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Michigan Curriculum Matrix for Mathematics

Copyright © 2006 International Center for Leadership in Education Math –

Michigan Mathematics Strands/Grade Level Content Expectations

Grade 3

Curriculum Survey of Essential SkillsNational Rankings

RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONSUnderstand and use number notation and place valueN.ME.03.01 Read and write numbers to 10,000 in both numerals and words, and relate them to the quantities they represent, e.g., relate numeral or written word to a display of dots or objects.

m19

Understand the definitions and properties of rational and irrational numbers. H H H

N.ME.03.02 Recognize and use expanded notation for numbers using place value to 10,000s place, e.g., 2,517 is 2 thousands, 5 hundreds, 1 ten, and 7 ones; 4 hundreds and 2 ones is 402. Identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place.

m19

Understand the definitions and properties of rational and irrational numbers.

H H H

N.ME.03.03 Compare and order numbers up to 10,000. m19 Understand the definitions and properties of rational and

irrational numbers. H H H

Count in steps, and understand even and odd numbersN.ME.03.04 Count orally by 6’s, 7’s, 8’s and 9’s starting with 0, making the connection between repeated addition and multiplication.

m1Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. H H H

m19 Understand the definitions and properties of rational and irrational numbers.

N.ME.03.05 Know that even numbers end in 0, 2, 4, 6,or 8; name a whole number quantity that can be shared in two equal groups or grouped into pairs with no remainders; recognize even numbers as multiples of 2. Know that odd numbers end in 1, 3, 5, 7, or 9, and work with patterns involving even and odd numbers.

m19


H H H

Add and subtract whole numbersN.FL.03.06 Add and subtract fluently two numbers: up to and including two-digit numbers with regrouping and up to four-digit numbers without regrouping.

m1

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. H H H

N.FL.03.07 Estimate the sum and difference of two numbers with three digits (sums up to 1,000), and judge reasonableness of estimates.



N.FL.03.08 Use mental strategies to fluently add m1 Perform operations with signed (positive and negative) H H HCopyright © 2006 International Center for Leadership in Education Math –


Grade 3


RankMEAP Curriculum

Survey Priority

and subtract two-digit numbers. numbers, including decimals, ratios, percents, and fractions.


Multiply and divide whole numbersN.MR.03.09 Use multiplication and division fact families to understand the inverse relationship of these two operations, e.g., because 3 x 8 = 24, we know that 24 ÷ 8 = 3 or 24 ÷ 3 = 8. Express a multiplication statement as an equivalent division statement.

m1Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. L H M

m19Understand the definitions and properties of rational and irrational numbers.

N.MR.03.10 Recognize situations that can be solved using multiplication and division including finding “How many groups?” and “How many in a group?” and write mathematical statements for those situations.

m1


N.FL.03.11 Find products fluently up to 10 x 10; find related quotients using multiplication and division relationships.

m1Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.

H H H

N.MR.03.12 Find solutions to open sentences such as 7 x = 42 or 12 ÷ = 4, using the inverse relationship between multiplication and division.


H H H

N.FL.03.13 Mentally calculate simple products and quotients up to a three-digit number by a one-digit number involving multiples of 10, e.g., 500 x 6, or 400 ÷ 8.

m1


N.MR.03.14 Solve simple division problems involving remainders, viewing remainder as the “number left over” (less than the divisor), e.g., 4 children per group; we have 25 children; there are 6 groups with 1 child left over; interpret based on problem context.

m1

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.

H H H

Problem-solving with whole numbersN.MR.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words (including “product” and “quotient”), and mathematical statements; solve.

m1


Understand simple fractions, relation to the whole, and addition and subtraction of fractionsN.ME.03.16 Understand that fractions may m19 Understand the definitions and properties of rational and H H H



Grade 3


RankMEAP Curriculum

Survey Priority

represent a portion of a whole unit that has been partitioned into parts of equal area or length; use the terms “numerator” and “denominator.”

irrational numbers.

N.ME.03.17 Recognize, name and use equivalent fractions with denominators 2, 4, and 8, using strips as area models.



N.ME.03.18 Place fractions with denominators of 2, 4, and 8 on the number line; relate the number line to a ruler; compare and order up to three fractions with denominators 2, 4, and 8.

m19


N.ME.03.19 Understand that any fraction can be written as a sum of unit fractions, e.g., 3/4 = 1/4 + 1/4 + 1/4.



N.MR.03.20 Recognize that addition and subtraction of fractions with equal denominators can be modeled by joining and taking away segments on the number line.



Understand simple decimal fractions in relation to moneyN.ME.03.21 Understand the meaning of $0.50 and $0.25 related to money, e.g., $1.00 shared by two people means $1.00 ÷ 2 = 1/2 dollar = $0.50.


H H H

MEASUREMENTMeasure and use units for length, weight, temperature and timeM.UN.03.01 Know and use common units of measurements in length, weight and time.

m33

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. H H H

s23

Measure properties of the environment using dimensional quantities such as time, length, mass, pressure, volume, acceleration, etc. Compare, estimate and predict measurements.

M.UN.03.02 Measure in mixed units within the m33 Use the technique of dimensional analysis to convert units H H H



Grade 3


RankMEAP Curriculum

Survey Priority

same measurement system for length, weight and time: feet and inches, meters and centimeters, kilograms and grams, pounds and ounces, liters and milliliters, hours and minutes, minutes and seconds, years and months.

of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.

s23


M.UN.03.03 Understand relationships between sizes of standard units, e.g., feet and inches, meters and centimeters. m33

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.

H H H

M.UN.03.04 Know benchmark temperatures such as freezing (32ºF, 0ºC); boiling, (212ºF, 100ºC); and compare temperatures to these, e.g., cooler, warmer. m33


H H Hs23


s31Know the concepts of temperature and absolute temperature. Know the temperature scales (Fahrenheit, Celsius, and Kelvin) and their relationships.

Understand meaning of area and perimeter and apply in problemsM.UN.03.05 Know the definition of area and perimeter and calculate the perimeter of a square and rectangle given whole number side lengths.

m13Compute the perimeter and area of two-dimensional figures. H H H

M.UN.03.06 Use square units in calculating area by covering the region and counting the number of square units. m33


H H H

M.UN.03.07 Distinguish between units of length and area and choose a unit appropriate in the context. m33


H H H

s23 Measure properties of the environment using dimensional



Grade 3


RankMEAP Curriculum

Survey Priority

quantities such as time, length, mass, pressure, volume, acceleration, etc. Compare, estimate and predict measurements.

M.UN.03.08 Visualize and describe the relative sizes of one square inch and one square centimeter.

m33


s23


Estimate perimeter and areaM.TE.03.09 Estimate the perimeter of a square and rectangle in inches and centimeters; estimate the area of a square and rectangle and square inches and square centimeters.

m33


s23


Solve measurement problemsM.PS.03.10 Add and subtract lengths, weights and times using mixed units within the same measurement system. m33


H H H

M.PS.03.11 Add and subtract money in dollars and cents. m1


H H H

m33


M.PS.03.12 Solve applied problems involving money, length and time.

m33


H H H

s23 Measure properties of the environment using dimensional Copyright © 2006 International Center for Leadership in Education Math –


Grade 3


RankMEAP Curriculum

Survey Priority

quantities such as time, length, mass, pressure, volume, acceleration, etc. Compare, estimate and predict measurements.

M.PS.03.13 Solve contextual problems about perimeters of rectangles and areas of rectangular regions.

m13 Compute the perimeter and area of two-dimensional figures.

H H Hm33


GEOMETRYRecognize the basic elements of geometric objectsG.GS.03.01 Identify points, line segments, lines and distance. m6 Understand the characteristics and applications of the

undefined terms of geometry (i.e., point, line, and plane). H H Hm9 Know how to compute the distance between two points

(i.e., length of a line segment) on a coordinate plane. G.GS.03.02 Identify perpendicular lines and parallel lines in familiar shapes and in the classroom.

m2Understand the characteristics of parallel, perpendicular, and intersecting lines. H H H

G.GS.03.03 Identify parallel faces of rectangular prisms, in familiar shapes and in the classroom. m2 Understand the characteristics of parallel, perpendicular,

and intersecting lines. H H H

m29Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.

Name and explore properties of shapesG.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices.

m10Understand the properties of circles (e.g., radius, arc, diameter, chord, secant, tangent, etc.).

H H H

m27Understand the properties and classification of quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid).

G.SR.03.05 Compose and decompose triangles and rectangles to form other familiar two-dimensional shapes, e.g., form a rectangle using two congruent right triangles, or decompose a parallelogram into a rectangle and two right triangles.

m14 Understand the angle relationships in triangles (i.e., acute, obtuse, right, interior, and exterior).

H H Hm27Understand the properties and classification of quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid).

m49 Apply transformation concepts to understand and create congruent and similar figures.

Explore and name three-dimensional solidsG.GS.03.06 Identify, describe, build and classify m29 Know the classification and properties of solid figures H H H



Grade 3


RankMEAP Curriculum

Survey Priority

familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices).

such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.

G.SR.03.07 Represent front, top, and side views of solids built with cubes. m29

Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.

H H H

DATA & PROBABILITYUse bar graphsD.RE.03.01 Read and interpret bar graphs in both horizontal and vertical forms. m5

Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences.

H H H

D.RE.03.02 Read scales on the axes and identify the maximum, minimum, and range of values in a bar graph.

m5Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences.

H H H

D.RE.03.03 Solve problems using information in bar graphs including comparison of bar graphs. m5


H H H



Grade 4


RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONUnderstand and use number notation and place valueN.ME.04.01 Read and write numbers to 1,000,000; relate them to the quantities they represent; compare and order.

m19Understand the definitions and properties of rational and irrational numbers. H H H

N.ME.04.02 Compose and decompose numbers using place value to 1,000,000’s, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones.

m19


N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place values of numbers, and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds.

m19


Use factors and multiplesN.ME.04.04 Find all factors of a whole number up to 50, and list factor pairs. m22

Understand factoring a composite number into its prime factors, and how to find the largest monomial factor of a polynomial to write the polynomial as the product of the monomial and a polynomial.

H H H

N.ME.04.05 List the first ten multiples of a given one-digit whole number; determine if a whole number is a multiple of a given one-digit whole number and if a one-digit number is a factor of a given whole number.


H H Hm22


N.MR.04.06 Know that some numbers including 2, 3, 5, 7, and 11 have exactly two factors (1 and the number itself) and are called prime numbers.


H H Hm22


N.MR.04.07 Solve problems about factors and multiples, e.g., since 100 = 4 x 25, and 200 = 2 x 100, then 200 = 2 x 4 x 25 = 8 x 25. m22


H H H

Add and subtract whole numbersN.FL.04.08 Add and subtract whole numbers fluently. m1


H H H

Multiply and divide whole numbersCopyright © 2006 International Center for Leadership in Education Math –


Grade 4


RankMEAP Curriculum

Survey Priority

N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property, e.g., 21 x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = 3 + 60 = 63

m3Understand basic algebraic properties (i.e., commutative: ab = ba; associative: ab(c) = a(bc); and distributive: a(b+c) = (ab)+(ac)).

H H H

N.FL.04.10 Multiply fluently any whole number by a one-digit number, and a three-digit number by a two-digit number; for a two-digit by one-digit multiplication, use distributive property to develop meaning for the algorithm.



N.FL.04.11 Divide numbers up to four digits by one-digit numbers and by 10. m1


H H H

N.FL.04.12 Find unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25. m7

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables.

H H H

N.MR.04.13 Use the relationship between multiplication and division to simplify computations and check results, e.g., 6840 ÷ 20 = (6840 ÷ 10) ÷ 2 = 684 ÷ 2 = 342.


L H M

m11

Use addition and multiplication to simplify an algebraic expression by identifying the order of operations and techniques necessary to carry out the operations (e.g., 5-3(x-2) = 5-3x+6 = 11-3x).

N.FL.04.14 Solve applied problems involving whole number multiplication and division. m1


H H Hm7


m8 Understand the correct order of operations for performing algebraic computations.

Read, interpret and compare decimal fractionsN.ME.04.15 Read and interpret decimals up to two decimal places; relate to money and place value decomposition.

m1 Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. H H H


N.ME.04.16 Know that terminating decimals represents fractions whose denominators are 10, 10 x 10, 10 x 10 x 10, etc., e.g., powers of 10.


m19 Understand the definitions and properties of rational and



Grade 4


RankMEAP Curriculum

Survey Priority

irrational numbers. N.ME.04.17 Locate tenths and hundredths on a number line. m19 Understand the definitions and properties of rational and


N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places. m19 Understand the definitions and properties of rational and


N.MR.04.19 Write tenths and hundredths in decimal and fraction forms, and know the decimal equivalents for halves and fourths.


Understand fractionsN.ME.04.20 Understand fractions as parts of a set of objects. m19 Understand the definitions and properties of rational and


N.MR.04.21 Explain why equivalent fractions are equal, using models such as fraction strips or the number line, for fractions with denominators of 12 or less, or equal to 100.

m19


N.MR.04.22 Locate and compare fractions on the number line, including improper fractions and mixed numbers with denominators of 12 or less.


N.MR.04.23 Understand the relationships among halves, fourths and eighths and among thirds, sixths and twelfths.


N.MR.04.24 Know that fractions of the form where m/n, is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line; express as mixed numbers.

m19


N.MR.04.25 Write improper fractions as mixed numbers, and understand that a mixed number represents the number of “wholes” and the part of a whole remaining, e.g., 5/4 = 1 + 1/4= 1 1/4



N.MR.04.26 Compare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12, including improper fractions and mixed numbers.


Add and subtract fractionsN.MR.04.27 Add and subtract fractions less than 1 with denominators 12 or less and including 100, in cases where the denominators are equal or when one denominator is a multiple of the other, e.g., 1/12 + 5/12= 6/12; 1/6 + 5/12 = 7/12; 3/10 - 23/100 = 7/100.

m1


H H H

N.FL.04.28 Solve fraction problems involving sums and differences for fractions where one denominator m1




Grade 4


RankMEAP Curriculum

Survey Priority

is a multiple of the other (denominators 2 through 12, and 100).N.MR.04.29 Solve for the unknown in equations such as: 1/8+ x = 5/8 or 3/4 - y =1/2. m1 Perform operations with signed (positive and negative)

numbers, including decimals, ratios, percents, and fractions.

H H Hm7


Multiply fractions by whole numbersN.MR.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models. m1 Perform operations with signed (positive and negative)

numbers, including decimals, ratios, percents, and fractions. H H H

Add and subtract decimal fractionsN.MR.04.31 Use mathematical statements to represent problems that use addition and subtraction of decimals with up to two-digits; solve.

m1 Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.

H H Hm7


N.FL.04.32 Add and subtract decimals up to two decimal places. m1 Perform operations with signed (positive and negative)


Multiply and divide decimal fractionsN.FL.04.33 Multiply and divide decimals up to two decimal places by a one-digit whole number where the result is a terminating decimal, e.g., 0.42 ÷ 3 = 0.14, but not 5 ÷ 3 = 1. 6

m1


H H H

EstimateN.FL.04.34 Estimate the answers to calculations involving addition, subtraction, or multiplication. m1


H H H

N.FL.04.35 Know when approximation is appropriate and use it to check the reasonableness of answers; be familiar with common place-value errors in calculations.



N.FL.04.36 Make appropriate estimations and calculations fluently with whole numbers using mental math strategies.





Grade 4


RankMEAP Curriculum

Survey Priority

Problem-solvingN.MR.04.37 Solve applied problems using the four basic arithmetic operations for appropriate fractions, decimals, and whole numbers.


H H Hm7



MEASUREMENTMeasure using common tools and appropriate unitsM.UN.04.01 Measure using common tools and select appropriate units of measure.

m33


s23


M.PS.04.02 Give answers to a reasonable degree of precision in the context of a given problem.

m33


H H H

s23


s81 Know how to round off numbers according to the correct number of significant figures.

M.UN.04.03 Measure and compare integer temperatures in degrees.

m33


H H H

s23 Measure properties of the environment using dimensional quantities such as time, length, mass, pressure, volume,



Grade 4


RankMEAP Curriculum

Survey Priority

acceleration, etc. Compare, estimate and predict measurements.

s31Know the concepts of temperature and absolute temperature. Know the temperature scales (Fahrenheit, Celsius, and Kelvin) and their relationships.

M.TE.04.04 Measure surface area of cubes and rectangular prisms by covering and counting area of the faces.


H H Hm33


Convert measurement unitsM.TE.04.05 Carry out the following conversions from one unit of measure to a larger or smaller unit of measure: meters to centimeters, kilograms to grams, liters to milliliters, hours to minutes, minutes to seconds, years to months, weeks to days, feet to inches, ounces to pounds (using numbers that involve only simple calculations).

m33


H H H

Use perimeter and area formulasM.TE.04.06 Know and understand the formulas for perimeter and area of a square and a rectangle; calculate the perimeters and areas of these shapes and combinations of these shape using the formulas.

m13

Compute the perimeter and area of two-dimensional figures. H H H

M.TE.04.07 Find one dimension of a rectangle given the other dimension and its perimeter or area. m13 Compute the perimeter and area of two-dimensional

figures. H H H


M.TE.04.08 Find the side of a square given its perimeter or area. m13 Compute the perimeter and area of two-dimensional

figures. H H H


M.PS.04.09 Solve contextual problems about perimeter and area of squares and rectangles in compound shapes.


H H Hm27

Understand the properties and classification of quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid).



Grade 4


RankMEAP Curriculum

Survey Priority

Understand right anglesM.TE.04.10 Identify right angles and compare angles to right angles. m4

Understand the characteristics and terminology of angles, e.g., degree measure, classification of angles by measure (acute, right, obtuse, and straight), supplementary and complementary angles, and vertical angles.

H H H

Problem-solvingM.PS.04.11 Solve contextual problems about surface area. m13 Compute the perimeter and area of two-dimensional

figures. H H H

GEOMETRYUnderstand perpendicular, parallel, and intersecting linesG.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner.

m2 Understand the characteristics of parallel, perpendicular, and intersecting lines.

H H Hm28

Use geometric methods (e.g., an unmarked straightedge and compass) to complete basic geometric constructions (e.g., perpendicular bisector of a line segment, angle bisector, etc.).

Identify basic geometric shapes and their components, and solve problemsG.GS.04.02 Identify basic geometric shapes including isosceles, equilateral and right triangles, and use their properties to solve problems.

m16Understand the properties and classification triangles by sides (i.e., scalene, isosceles, and equilateral). H H H

G.SR.04.03 Identify and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces.

m29

Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres. H H H

Recognize symmetry and transformationsG.TR.04.04 Recognize plane figures that have line symmetry. m55

Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation.

H M H

G.TR.04.05 Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. m55


H M H

DATA & PROBABILITYRepresent and solve problems for given dataD.RE.04.01 Construct tables and bar graphs from given data. m5


H H H

D.RE.04.02 Order a given set of data, find the median, and specify the range of values.

m5 Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences.

H H H



Grade 4


RankMEAP Curriculum

Survey Priority

m15 Understand the characteristics of measures of central tendency (i.e., mean, median, and mode).

m36Understand the characteristics of measures of dispersion (i.e., range, mean deviation, variance, and standard deviation).

D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs and read bar graphs showing two data sets.

m5

Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences. H H H



Grade 5


RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONSUnderstand division of whole numbersN.MR.05.01 Understand the meaning of division of whole numbers, with and without remainders; relate division to fractions and to repeated subtraction.



N.MR.05.02 Relate division of whole numbers with remainders to the form a = bq + r, e.g., 34 ÷ 5 = 6 r 4, so 5 • 6 + 4 = 34; note remainder (4) is less than divisor (6).

m1


H H H

N.MR.05.03 Write mathematical statements involving division for given situations. m1 Perform operations with signed (positive and negative)


H H Hm7


Multiply and divide whole numbersN.FL.05.04 Multiply a multi-digit number by a two-digit number; recognize and be able to explain common computational errors such as not accounting for place value.



N.MR.05.05 Solve applied problems involving multiplication and division of whole numbers. m1 Perform operations with signed (positive and negative)


H H Hm7



N.FL.05.06 Divide fluently up to a four-digit number by a two-digit number. m1 Perform operations with signed (positive and negative)


Find prime factorizations of whole numbersN.MR.05.07 Find the prime factorization of numbers between 1 and 50, express in exponential notation, e.g., 24 = 233 x 311, and understand that every whole number can be expressed as a product of primes.

m22


M H H

Understand meaning of decimal fractions and percentages



Grade 5


RankMEAP Curriculum

Survey Priority

N.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the relationship of each place value to the place to its right, e.g., 1 is 10 tenths, one tenth is 10 hundredths.

m19

Understand the definitions and properties of rational and irrational numbers. M H H

N.ME.05.09 Understand percentages as parts out of 100, use % notation, and express a part of a whole as a percentage.

m19Understand the definitions and properties of rational and irrational numbers. M H H

Understand fractions as division statements; find equivalent fractionsN.ME.05.10 Understand a fraction as a statement of division, e.g., 2 ÷ 3 = 2/3 using simple fractions and pictures to represent.


N.ME.05.11 Given two fractions, express them as equivalent fractions with a common denominator, but not necessarily a least common denominator, e.g., 1/2 = 4/8 and 3/4 = 6/8; use denominators less than 12 or factors of 100.

m19


M H H

Multiply and divide fractionsN.FL.05.12 Find the product of two unit fractions with small denominators using area model. m1


H H H

N.FL.05.13 Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions.


H H H

Add and subtract fractions using common denominatorsN.FL.05.14 Add and subtract fractions with unlike denominators of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g.,3/8 + 7/10 = (3 x 10) + (7 x 8)= 30 + 56 80= 86/80


H H H

m8

Understand the correct order of operations for performing algebraic computations.

Multiply and divide by powers of tenN.MR.05.15 Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1,000; and identify patterns.


m24 Understand the basic properties and laws of exponents and scientific notation.



Grade 5


RankMEAP Curriculum

Survey Priority

N.FL.05.16 Divide numbers by 10’s, 100’s, 1,000’s, using mental strategies. m1



N.MR.05.17 Multiply one-digit whole numbers by decimals up to two decimal places. m1


H H H

Solve applied problems with fractionsN.FL.05.18 Given an applied situation involving addition and subtraction of fractions, write mathematical statements describing the situation.


H H H

m7


N.MR.05.19 Solve word problems that involve finding sums and differences of fractions with unlike denominators using knowledge of equivalent fractions.



N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness; use examples involving money.



N.MR.05.21 Solve for the unknown in such equations as: ¼ + x = 7/12. m1


H H H

m7


Express, interpret, and use ratios; find equivalencesN.MR.05.22 Express fractions and decimals as percentages and vice versa. m1


M H H

N.ME.05.23 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3 : 5,

m1 Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and

M H H



Grade 5


RankMEAP Curriculum

Survey Priority

3/5; recognize and find equivalent ratios. fractions. MEASUREMENTKnow, and convert among, measurement units within a given systemM.UN.05.01 Recognize the equivalence of 1 liter, 1.000 ml and 1000 cm3 and include conversions among liters, milliliters, and cubic centimeters. m33


H H H

M.UN.05.02 Know the units of measure of volume: cubic centimeter, cubic meter, cubic inches, cubic feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3).

m33


s23


M.UN.05.03 Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one cubic meter. m33


H H H

M.UN.05.04 Convert measurements of length, weight, area, volume, and time within a given system using easily manipulated numbers. m33


H H H

Find areas of geometric shapes using formulasM.PS.05.05 Represent relationships between areas of rectangles, triangles, and parallelograms using models.

m13 Compute the perimeter and area of two-dimensional figures. H H H


M.TE.05.06 Understand and know how to use the area formula of a triangle: A = 1/2 bh (where b is length of the base and h is the height), and represent using models and manipulatives.


m16 Understand the properties and classification triangles by sides (i.e., scalene, isosceles, and equilateral).

M.TE.05.07 Understand and know how to use the area formula for a parallelogram: A = bh, and represent using models and manipulatives.


m27 Understand the properties and classification of Copyright © 2006 International Center for Leadership in Education Math –


Grade 5


RankMEAP Curriculum

Survey Priority

quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid).

Understand the concept of volumeM.TE.05.08 Build solids with unit cubes and state their volumes. m29

Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.

H H H

m33


M.TE.05.09 Use filling (unit cubes or liquid), and counting or measuring to find the volume of a cube and rectangular prism.


H H Hm33


s23


M.PS.05.10 Solve applied problems about the volumes of rectangular prisms using multiplication and division and using the appropriate units.

m17Compute the volume of three-dimensional figures (solids).

H H H

GEOMETRYKnow the meaning of angles, and solve problemsG.TR.05.01 Associate an angle with a certain amount of turning; know that angles are measured in degrees; understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, and 3/4 and full turns.

m4


H H H

G.GS.05.02 Measure angles with a protractor, and classify them as acute, right, obtuse, or straight. m4


H H H

G.GS.05.03 Identify and name angles on a straight line and vertical angles. m4


H H H



Grade 5


RankMEAP Curriculum

Survey Priority

G.GS.05.04 Find unknown angles in problems involving angles on a straight line, angles surrounding a point and vertical angles.

m4


H H H

G.GS.05.05 Know that angles on a straight line add up to 180°and angles surrounding a point add up to 360°; justify informally by “surrounding” a point with angles.

m4


H H H

G.GS.05.06 Understand why the sum of the interior angles of a triangle is 180°and the sum of the interior angles of a quadrilateral is 360°, and use these properties to solve problems.


H H Hm27


Solve problems about geometric shapesG.GS.05.07 Find unknown angles using the properties of: triangles, including right,isosceles, and equilateral triangles; parallelograms, including rectangles and rhombuses; and trapezoids.

m4


H H Hm14 Understand the angle relationships in triangles (i.e., acute, obtuse, right, interior, and exterior).


DATA & PROBABILITYConstruct and interpret line graphsD.RE.05.01 Read and interpret line graphs, and solve problems based on line graphs, e.g., distance-time graphs, and problems with two or three line graphs on same axes, comparing different data.

m5

Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences. H H H

D.RE.05.02 Construct line graphs from tables of data; include axis labels and scale. m5


H H H

Find and interpret mean and mode for a given set of dataD.AN.05.03 Given a set of data, find and interpret the mean (using the concept of fair share) and mode. m15 Understand the characteristics of measures of central

tendency (i.e., mean, median, and mode). H H H

D.AN.05.04 Solve multi-step problems involving means. m15 Understand the characteristics of measures of central

tendency (i.e., mean, median, and mode). H H H



Grade 6


RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONSMultiply and divide fractionsN.MR.06.01 Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = , then 2/3 x = 4/5, so = 4/5 • 2/3 = 12/10.


H H H

N.FL.06.02 Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation.


H H H

m7


N.MR.06.03 Solve for the unknown in equations such as: 1/4÷ = 1 3/4 ÷ = 1/4 and 1/2 = 1 • . m1


H H H

N.FL.06.04 Multiply and divide any two fractions, including mixed numbers, fluently. m1


H H H

Represent rational numbers as fractions or decimalsN.ME.06.05 Order rational numbers and place them on the number line. m19 Understand the definitions and properties of rational and

irrational numbers. M H H

N.ME.06.06 Represent rational numbers as fractions or terminating decimals when possible, and translate between these representations.


N.ME.06.07 Understand that a fraction or a negative fraction is a quotient of two integers, e.g., -8/3 is -8 divided by 3.


Add and subtract integers and rational numbersN.MR.06.08 Understand integer subtraction as the inverse of integer addition; add and subtract integers using integers from 10 to -10.


M H H

N.FL.06.09 Add, subtract, multiply, and divide integers between -10 and 10; use number line and strip models for addition and subtraction.


H H H

N.FL.06.10 Add, subtract, multiply and divide positive rational numbers fluently. m1


H H H

Find equivalent ratios



Grade 6


RankMEAP Curriculum

Survey Priority

N.ME.06.11 Find equivalent ratios by scaling up or scaling down. m1


M H H

m33


Solve decimal, percentage and rational number problemsN.FL.06.12 Calculate part of a number given the percentage and the number. m1


H H H

N.FL.06.13 Solve word problems involving percentages in such contexts as sales taxes and tips, and involving positive rational numbers.


H H H

N.FL.06.14 For applied situations, estimate the answers to calculations involving operations with rational numbers.



N.FL.06.15 Solve applied problems that use the four operations with appropriate decimal numbers. m1


H H H

Use exponentsN.ME.06.16 Understand and use integer exponents, excluding powers of negative numbers; express numbers in scientific notation.

m24Understand the basic properties and laws of exponents and scientific notation. M H H

Understand rational numbers and their location on the number lineN.ME.06.17 Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0, and are on opposite sides and at equal distance from 0 on a number line.

m19


M H H

N.ME.06.18 Understand that rational numbers are quotients of integers (non-zero denominators), e.g., a rational number is either a fraction or a negative fraction.

m19

Understand the definitions and properties of rational and irrational numbers. M H H

N.ME.06.19 Understand that 0 is an integer that is m19 Understand the definitions and properties of rational and M H H



Grade 6


RankMEAP Curriculum

Survey Priority

neither negative nor positive. irrational numbers. N.ME.06.20 Know that the absolute value of a number is the value of the number, ignoring the sign, or is the distance of the number from 0.


ALGEBRACalculate ratesA.PA.06.01 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will it go in 3 ½ hours? m33


H H H

Understand the coordinate planeA.RP.06.02 Plot ordered pairs of integers and use ordered pairs of integers to identify points in all four quadrants of the coordinate plane. m23

Know the components and properties of the rectangular coordinate system, (i.e., x - y axis, origin, quadrants, abscissa (x-coordinate) and ordinate (y-coordinate), and the general representation of a point (x,y)).

H H H

Use variables, write expressions and equations, and combine like termsA.FO.06.03 Use letters, with units, to represent quantities in a variety of contexts, e.g., y lbs., k minutes, x cookies. m7


H H H

A.FO.06.04 Distinguish between an algebraic expression and an equation. m7


H H H

A.FO.06.05 Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means “two times x, plus 1” and 2(x + 1) means “two times the quantity (x + 1).”

m7


H H H

A.FO.06.06 Represent information given in words using algebraic expressions and equations. m7


H H H

A.FO.06.07 Simplify expressions of the first degree by combining like terms, and evaluate using specific values. m7


H H H

m11 Use addition and multiplication to simplify an algebraic expression by identifying the order of operations and techniques necessary to carry out the operations (e.g., 5-



Grade 6


RankMEAP Curriculum

Survey Priority

3(x-2) = 5-3x+6 = 11-3x). Represent linear functions using tables, equations, and graphsA.RP.06.08 Understand that relationships between quantities can be suggested by graphs and tables. m40

Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.).

H M H

A.PA.06.09 Graph and write equations for linear functions of the form y = mx, and solve related problems, e.g., given n chairs, the “leg function” is f(n) = 4n; if you have 5 chairs, how many legs?; if you have 12 legs, how many chairs?

m40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.). H M H

m64Know how to express a linear function (e.g., y = 1/3x+5) using the functional notation f(x) = 1/3x+5, and determine the ordered pairs.

A.RP.06.10 Represent simple relationships between quantities, using verbal descriptions, formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches.



Solve equationsA.FO.06.11 Relate simple linear equations with integer coefficients to particular contexts, and solve, e.g., 3x = 8 or x + 5 = 10. m7

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. H H H

m11


A.FO.06.12 Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution. m11


L H M

A.FO.06.13 Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solutions.

m11


M H H

A.FO.06.14 Solve equations of the form ax + b = c, e.g., 3x + 8 = 15 by hand for positive integer coefficients less than 20, using calculators otherwise, and interpret the results.

m11


L H M

m35 Find the solution of linear equations and inequalities Copyright © 2006 International Center for Leadership in Education Math –


Grade 6


RankMEAP Curriculum

Survey Priority

where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x).

MEASUREMENTConvert within measurement systemsM.UN.06.01 Convert between basic units of measurement within a single measurement system, e.g., square inches to square feet. m33


H H H

Find volume and surface areaM.PS.06.02 Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets).


H H H

m33


M.TE.06.03 Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides using formulas.


m17 Compute the volume of three-dimensional figures (solids).GEOMETRYG.GS.06.01 Understand and apply basic properties of lines, angles, and triangles, including:—triangle inequality—relationships of vertical angles, complementary angles, supplementary angles—congruence of corresponding and alternate interior angles when parallel lines —are cut by a transversal, and that such congruencies imply parallel lines—locate interior and exterior angles of any triangle, and use the property that an exterior —angle of a triangle is equal to the sum of the remote (opposite) interior angles—know that the sum of the exterior angles of a convex polygon is 360º.


H H H

m4






Understand the concept of congruence and basic transformationsG.GS.06.02 Understand that for polygons, m49 Apply transformation concepts to understand and create H M H



Grade 6


RankMEAP Curriculum

Survey Priority

congruence means corresponding sides and angles have equal measures.

congruent and similar figures.

G.TR.06.03 Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and apply them to solve problems.

m49

Apply transformation concepts to understand and create congruent and similar figures. H M H

G.TR.06.04 Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.

m55Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation.

H M H

Construct geometric shapesG.SR.06.05 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors; justify informally.

m28


H H H

DATA & PROBABILITYUnderstand the concept of probability and solve problemsD.PR.06.01 Express probabilities as fractions, decimals or percentages between 0 and 1; know that 0 probability means an event will not occur and that probability 1 means an event will occur.

m25

Determine the probability of single and compound events using the basic premise that the probability of an event is equal to the number of ways it can occur divided by the total number of outcomes.

M H H

D.PR.06.02 Compute probabilities of events from simple experiments with equally likely outcomes, e.g., tossing dice, flipping coins, spinning spinners, by listing all possibilities and finding the fraction that meets given conditions.

m20

Understand the characteristic differences between theoretical and empirical probability (e.g., the theoretic probability of rolling a six and a die is 1/6; empirical probability is derived from repeated experimentation or accumulated statistics).

M H H



Grade 7


RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONSUnderstand derived quantitiesN.ME.07.01 Understand derived quantities such as density, velocity, and weighted averages. s23


M H H

N.FL.07.02 Solve problems involving derived quantities.

m33


s23


Understand and solve problems involving rates, ratios, and proportionsN.FL.07.03 Calculate rates of change including speed. m1


H H H

m33


N.MR.07.04 Convert ratio quantities between different systems of units such as feet per second to miles per hour. m33


M H H

N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

m33


H H H

m52 Find the solution of proportions with monomial monomial and binomial terms (e.g., x/(x-2) = 6/5, therefore, x = 12).

Recognize irrational numbersN.MR.07.06 Understand the concept of square root and cube root, and estimate using calculators. m19 Understand the definitions and properties of rational and

irrational numbers. M H H



Grade 7


RankMEAP Curriculum

Survey Priority

Compute with rational numbersN.FL.07.07 Solve problems involving operations with integers. m1 Perform operations with signed (positive and negative)


N.FL.07.08 Add, subtract, multiply and divide negative rational numbers. m1 Perform operations with signed (positive and negative)


N.FL.07.09 Estimate results of computations with rational numbers. m1 Perform operations with signed (positive and negative)

numbers, including decimals, ratios, percents, and fractions. H H Hm19 Understand the definitions and properties of rational and

irrational numbers. ALGEBRAUnderstand and apply directly proportional relationships and relate to linear relationshipsA.PA.07.01 Recognize when information given in a table, graph, or formula suggests a proportional or linear relationship.

m40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.).

H M H

A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.

m7


H H Hm33




A.PA.07.03 Given a directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = kx for specific x values, given k, e.g., weight vs. volume of water, base cost plus cost per unit.

m34 Know the equation for the slope of a line and compute slope given the coordinates of two points.

H H Hm45Know the equation of a line and interpret graphically using the slope-intercept form (i.e., y = mx+b), and the point-slope form (i.e., y-b = m(x-a)).


A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and

m33 Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including

H H H



Grade 7


RankMEAP Curriculum

Survey Priority

equations, e.g., the heights and volume of a container with uniform cross-section, height of water in a tank being filled at a constant rate, degrees Celsius and degrees Fahrenheit, distance and time under constant speed.

drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.


m45Know the equation of a line and interpret graphically using the slope-intercept form (i.e., y = mx+b), and the point-slope form (i.e., y-b = m(x-a)).


A.PA.07.05 Understand and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.


H H Hm40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.).


Understand and represent linear functionsA.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change.


M H Hm40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.).


A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.


H H Hm45Know the equation of a line and interpret graphically using the slope-intercept form (i.e., y = mx+b), and the point-slope form (i.e., y-b = m(x-a)).


A.FO.07.08 Know that the solution to a linear equation corresponds to the point at which its graph crosses the x-axis.


L M M

Understand and solve problems about inversely proportional relationships



Grade 7


RankMEAP Curriculum

Survey Priority

A.PA.07.09 Recognize inversely proportional relationships in contextual situations; know that quantities are inversely proportional if their product is constant, e.g., the length and width of a rectangle with fixed area, and that an inversely proportional relationship is of the form y = k/x where k is some non-zero number.


L M M

m73

Understand inverse functions as the set of ordered pairs obtained by interchanging the first and second elements of each pair belonging to a one-on-one function. Use one-on-one functions to create symmetric figures consisting of the graphs of a function and its inverse function.

A.RP.07.10 Know that the graph of y = k/x is not a line; know its shape; and know that it crosses neither the x nor the y-axis.


L M M

Apply basic properties of real numbers in algebraic contextsA.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition.

m3Understand basic algebraic properties (i.e., commutative: ab = ba; associative: ab(c) = a(bc); and distributive: a(b+c) = (ab)+(ac)). H H H


Combine algebraic expressions and solve equationsA.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or – 2x (5x – 4), and justify using properties of real numbers.

m11

Use addition and multiplication to simplify an algebraic expression by identifying the order of operations and techniques necessary to carry out the operations (e.g., 5-3(x-2) = 5-3x+6 = 11-3x). H H H


A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. m35

Find the solution of linear equations and inequalities where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x).

L H M

GEOMETRYDraw and construct geometric objectsG.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles and parallelograms with specified dimensions. m28


H H H

G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand

m28 Use geometric methods (e.g., an unmarked straightedge and compass) to complete basic geometric constructions (e.g., perpendicular bisector of a line segment, angle bisector, etc.).

H H H



Grade 7


RankMEAP Curriculum

Survey Priority

informal justifications.Understand the concept of similar polygons, and solve related problemsG.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor.

m33


H H H


G.TR.07.04 Solve problems about similar figures and scale drawings.

m33


H H H


G.TR.07.05 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments.


H H H


m33



G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r2. m33


H H H


DATA & PROBABILITYRepresent data and interpretD.RE.07.01 Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-and-whisker plots, and select appropriate


H H H



Grade 7


RankMEAP Curriculum

Survey Priority

representation to address specific questions.D.AN.07.02 Create and interpret scatter plots and find line of best fit and use an estimated line of best fit to answer questions about the data.


H H H

Compute statistics about datasetsD.AN.07.03 Calculate and interpret relative frequencies and cumulative frequencies for given data sets.


L H M

D.AN.07.04 Find and interpret the median, quartiles, and interquartile range of a given set of data.


H H Hm42

Understand the concepts and applications of quartiles (i.e., distributing groups into four equal frequencies) and percentiles (i.e., distributing individuals into one-hundred groups of equal frequency).



Grade 8


RankMEAP Curriculum

Survey Priority

NUMBER & OPERATIONSUnderstand real number conceptsN.ME.08.01 Understand the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to the volume of a cube.

m19


M H H

N.ME.08.02 Understand meanings for zero and negative integer exponents. m19 Understand the definitions and properties of rational and

irrational numbers. M H Hm24 Understand the basic properties and laws of exponents and

scientific notation. N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g., 0.1= 1/9; 0.3= 1/3 .

m19


M H H

N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, (e.g.,√2 , √3 , π) on the number line.

m19


M H H

N.FL.08.05 Estimate and solve problems with square roots and cube roots using calculators.

m44

Perform operations with radicals such as addition, subtraction, multiplication, and division of two or more irrational numbers and express as the square root of a positive integer or as the product of a rational number and the square root of a positive integer.

M M M

m68 Apply arithmetic methods for obtaining a rational approximation of an irrational number (e.g., radical).

N.FL.08.06 Find square roots of perfect squares and approximate the square roots of nonperfect squares by locating between consecutive integers, e.g., √130 is between 11 and 12.

m44

Perform operations with radicals such as addition, subtraction, multiplication, and division of two or more irrational numbers and express as the square root of a positive integer or as the product of a rational number and the square root of a positive integer.

M M M


Solve problemsN.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g.,

m1 Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and

M H H



Grade 8


RankMEAP Curriculum

Survey Priority

3% increase of a quantity x is x + .03x = 1.03x. fractions.

m7


N.MR.08.08 Solve problems involving percent increases and decreases. m1


M H H

m7


N.FL.08.09 Solve problems involving compounded interest or multiple discounts. m1


M H H

m7


N.MR.08.10 Calculate weighted averages such as course grades, consumer price indices, and sports ratings.


M H H

m7


N.MR.08.11 Solve problems involving ratio units such as miles per hour, dollars per pound, or persons per square mile.


M H Hm7


m33


ALGEBRAUnderstand the concept of non-linear functions Copyright © 2006 International Center for Leadership in Education Math –


Grade 8


RankMEAP Curriculum

Survey Priority

using basic examplesA.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inverse functions (y = k/x), cubics (y = ax3) roots, (y =√x ), and exponentials (y = ax , a > 0), using tables, graphs, and equations.


H M H



m69 Graph the exponential function and understand its characteristics.

m73


A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.


m81 Solve and graphically sketch problems involving two variables that exhibit direct and indirect variation.

A.PA.08.03 Recognize basic functions in problem context, e.g., area of a circle is π r2, volume of a sphere is 4/3 π r3, and represent them using tables, graphs, and formulas.


L H M

m17 Compute the volume of three-dimensional figures (solids).

m30Know how to measure circle quantities (e.g., area, angle formed by two secants, circumference, length of segments, etc.).


A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.

m32

Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

L H M




Grade 8


RankMEAP Curriculum

Survey Priority

Understand and represent quadratic functionsA.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function.

m40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.). L M M

m53Apply the zero property of multiplication to find the solution of quadratic equations.

A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2.

m86

Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations.

L L L

Recognize, represent, and apply common formulasA.FO.08.07 Recognize and apply the common formulas:(a + b)2 = a2 + 2 ab + b2

(a – b)2 = a2 – 2 ab + b2

(a + b) (a – b) = a2 – b2 ; represent geometrically.

m81

Solve and graphically sketch problems involving two variables that exhibit direct and indirect variation.

L L L

A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g., x2

+ 6x + 9, x2 + 2x –

3 and x2 – 4; solve simple quadratic equations, e.g., x2

= 16 or x2 = 5 (by taking square roots); x2

– x – 6 = 0, x2

– 2x = 15 (by factoring); verify solutions by evaluation.

m22

Understand factoring a composite number into its prime factors, and how to find the largest monomial factor of a polynomial to write the polynomial as the product of the monomial and a polynomial. L H M

m53 Apply the zero property of multiplication to find the solution of quadratic equations.

A.FO.08.09 Solve applied problems involving simple quadratic equations. m22

Understand factoring a composite number into its prime factors, and how to find the largest monomial factor of a polynomial to write the polynomial as the product of the monomial and a polynomial. L H M


Understand solutions and solve equations, simultaneous equations, and linear inequalitiesA.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).

m12

Analyze the truth value of simple sentences by stating whether a simple objective statement (closed sentence) is true or false, or whether a statement containing pronouns or variables (open sentence) becomes true or false upon replacement of those pronouns or variables.

H H H

m40 Understand appropriate terminology used to define relations and functions and their properties (e.g., domain,



Grade 8


RankMEAP Curriculum

Survey Priority

range, function composition, inverses, etc.).

m71Know how to find the graphic solution of systems of linear equations (e.g., find the point(s) common to a quadratic-linear pair).

A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.

m45Know the equation of a line and interpret graphically using the slope-intercept form (i.e., y = mx+b), and the point-slope form (i.e., y-b = m(x-a)). L M M

m71Know how to find the graphic solution of systems of linear equations (e.g., find the point(s) common to a quadratic-linear pair).

A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets. m35

Find the solution of linear equations and inequalities where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x). H H H

m82Know how to find the graphic solution of systems of linear inequalities (e.g., graph the solution set or region of the coordinate plane common to both inequalities).

A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities.

m71Know how to find the graphic solution of systems of linear equations (e.g., find the point(s) common to a quadratic-linear pair). L L L


GEOMETRYUnderstand and use the Pythagorean TheoremG.GS.08.01 Understand at least one proof of the Pythagorean Theorem; use the Pythagorean Theorem and its converse to solve applied problems including perimeter, area, and volume problems.


H H Hm17 Compute the volume of three-dimensional figures (solids).

m21 Use the Pythagorean theorem to compute side lengths of right triangles.

G.LO.08.02 Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem.

m9 Know how to compute the distance between two points (i.e., length of a line segment) on a coordinate plane. H H H


Solve problems about geometric figuresG.SR.08.03 Understand the definition of a circle; know and use the formulas for circumference and area of a circle to solve problems.

m10 Understand the properties of circles (e.g., radius, arc, diameter, chord, secant, tangent, etc.).

H H H

m30 Know how to measure circle quantities (e.g., area, angle formed by two secants, circumference, length of segments,



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etc.). G.SR.08.04 Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals, triangles, circles).


H H H




G.SR.08.05 Solve applied problems involving areas of triangles, quadrilaterals, and circles. m13 Compute the perimeter and area of two-dimensional

figures.

H H Hm21 Use the Pythagorean theorem to compute side lengths of right triangles.


Understand concepts of volume and surface area, and apply formulas G.SR.08.06 Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and pyramids ( 1/3(area of base) x height) and spheres ( 4/3 π (radius) 3 ) and apply them to solve problems.

m17

Compute the volume of three-dimensional figures (solids).

H H H

G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and cylinders.


H H Hm30

Know how to measure circle quantities (e.g., area, angle formed by two secants, circumference, length of segments, etc.).

Visualize solidsG.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets, use such two-dimensional representations to help solve problems.


H H Hm33



m55 Understand the concepts of symmetry and transformations Copyright © 2006 International Center for Leadership in Education Math –


Grade 8


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Survey Priority

and graphically apply line reflections, rotation, translations, and dilation.

m75

Understand the concepts of direct and opposite isometries (i.e., transformations that preserve distance such as reflections, rotations, translations, and glide reflections, and be able to graphically apply them.

Understand and apply concepts of transformation and symmetryG.TR.08.09 Understand the definition of a dilation from a point in the plane, and relate it to the definition of similar polygons.

m49Apply transformation concepts to understand and create congruent and similar figures. H M H

G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes, and relate them to transformations to solve problems.


H M H

DATA & PROBABILITYDraw, explain, and justify conclusions based on dataD.AN.08.01 Determine which measure of central tendency (mean, median, mode) best represents a data set, e.g., salaries, home prices for answering certain questions; justify the choice made.

m15

Understand the characteristics of measures of central tendency (i.e., mean, median, and mode). H H H

D.AN.08.02 Recognize practices of collecting and displaying data that may bias the presentation or analysis.


H H H



m42


Understand probability concepts for simple and compound eventsD.PR.08.03 Compute relative frequencies from a table of experimental results for a repeated event, and be able to answer questions about the result, using relationship of probability to relative frequency.

m5Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences. M H H

m20Understand the characteristic differences between theoretical and empirical probability (e.g., the theoretic



Grade 8


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probability of rolling a six and a die is 1/6; empirical probability is derived from repeated experimentation or accumulated statistics).

D.PR.08.04 Apply the Basic Counting Principle to find total number of outcomes possible for independent and dependent events, and calculate the probabilities using organized lists or tree diagrams.

m56

Use the Counting Principle to determine the probability of events occurring jointly (e.g., if one activity can occur in any of m ways and another in any one of n ways, then the total number of ways both activities can occur is mn).

M M M

D.PR.08.05 Understand the relationship of probability to relative frequency.

m20


L H M

D.PR.08.06 Understand the difference between independent and dependent events, and recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll.


M H H

m20


D.AN.08.07 Compute relative frequencies from a table of experimental results for a repeated event; understand the relationship of experimental probability to relative frequency; answer questions regarding the results.


L H M

m20



Michigan MathematicsStandards/Benchmarks

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MEAP11th Grade

Curriculum Survey Priority

STRAND 1: QUANTITATIVE LITERACY AND LOGICSTANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONSBased on their knowledge of the properties of arithmetic, students understand and reason about numbers, number systems, and the relationships between them. They represent quantitative relationships using mathematical symbols, and interpret relationships from those representations. L1.1 Number Systems and Number SenseL1.1.1 Know the different properties that hold in different number systems, and recognize that the applicable properties change in the transition from the positive integers, to all integers, to the rational numbers, and to the real numbers.

m3Understand basic algebraic properties (i.e., commutative: ab = ba; associative: ab(c) = a(bc); and distributive: a(b+c) = (ab)+(ac)). H


L1.1.2 Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse of a number has the opposite sign.

m19Understand the definitions and properties of rational and irrational numbers. H

L1.1.3 Explain how the properties of associativity, commutativity, and distributivity, as well as identity and inverse elements, are used in arithmetic and algebraic calculations.


H

m7


m11



L1.1.4 Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number by a number less than 0, a number between 0 and 1, and a number greater than 1.

m19 Understand the definitions and properties of rational and irrational numbers. H


L1.1.5 Justify numerical relationships (e.g., show that the sum of even integers is even; that every

m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of

H



High School


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integer can be written as 3m+k, where k is 0, 1, or 2, and m is an integer; or that the sum of the first n positive integers is n (n+1)/2).

Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

L1.1.6 Explain the importance of the irrational numbers and in basic right triangle trigonometry; the importance of π because of its role in circle relationships; and the role of e in applications such as continuously compounded interest.


Hm57

Understand the concepts of right triangle trigonometry and solve right triangles using basic trigonometric ratios (sine, cosine, tangent).

m61Understand the concepts recurrence relations and how they are applicable to such things as compound interest and annuity.


L1.2 Representations and RelationshipsL1.2.1 Use mathematical symbols (e.g., interval notation, set notation, summation notation) to represent quantitative relationships and situations.

m47 Know how to represent the solution set of an open sentence (e.g., x<-1) on a number line.

Mm72

Understand the characteristics and uses of finite sequence and series (e.g., it allows a systematic and useful means of quantifying things).

L1.2.2 Interpret representations that reflect absolute value relationships (e.g. l x - a l ≤ b, or a ± b) in such contexts as error tolerance. m33


H

L1.2.3 Use vectors to represent quantities that have magnitude and direction; interpret direction and magnitude of a vector numerically, and calculate the sum and difference of two vectors.

m70

Understand the characteristics and uses of vectors (e.g., representations of velocity and force) and perform basic operations on vectors (e.g., vector addition and scalar multiplication). A vector is a physical element possessing magnitude and direction.

M

L1.2.4 Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.


Hm15 Understand the characteristics of measures of central tendency (i.e., mean, median, and mode).




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L1.2.5 Read and interpret representations from various technological sources, such as contour or isobar diagrams.


L1.3 Counting and Probabilistic ReasoningL1.3.1 Describe, explain, and apply various counting techniques (e.g., finding the number of different 4-letter passwords; permutations; and combinations); relate combinations to Pascal’s triangle; know when to use each technique.

m43 Know how to determine combinations (i.e., the various grouping a set may be arranged in without regard to order).

Mm56


m66a Know how to determine permutations (i.e., arrangements of a set where order matters).

L1.3.2 Define and interpret commonly used expressions of probability (e.g., chances of an event, likelihood, odds). m25


H

L1.3.3 Recognize and explain common probability misconceptions such as “hot streaks” and “being due.” m20

Understand the characteristic differences between theoretical and empirical probability (e.g., the theoretic probability of rolling a six and a die is 1/6; empirical probability is derived from repeated experimentation or accumulated statistics). H

m25


STANDARD L2: CALCULATION, ALGORITHMS, AND ESTIMATIONStudents calculate fluently, estimate proficiently, and describe and use algorithms in appropriate situations (e.g., approximating solutions to equations.) They understand the basic ideas of iteration and algorithms.

L2.1 Calculation Using Real and Complex NumbersL2.1.1 Explain the meaning and uses of weighted averages (e.g., GNP, consumer price index, grade point average).


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L2.1.2 Calculate fluently with numerical expressions involving exponents; use the rules of exponents; evaluate numerical expressions involving rational and negative exponents; transition easily between roots and exponents.

m24

Understand the basic properties and laws of exponents and scientific notation.

H

L2.1.3 Explain the exponential relationship between a number and its base 10 logarithm, and use it to relate rules of logarithms to those of exponents in expressions involving numbers.

m24 Understand the basic properties and laws of exponents and scientific notation. H

m75 Graph the logarithmic function and understand its characteristics.

L2.1.4 Know that the complex number i is one of two solutions to x2 = -1. m60

Understand the concept of the imaginary unit, i, and know how to simplify square roots involving a negative radicand.

Mm65

Know the standard form of a complex number is expressed as a + bi where a and b are real numbers, and represent graphically on the complex plane where the horizontal axis is the real axis and the vertical axis is the imaginary axis.

m76 Find the solution of quadratic equations with imaginary roots and understand the characteristics of the roots.

L2.1.5 Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of ) complex numbers.

m39Execute basic operations with complex numbers (i.e., addition, multiplication, and inverse), and graphically interpret complex numbers using the complex plane.

2.1.6 Recognize when exact answers aren’t always possible or practical; use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots)

m33

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. M

m62Understand the characteristics of algorithms and how they are used for finding the greatest common denominator of two numbers and the solutions of quadratic equations.

L2.1.7 Understand the mathematical bases for the differences among voting procedures. m62

Understand the characteristics of algorithms and how they are used for finding the greatest common denominator of two numbers and the solutions of quadratic equations.

M

L2.2 Sequences and IterationL2.2.1 Find the nth term in arithmetic, geometric, or other simple sequences. m40


M

L2.2.2 Compute sums of finite arithmetic and m72 Understand the characteristics and uses of finite sequence LCopyright © 2006 International Center for Leadership in Education Math –


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MEAP11th Grade


geometric sequences. and series (e.g., it allows a systematic and useful means of quantifying things).

m77Apply summation notation to taking the sum of an expression using limits (e.g., take the sum of 3i+1, from i = 1 to 5).

L2.2.3 Use iterative processes in such examples as computing compound interest or applying approximation procedures.

m61Understand the concepts recurrence relations and how they are applicable to such things as compound interest and annuity. M


L2.2.4 Compute sums of infinite geometric sequences. m40

Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.). M

m48Understand the concepts and apply the uses of functions and limits (i.e., conduct limiting processes using functions to investigate infinite series and sequences).

STANDARD L3: MEASUREMENT AND PRECISIONStudents apply measurement units and calculations, and understand the concept of error.L3.1 Measurement Units, Calculations, and ScalesL3.1.1 Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly.

m33


H

L3.1.2 Describe and interpret logarithmic relationships in such contexts as the Richter scale, the pH scale, or decibel measurements (e.g., explain why a small change in the scale can represent a large change in intensity); solve applied problems.

m33


H


L3.2 Understanding ErrorL3.2.1 Determine what degree of accuracy is reasonable for measurements in a given situation; express accuracy through use of significant digits, error tolerance, or percent of error; describe how errors in measurements are magnified by

m33 Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.

H



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MEAP11th Grade


computation; recognize accumulated error in applied situations.L3.2.2 Describe and explain round-off error, rounding, and truncating.

m33


H

L3.2.3 Know the meaning of and interpret statistical significance, margin of error, and confidence level.

m5Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences. H


STANDARD L4: MATHEMATICAL REASONING, LOGIC, AND PROOFStudents understand mathematical reasoning as being grounded in logic and proof and can distinguish mathematical arguments from other types of arguments. They can interpret arguments made about quantitative situations in the popular media. Students know the language and laws of logic and can apply them in both mathematical and everyday settings. They write proofs using direct and indirect methods and use counterexamples appropriately to show that statements are false.L4.1 Mathematical ReasoningL4.1.1 Distinguish between inductive and deductive reasoning, identifying and providing examples of each.

m32


H

L4.1.2 Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic.


H

m31

Analyze the truth value of compound sentences that include the connectives AND (conjunction), OR (disjunction), IF-THEN (conditional), and IF AND ONLY IF (bi-conditional) and summarize by creating truth tables.

m32 Use direct proof and indirect proof sequencing techniques Copyright © 2006 International Center for Leadership in Education Math –


High School


Rank

MEAP11th Grade


to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.


L4.1.3 Define and explain the roles of axioms (postulates), definitions, theorems, counterexamples, and proofs in the logical structure of mathematics; identify and give examples of each.


H

m6 Understand the characteristics and applications of the undefined terms of geometry (i.e., point, line, and plane).


m32


L4.2 Language and Laws of LogicL4.2.1 Know and use the terms of basic logic (e.g., proposition, negation, truth and falsity, implication, if and only if, contrapositive, and converse). m12

Analyze the truth value of simple sentences by stating whether a simple objective statement (closed sentence) is true or false, or whether a statement containing pronouns or variables (open sentence) becomes true or false upon replacement of those pronouns or variables. H

m31


L4.2.2 Use the connectives “NOT,” “AND,” “OR,” and “IF…,THEN,” in mathematical and everyday settings. Know the truth table of each connective and how to logically negate statements involving these connectives.

m31


H

L4.2.3 Use the quantifiers “THERE EXISTS” and “ALL” in mathematical and everyday settings and know how to logically negate statements involving

m12 Analyze the truth value of simple sentences by stating whether a simple objective statement (closed sentence) is true or false, or whether a statement containing pronouns

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High School


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MEAP11th Grade


them. or variables (open sentence) becomes true or false upon replacement of those pronouns or variables.

m31


L4.2.4 Write the converse, inverse, and contrapositive of an “If…, then…” statement; use the fact, in mathematical and everyday settings, that the contrapositive is logically equivalent to the original while the inverse and converse are not.

m31


H

L4.3 ProofL4.3.1 Know the basic structure for the proof of an “If…, then…” statement (assuming the hypothesis and ending with the conclusion) and know that proving the contrapositive is equivalent.

m31


H

m32


L4.3.2 Construct proofs by contradiction; use counterexamples, when appropriate, to disprove a statement.

m32


H

L4.3.3 Explain the difference between a necessary and a sufficient condition within the statement of a theorem; determine the correct conclusions based on interpreting a theorem in which necessary or sufficient conditions in the theorem or hypothesis are satisfied.

m12

Analyze the truth value of simple sentences by stating whether a simple objective statement (closed sentence) is true or false, or whether a statement containing pronouns or variables (open sentence) becomes true or false upon replacement of those pronouns or variables.

H

m31


m32 Use direct proof and indirect proof sequencing techniques Copyright © 2006 International Center for Leadership in Education Math –


High School


Rank

MEAP11th Grade


to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

STRAND 2: ALGEBRA AND FUNCTIONSSTANDARD A1: EXPRESSIONS, EQUATIONS, AND INEQUALITIESStudents recognize, construct, interpret, and evaluate expressions. They fluently transform symbolic expressions into equivalent forms. They determine appropriate techniques for solving each type of equation, inequality, or system of equations, apply the techniques correctly to solve, justify the steps in the solutions, and draw conclusions from the solutions. They know and apply common formulas.A1.1 Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.

m7

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. H


A1.1.2 Know the definitions and properties of exponents and roots, transition fluently between them, and apply them in algebraic expressions.

m24Understand the basic properties and laws of exponents and scientific notation. H

A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes).

m22


H

A1.1.4 Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x – 1) (1 – x2 + 3); simplify 9x - x3x + 3)

m37 Perform addition of polynomials to express them in their simplest form (e.g., (2a+2)+(3a-1) = 5a+1).

M

m41 Perform multiplication of polynomials by understanding the meaning of a positive, integral exponent, and using



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exponents correctly when multiplying powers with like bases.

A1.1.5 Divide a polynomial by a monomial.

m46

Perform division of a polynomial by a monomial by knowing how to divide powers with like bases, use integral exponents to express decimal numbers in scientific notation, use the rules for the division of powers with like bases to simplify fractions with monomial denominators, and reduce fractions to lowest terms.

M

A1.1.6 Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms including the inverse relationship between exponents and logarithms.


Hm69 Graph the exponential function and understand its characteristics.


A1.1.7 Transform trigonometric expressions into equivalent forms using basic identities such as sin cos sin2 + cos2 =1, tan = and tan2 + 1 = sec2Needs formula attention

m58

Be able to prove trigonometric identities and solve equations (linear and quadratic). M

A1.2 Solutions of Equations and Inequalities (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)A1.2.1 Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve. m7

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. H

m35


A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation. m35

Find the solution of linear equations and inequalities where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x). H


A1.2.3 Solve (and justify steps in the solutions) linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns; apply the quadratic formula

m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial

H



High School


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MEAP11th Grade


appropriately. assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

m35





A1.2.4 Solve absolute value equations and inequalities, (e.g. solve l x - 3 l ≤ 6), and justify steps in the solution.

m32


H

m35


A1.2.5 Solve polynomial equations and equations involving rational expressions (e.g. solve -2x(x2 + 4x+3) = 0; solve x - 1x + 6 = 3), and justify steps in the solution. m32


H


A1.2.6 Solve power equations (e.g., (x + 1)3 = 8) and equations including radical expressions (e.g., 3x - 7 = 7), justify steps in the solution, and explain how extraneous solutions may arise.


H

m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial



High School


Rank

MEAP11th Grade


assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

A1.2.7 Solve exponential and logarithmic equations (e.g., 3(2x) = 24), 2 ln(x + 1) = 4), and justify steps in the solution.

m32


H



A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.


Hm32


m35


A1.2.9 Know common formulas (e.g., slope, distance between two points, quadratic formula, compound interest, distance = velocity • time), and apply appropriately in contextual situations.

m9 Know how to compute the distance between two points (i.e., length of a line segment) on a coordinate plane.

H

m33



m61Understand the concepts recurrence relations and how they are applicable to such things as compound interest and annuity.

A1.2.10 Use special values of the inverse m58 Be able to prove trigonometric identities and solve MCopyright © 2006 International Center for Leadership in Education Math –


High School


Rank

MEAP11th Grade


trigonometric functions to solve trigonometric equations over specific intervals (e.g., 2sin x – I = 0 for 0 ≤ x ≤ 2).

equations (linear and quadratic).

m73


STANDARD A2: FUNCTIONSStudents understand functions, their representations, and their attributes. They perform transformations, combine and compose functions, and find inverses. Students classify functions and know the characteristics of each family. They work with functions with real coefficients fluently.A2.1 Definitions, Representations, and Attributes of FunctionsA2.1.1 Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range.



A2.1.2 Read, interpret, and use function notation, and evaluate a function at a value in its domain. m40



A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.



A2.1.4 Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined (e.g., absolute value and greatest integer functions).

m40


A2.1.5 Recognize that functions may be defined recursively, and compute values of and graph simple recursively defined functions (e.g., f(0) = 5,

m40 Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.).

M



High School


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MEAP11th Grade


and f(n) = f(n-1) + 2 ).m61

Understand the concepts recurrence relations and how they are applicable to such things as compound interest and annuity.

A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches postive or negative infinity, given the symbolic and graphical representations.


Mm48Understand the concepts and apply the uses of functions and limits (i.e., conduct limiting processes using functions to investigate infinite series and sequences).


A2.1.7 Identify and interpret the key features of a function from its graph or its formula(e), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity).


H



m59Understand the characteristics of maxima and minima and be able to mathematically determine maximum and minimum points on a graph or curve.

A2.2 Operations and TransformationsA2.2.1 Combine functions by addition, subtraction, multiplication, and division. m40


M

A2.2.2 Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x- and y-axes) to basic functions, and represent symbolically.

m55

Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation. M

A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f(x) = x3 and g(x) = x1/3).


M

m73


A2.2.4 If a function has an inverse, find the expression(s) for the inverse.

m73 Understand inverse functions as the set of ordered pairs obtained by interchanging the first and second elements of

L



High School


Rank

MEAP11th Grade


each pair belonging to a one-on-one function. Use one-on-one functions to create symmetric figures consisting of the graphs of a function and its inverse function

A2.2.5 Write an expression for the composition of one function with another; recognize component functions when a function is a composition of other functions.

m40


A2.2.6 Know and interpret the function notation for inverses and verify that two functions are inverses using composition.


M

m73

Understand inverse functions as the set of ordered pairs obtained by interchanging the first and second elements of each pair belonging to a one-on-one function. Use one-on-one functions to create symmetric figures consisting of the graphs of a function and its inverse function

A2.3 Families of Functions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)A2.3.1 Identify a function as a member of a family of functions based on its symbolic, or graphical representation; recognize that different families of functions have different asymptotic behavior at infinity, and describe these behaviors.

m40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.). M

m48Understand the concepts and apply the uses of functions and limits (i.e., conduct limiting processes using functions to investigate infinite series and sequences).

A2.3.2 Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.


Hm45Know the equation of a line and interpret graphically using the slope-intercept form (i.e., y = mx+b), and the point-slope form (i.e., y-b = m(x-a)).

m63Use the process of differentiation (i.e., derivatives) to determine tangents, maxima and minima, velocity, and acceleration.

A2.3.3 Write the general symbolic forms that characterize each family of functions. (e.g., f(x) = A0ax; f(x) = AsinBx )


M


m74 Understand the trigonometric properties of the unit circle and sketch the graphs of basic circular functions (i.e., y =



High School


Rank

MEAP11th Grade


sin x, y = cos x, and y = tan x) where the measure of the angle x is expressed in radians.

A2.4 Lines and Linear FunctionsA2.4.1 Write the symbolic forms of linear functions (standard [i.e., Ax + By = C, where B ≠ 0], point-slope, and slope-intercept) given appropriate information, and convert between forms.




A2.4.2 Graph lines (including those of the form x = h and y = k) given appropriate information. m34 Know the equation for the slope of a line and compute

slope given the coordinates of two points.H


A2.4.3 Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph. m34 Know the equation for the slope of a line and compute

slope given the coordinates of two points.H


A2.4.4 Find an equation of the line parallel or perpendicular to given line, through a given point; understand and use the facts that non-vertical parallel lines have equal slopes, and that non-vertical perpendicular lines have slopes that multiply to give -1.


Hm34 Know the equation for the slope of a line and compute slope given the coordinates of two points.


A2.5 Exponential and Logarithmic FunctionsA2.5.1 Write the symbolic form and sketch the graph of an exponential function given appropriate information. (e.g., given an initial value of 4 and a rate of growth of 1.5, write f(x) = 4 (1.5)x).

m69

Graph the exponential function and understand its characteristics. M

A2.5.2 Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions (e.g., f(x) = 10 x, f(x) = log x, f(x) = ex, f(x) = ln x); recognize the logarithmic function as the inverse of the exponential function.


Mm78

Graph the logarithmic function and understand its characteristics.

A2.5.3 Apply properties of exponential and logarithmic functions (e.g., ax+y = axa y; log(ab)=


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log a + log b). m78 Graph the logarithmic function and understand its characteristics.

A2.5.4 Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay.

m69

Graph the exponential function and understand its characteristics. M

A2.5.5 Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.

m69 Graph the exponential function and understand its characteristics. M


A2.6 Quadratic FunctionsA2.6.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate information (e.g., vertex, intercepts, etc.).


Mm55


A2.6.2 Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.

m40Understand appropriate terminology used to define relations and functions and their properties (e.g., domain, range, function composition, inverses, etc.). M


A2.6.3 Convert quadratic functions from standard to vertex form by completing the square. m40



A2.6.4 Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function.

m53 Apply the zero property of multiplication to find the solution of quadratic equations. M


A2.6.5 Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros.


Mm59

Understand the characteristics of maxima and minima and be able to mathematically determine maximum and minimum points on a graph or curve.

A2.7 Power Functions (including roots, cubics, quartics, etc.)A2.7.1 Write the symbolic form and sketch the graph of power functions.


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A2.7.2 Express direct and inverse relationships as functions (e.g., y = kxn and y = kx-n, n > 0) and recognize their characteristics (e.g., in y = x3, note that doubling x results in multiplying y by a factor of 8).

m81

Solve and graphically sketch problems involving two variables that exhibit direct and indirect variation.

L

A2.7.3 Analyze the graphs of power functions, noting reflectional or rotational symmetry. m5

Understand the best procedures for statistical data collection, organization, and display including making estimates and predictions and drawing inferences. H


A2.8 Polynomial FunctionsA2.8.1 Write the symbolic form and sketch the graph of simple polynomial functions. m23




A2.8.2 Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.


Hm55


A2.8.3 Determine the maximum possible number of zeros of a polynomial function, and understand the relationship between the x-intercepts of the graph and the factored form of the function.

m53

Apply the zero property of multiplication to find the solution of quadratic equations. M

A2.9 Rational FunctionsA2.9.1 Write the symbolic form and sketch the graph of simple rational functions.

m46 Perform division of a polynomial by a monomial by knowing how to divide powers with like bases, use integral exponents to express decimal numbers in scientific notation, use the rules for the division of powers with like bases to simplify fractions with monomial denominators,

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and reduce fractions to lowest terms.A2.9.2 Analyze graphs of simple rational functions (e.g., 2x + 1x - 1xx2 - 4;f(x) = g(x) = ) and understand the relationship between the zeros of the numerator and denominator and the function’s intercepts, asymptotes, and domain.


Mm48Understand the concepts and apply the uses of functions and limits (i.e., conduct limiting processes using functions to investigate infinite series and sequences).


A2.10 Trigonometric FunctionsA2.10.1 Use the unit circle to define sine and cosine; approximate values of sine and cosine (e.g., sin 3, or cos 0.5); use sine and cosine to define the remaining trigonometric functions; explain why the trigonometric functions are periodic.

m32


H

m74

Understand the trigonometric properties of the unit circle and sketch the graphs of basic circular functions (i.e., y = sin x, y = cos x, and y = tan x) where the measure of the angle x is expressed in radians.

A2.10.2 Use the relationship between degree and radian measures to solve problems. m74


L

A2.10.3 Use the unit circle to determine the exact values of sine and cosine, for integer multiples of ⁄6 and ⁄4. m74


L

A2.10.4 Graph the sine and cosine functions; analyze graphs by noting domain, range, period, amplitude, andlocation of maxima and minima.


H


m59Understand the characteristics of maxima and minima and be able to mathematically determine maximum and minimum points on a graph or curve.

m74 Understand the trigonometric properties of the unit circle and sketch the graphs of basic circular functions (i.e., y =



High School


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MEAP11th Grade


sin x, y = cos x, and y = tan x) where the measure of the angle x is expressed in radians.

A2.10.5 Graph transformations of basic trigonometric functions (involving changes in period, amplitude, and midline) and understand the relationship between constants in the formula and the transformed graph.


Hm55Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation.

m74


STANDARD A3: MATHEMATICAL MODELINGStudents construct or select a function to model a real-world situation in order to solve applied problems. They draw on their knowledge of families of functions to do so.

A3.1 Models of Real-world Situations Using Families of Functions.A3.1.1 Identify the family of function best suited for modeling a given real-world situation (e.g., quadratic functions for motion of an object under the force of gravity; exponential functions for compound interest; trigonometric functions for periodic phenomena. In the example above, recognize that the appropriate general function is exponential (P = P0at)

m33


Hm69 Graph the exponential function and understand its characteristics.

m74


A3.1.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute the given values P0 = 300 and a = 1.02 to obtain P = 300(1.02)t.

m33

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min) including drawing to scale and applying ratios. Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. H


m74 Understand the trigonometric properties of the unit circle



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and sketch the graphs of basic circular functions (i.e., y = sin x, y = cos x, and y = tan x) where the measure of the angle x is expressed in radians.

A3.1.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. In the example above, the exact solution is 365.698, but for this problem an appropriate approximation is 365.

m32

Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise. H


m74


A3.1.4 Use methods of linear programming to represent and solve simple real-life problems. NA There is no essential skill which matches this benchmark. L

STRAND 3: GEOMETRY AND TRIGONOMETRYSTANDARD G1: FIGURES AND THEIR PROPERTIESStudents represent basic geometric figures, polygons, and conic sections and apply their definitions and properties in solving problems and justifying arguments, including constructions and representations in the coordinate plane. Students represent three-dimensional figures, understand the concepts of volume and surface area, and use them to solve problems. They know and apply properties of common three-dimensional figures.G1.1 Lines and Angles; Basic Euclidean and Coordinate GeometryG1.1.1 Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles.

m4


H

m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps



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MEAP11th Grade


leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may be proved otherwise.

G1.1.2 Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.


H

m4


m32


G1.1.3 Perform and justify constructions, including midpoint of a line segment and bisector of an angle, using straightedge and compass. m28


H

m32


G1.1.4 Given a line and a point, construct a line through the point that is parallel to the original line using straightedge and compass; given a line and a point, construct a line through the point that is perpendicular to the original line; justify the steps of the constructions.


H

m28


m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may



High School


Rank

MEAP11th Grade


be proved otherwise.G1.1.5 Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint.

m9 Know how to compute the distance between two points (i.e., length of a line segment) on a coordinate plane. H

m38 Know how to compute the midpoint of a line segment between two points on a coordinate plane.

G1.1.6 Recognize Euclidean Geometry as an axiom system; know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, plane), axioms, definitions, and theorems.


H

m6 Understand the characteristics and applications of the undefined terms of geometry (i.e., point, line, and plane).

m32


G1.2 Triangles and Their PropertiesG1.2.1 Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles.


Hm32


G1.2.2 Construct and justify arguments and solve multi-step problems involving angle measure, side length, perimeter, and area of all types of triangles.


Hm32


G1.2.3 Know a proof of the Pythagorean Theorem and use the Pythagorean Theorem and its converse to solve multi-step problems.


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G1.2.4 Prove and use the relationships among the side lengths and the angles of 30º- 60º- 90º triangles and 45º- 45º- 90º triangles.

m16 Understand the properties and classification of triangles by sides (i.e., scalene, isosceles, and equilateral).

Hm32


G1.2.5 Solve multi-step problems and construct proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle; using a straightedge and compass, construct these lines.

m28


H

m32


G1.3 Triangles and TrigonometryG1.3.1 Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides; solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles.

m18 Know the basic trigonometric functions and ratios.

Hm57Understand the concepts of right triangle trigonometry and solve right triangles using basic trigonometric ratios (sine, cosine, tangent).

G1.3.2 Know and use the Law of Sines and the Law of Cosines and use them to solve problems; find the area of a triangle with sides a and b and included angleusing the formula Area = (1/2) a b sin.

m54

Perform the general solution of triangles by using the law of sines and law of cosines to obtain the angle and side length measurements of any triangle. M

G1.3.3 Determine the exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples, and apply in various contexts.

m18 Know the basic trigonometric functions and ratios.

Hm57Understand the concepts of right triangle trigonometry and solve right triangles using basic trigonometric ratios (sine, cosine, tangent).

G1.4 Quadrilaterals and Their PropertiesG1.4.1 Solve multi-step problems and construct m13 Compute the perimeter and area of two-dimensional HCopyright © 2006 International Center for Leadership in Education Math –


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MEAP11th Grade


proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.

figures.

m26Understand the properties and classification of polygons (e.g., triangle, quadrilaterals, pentagon, hexagon, etc.) as well as knowledge of geometric shapes.


m32


G1.4.2 Solve multi-step problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry.


H

m32


G1.4.3 Describe and justify hierarchical relationships among quadrilaterals, (e.g. every rectangle is a parallelogram).


H

m32


G1.4.4 Prove theorems about the interior and exterior angle sums of a quadrilateral. m27


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G1.4.5 Understand the definition of a cyclic quadrilateral, and know and use the basic properties of cyclic quadrilaterals.

m27 Understand the properties and classification of quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid).

H

G1.5 Other Polygons and Their PropertiesG1.5.1 Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, non-regular pentagon).


Hm30


G1.5.2 Know, justify, and use formulas for the perimeter and area of a regular n-gon and formulas to find interior and exterior angles of a regular n-gon and their sums.


H


m32


G1.6 Circles and Their PropertiesG1.6.1 Solve multi-step problems involving circumference and area of circles. m10

Understand the properties of circles (e.g., radius, arc, diameter, chord, secant, tangent, etc.)

Hm30

Know how to measure circle quantities (e.g., area, angle formed by two secants, circumference, length of segments, etc.)

G1.6.2 Solve problems and justify arguments about chords (e.g., if a line through the center of a circle is perpendicular to a chord, it bisects the chord) and lines tangent to circles (e.g., a line tangent to a circle is perpendicular to the radius drawn to the point of tangency).


H

m32 Use direct proof and indirect proof sequencing techniques to reach a conclusion. Direct proof uses the Laws of Reasoning to create an orderly arrangement of steps leading to a conclusion. Indirect proof uses an initial assumption that the conclusion is false, and through a series of logically sound reasoning steps the statement may



High School


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MEAP11th Grade


be proved otherwise.G1.6.3 Solve problems and justify arguments about central angles, inscribed angles and triangles in circles.


H


m32


G1.6.4 Know and use properties of arcs and sectors, and find lengths of arcs and areas of sectors.


Hm30


G1.7 Conic Sections and Their PropertiesG.1.7.1 Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius.


Hm86

Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations.

G1.7.2 Identify and distinguish among geometric representations of parabolas, circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones.

m86

Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations. L

G1.7.3 Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations. m23

Know the components and properties of the rectangular coordinate system, (i.e., x - y axis, origin, quadrants, abscissa (x-coordinate) and ordinate (y-coordinate), and the general representation of a point (x,y)). H

m86Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations.

G1.7.4 Know and use the relationship between the vertices and foci in an ellipse, the vertices and foci in a hyperbola, and the directrix and focus in a parabola; interpret these relationships in applied contexts.

m86

Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations. L



High School


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MEAP11th Grade


G1.8 Three- Dimensional FiguresG1.8.1 Solve multi-step problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

m13 Compute the perimeter and area of two-dimensional figures. H

m17 Compute the volume of three-dimensional figures (solids).G1.8.2 Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres. m29

Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres. H


STANDARD G2: RELATIONSHIPS BETWEEN FIGURESStudents use and justify relationships between lines, angles, area and volume formulas, and 2- and 3-dimensional representations. They solve problems and provide proofs about congruence and similarity.G2.1 Relationships Between Area and Volume FormulasG2.1.1 Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid.


Hm26

Understand the properties and classification of polygons (e.g., triangle, quadrilaterals, pentagon, hexagon, etc.) as well as knowledge of geometric shapes.

G2.1.2 Know and demonstrate the relationships between the area formulas of various quadrilaterals (e.g., explain how to find the area of a trapezoid based on the areas of parallelograms and triangles).


Hm27


G2.1.3 Know and use the relationship between the volumes of pyramids and prisms (of equal base and height) and cones and cylinders (of equal base and height).


Hm29Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres.

G2.2 Relationships Between Two-dimensional and Three-dimensional RepresentationsG2.2.1 Identify or sketch a possible 3-dimensional figure, given 2-dimensional views (e.g., nets, multiple views); create a 2-dimensional representation of a 3-dimensional figure.


H

m29 Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular



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cylinders, cones, and spheres.


G2.2.2 Identify or sketch cross-sections of 3-dimensional figures; identify or sketch solids formed by revolving 2-dimensional figures around lines.

m29Know the classification and properties of solid figures such as prisms, rectangular solids, pyramids, right circular cylinders, cones, and spheres. H

G2.3 Congruence and SimilarityG2.3.1 Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria, and for right triangles, the hypotenuse-leg criterion.

m32


H


G2.3.2 Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates. m23


Hm32



G2.3.3 Prove that triangles are similar by using SSS, SAS, and AA conditions for similarity.

m32


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G2.3.4 Use theorems about similar triangles to solve problems with and without use of coordinates. m23


Hm32



G2.3.5 Know and apply the theorem stating that the effect of a scale factor of k relating one two dimensional figure to another or one three dimensional figure to another, on the length, area, and volume of the figures is to multiply each by k, k2, and k3, respectively.


H


m33


STANDARD G3: TRANSFORMATIONS OF FIGURES IN THE PLANEStudents will solve problems about distance-preserving transformations and shape-preserving transformations. The transformations will be described synthetically and, in simple cases, by analytic expressions in coordinates.G3.1 Distance-preserving Transformations: IsometriesG3.1.1 Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.

m55Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation. M


G3.1.2 Given two figures that are images of each other under an isometry, find the isometry and describe it completely.


m75 Understand the concepts of symmetry and transformations Copyright © 2006 International Center for Leadership in Education Math –


High School


Rank

MEAP11th Grade


and graphically apply line reflections, rotation, translations, and dilation.

G3.1.3 Find the image of a figure under the composition of two or more isometries, and determine whether the resulting figure is a reflection, rotation, translation, or glide reflection image of the original figure.



G3.2 Shape-preserving Transformations: Dilations and IsometriesG3.2.1 Know the definition of dilation, and find the image of a figure under a given dilation. m55


M

G3.2.2 Given two figures that are images of each other under some dilation, identify the center and magnitude of the dilation.


M

G3.2.3 Find the image of a figure under the composition of a dilation and an isometry. m55

Understand the concepts of symmetry and transformations and graphically apply line reflections, rotation, translations, and dilation. M


STRAND 4: STATISTICS AND PROBABILITYSTANDARD S1: UNIVARIATE DATA- EXAMINING DISTRIBUTIONSStudents plot and analyze univariate data by considering the shape of distributions and analyzing outliers; they find and interpret commonly-used measures of center and variation; and they explain and use properties of the normal distribution.S1.1 Producing and Interpreting PlotsS1.1.1 Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics.



m36 Understand the characteristics of measures of dispersion



High School


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MEAP11th Grade


(i.e., range, mean deviation, variance, and standard deviation).

S1.1.2 Given a distribution of a variable in a data set, describe its shape, including symmetry or skewness, and state how the shape is related to measures of center (mean and median) and measures of variation (range and standard deviation) with particular attention to the effects of outliers on these measures.




S1.2 Measures of Center and VariationS1.2.1 Calculate and interpret measures of center including: mean, median, and mode; explain uses, advantages and disadvantages of each measure given a particular set of data and its context.



S1.2.2 Estimate the position of the mean, median, and mode in both symmetrical and skewed distributions, and from a frequency distribution or histogram.



S1.2.3 Compute and interpret measures of variation, including percentiles, quartiles, interquartile range, variance, and standard deviation.


M

m42


S1.3 The Normal DistributionS1.3.1 Explain the concept of distribution and the relationship between summary statistics for a data set and parameters of a distribution.


M

m42


S1.3.2 Describe characteristics of the normal distribution, including its shape and the relationships among its mean, median, and mode.


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S1.3.3 Know and use the fact that about 68%, 95%, and 99.7% of the data lie within one, two, and three standard deviations of the mean, respectively in a normal distribution.

m36

Understand the characteristics of measures of dispersion (i.e., range, mean deviation, variance, and standard deviation). M

S1.3.4 Calculate z-scores, use z-scores to recognize outliers, and use z-scores to make informed decisions.


M

STANDARD S2: BIVARIATE DATA – EXAMINING RELATIONSHIPSStudents plot and interpret bivariate data by constructing scatterplots, recognizing linear and nonlinear patterns, and interpreting correlation coefficients; they fit and interpret regression models, using technology as appropriate.S2.1 Scatterplots and CorrelationS2.1.1 Construct a scatterplot for a bivariate data set with appropriate labels and scales. m5


H

S2.1.2 Given a scatterplot, identify patterns, clusters, and outliers; recognize no correlation, weak correlation, and strong correlation.


H

S2.1.3 Estimate and interpret Pearson’s correlation coefficient for a scatterplot of a bivariate data set; recognize that correlation measures the strength of linear association.

m5


S2.1.4 Differentiate between correlation and causation; know that a strong correlation does not imply a cause-and-effect relationship; recognize the role of lurking variables in correlation.

m5


S2.2 Linear RegressionS2.2.1 For bivariate data which appear to form a linear pattern, find the least squares regression line by estimating visually and by calculating the equation of the regression line; interpret the slope of the equation for a regression line.



S2.2.2 Use the equation of the least squares regression line to make appropriate predictions.

m5 Understand the best procedures for statistical data collection, organization, and display including making

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estimates and predictions and drawing inferences.STANDARD S3: SAMPLES, SURVEYS, AND EXPERIMENTSStudents understand and apply sampling and various sampling methods, examine surveys and experiments, identify bias in methods of conducting surveys, and learn strategies to minimize bias. They understand basic principles of good experimental design.S3.1 Data Collection and AnalysisS3.1.1 Know the meanings of a sample from a population and a census of a population, and distinguish between sample statistics and population parameters.

m5


S3.1.2 Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates.

m5


H

S3.1.3 Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each.


H

S3.1.4 Design simple experiments or investigations to collect data to answer questions of interest; interpret and present results.


H

S3.1.5 Understand methods of sampling, including random sampling, stratified sampling, and convenience samples, and be able to determine, in context, the advantages and disadvantages of each.

m5


S3.1.6 Explain the importance of randomization, double-blind protocols, replication, and the placebo effect in designing experiments and interpreting the results of studies.


m66b Understand the concepts and theories of random distribution.

S3.2.1 Explain the basic ideas of statistical process control, including recording data from a process over time.


H

S3.2.2 Read and interpret basic control charts; m5 Understand the best procedures for statistical data HCopyright © 2006 International Center for Leadership in Education Math –


High School


Rank

MEAP11th Grade


detect patterns and departures from patterns. collection, organization, and display including making estimates and predictions and drawing inferences.

STANDARD S4: PROBABILITY MODELS AND PROBABILITY CALCULATIONStudents understand probability and find probabilities in various situations, including those involving compound events, using diagrams, tables, geometric models and counting strategies; they apply the concepts of probability to make decisions.S4.1 ProbabilityS4.1.1 Understand and construct sample spaces in simple situations (e.g., tossing two coins, rolling two number cubes and summing the results). m20


m25


S4.1.2 Define mutually exclusive events, independent events, dependent events, compound events, complementary events and conditional probabilities; and use the definitions to compute probabilities.

m20


Hm25


m56


S4.1.3 Design and carry out an appropriate simulation using random digits to estimate answers to questions about probability; estimate probabilities using results of a simulation; compare results of simulations to theoretical probabilities.

m20


H

m25 Determine the probability of single and compound events using the basic premise that the probability of an event is



High School


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MEAP11th Grade


equal to the number of ways it can occur divided by the total number of outcomes.

S4.2 Application and RepresentationS4.2.1 Compute probabilities of events using tree diagrams, formulas for combinations and permutations, Venn diagrams, or other counting techniques.

m20


Hm25


m43 Know how to determine combinations (i.e., the various grouping a set may be arranged in without regard to order).

m66a Know how to determine permutations (i.e., arrangements of a set where order matters).

S4.2.2 Apply probability concepts to practical situations, in such settings as finance, health, ecology, or epidemiology, to make informed decisions.

m20


m25



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