.

12. Identify coins and determine the value of a given set of

coins.

13. Identify two-dimensional and three-dimensional figures and

describe similarities and differences between figures.

14. Identify congruent figures and lines of symmetry.

15. Measure objects using both nonstandard units and standard

units (cm, in. and ft.).

16. Order a set of objects given some measurable attribute.

17. Determine length, capacity, weight, area, and time.

18. Collect data and make pictographs and bar graphs of the data.

19. Draw conclusions and make informal predictions based on

experience or graphed data.

20. Identify some events that are sure to happen and some that

are not sure to happen.

21. Orally identify halves, thirds, and fourths of regions.

22. Duplicate, continue, and reverse a pattern of concrete

objects.

23. Identify and describe patterns that occur in real-life

situations.

OBJECTIVES FOR GRADE 2

By the end of grade 2, students will be able to:

1. Demonstrate an understanding of the concept of place value

using various proportional and nonproportional models.

2. Read, write, and order any set of numerals between 1 and

1,000.

3. Write a number sentence that describes the relationship

between any pair of whole numbers.

4. Count by ones to any whole number, and skip count by twos,

threes, fours, fives, and tens.

5. Identify whether a number is even or odd.

6. Find the sum of three or four single-digit addends.

7. Estimate and find the sum or difference of two-digit and

three-digit numbers.

8. Round two-digit numbers to the nearest ten, and round

three-digit numbers to the nearest ten and to the nearest

hundred.

9. Write number sentences that describe modeled multiplication

sentences.

10. Use a calculator to make mathematical discoveries and to do

up to three-digit addition and subtraction problems.

11. Identify coins and bills and determine the value of a given

set of coins and bills.

12. Identify, describe, and compare two- and three- dimensional

figures.

13. Identify congruent and symmetrical figures.

14. Estimate and measure length, perimeter, capacity, weight

(mass), temperature, and area by using various nonstandard,

<*dv_3*>metric, and English units.

15. Tell time on a traditional (analog) clock to the nearest

hour, half-hour, quarter-hour, and five minutes.

16. Collect data and make pictographs and bar graphs of the data.

17. Describe data displayed on a graph and make predictions and

draw conclusions based on the graphed data.

18. Determine the likelihood that an event will occur.

19. Locate on a graph in a coordinate plane the point whose

coordinates are a given pair of numbers between 0 and 15.

20. Recognize different physical representations for the same

fraction.

21. Give the appropriate fraction symbol and name for a fraction

model.

22. Use different strategies to determine basic facts.

23. Identify and extend patterns of objects and symbols.

OBJECTIVES FOR GRADE 3

By the end of grade 3, students will be able to

1. Count by ones to any whole number needed and skip count by

twos, threes, fives, and tens.

2. Read, write, order, and use numerals through 999,000 and

decimals to the hundredths.

3. Write a number sentence that describes the relationship

between any pair of whole numbers.

4. Identify the place value of any numeral up to 6 spaces to the

left of the decimal point and two spaces to the right of the

decimal point.

5. Round a number to the nearest ten, hundred, or thousand.

6. Estimate and find the sum of three or more whole numbers and

the sum or difference of two-, three-, and four-digit numbers.

7. Write number sentences that describe modeled multiplication or

division sentences.

8. Do mental calculations by using various properties of addition

and subtraction.

9. Demonstrate the relationship between addition and

multiplication, subtraction and division, and multiplication and

division.

10. Find the product of two one-digit whole numbers and a

one-digit number multiplied by a two-digit number.

11. Find the quotient when the dividend is a two-digit whole

number and the divisor is a one-digit whole number.

12. Use a calculator to make mathematical discoveries, add or

subtract any pair of whole numbers, and multiply any two whole

numbers.

13. Compare, order, and round money amounts; make change for

dollar amounts up to $5; express the value for a given amount of

money in words; and add and subtract money using models.

14. Identify, describe, and compare two- and three-dimensional

figures.

15. Identify congruent and symmetrical figures.

16. Construct, using cubes, a solid to match a given solid.

17. Find the area and the perimeter of two-dimensional figures by

using both nonstandard units and standard units.

18. Determine elapsed time.

19. Choose the appropriate metric or English unit for making a

measurement.

20. Convert linear measurements from centimeters to meters,

inches to feet, and vice versa.

21. Collect and display data in the form of tables, bar graphs,

and pictographs. Formulate questions and make predictions based

on organized data.

22. Locate or name ordered pairs on a coordinate grid.

23. Compare and order fractions and mixed numbers using concrete

models. (To be able to do this students will need to be able to

model several different equivalent fractions for a given

fraction.)

24. Use different strategies to determine basic multiplication

and division facts.

25. Determine the relationship that exists between each pair of

elements in a given set of ordered pairs and then use this

relationship (rule) to generate additional ordered pairs.

OBJECTIVES FOR GRADE 4

By the end of grade 4, students will be able to

1. Read, write, order, and use numerals through 1,000,000,000 and

decimals to the hundredth, and mixed numbers.

2. Write a number sentence that describes the relationship

between any pair of whole numbers.

3. Round a number to the nearest ten, hundred, thousand, ten

thousand, or hundred thousand and round money amounts to the

nearest $.10, $1.00, or $10.00.

4. Estimate and find the sum or difference of two-, three-, and

four-digit numbers.

5. Illustrate how the distributive property of multiplication

over addition can be used to find the product of a one-digit

number and a two- or three-digit number.

6. Estimate and find the product of any two-digit number

multiplied by a one- or two-digit number.

7. Estimate and find the quotient of a two-digit whole number

dividend and a one-digit whole number divisor.

8. Do mental calculations by using various properties of

addition, subtraction, and multiplication.

9. Be able to use a calculator to make mathematical discoveries,

add several numbers, and subtract or multiply a given pair of

whole numbers.

10. Estimate and find the sum, difference, or product of decimals

to the nearest hundredth.

11. Make change for dollar amounts up to $20; express the value

for a given amount of money in words; and find sums and

differences of money amounts.

12. Identify and construct models of a line; a line segment; a

ray; an angle, including its sides and its vertex; a right angle;

two parallel lines; two intersecting lines; two perpendicular

lines; a radius; a diameter; and certain two- and

three-dimensional figures.

13. Identify congruent, similar, and symmetrical figures.

14. Transform plane figures, i.e., be able to illustrate the

reflection, the rotation, and the translation of a geometric

figure using concrete models.

15. Estimate and measure length, perimeter, capacity, weight

(mass), temperature, and area by using various nonstandard,

metric, and English units.

16. Convert linear measurements in centimeters, decimeters, or

meters from one unit to another or in inches, feet, or yards from

one unit to another.

17. Collect, record, and organize data into tables, charts, bar

graphs, line graphs, and pictographs.

18. Formulate questions and make predictions based on organized

data.

19. Find the likelihood (probability) of an event and make

predictions. In order to determine the likelihood, students will

need to be able to list the possible outcomes for various

experiments and list the different arrangements (permutations)

for a given set of objects.

20. Find the mean (average), median, and range for a set of data.

21. Locate or name ordered pairs on a coordinate grid.

22. Find factors and multiples of numbers and identify prime and

composite numbers.

23. Order fractions, mixed numbers, and decimals.

24. Find equivalent fractions and simplify fractions.

25. Find the sum of any two fractions or mixed numbers which have

a common denominator.

26. Determine the relationship that exists between each pair of

elements in a given set of ordered pairs and then use this

relationship (rule) to generate additional ordered pairs.

OBJECTIVES FOR GRADE 5

By the end of grade 5, students will be able to

1. Read, write, round, order, and use numerals through billions,

decimals to thousandths, fractions, and mixed numbers.

2. Estimate and find the sum or difference of two 3 5 digit whole

numbers, the product of a one-, two-, or a three-digit whole

number by a one-, two-, or a three-digit whole number by a one-,

two-, or three-digit whole number, and to find the quotient for

division problems that have one- or two-digit divisors.

3. Estimate and find the sum or difference of any two decimals to

the thousandths.

4. Multiply and divide decimals by whole numbers.

5. Use a calculator to find the sum or difference of any two

decimal numerals, the product of any decimal and whole number,

and the quotient of a decimal divided by a whole number.

6. Determine the prime factorization of a number. (Finding the

prime factorization is easier if students know the tests for

divisibility by 2, 3, 4, 5, and 10.)

7. Find the greatest common factor and the least common multiple

of two or more numbers.

8. Develop the ability to find equivalent fractions for a given

fraction and to reduce fractions.

9. Add and subtract fractions and mixed numbers with like and

unlike denominators.

10. Multiply a whole number by a fraction, a fraction by a whole

number, and a fraction by a fraction.

11. Convert a common fraction or mixed numeral to a decimal and a

decimal to a common fraction or mixed numeral.

12. Simplify an expression, including symbols of inclusion.

13. Use formulas to compute the circumference of a circle, and

the area of a square, a rectangle, a triangle, and a

parallelogram.

14. Determine the volume of solids by counting nonstandard units

and standard units.

15. Estimate and calculate the volume of a rectangular prism or

cube.

16. Describe the relationships that exist between various units

of volume and between volume and capacity for the metric system.

17. Convert from one unit of measure to another unit of measure

within the same measurement system.

18. Express a relationship as a ratio, determine if two ratios

are equal, and determine the missing term given two equivalent

ratios.

19. Interpret and use scale drawings.

20. Represent situations and number patterns with tables, graphs,

verbal rules, and equations that include variables.

21. Analyze tables and graphs to identify properties and

relationships.

22. Systematically collect, organize, and summarize data in a

table or a pictograph. Construct, read, and interpret tables,

charts, and graphs. Compute measures of central tendency (mean,

median, and mode) and the range.

23. Determine the empirical probability of a simple event by

conducting experiments and finding the theoretical probability of

a simple event by constructing a sample space for the set of all

possible outcomes and the set of all favorable outcomes.

24. Predict outcomes based on theoretical probability and

empirical probability.

25. Identify by name polygons with 4, 5, 6, 8, or 10 sides and

classify plane figures, angles, and space figures.

26. Construct circles and identify the radius, diameter, chord,

center, and circumference of circles.

27. Measure and draw angles using a protractor.

28. Transform plane figures and identify how a figure was

transformed.

29. Construct three-dimensional models and describe the model

when looking at it from different perspectives.

OBJECTIVES FOR GRADE 6

By the end of grade 6, students will be able to

1. Read, write, round, compare, order, and use whole numbers,

decimals, fractions, and mixed numbers.

2. Estimate and find the sum, difference, or product of any two

whole numbers or decimals.

3. Estimate and find the quotient of a decimal divided by a whole

number or by a decimal with two digits.

4. Express a number which has repeated factors in exponential

form and evaluate expressions written in exponential form.

5. Find the greatest common factor and the least common multiple

of two or more numbers.

6. Estimate and find sums and differences of fractions and mixed

numbers.

7. Find the products of mixed numbers and fractions.

8. Demonstrate the meaning of percent with concrete models and

express a given percent as a decimal fraction or decimal and vice

versa.

9. Use the concepts of ratio, proportion, and percent to solve

application problems.

10. Express large numbers in scientific notation and rewrite

numbers written in scientific notation in regular decimal

notation.

11. Use a calculator to find a given power of a given number and

a given percent of a given number.

12. Simplify expressions that include symbols of inclusion.

13. Approximate the area of irregular figures by using grids;

compute the area of common polygons (triangle, trapezoid,

parallelogram, square, and rectangle) by using formulas; and

compute the circumference and the area of a circle of a given

radius.

14. Determine and describe the effect changing the linear

dimensions of a figure has on the area of the figure.

15. Use formulas to find the volume of a rectangular prism, a

cube, a cylinder, a prism, and a pyramid.

16. Convert from one unit of measure to another unit of measure

within the same measurement system.

17. Interpret and use scale drawings.

18. Find the sum of any two integers using various models.

19. Represent situations and number patterns with tables, graphs,

verbal rules, and equations.

20. Analyze tables and graphs to identify properties and

relationships.

21. Plot integers on a number line and solve simple linear

equations.

22. Systematically collect, organize, and summarize data;

construct, read, and interpret tables, charts, and graphs; and

compute measures of central tendency (mean, median, and mode) and

the range.

23. Determine the empirical probability of simple events by

conducting experiments and the theoretical probability of a

simple event by constructing a sample space for the set of all

possible outcomes. (Students should be able to express the

probability as a fraction, a ratio, a decimal, or a percent.)

24. Make and refine predictions by determining probabilities for

different sample sizes.

25. Classify angles, pairs of lines, triangles, quadrilateral,

and polygons.

26. Identify congruent, similar, or symmetric figures.

27. Identify transformations of given figures.

28. Build models of three-dimensional figures such as pyramids,

cones, or prisms with polygonal bases and determine some of the

properties of these solids.

29. Use a compass and a straightedge to locate the midpoint of a

segment and to construct perpendicular lines, congruent angles,

and angle bisectors.

OBJECTIVES FOR GRADE 7

By the end of grade 7, students will be able to

<*dv_1*>1. Read, write, round, compare and order, and use whole numbers,

decimals, fractions, and mixed numbers.

2. Estimate and find the sum, difference, or product of any two

whole numbers and decimals on paper and with a calculator.

3. Estimate and find the quotient of any two whole numbers or of

a decimal divided by a whole number or a decimal with two digits

on paper and with a calculator.

4. Convert between whole numbers, fractions, decimals, and

percents mentally, on paper, and with a calculator.

5. Estimate and find sums, differences, products, and quotients

of fractions and mixed numbers on paper, and with a calculator.

6. Use the concepts of ratio, proportion, and percent to solve

application problems.

7. Evaluate expressions written in exponential form which have

integral exponents and find the product of two powers which have

the same base.

8. Multiply large numbers and small numbers, using scientific

notation.

9. Use a calculator to find the square root and the square of a

given number.

10. Find the missing terms and the sum of a sequence of numbers.

11. Find the area of a trapezoid and the surface area of

three-dimensional figures.

12. Find and use formulas for finding volume of prisms,

cylinders, cones, and pyramids.

13. Determine and describe the effect changing the linear

dimensions of a figure has on its volume.

14. Convert from one unit of measure to another unit of measure

within the same measurement system and interpret and use scale

drawings.

15. Represent situations and number patterns with tables, graphs,

verbal rules, and equations.

16. Analyze tables and graphs to identify properties and

relationships.

17. Graph ordered pairs on a four-quadrant grid.

18. Find the sum, difference, product, or quotient of any two

integers and the absolute value of any integer.

19. Solve simple linear equations and solve simple linear

inequalities. (Students should also be able to graph the solution

on a number line.)

20. Translate word phrases and sentences into algebraic

expressions and evaluate algebraic express-ions.

21. Systematically collect, organize, and summarize data

(students should be able to use box and whisker graphs, stem and

leaf plots, and histograms to display information); construct,

read, and interpret tables, charts, and graphs; and compute

measures of central tendency (mean, median, and mode) and the

range.

22. Determine the empirical probability of simple events by

conducting experiments and the theoretical probability of simple

<*dv_0*>events by constructing a sample space for the set of all possible

outcomes and the set of all favorable outcomes.

23. Make and refine predictions by determining probabilities for

different sample sizes.

24. Identify and classify angles, pairs of lines, triangles,

quadrilaterals, and polygons.

25. Identify congruent, similar, or symmetric figures and

identify transformations of given figures.

<*dv_2*>26. Use compass and straightedge to construct the perpendicular

bisector of a line segment, perpendicular lines, parallel lines,

congruent angles, angle bisectors, and triangles.

27. Construct a model of a three-dimensional figure when shown

the top, side, and front views.

28. Discover geometric relationships such as the sum of the

interior angles of a polygon, the number of diagonals of a

polygon, etc.

OBJECTIVES FOR GRADE 8

By the end of grade 8, students will be able to

1. Read, write, round, compare and order, and use whole numbers,

decimals, fractions, and mixed numbers.

2. Estimate and find the sum, difference, product, or quotient of

any two decimals.

3. Convert between whole numbers, fractions, decimals, and

percents mentally, and on paper.

4. Estimate and find sums, differences, products, and quotients

of fractions and mixed numbers.

5. Use the concepts of ratio, proportion, and percent to solve

application problems.

6. Use a calculator to perform all arithmetic operations,

including work with percents, square roots, powers, and use of

calculator memory.

7. Identify a real number as rational or irrational and find a

real number that lies between any two distinct real numbers.

8. Describe some properties of rational, irrational, and real

numbers.

9. Use radical notation and fractional notation to write square

and cube roots.

10. Find the nth term in an arithmetic or geometric sequence.

11. Find the product or quotient of two powers that have the same

base.

12. Multiply and divide large numbers and small numbers using

scientific notation.

13. Identify and give examples of well-defined sets, equivalent

sets, equal sets, and the empty set.

<*dv_4*>14. Find subsets of a given set, perform the operations of

intersection and union on sets, and find the complement of a

given set of the universal set.

15. Find the perimeter and the area of two-dimensional figures

and find the volume and surface area of prisms, pyramids, cones,

cylinders, and spheres.

16. Convert from one unit of measure to another unit of measure

within the same measurement system.

17. Describe the difference between the accuracy and the

precision of a measurement and determine the amount of error

possible in a measurement given the precision of the measurement.

18. Graph relations of real numbers in order to determine whether

the relation represents a function.

19. Solve a formula for any given variable.

20. Translate word phrases and sentences into algebraic

expressions and evaluate algebraic expressions.

21. Use the Pythagorean theorem to determine the measure of one

side of a triangle, given the measure of the other two sides, and

to determine whether a triangle is a right triangle.

22. Solve word problems involving direct or inverse variation or

applications of the Pythagorean theorem or which require writing

and solving a simple linear equation or inequality.

23. Find the slope, the x-intercept, and the y-intercept of a

linear equation in two variables.

24. Add and subtract polynomial expressions.

25. Solve a system of two equations in two unknowns.

26. Find horizontal, vertical, and diagonal lengths in the

coordinate plane.

27. Systematically collect, organize, and summarize data;

construct, read, and interpret tables, charts, and graphs; and

find the mean, the median, and the mode of a given set of

numbers. (Students need to be able to interpret and display data

from frequency tables, bar graphs, line graphs, circle graphs,

histograms, scattergrams, stem-and-leaf plots, and

box-and-whisker plots.)

28. Distinguish between useful and misleading graphs and between

useful and misleading statistics.

29. Determine the probability of independent and dependent

events.

30. Determine the empirical probability of simple events and

compound events by conducting experiments and determine the

theoretical probability of simple and compound events by

constructing sample spaces for the sets of all possible outcomes

and the sets of all favorable outcomes.

31. Find the number of permutations and the number of

combinations using factorial notation.

32. Use SSS, SAS, and ASA to identify congruent triangles.

33. Identify transformations of given figures.

34. Construct congruent line segments, congruent angles, the

perpendicular bisector of a line segment, an angle bisector, the

perpendicular from a point to a line, and the perpendicular to a

point on a line.

35. Construct a geometric figure congruent to a given geometric

figure.

36. Construct a model of a three-dimensional figure shown from

different perspectives.

37. Identify similar triangles and find the missing parts of

similar triangles.

38. Graph similar figures, reflections, and translations in a

coordinate plane.

39. Identify a chord, a tangent, and a secant of a circle and

complementary or supplementary angles.

40. Discover and describe the relationships between angles formed

by two lines and a transversal.