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UNION PUBLIC SCHOOLSWHAT EVERT STUDENT MUST KNOW BY THE END OF PREKINDERGARTEN—MATHEMATICS

Recognize and identify two-dimensional geometric shapes: circle, square, triangle, rectangle, oval, heart, diamond, star

Rote count by ones from 1-10 or higher Recognize and identify numerals 0-10 Establish a one-to-one correspondence by counting objects while saying aloud the number word Count sets of objects 1-10 Sort objects by one attribute Recognize size (small, medium, large) Demonstrate knowledge of opposites Complete an AB pattern Identify relative positions using appropriate terminology (up/down, near/far, in front of/behind, on top

of/beneath, around, under, above, last, second, first)

UNION PUBLIC SCHOOLS

WHAT EVERY STUDENT MUST KNOW BY THE END OF KINDERGARTEN – MATHEMATICS

EACH STUDENT WILL BE ABLE TO:

Counting and Cardinality: Recite and count numbers forward to 100 by ones and by tens. Count forward beginning from a given number within the known sequence. Count objects in a given set up to 20. Recognizes numerals 0 – 20 out of sequence. Write numbers in correct formation 0 – 20. Fill in missing numbers, forwards and backwards up to 20 ex. (0, 1, __, 3, __, 5) ex. (10, 9, __, 7, __, 5). Compare two numbers between 1 and 10 presented as written numerals (less than, greater than, equal to).

Operations and Algebraic Thinking Represent addition and subtraction with objects, situations, expressions, etc. Solve addition and subtraction word problems within 10. Decompose numbers less than or equal to 10 into pairs in more than one way. For any number from 1 to 9, find the number that makes 10 when added to that number. Fluently add and subtract within 5.

Number & Operations in Base Ten Compose and decompose numbers from 11 to 19 into ten ones and some further ones.

Measurement and Data Measuring

o Compare and order objects by weight, height, and length.o Use non-standard units to measure weight, height, length, and capacity.o Sort objects by visual observation according to length, height, and width

Classify objects and sort the groups by count (limit count to 10 or less). Sort and describe objects by color, shape, or size.

Geometry Describe and understand basic shapes (square, circle, triangle, rectangle, hexagon) as well as solid shapes

(sphere, cube, prism, cylinder, pyramid, cone). Understand and use positional /size/ location words such as (more, less, fewer, above, below, top, bottom, middle, next to, left, right, most, least, equal). Analyze and compare two- and three-dimensional shapes. Model shapes in the world by building them from components and drawing them. Use simple shapes to construct larger shapes. Use appropriate pencil grip.


WHAT EVERY STUDENT MUST KNOW BY THE END OF GRADE 1 – MATHEMATICS


Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction within 20. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20. Understand and apply properties of numbers (commutative and associative) to add. Understand subtraction as an unknown-addend problem. Add and subtract within 20. Fluently add and subtract within 10. Understand the meaning of the equal sign and determine if equations involving addition and subtraction are

true or false. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers,

(example: 8 + ? = 11)

Number & Operations in Base Ten Count to 120 Read and write numerals and represent a number of objects with a written numeral within 120. Understand that the two digits of a two-digit number represent amounts of tens and ones. Use the symbols <, >, and = to compare two two-digit numbers. Within 100, add a two-digit number and a one-digit number, and a two-digit number and a multiple of 10. Find 10 more or 10 less than a two-digit number without having to count. Within the 10 – 90 range, subtract multiples of 10 from multiples of 10.

Measurement and Data Measuring

o Compare and order three objects by lengtho Express the length of an object as a whole number of length units.

Tell and write time in hours and half-hours using analog and digital clocks. Organize, represent, and interpret data with up to three categories.

Geometry Distinguish between defining attributes (closed figure, three-sided) and non-defining attributes (color,

orientation). Build and draw shapes with defining attributes. Compose two- or three-dimensional shapes to form composite shapes. Partition circles and rectangles into two and four equal shares; describe the shares using the words halves,

fourths, and quarters. Use the phrases half of, fourth of, and quarter of.


WHAT EVERY STUDENT MUST KNOW BY THE END OF GRADE 2 – MATHEMATICS


Operations and Algebraic Thinking Use addition and subtraction within 100 to solve one- and two-step word problems with unknowns in all

positions. Use drawings and equations with a symbol for the unknown number to represent problems. Fluently add and subtract within 20 using mental strategies. Know from memory all sums of two one-digit numbers. Determine whether a group of objects (up to 20) has an odd or even number of members. Write an equation to express an even number as a sum of two equal addends. Use addition to find the total number of objects in rectangular arrays of up to 5 rows and columns; write an

equation to express the total as a sum of equal addends.

Number & Operations in Base Ten Count within 1000 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Use the symbols <, >, and = to compare two three-digit numbers. Fluently add and subtract within 100. Add up to four two-digit numbers. Add and subtract within 1000. Mentally add 10 or 100 to a given number within 100 – 900 range. Mentally subtract 10 or 100 from a given number within 100 – 900 range.

Measurement and Data Measure the length of an object by selecting and using appropriate tools. Measure the length of an object twice, using different units of measure; describe how the two

measurements relate to the size of the unit chosen. Estimate length using units of inches, feet, centimeters, and meters. Measure to determine how much longer one object is than another. Tell and write time using analog and digital clocks to the nearest 5 minutes, using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols

appropriately. Represent data by making a line plot, where horizontal scale is marked off in whole-number units. Draw a picture graph and a bar graph to represent a data set with up to four categories; answer questions

using information presented in a bar graph.

Geometry Recognize and draw shapes having specified attributes. Identify triangles, quadrilaterals, pentagons, hexagons, and circles. Partition a rectangle into rows and columns of same-size squares and count them. Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words

halves, thirds, half of, a third of, etc.


WHAT EVERY STUDENT MUST KNOW BY THE END OF 3rd GRADE – MATHEMATICSRevised June 2011

Number Sense, Numeration, and Numerical Operations Use place value to read, write, and describe the value of whole numbers through 10,000 Use expanded notation to the hundreds place Compare and order whole numbers Use fraction names to describe fractional parts of whole objects (denominators 2 – 8) Compare and order fractions with like denominators Add and subtract to solve problems involving whole numbers up to the thousands place Use the identity and commutative properties fro addition and multiplication Know multiplication facts up to twelve (by June) Demonstrate an understanding of division and its relationship to multiplication Identify the operation(s) necessary to solve a word problem (addition, subtraction, multiplication,

division) Round 2 & 3 digit numbers to the nearest ten & hundred & estimation Open-Ended 1 Step problem (by January) show work Open-Ended 2 – 3 step problem (by June) show work

Spatial Sense, Measurement, and Geometry Identify the appropriate unit of measurement (length, weight, and capacity) Estimate and measure length to the nearest ¼ inch, weight to the nearest pound, and capacity Compare units within the customary system Determine the value of sets of coins and make change up to a dollar Use digital and analog clocks to tell time to the nearest five minutes Name, describe, and draw a square, rectangle, triangle, circle, and their solid equivalents Identify congruent shapes Identify lines of symmetry Area and perimeter and volume

Patterns, Relationships, and Functions Recognize numerical patterns Extend and create numerical patterns

Data, Probability, and Statistics Gather, organize, interpret and display data using charts and graphs (bar, picture, line)


WHAT EVERY STUDENT MUST KNOW BY THE END OF 4th GRADE – MATHEMATICSRevised June 2011

Read, write, and round rationale numbers to the hundred millions Money - Count, compare, order, and make change using a variety of strategies. Add and subtract using regrouping up to four-digit whole numbers Use median, mode and range to describe a set of data Collect, construct, display and interpret data, charts, graphs, and plots Perform multiplication of two-digit multipliers Perform division using a single-digit divisor Identify point, lines, segment, and angles Identify properties of plane and solid figures, and recognize the relationship of objects in the environment Determine the perimeter and area of polygons Understand the concepts of and recognize geometric transformations (rotations, reflections, and

translations) Recognize congruent plane figures after performing geometric transformations Estimate and measure length, weight, and capacity using metric and customary units Use ordered pairs to locate points and plot positions on a coordinate grid Solve real-world problems involving length, weight, capacity, money, time, elapsed time, temperature,

perimeter, and volume Model fractions, mixed numbers, and find equivalent fractions Compare and order whole numbers, decimals, fractions, and mixed numbers Add and subtract decimals, fractions with like denominators Identify and extend upon geometric and numerical patterns by stating their rules Problem solving strategies should be used throughout

UNION PUBLIC SCHOOLSWHAT EVERY STUDENT MY KNOW BY THE END OF 5TH GRADE – MATHEMATICS

Revised June 2011EACH STUDENT WILL BE ABLE TO:Number Sense, Numeration and Numerical Operations

Demonstrate a knowledge of multiplication and division up to and including 3 digit by 2 digit Add and subtract decimals in regards to money Read and write rational numbers Round whole numbers and decimals Identify equivalent fractions Estimate and solve problems involving whole numbers, fractions and decimals Find multiples, common multiples and least common multiples Relate exponential notation to repeated multiplication through prime factorization Find factors, common factors and greatest common factors of numbers Identify prime and composite numbers Add and subtract fractions with like and unlike denominators without regrouping Solve word problems involving addition, subtraction, multiplication and division using a variety of strategies

Spatial Sense, Measurement and Geometry Identify, construct and measure points, lines, segments and angles using a ruler and/or a protractor Identify geometric shapes and their characteristics including: similarity, congruence and symmetry Identify that a circle is a set of points equidistant from a center point Translations, rotations and reflections Identify, classify and describe triangles and quadrilaterals Compare and convert units of measure within the standard system Determine the perimeter and area of squares and rectangles Use measurement, standard and metric, concepts involving length, weight, money and time

Patterns, Relationships and Functions Identify and extend numerical and geometric patterns Use non-numeric symbols and variables to represent quantities and relationships in simple expressions or

equations

Data, Probability and Statistics Use mean, median, mode and range to describe a set of data Interpret data using tables, graphs, line plots and Venn diagrams Demonstrate the relationship between probability, chance and fraction


WHAT EVERY STUDENT MUST KNOW BY THE END OF 6th GRADE – MATHEMATICS


Number Sense Use the Order of Operations (whole #’s only) Add, subtract, multiply, and divide decimals (up to the hundredths place) Identify place value (up to ten-thousandths) & round decimals given indicated place value position Identify prime and composite numbers and write the prime factorization of composite numbers Define and find the LCM and GCF of 2 numbers Convert improper fractions to mixed numbers and vice versa Add, subtract, multiply, and divide fractions Convert fractions to decimals and vice versa Identify, graph, compare, and order integers Covert decimals to percents and vice versa Use estimation and mental math

Patterns and Algebra Solve simple one step equations (whole numbers) Evaluate/simplify expressions using substitution and using given formulas Identify and plot points on the coordinate plane (Quadrant 1) Identify ratios and solve proportions (whole #’s)

Geometry Calculate area and perimeter of rectangles, triangles, squares, & parallelograms Identify angles, triangles, and quadrilaterals Identify circle parts and understand Pi Identify 3-dimensional figures

Data, Probability, and Statistics Organize, display, interpret, and analyze data using tables and graphs (bar, line, and circle) Find mean, median, mode, and range (whole #’s & decimals) Demonstrate an understanding of probability using dice and spinners; express the probability as a

fraction




Number Sense, Numeration, and Numerical Operations Solve problems using order of operations with exponents Express numbers in exponential form, scientific notation, and expanded form Examine logic problems Estimate and compute square roots of whole numbers Understand percents (larger than 100% and smaller than 1%) Solve problems with percents Explore ratio, proportion, and equivalency (fractions, decimals, percents) Read, write, compose and order integers Perform operations with integers

Spatial Sense, Measurement, and Geometry Calculate circumference, area, and perimeter of plane figures Measure with protractors Identify congruent figures and name their corresponding parts Transformations of objects Describe and use angles based on their measures and relationships to other angles

Patterns, Relationships, Functions Recognize sequences and predict subsequent terms Use patterns to solve problems Solve and graph two step equations/ inequalities on a number line Solve input/output functions Translate a word phrase or sentence into expressions, equations and inequality

Data, Probability, and Statistics Analyze data using mean, median, mode, and range Determine probability of events (example: flipping coins, spinners, dice, etc.) Solve basic combinations and permutation problems




Number Sense, Numeration and Numerical Operation Solve and simplify expressions using order of operations and variables Express numbers in exponential form, scientific notation and expanded form Use calculators to enhance understanding of problem solving (not to replace mental math and paper and

pencil computational skills) Understand percentages larger than 100% and smaller than 1% Solve problems with percentages Demonstrate calculation and application of ratio, proportion and equivalency including similarity Demonstrate applications and operations with integers Solve and graph basic inequalities

Spatial Sense, Measurement and Geometry Calculate area, perimeter, circumference, volume, and surface area of basic shapes Measure with protractors Use Pythagorean Theorem for distance problems

Patterns, Relationships, Functions Locate and identify parts of a coordinate plane and plot points Solve one- and two-step equations Use patterns to solve problems

Data, Probability, and Statistics Use charts and graphs to solve problems and make predictions Analyze data using mean, median and mode Determine probability of events

TOWNSHIP OF UNION PUBLIC SCHOOLSAlgebra I

WHAT EVERY STUDENT MUST KNOW BY THE END OF THE YEAR

EACH STUDENT WILL BE ABLE TO:A. Operations with Numbers, Expressions and Equations

1. Use the properties of number systems.2. Use rates, ratios, and proportions to solve problems.3. Solve equations for one variable.4. Solve formulas for one variable in terms of the others.5. Apply the laws of exponents.6. Use the properties of radicals to simplify expressions and solve problems.7. Add, subtract, and multiply polynomial expressions.8. Factor polynomial expressions.

B. Linear Relationships9. Recognize, describe, represent and analyze linear relationships using words, tables, numerical patterns,

graphs, and equations.10. Solve problems that can be modeled using a linear relationship.11. Solve systems of linear equations algebraically and graphically.

C. Non-Linear Relationships12. Recognize, describe, represent, and analyze non-linear relationships using words, tables, numerical

patterns, graphs, or equations.13. Solve problems that can be modeled using a quadratic equation.

D. Data, Statistics, and Probability14. Use measures of central tendency to compare and analyze data sets.15. Use the counting principle to determine the number of ways an event can occur.16. Apply probability concepts to determine the likelihood an event will occur.

TOWNSHIP OF UNION PUBLIC SCHOOLS

Geometry

WHAT EVERY STUDENT MUST KNOW BY THE END OF YEAR


Understand and solve problems using points, lines, planes and angles

Use the laws of inductive and deductive reasoning to draw conclusions

Apply properties of parallel and perpendicular lines

Prove geometric theorems and statements

Understand congruence of triangles and apply properties for problemsolving

Understand and apply properties of triangles and their parts

Understand similarity, right triangles and trigonometry Define trigonometric ratios Solve problems with right triangles and similarity

Understand and apply properties of quadrilaterals to solve problems

Understand and apply properties of circles to solve problems

Identify a geometric equation based on a diagram, convert to an algebraic equation, and solve

Understand and calculate area, surface area, and volume of figures

Understand and perform transformations

Make a geometric construction Use geometry tools including ruler, protractor and compass


Algebra II



1. Solve linear equations and inequalities.

2. Solve and graph absolute value inequalities.

3. Model real-life problems using direct, indirect and joint variation.

4. Write and graph linear equations given specific conditions.

5. Solve systems of equations algebraically and graphically.

6. Solve quadratics by using the quadratic formula, factoring, completing the square and graphing.

7. Add, subtract and multiply complex numbers.

8. Use properties of radicals in order to simplify and evaluate expressions containing radicals with various indices.

9. Evaluate and simplify expressions written in exponential form or radical form.

10. Solve polynomial equations by various methods including factoring, synthetic division and long division.

11. Simplify rational expressions and solve rational equations.

12. Use the properties of logarithms to simplify expressions and solve equations.

13. Apply formulas of geometric and arithmetic sequences and series.

14. Calculate the probability, odds, combinations and permutations of given events.

15. Apply knowledge of matrices to solve problems.


General Math 3



1) Convert between fractions, decimals, and percentages.2) Solve all types of percentage problems, including percent of increase and decrease.3) Solve linear equations and inequalities, absolute values, and graph solutions.4) Use rules of exponents to simplify expressions.5) Identify the slope and intercept of a linear equation and find slope and intercept given two points on the line.6) Determine parallel and perpendicular lines given their slopes.7) Apply the Pythagorean Theorem to solve real-world problems.8) Use proportions to find missing parts of similar figures and scale factors for real-life problems.9) Identify types and characteristics of quadrilaterals.10) Use formulas, including simple and compound interest, area and volume.11) Identify relationships among angles formed by parallel lines cut by a transversal.12) Find the measures of interior and exterior angles of a polygon.13) Calculate geometric probability of a figure.14) Identify and use properties of transformations to solve problems.15) Use the Fundamental Counting Principal to solve real-world problems.16) Prepare for the HSPA by practicing HSPA-related problems17) Factor quadratic expressions and solve quadratic equations.18) Distinguish between and use arithmetic and geometric patterns to solve problems.19) Calculate measures of central tendency.20) State the parts and truth values of conditionals, conjunctions, and disjunctions.21) Understand and use basic set theory.22) Identify sine, cosine, and tangent of an angle within a right triangle.23) Draw the line of best fit and identify the type of correlation between two variables is a dataset.


General Math 4



Find the mean, median, mode, and range of a set of data. Recognize the effects of an outlier on the measures of central tendency for a set of data. Represent data in the form of tables, charts, and graphs. Use graphs and charts to interpret data and identify misleading information. Collect, organize, and interpret data. Identify a pattern and be able to find the next term in the sequence. Find missing term of a proportion. Write checks and deposit slips and record the items and their balance in the checkbook register. Reconcile a check register and a bank statement. Compute the net salary per pay period including straight-time, overtime, tips, deductions and commission. Become familiar with insurance terms. Convert between decimals, fractions and percents. Analyze and compare the terms for charge accounts. Determine how variations in the term of the loan, APR, and down payment affect the amount of interest and

maturity value on both a loan. Fill out W-4 and 1040 EZ and accompanying schedules using information from W-2 and 1099INT. Read and use Federal and State Tax Tables.


College Algebra



1. Perform the four basic operations with Real, Imaginary, and Complex numbers

2. Perform operations with percents

3. Perform the four basic operations with polynomials

4. Simplify and solve polynomial rational expressions and equations

5. Solve systems of equations using various methods

6. *** Solve quadratic functions through the use of factoring, quadratic formula, completing the square, and graphing

7. *** Solve and graph other higher order equations and inequalities

8. *** Identify, solve and graph functions

9. *** Simplify and solve exponential and logarithmic expressions and functions

10. *** Identify and evaluate trigonometry functions

11. *** Solve right triangles using trigonometry

12. *** Convert degrees to radians and vice versa along with solving modeling problems

13. *** Solve circular functions

14. *** Graph Sine and Cosine functions

15. Use fundamental trigonometric identities to simplify expressions and solve equations

*** Use of the graphing calculator is required


Statistics



Read and understand terminology in published statistical reports and journals

Create and interpret graphs from data and calculate descriptive statistics

Calculate and interpret correlation between two variables

Determine the influence of one variable on another by using regression methods

Identify the characteristics of and the differences between observational studies and experiments

Compare and contrast the different ways of selecting samples from a population

Know how to design a valid statistical study and be aware of the biases that may exist

Calculate the probabilities of real world phenomena

Understand and use sampling distributions to solve real-world problems

Calculate and interpret confidence intervals in real world situations

Perform significance tests and draw valid conclusions from their findings

Perform and interpret chi-squared tests on categorical data

Perform and interpret non-parametric tests when other significance tests are deemed invalid

Select and perform the best statistical analysis possible for a specific real world situation


AP Calculus


EACH STUDENT WILL BE ABLE TO:A. LIMITS AND THEIR PROPERTIES

1. Estimate a limit using numerical and graphical approaches.

2. Find the slope of the tangent line to a graph at a given point.

3. Write the equation of the tangent line to a graph at a given point.

4. Find higher-order derivatives of a function.

5. Use implicit differentiation to find the derivative of a function.

6. Use related rates to solve real-life problems.

B. DIFFERENTIATION7. Use the limit definition to find the derivative of a function.

8. Evaluate a limit using different strategies such as dividing out and rationalizing.

9. Determine one-sided limits.

10. Determine infinite limits from the left and from the right side.

11. Use the differentiation rules to find the derivative of a function.

12. Use related rates to solve real-life problems.

C. APPLICATIONS OF DIFFERENTIATION

13. Find extrema on a closed interval.

14. State and use Rolle’s Theorem and the Mean Value Theorem.

15. Use the First Derivative Test to locate absolute or relative extrema.

16. Use the Concavity Test to determine properties of concavity of a graph and inflection points.

17. Apply the Second Derivative Test to find the relative extrema of a function.

18. Determine limits at infinity.

19. Analyze and sketch the graph of a function using the tests involving the derivative.

20. Solve optimization problems.

D. INTEGRATION

21. Find indefinite integrals by using the integration techniques.

22. Find the general or particular solution of a differential equation.

23. Approximate area of a plane region using sum of areas of n rectangles.

24. State and use the definition of Reimann Sum to find a definite integral.

25. Evaluate definite integrals of using the First Fundamental Theorem of Calculus.

26. Use the Second Fundamental Theorem of Calculus to differentiate a function

in integral form.E. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS

27. Find the derivative of a function involving the natural logarithmic function.

28. Use the Log Rule for integration of a rational function.

29. Integrate trigonometric functions.

30. Determine the derivative of an inverse function.

31. Differentiate a natural exponential function.

32. Integrate a natural exponential function.

33. Differentiate and integrate an exponential function with a base other than e.

34. Differentiate a logarithmic function with base different than e.

35. Differentiate inverse trigonometric functions.

36. Integrate a function whose antiderivative involves an inverse trigonometric function.

F. APPLICATIONS OF INTEGRATION

37. Find the area between two curves using integration.

38. Find the volume of a solid of revolution using the disk method.

39. Find the volume of a solid of revolution using the washer method.

40. Find the volume of a solid of revolution using the shell method.

41. Find the arc length of a smooth curve using the integration formula.

42. Find the area of a surface of revolution using the integration formula.

43. Find the work done by a constant or variable force.

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