michigan standards alignment kindergarten through grade twelve

Michigan Standards Alignment Kindergarten through Grade Twelve

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Michigan Standards Alignment

Standards list with Aligned Product Skills

The Standards list with Aligned Product Skills Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product.

Note to Educator ............................................................... iii

Kindergarten ................................................................1

Grade 1 ................................................................3

Grade 2 ................................................................7

Grade 3 ..............................................................13

Grade 4 ..............................................................20

Grade 5 ..............................................................28

Grade 6 ..............................................................35

Grade 7 ..............................................................45

Grade 8 ..............................................................54

Grades 9 - 12 ..............................................................62

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Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) 338-4204. Sincerely, Renaissance Sales and Funding Staff

P.O. Box 8036 Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204 Fax: (715) 424-4242

www.renlearn.com

Agency Tag Set NameMichigan, Math, 2006, Kindergarten, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Count, write, and order numbers

MI N.ME.00.01 - Count objects in sets up to 30.

Domain 1 - Number and Operations (NO)

Skill 1 - Count objects to 20

MI N.ME.00.02 - Use one-to-one correspondence to compare and order sets of objects to 30 using phrases such as "same number", "more than", or "less than"; use counting and matching.MI N.ME.00.03 - Compare and order numbers to 30 using phrases such as "more than" or "less than."

MI N.ME.00.04 - Read and write numbers to 30 and connect them to the quantities they represent.MI N.ME.00.05 - Count orally to 100 by ones. Count to 30 by 2's, 5's and 10's using grouped objects as needed. - Compose and decompose numbersMI N.ME.00.06 - Understand the numbers 1 to 30 as having one, or two, or three groups of ten and some ones. Also count by tens with objects in ten-groups to 100.MI N.MR.00.07 - Compose and decompose numbers from 2 to 10, e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of number systems, e.g., 6 is one more than 5, 7 is one more than 6.


Skill 47 - Determine equivalent forms of a number, up to 10

MI N.MR.00.08 - Describe and make drawings to represent situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting.

- Add and subtract numbersMI N.MR.00.09 - Record mathematical thinking by writing simple addition and subtraction sentences, e.g., 7 + 2 = 9, 10 - 8 = 2.

- Explore number patternsMI N.MR.00.10 - Create, describe, and extend simple number patterns.

Standards List with Aligned Product SkillsProduct NameSTAR Math Enterprise

STAR Math Enterprise Kindergarten

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Agency Tag Set NameMichigan, Math, 2006, Kindergarten, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


MI M - Measurement - Explore concepts of timeMI M.UN.00.01 - Know and use the common words for the parts of the day (morning, afternoon, evening, night) and relative time (yesterday, today, tomorrow, last week, next year).MI M.TE.00.02 - Identify tools that measure time (clocks measure hours and minutes; calendars measure days, weeks, and months).

MI M.UN.00.03 - Identify daily landmark times to the nearest hour (lunchtime is 12 o'clock; bedtime is 8 o'clock). - Explore other measurement attributesMI M.UN.00.04 - Compare two or more objects by length, weight and capacity, e.g., which is shorter, longer, taller?

Domain 3 - Geometry and Measurement (GM)

Skill 412 - Compare objects using the vocabulary of measurement

MI M.PS.00.05 - Compare length and weight of objects by comparing to reference objects, and use terms such as shorter, longer, taller, lighter, heavier.MI G - Geometry - Create, explore, and describe shapesMI G.GS.00.01 - Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism.

MI G.GS.00.02 - Identify, sort, and classify objects by attribute and identify objects that do not belong in a particular group.


Skill 413 - Identify a shape with given attributes

- Explore geometric patternsMI G.GS.00.03 - Create, describe, and extend simple geometric patterns.

STAR Math Enterprise Kindergarten

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Agency Tag Set NameMichigan, Math, 2006, First Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Count, write, and order numbers

MI N.ME.01.01 - Count to 110 by 1's, 2's, 5's, and 10's, starting from any number in the sequence; count to 500 by 100's and 10's; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd.


Skill 3 - Count on by ones from a number less than 100

Skill 5 - Answer a question involving an ordinal number up to "tenth"

Skill 11 - Count by 2s to 50 starting from a multiple of 2Skill 12 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectivelySkill 14 - Complete a skip pattern starting from a multiple of 2, 5, or 10

Skill 15 - Complete a skip pattern of 2 or 5 starting from any numberSkill 16 - Complete a skip pattern of 10 starting from any number

MI N.ME.01.02 - Read and write numbers to 110 and relate them to the quantities they represent.


Skill 1 - Count objects to 20

MI N.ME.01.03 - Order numbers to 110; compare using phrases such as "same as", "more than", "greater than", "fewer than"; use = symbol. Arrange small sets of numbers in increasing or decreasing order, e.g., write the following from smallest to largest: 21, 16, 35, 8.


Skill 23 - Compare whole numbers to 100 using words

Skill 24 - Order whole numbers to 100 in ascending order

MI N.ME.01.04 - Identify one more than, one less than, 10 more than, and 10 less than for any number up to 100.


Skill 8 - Determine one more than or one less than a given number

Skill 9 - Determine one more than or one less than a given number across decadesSkill 10 - Determine ten more than or ten less than a given number


STAR Math Enterprise Grade 1

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Agency Tag Set NameMichigan, Math, 2006, First Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


MI N.ME.01.05 - Understand that a number to the right of another number on the number line is bigger and that a number to the left is smaller.MI N.ME.01.06 - Count backward by 1's starting from any number between 1 and 100.


Skill 4 - Count back by ones from a number less than 20

- Explore place valueMI N.ME.01.07 - Compose and decompose numbers through 30, including using bundles of tens and units, e.g., recognize 24 as 2 tens and 4 ones, 10 and 10 and 4, 20 and 4, and 24 ones. - Add and subtract whole numbersMI N.ME.01.08 - List number facts (partners inside of numbers) for 2 through 10, e.g., 8 = 7 + 1 = 6 + 2 = 5 + 3 = 4 + 4; 10 = 8 + 2 = 2 + 8.


Skill 47 - Determine equivalent forms of a number, up to 10

MI N.MR.01.09 - Compare two or more sets in terms of the difference in number of elements.MI N.MR.01.10 - Model addition and subtraction for numbers through 30 for a given contextual situation using objects or pictures; explain in words; record using numbers and symbols; solve.


Skill 51 - WP: Use basic addition facts to solve problems

Skill 52 - WP: Use basic subtraction facts to solve problems

MI N.MR.01.11 - Understand the inverse relationship between addition and subtraction, e.g., subtraction "undoes" addition: if 3 + 5 = 8, we know that 8 - 3 = 5 and 8 - 5 = 3; recognize that some problems involving combining, "taking away," or comparing can be solved by either operation.MI N.FL.01.12 - Know all the addition facts up to 10 + 10, and solve the related subtraction problems fluently.


Skill 49 - Know basic addition facts to 10 plus 10

Skill 50 - Know basic subtraction facts to 20 minus 10


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MI N.MR.01.13 - Apply knowledge of fact families to solve simple open sentences for addition and subtraction, such as: __ + 2 = 7 and 10 - __= 6.

Domain 2 - Algebra (AL) Skill 335 - Determine a missing addend in a basic addition-fact number sentence

Skill 337 - Determine a missing subtrahend in a basic subtraction-fact number sentence

MI N.FL.01.14 - Add three one-digit numbers.


Skill 68 - Add three 1-digit numbers

MI N.FL.01.15 - Calculate mentally sums and differences involving: a two-digit number and a one-digit number without regrouping; a two-digit number and a multiple of 10.


Skill 53 - Add a 2-digit number and a 1-digit number without regrouping

Skill 56 - Subtract a 1-digit number from a 2-digit number without regrouping

MI N.FL.01.16 - Compute sums and differences through 30 using number facts and strategies, but no formal algorithm.MI M - Measurement - Estimate and measure lengthMI M.UN.01.01 - Measure the lengths of objects in non-standard units, e.g., pencil lengths, shoe lengths, to the nearest whole unit.MI M.UN.01.02 - Compare measured lengths using the words shorter, shortest, longer, longest, taller, tallest, etc. - Tell timeMI M.UN.01.03 - Tell time on a twelve-hour clock face to the hour and half-hour.


Skill 446 - Tell time to the hour and half hour

- Work with moneyMI M.UN.01.04 - Identify the different denominations of coins and bills.


Skill 407 - Identify a coin or the value of a coin

MI M.UN.01.05 - Match one coin or bill of one denomination to an equivalent set of coins/bills of other denominations, e.g., 1 quarter = 2 dimes and 1 nickel.MI M.UN.01.06 - Tell the amount of money: in cents up to $1, in dollars up to $100. Use the symbols $ and ¢.


Skill 409 - Determine the value of groups of coins to $1.00


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MI M.PS.01.07 - Add and subtract money in dollars only or in cents only.

- Solve problemsMI M.PS.01.08 - Solve one-step word problems using addition and subtraction of length, money and time, including "how much more/less", without mixing units.


Skill 408 - Determine cent amounts that total a dollar

MI G - Geometry - Create and describe shapesMI G.GS.01.01 - Create common two-dimensional and three-dimensional shapes, and describe their physical and geometric attributes, such as color and shape.

MI G.LO.01.02 - Describe relative position of objects on a plane and in space, using words such as above, below, behind, in front of.


Skill 415 - Use basic terms to describe position

- Create and describe patterns involving geometric objectsMI G.SR.01.03 - Create and describe patterns, such as repeating patterns and growing patterns using number, shape, and size.

MI G.SR.01.04 - Distinguish between repeating and growing patterns.

MI G.SR.01.05 - Predict the next element in a simple repeating pattern.

MI G.SR.01.06 - Describe ways to get to the next element in simple repeating patterns.MI D - Data and Probability - Use pictographsMI D.RE.01.01 - Collect and organize data to use in pictographs.

MI D.RE.01.02 - Read and interpret pictographs.

Domain 4 - Data Analysis, Statistics, and Probability (SP)

Skill 523 - Read a simple pictograph

MI D.RE.01.03 - Make pictographs of given data using both horizontal and vertical forms of graphs; scale should be in units of one and include symbolic representations, e.g., "smiley face" represents one child.


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Agency Tag Set NameMichigan, Math, 2006, Second Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Count, write, and order whole numbersMI N.ME.02.01 - Count to 1000 by 1's, 10's and 100's starting from any number in the sequence.


Skill 16 - Complete a skip pattern of 10 starting from any number

Skill 17 - Count on by 100s from any number

MI N.ME.02.02 - Read and write numbers to 1000 in numerals and words, and relate them to the quantities they represent.


Skill 13 - Count objects grouped in tens and ones

Skill 22 - Relate a whole number to the word form of the number to 100

Skill 30 - Relate a 3-digit whole number to its word form

MI N.ME.02.03 - Compare and order numbers to 1000; use the symbols > and <.


Skill 31 - Compare whole numbers to 1,000 using the symbols <, >, and =

MI N.ME.02.04 - Count orally by 3's and 4's starting with 0, and by 2's, 5's, and 10's starting from any whole number. - Understand place valueMI N.ME.02.05 - Express numbers through 999 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials.


Skill 26 - Represent a 3-digit number as hundreds, tens, and ones

- Add and subtract whole numbersMI N.FL.02.06 - Decompose 100 into addition pairs, e.g., 99 + 1, 98 + 2...


Skill 69 - Determine a number pair that totals 100

MI N.MR.02.07 - Find the distance between numbers on the number line, e.g., how far is 79 from 26?MI N.MR.02.08 - Find missing values in open sentences, e.g., 42 + __ = 57; use relationship between addition and subtraction.

Domain 2 - Algebra (AL) Skill 335 - Determine a missing addend in a basic addition-fact number sentence

Skill 337 - Determine a missing subtrahend in a basic subtraction-fact number sentenceSkill 339 - Determine a missing addend in a number sentence involving 2-digit numbers



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Agency Tag Set NameMichigan, Math, 2006, Second Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


MI N.MR.02.09 - Given a contextual situation that involves addition and subtraction using numbers through 99: model using objects or pictures; explain in words; record using numbers and symbols; solve.


Skill 54 - WP: Add a 2-digit number and a 1-digit number without regrouping

Skill 59 - WP: Subtract a 1-digit number from a 2-digit number without regroupingSkill 60 - WP: Add two 2-digit numbers without regroupingSkill 61 - WP: Subtract a 2-digit number from a 2-digit number without regroupingSkill 71 - WP: Add a 2-digit number and a 1- or 2-digit number with regroupingSkill 75 - WP: Subtract a 1- or 2-digit number from a 2-digit number with one regrouping

MI N.FL.02.10 - Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99.


Skill 55 - Add two 2-digit numbers without regrouping

Skill 56 - Subtract a 1-digit number from a 2-digit number without regroupingSkill 58 - Subtract a 2-digit number from a 2-digit number without regroupingSkill 70 - Add a 2-digit number and a 1- or 2-digit number with regrouping

MI N.FL.02.11 - Estimate the sum of two numbers with three digits.MI N.FL.02.12 - Calculate mentally sums and differences involving: three-digit numbers and ones; three-digit numbers and tens; three-digit numbers and hundreds. - Understand meaning of multiplication and divisionMI N.MR.02.13 - Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 x 5 gives the number of objects in 3 groups of 5 objects, or 3 x 5 = 5 + 5 + 5 = 15.


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MI N.MR.02.14 - Represent multiplication using area and array models.


Skill 86 - Use a multiplication sentence to represent an area or an array model

MI N.MR.02.15 - Understand division (÷) as another way of expressing multiplication, using fact families within the 5 x 5 multiplication table; emphasize that division "undoes" multiplication, e.g., 2 x 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2.

MI N.MR.02.16 - Given a situation involving groups of equal size or of sharing equally, represent with objects, words, and symbols; solve.


Skill 103 - WP: Divide objects into equal groups by sharing

Domain 2 - Algebra (AL) Skill 317 - Use a division sentence to represent objects divided into equal groups

MI N.MR.02.17 - Develop strategies for fluently multiplying numbers up to 5 x 5. - Work with unit fractionsMI N.ME.02.18 - Recognize, name, and represent commonly used unit fractions with denominators 12 or less; model 1/2, 1/3, and 1/4 by folding strips.MI N.ME.02.19 - Recognize, name, and write commonly used fractions: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4.

MI N.ME.02.20 - Place 0 and halves, e.g., 1/2, 1 1/2, 2 1/2, on the number line; relate to a ruler.MI N.ME.02.21 - For unit fractions from 1/12 to 1/2 understand the inverse relationship between the size of a unit fraction and the size of the denominator; compare unit fractions from 1/12 to 1/2.MI N.ME.02.22 - Recognize that fractions such as 2/2, 3/3, and 4/4 are equal to the whole (one).MI M - Measurement - Measure, add, and subtract length


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MI M.UN.02.01 - Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations: cm, m, in, ft, yd.


Skill 430 - Measure length in inches

Skill 431 - Measure length in centimeters

MI M.PS.02.02 - Compare lengths; add and subtract lengths (no conversion of units). - Understand the concept of area

MI M.UN.02.03 - Measure area using non-standard units to the nearest whole unit.MI M.TE.02.04 - Find the area of a rectangle with whole number side lengths by covering with unit squares and counting, or by using a grid of unit squares; write the area as a product. - Tell time and solve time problemsMI M.UN.02.05 - Using both A.M. and P.M., tell and write time from the clock face in 5 minute intervals and from digital clocks to the minute; include reading time: 9:15 as nine-fifteen and 9:50 as nine-fifty. Interpret time both as minutes after the hour and minutes before the next hour, e.g., 8:50 as eight-fifty and ten to nine. Show times by drawing hands on clock face.


Skill 447 - Tell time to the quarter hour

Skill 448 - Tell time to 5-minute intervals

MI M.UN.02.06 - Use the concept of duration of time, e.g., determine what time it will be half an hour from 10:15.

- Record, add and subtract money

MI M.UN.02.07 - Read and write amounts of money using decimal notations, e.g., $1.15.


Skill 410 - Translate between a dollar sign and a cent sign

MI M.PS.02.08 - Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10.


Skill 186 - WP: Determine the amount of change from whole dollar amounts

Skill 187 - Determine money amounts that total $10


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- Read thermometersMI M.UN.02.09 - Read temperature using the scale on a thermometer in degrees Fahrenheit. - Solve measurement problemsMI M.PS.02.10 - Solve simple word problems involving length and money.



MI M.TE.02.11 - Determine perimeters of rectangles and triangles by adding lengths of sides, recognizing the meaning of perimeter.


Skill 452 - Determine the perimeter of a triangle

Skill 453 - Determine the perimeter of a rectangle given a picture showing length and width

MI G - Geometry - Identify and describe shapesMI G.GS.02.01 - Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, and rectangular prisms.


Skill 414 - Identify a circle, a triangle, a square, or a rectangle

MI G.GS.02.02 - Explore and predict the results of putting together and taking apart two-dimensional and three-dimensional shapes.

MI G.GS.02.04 - Distinguish between curves and straight lines and between curved surfaces and flat surfaces.MI G.SR.02.05 - Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, by common attributes such as shape, size, color, roundness, or number of corners and explain which attributes are being used for classification.

MI G.TR.02.06 - Recognize that shapes that have been slid, turned, or flipped are the same shape, e.g., a square rotated 45° is still a square.


Skill 480 - Identify figures that are the same size and shape

- Use coordinate systems


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MI G.LO.02.07 - Find and name locations using simple coordinate systems such as maps and first quadrant grids.MI D - Data and Probability - Create, interpret, and solve problems involving pictographsMI D.RE.02.01 - Make pictographs using a scale representation, using scales where symbols equal more than one.MI D.RE.02.02 - Read and interpret pictographs with scales, using scale factors of 2 and 3.MI D.RE.02.03 - Solve problems using information in pictographs; include scales such as each "box" represents 2 apples; avoid partial cases.


Skill 524 - Answer a question using information from a pictograph (1 symbol = more than 1 object)


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Agency Tag Set NameMichigan, Math, 2006, Third Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Understand and use number notation and place valueMI N.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.


Skill 30 - Relate a 3-digit whole number to its word form

MI N.ME.03.02 - Identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. Recognize and use expanded notation for numbers using place value through 9,999, e.g., 2,517 is 2000+ 500+10+ 7; 4 hundreds and 2 ones is 402.


Skill 35 - Represent a 4-digit whole number as thousands, hundreds, tens, and ones

Skill 36 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Skill 37 - Represent a 4-digit whole number in expanded form

MI N.ME.03.03 - Compare and order numbers up to 10,000.


Skill 39 - Order 4-digit whole numbers in ascending or descending order

- Count in steps, and understand even and odd numbers

MI N.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.

MI 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.


Skill 18 - Identify odd and even numbers less than 100

- Add and subtract whole numbersMI N.FL.03.06 - Add and subtract fluently two numbers through 999 with regrouping and through 9,999 without regrouping.


Skill 72 - Add 2- and 3-digit numbers with no more than one regrouping



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Agency Tag Set NameMichigan, Math, 2006, Third Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


Skill 73 - Add two 3-digit numbers with one regroupingSkill 74 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 76 - Subtract a 1- or 2-digit number from a 3-digit number with one regroupingSkill 77 - Subtract a 3-digit number from a 3-digit number with one regroupingSkill 80 - Subtract a 2- or 3-digit number from a 3-digit number with two regroupings

MI 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.

MI N.FL.03.08 - Use mental strategies to fluently add and subtract two-digit numbers. - Multiply and divide whole numbersMI N.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.MI 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 to represent those situations.

Domain 2 - Algebra (AL) Skill 316 - WP: Determine a multiplication or division sentence for a given situation

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


Skill 87 - Know basic multiplication facts to 10 x 10

Skill 104 - Know basic division facts to 100 ÷ 10

MI 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.


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MI 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.MI N.MR.03.14 - Solve division problems involving remainders, viewing the remainder as the "number left over"; interpret based on problem context, e.g. , when we have 25 children with 4 children per group then there are 6 groups with 1 child left over. - Problem-solving with whole numbersMI N.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.


Skill 64 - WP: Add two 3-digit numbers without regrouping

Skill 65 - WP: Subtract a 3-digit number from a 3-digit number without regroupingSkill 71 - WP: Add a 2-digit number and a 1- or 2-digit number with regroupingSkill 75 - WP: Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 88 - WP: Multiply using basic facts to 10 x 10Skill 90 - WP: Multiply a 2-digit whole number by a 1-digit whole number without regroupingSkill 103 - WP: Divide objects into equal groups by sharingSkill 105 - WP: Divide using basic facts to 100 ÷ 10Skill 107 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Domain 2 - Algebra (AL) Skill 315 - WP: Determine the operation needed for a given situation

Skill 316 - WP: Determine a multiplication or division sentence for a given situation


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- Understand simple fractions, relation to the whole, and addition and subtraction of fractions

MI N.ME.03.16 - Understand that fractions may represent a portion of a whole unit that has been partitioned into parts of equal area or length; use the terms "numerator" and "denominator".MI N.ME.03.17 - Recognize, name, and use equivalent fractions with denominators 2, 4, and 8, using strips as area models.MI 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.MI N.ME.03.19 - Understand that any fraction can be written as a sum of unit fractions, e.g., ¾ = ¼ + ¼ + ¼.

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

- Understand simple decimal fractions in relation to moneyMI N.ME.03.21 - Understand and relate decimal fractions to fractional parts of a dollar, e.g., ½ dollar = $0.50; ¼ dollar = $0.25.MI M - Measurement - Measure and use units for length, weight, temperature and timeMI M.UN.03.01 - Know and use common units of measurements in length, weight, and time.


Skill 430 - Measure length in inches

Skill 431 - Measure length in centimeters


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MI M.UN.03.02 - Measure in mixed units within the 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.

MI M.UN.03.03 - Understand relationships between sizes of standard units, e.g., feet and inches, meters and centimeters.MI M.UN.03.04 - Know benchmark temperatures such as freezing (32°F, 0°C); boiling (212°F, 100°C); and compare temperatures to these, e.g., cooler, warmer. - Understand meaning of area and perimeter and apply in problems

MI M.UN.03.05 - Know the definition of area and perimeter and calculate the perimeter of a square and rectangle given whole number side lengths.



Skill 454 - Determine the perimeter of a squareSkill 455 - WP: Determine the perimeter of a rectangle

MI M.UN.03.06 - Use square units in calculating area by covering the region and counting the number of square units.MI M.UN.03.07 - Distinguish between units of length and area and choose a unit appropriate in the context.

MI M.UN.03.08 - Visualize and describe the relative sizes of one square inch and one square centimeter. - Estimate perimeter and areaMI M.TE.03.09 - Estimate the perimeter of a square and rectangle in inches and centimeters; estimate the area of a square and rectangle in square inches and square centimeters. - Solve measurement problems


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MI M.PS.03.10 - Add and subtract lengths, weights, and times using mixed units within the same measurement system.MI M.PS.03.11 - Add and subtract money in dollars and cents.


Skill 186 - WP: Determine the amount of change from whole dollar amountsSkill 187 - Determine money amounts that total $10

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



MI M.PS.03.13 - Solve contextual problems about perimeters of rectangles and areas of rectangular regions.MI G - Geometry - Recognize the basic elements of geometric objectsMI G.GS.03.01 - Identify points, line segments, lines, and distance.MI G.GS.03.02 - Identify perpendicular lines and parallel lines in familiar shapes and in the classroom.


Skill 419 - Identify parallel lines

Skill 426 - Identify perpendicular lines

MI G.GS.03.03 - Identify parallel faces of rectangular prisms in familiar shapes and in the classroom.

- Name and explore properties of shapesMI G.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 on the number of sides and vertices.MI 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.


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- Explore and name three-dimensional solidsMI G.GS.03.06 - Identify, describe, build, and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices).MI G.SR.03.07 - Represent front, top, and side views of solids built with cubes.MI D - Data and Probability - Use bar graphsMI D.RE.03.01 - Read and interpret bar graphs in both horizontal and vertical forms.


Skill 527 - Read a bar graph

Skill 528 - Answer a question using information from a bar graph

MI D.RE.03.02 - Read scales on the axes and identify the maximum, minimum, and range of values in a bar graph.MI D.RE.03.03 - Solve problems using information in bar graphs, including comparison of bar graphs.


Skill 528 - Answer a question using information from a bar graph


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Agency Tag Set NameMichigan, Math, 2006, Fourth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Understand and use number notation and place valueMI N.ME.04.01 - Read and write numbers to 1,000,000; relate them to the quantities they represent; compare and order.


Skill 38 - Relate a 4- or 5-digit whole number to its word form

Skill 43 - Order 4- to 6-digit whole numbers in ascending or descending order

MI 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.


Skill 41 - Determine the 4- or 5-digit whole number represented in expanded form

Skill 42 - Represent a 5-digit whole number in expanded form

MI 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.


Skill 40 - Determine the value of a digit in a 6-digit number

- Use factors and multiplesMI N.ME.04.04 - Find all factors of any whole number through 50, list factor pairs, and determine if a one-digit number is a factor of a given whole number.MI 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.MI 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.MI N.MR.04.07 - Use factors and multiples to compose and decompose whole numbers. - Add and subtract whole numbersMI N.FL.04.08 - Add and subtract whole numbers fluently.


Skill 73 - Add two 3-digit numbers with one regroupingSkill 78 - Add 3- and 4-digit whole numbers with regroupingSkill 79 - Add four 1- to 4-digit whole numbers



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Agency Tag Set NameMichigan, Math, 2006, Fourth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


Skill 80 - Subtract a 2- or 3-digit number from a 3-digit number with two regroupingsSkill 81 - Subtract 3- and 4-digit whole numbers with regroupingSkill 82 - Subtract two 2- to 6-digit whole numbers

- Multiply and divide whole numbersMI 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.MI 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.


Skill 89 - Multiply a 2-digit whole number by a 1-digit whole number with no regrouping

Skill 94 - Multiply a 3- or 4-digit whole number by a 1-digit whole number

Skill 95 - Multiply a 2-digit whole number by a 1- or 2-digit whole number with regroupingSkill 97 - Multiply a 2-digit whole number by a 2-digit whole numberSkill 98 - WP: Multiply a multi-digit whole number by a 1-digit whole number

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


Skill 106 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientSkill 115 - Divide a 2- or 3-digit whole number by a 1-digit whole number with a remainder in the quotient

MI N.FL.04.12 - Find the value of the unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25.MI N.MR.04.13 - Use the relationship between multiplication and division to simplify computations and check results.MI N.MR.04.14 - Solve contextual problems involving whole number multiplication and division.


Skill 90 - WP: Multiply a 2-digit whole number by a 1-digit whole number without regrouping


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Skill 96 - WP: Multiply a 2-digit whole number by a 1- or 2-digit whole numberSkill 98 - WP: Multiply a multi-digit whole number by a 1-digit whole numberSkill 101 - WP: Multiply whole numbersSkill 107 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 109 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 116 - WP: Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient

Skill 117 - WP: Divide a 2- or 3- digit whole number by a 1-digit whole number with a remainder in the quotient

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


Skill 168 - Determine the decimal number from a pictorial model of tenths or hundredths

Skill 169 - Identify a pictorial model of tenths or hundredths of a decimal numberSkill 177 - Identify the place of a digit in a decimal number through hundredths

MI 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.MI N.ME.04.17 - Locate tenths and hundredths on a number line.


Skill 170 - Identify a decimal number to tenths represented by a point on a number line

MI N.ME.04.18 - Read, write, interpret, and compare decimals up to two decimal places.


Skill 172 - Read a decimal number through the hundredths place

Skill 173 - Compare decimal numbers through the hundredths place


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MI N.MR.04.19 - Write tenths and hundredths in decimal and fraction forms, and know the decimal equivalents for halves and fourths. - Understand fractionsMI N.ME.04.20 - Understand fractions as parts of a set of objects.


Skill 123 - Determine a pictorial model of a fraction of a set of objects

MI 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.


Skill 128 - Identify equivalent fractions using models

MI N.MR.04.22 - Locate fractions with denominators of 12 or less on the number line; include mixed numbers.


Skill 125 - Locate a fraction on a number line

Skill 129 - Locate a mixed number on a number line

MI N.MR.04.23 - Understand the relationships among halves, fourths, and eighths and among thirds, sixths, and twelfths.MI N.ME.04.24 - Know that fractions of the form m/n where m is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line.MI 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.


Skill 161 - Convert a mixed number to an improper fraction

Skill 162 - Convert an improper fraction to a mixed number

MI 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 fractions


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MI N.MR.04.27 - Add and subtract fractions less than 1 with denominators through 12 and/or 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.


Skill 133 - Add fractions with like 1-digit denominators

Skill 135 - Subtract fractions with like 1-digit denominatorsSkill 145 - Add fractions with unlike denominators that have factors in common and simplify the sum

Skill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the difference

MI N.MR.04.28 - Solve contextual problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100).MI N.MR.04.29 - Find the value of an unknown in equations such as 1/8 + x = 5/8 or 3/4 - y = 1/2. - Multiply fractions by whole numbersMI N.MR.04.30 - Multiply fractions by whole numbers, using repeated addition and area or array models. - Add and subtract decimal fractionsMI N.MR.04.31 - For problems that use addition and subtraction of decimals through hundredths, represent with mathematical statements and solve.



MI N.FL.04.32 - Add and subtract decimals through hundredths. - Multiply and divide decimal fractionsMI N.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 repeating. - Estimate


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MI N.FL.04.34 - Estimate the answers to calculations involving addition, subtraction, or multiplication.


Skill 91 - Estimate the product of a 2-digit number and a 1-digit number

Skill 99 - Estimate the product of whole numbers using any method

MI 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.

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


Skill 91 - Estimate the product of a 2-digit number and a 1-digit number

Skill 99 - Estimate the product of whole numbers using any methodSkill 110 - Estimate the quotient of a 2-digit whole number divided by a 1-digit whole number with no remainder in the quotient

MI M - Measurement - Measure using common tools and appropriate unitsMI M.UN.04.01 - Measure using common tools and select appropriate units of measure.MI M.PS.04.02 - Give answers to a reasonable degree of precision in the context of a given problem.MI M.UN.04.03 - Measure and compare integer temperatures in degrees.MI M.TE.04.04 - Measure surface area of cubes and rectangular prisms by covering and counting area of the faces. - Convert measurement unitsMI M.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).


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- Use perimeter and area formulas

MI M.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 shapes using the formulas.



Skill 454 - Determine the perimeter of a squareSkill 455 - WP: Determine the perimeter of a rectangleSkill 460 - Determine the area of a squareSkill 461 - Determine the area of a rectangle given the length and width

MI M.TE.04.07 - Find one dimension of a rectangle given the other dimension and its perimeter or area.


Skill 456 - Determine the missing side length of a rectangle given a side length and the perimeter

Skill 463 - Determine the missing side length of a rectangle given a side length and the area

MI M.TE.04.08 - Find the side of a square given its perimeter or area.MI M.PS.04.09 - Solve contextual problems about perimeter and area of squares and rectangles in compound shapes. - Understand right anglesMI M.TE.04.10 - Identify right angles and compare angles to right angles.

- Problem-solvingMI M.PS.04.11 - Solve contextual problems about surface area.


Skill 490 - WP: Find the surface area of a rectangular prism

MI G - Geometry - Understand perpendicular, parallel, and intersecting linesMI G.GS.04.01 - Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90°) corner.


Skill 419 - Identify parallel lines

Skill 420 - Identify intersecting line segmentsSkill 426 - Identify perpendicular lines


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- Identify basic geometric shapes and their components, and solve problemsMI G.GS.04.02 - Identify basic geometric shapes including isosceles, equilateral, and right triangles, and use their properties to solve problems.MI 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. - Recognize symmetry and transformationsMI G.TR.04.04 - Recognize plane figures that have line symmetry.


Skill 418 - Identify a line of symmetry

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


Skill 482 - Determine the result of a flip, a turn, or a slide

MI D - Data and Probability - Represent and solve problems for given dataMI D.RE.04.01 - Construct tables and bar graphs from given data.


Skill 543 - Use a bar graph with a y-axis scale by 2s to represent data

Skill 546 - Use a double-bar graph to represent data

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


Skill 551 - Determine the median of an odd number of data values

MI 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.


Skill 526 - Answer a question using information from a table

Skill 528 - Answer a question using information from a bar graphSkill 536 - Read a double-bar graph

Skill 537 - Answer a question using information from a double-bar graph


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Agency Tag Set NameMichigan, Math, 2006, Fifth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Understand division of whole numbersMI N.MR.05.01 - Understand the meaning of division of whole numbers with and without remainders; relate division to fractions and to repeated subtraction.

MI 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 (5).


Skill 115 - Divide a 2- or 3-digit whole number by a 1-digit whole number with a remainder in the quotient

Skill 118 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotient

MI N.MR.05.03 - Write mathematical statements involving division for given situations.

Domain 2 - Algebra (AL) Skill 316 - WP: Determine a multiplication or division sentence for a given situation

- Multiply and divide whole numbersMI N.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.


Skill 97 - Multiply a 2-digit whole number by a 2-digit whole number

MI N.FL.05.05 - Solve applied problems involving multiplication and division of whole numbers.


Skill 98 - WP: Multiply a multi-digit whole number by a 1-digit whole numberSkill 101 - WP: Multiply whole numbersSkill 107 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 109 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 116 - WP: Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient

Skill 117 - WP: Divide a 2- or 3- digit whole number by a 1-digit whole number with a remainder in the quotient



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Agency Tag Set NameMichigan, Math, 2006, Fifth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


Skill 121 - WP: Divide a whole number and interpret the remainder

MI N.FL.05.06 - Divide fluently up to a four-digit number by a two-digit number.


Skill 106 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientSkill 118 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotient

- Find prime factorizations of whole numbersMI N.MR.05.07 - Find the prime factorization of numbers from 2 through 50, express in exponential notation, e.g., 24 = 2³ x 3¹, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes.


Skill 142 - Identify the prime factors of a 2-digit number

- Understand meaning of decimal fractions and percentages

MI 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., one is 10 tenths, one tenth is 10 hundredths.

MI N.ME.05.09 - Understand percentages as parts out of 100, use % notation, and express a part of a whole as a percentage. - Understand fractions as division statements; find equivalent fractionsMI N.ME.05.10 - Understand a fraction as a statement of division, e.g., 2 ÷ 3 = 2/3, using simple fractions and pictures to represent.MI N.ME.05.11 - Given two fractions, e.g., 1/2 and 1/4, express them as 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. - Multiply and divide fractions


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MI N.ME.05.12 - Find the product of two unit fractions with small denominators using an area model.MI N.MR.05.13 - Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions. - Add and subtract fractions using common denominatorsMI N.FL.05.14 - Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g., 3/8 + 7/10; use 80 as the common denominator.


Skill 145 - Add fractions with unlike denominators that have factors in common and simplify the sum

Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominators

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

MI N.FL.05.16 - Divide numbers by 10's, 100's, 1,000's using mental strategies.MI N.MR.05.17 - Multiply one-digit and two-digit whole numbers by decimals up to two decimal places.

- Solve applied problems with fractionsMI N.FL.05.18 - Use mathematical statements to represent an applied situation involving addition and subtraction of fractions.MI N.MR.05.19 - Solve contextual problems that involve finding sums and differences of fractions with unlike denominators using knowledge of equivalent fractions.


Skill 147 - WP: Add fractions with unlike 1-digit denominators


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Skill 154 - WP: Subtract fractions with unlike 1-digit denominators

MI N.FL.05.20 - Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness.


Skill 147 - WP: Add fractions with unlike 1-digit denominators

Skill 154 - WP: Subtract fractions with unlike 1-digit denominatorsSkill 189 - WP: Determine the sum of a decimal number and a whole numberSkill 202 - WP: Subtract a decimal number from a whole number

MI N.MR.05.21 - Solve for the unknown in equations such as 1/4 + x = 7/12. - Express, interpret, and use ratios; find equivalencesMI N.MR.05.22 - Express fractions and decimals as percentages and vice versa.


Skill 242 - Convert a decimal number to a percentage

Skill 243 - Convert a percentage to its decimal equivalent

MI N.ME.05.23 - Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3 : 5, 3/5; recognize and find equivalent ratios.


Skill 247 - Determine if ratios are equivalent

MI M - Measurement - Know, and convert among, measurement units within a given systemMI M.UN.05.01 - Recognize the equivalence of 1 liter, 1,000 ml and 1,000 cm³ and include conversions among liters, milliliters, and cubic centimeters.MI 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).

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


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


Skill 435 - Convert between inches, feet, and yards

Skill 436 - Convert between customary units of capacitySkill 437 - Convert within metric units of mass, length, and capacity

- Find areas of geometric shapes using formulasMI M.PS.05.05 - Represent relationships between areas of rectangles, triangles, and parallelograms using models.MI M.TE.05.06 - Understand and know how to use the area formula of a triangle: A = ½bh (where b is length of the base and h is the height), and represent using models and manipulatives.


Skill 465 - Determine the area of a right triangle

Skill 466 - Use a formula to determine the area of a triangle

MI M.TE.05.07 - Understand and know how to use the area formula for a parallelogram: A = bh, and represent using models and manipulatives. - Understand the concept of volumeMI M.TE.05.08 - Build solids with unit cubes and state their volumes.MI M.TE.05.09 - Use filling (unit cubes or liquid), and counting or measuring to find the volume of a cube and rectangular prism.MI M.PS.05.10 - Solve applied problems about the volumes of rectangular prisms using multiplication and division and using the appropriate units.


Skill 488 - WP: Determine the volume of a rectangular prism

MI G - Geometry - Know the meaning of angles, and solve problemsMI G.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 ¼, ½, and ¾, and full turns.


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


Skill 421 - Classify a right angle or a straight angle given a picture

Skill 422 - Classify an obtuse angle or an acute angle given a picture

Skill 423 - Classify an angle given its measureSkill 438 - Identify an angle given its measure

MI G.GS.05.03 - Identify and name angles on a straight line and vertical angles.MI G.GS.05.04 - Find unknown angles in problems involving angles on a straight line, angles surrounding a point, and vertical angles.


Skill 443 - Determine the measure of a vertical angle or a supplementary angle

Skill 444 - Identify angle relationships formed by intersecting lines

MI 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.MI 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.


Skill 501 - Determine a missing angle measure in a triangle

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


Skill 501 - Determine a missing angle measure in a triangle

MI D - Data and Probability - Construct and interpret line graphsMI D.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.


Skill 534 - Read a line graph


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Skill 535 - Answer a question using information from a line graph

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


Skill 545 - Use a line graph to represent data

- Find and interpret mean and mode for a given set of dataMI D.AN.05.03 - Given a set of data, find and interpret the mean (using the concept of fair share) and mode.


Skill 550 - Determine the mean of a set of whole number data

MI D.AN.05.04 - Solve multi-step problems involving means.


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Agency Tag Set NameMichigan, Math, 2006, Sixth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Multiply and divide fractionsMI N.MR.06.01 - Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = __, then 2/3 * __ = 4/5, so __ = 4/5 * 3/2 = 12/10.


Skill 210 - Determine the reciprocal of a positive whole number, a proper fraction, or an improper fraction

MI N.FL.06.02 - Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation.MI N.MR.06.03 - Solve for the unknown in equations such as ¼ ÷ __ = 1, ¾ ÷ __ = ¼, and ½ = 1 * __.

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


Skill 207 - Multiply a fraction by a fraction

Skill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fractionSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbers

- Represent rational numbers as fractions or decimalsMI N.ME.06.05 - Order rational numbers and place them on the number line.


Skill 125 - Locate a fraction on a number line

Skill 129 - Locate a mixed number on a number lineSkill 132 - Order fractions with unlike denominators in ascending or descending orderSkill 171 - Locate a decimal number to tenths on a number lineSkill 174 - Order decimal numbers through the hundredths placeSkill 179 - Order decimal numbers of differing places to thousandths in ascending or descending orderSkill 183 - Order numbers in decimal and fractional forms

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


Skill 164 - Convert a fraction or mixed number in hundredths or thousandths to a decimal number

Skill 166 - Convert a decimal number in hundredths or thousandths to a fraction



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Agency Tag Set NameMichigan, Math, 2006, Sixth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


MI 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 numbersMI N.MR.06.08 - Understand integer subtraction as the inverse of integer addition. Understand integer division as the inverse of integer multiplication.MI N.FL.06.09 - Add and multiply integers between -10 and 10; subtract and divide integers using the related facts. Use the number line and chip models for addition and subtraction.


Skill 279 - Multiply integers

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



Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominatorsSkill 192 - Add two decimal numbers of differing places to thousandths

Skill 196 - Subtract two decimal numbers of differing places to thousandthsSkill 201 - Subtract a decimal number from a whole numberSkill 204 - Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths


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Skill 205 - Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths

Skill 207 - Multiply a fraction by a fractionSkill 208 - Multiply a mixed number by a whole numberSkill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fractionSkill 212 - Divide a whole number by a fraction resulting in a fractional quotientSkill 214 - Divide a fraction by a whole number resulting in a fractional quotientSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbersSkill 221 - Multiply a decimal number through thousandths by a whole numberSkill 226 - Multiply decimal numbers less than one in hundredths or thousandthsSkill 227 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Skill 228 - Divide a decimal number by 10, 100, or 1,000Skill 229 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places

Skill 231 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberSkill 233 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Skill 234 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed


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Skill 235 - Divide decimal numbersSkill 237 - Divide a decimal number by a decimal number through thousandths, rounded quotient if needed

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


Skill 247 - Determine if ratios are equivalent

Skill 248 - WP: Determine if ratios are equivalent

- Solve decimal, percentage and rational number problemsMI N.FL.06.12 - Calculate part of a number given the percentage and the number.


Skill 255 - Determine a given percent of a number

MI N.MR.06.13 - Solve contextual problems involving percentages such as sales taxes and tips.


Skill 290 - WP: Determine the result of applying a percent of decrease to a valueSkill 291 - WP: Determine the result of applying a percent of increase to a value

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


Skill 158 - Estimate the sum of fractions with unlike 1-digit denominators

Skill 159 - Estimate the difference between fractions with unlike 1-digit denominatorsSkill 193 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any methodSkill 223 - WP: Estimate the product of two decimalsSkill 239 - WP: Estimate the quotient of two decimalsSkill 256 - Estimate a given percent of a number

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


Skill 197 - WP: Add or subtract decimal numbers through thousandths

Skill 202 - WP: Subtract a decimal number from a whole number

Skill 222 - WP: Multiply a decimal number through thousandths by a whole numberSkill 225 - WP: Multiply two decimal numbers


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Skill 230 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberSkill 232 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededSkill 236 - WP: Divide a whole number by a decimal numberSkill 238 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededSkill 240 - WP: Solve a 2-step problem involving decimalsSkill 241 - WP: Solve a multi-step problem involving decimal numbers

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


Skill 46 - Convert a whole number greater than 10 to scientific notation

Skill 184 - Convert a number less than 1 to scientific notationSkill 268 - Evaluate or represent an expression of a whole number raised to a whole number power

- Understand rational numbers and their location on the number lineMI N.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.MI 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.MI N.ME.06.19 - Understand that 0 is an integer that is neither negative nor positive.MI 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.MI A - Algebra


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- Calculate ratesMI A.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 3½ hours?


Skill 259 - WP: Determine a unit rate

Skill 260 - WP: Use a unit rate to solve a problem

- Understand the coordinate plane

MI A.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.

Domain 2 - Algebra (AL) Skill 319 - Determine the ordered pair of a point in any quadrant

- Use variables, write expressions and equations, and combine like termsMI A.FO.06.03 - Use letters, with units, to represent quantities in a variety of contexts, e.g., y lbs., k minutes, x cookies.MI A.FO.06.04 - Distinguish between an algebraic expression and an equation.MI 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)."

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

Domain 2 - Algebra (AL) Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportion

Skill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 355 - Use a 1-variable, 1-step equation to represent a verbal statementSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation

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

Domain 2 - Algebra (AL) Skill 331 - Evaluate a 2-variable expression, with two or three operations, using whole number substitutionSkill 333 - Evaluate a 2-variable expression, with two or three operations, using integer substitution


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Skill 375 - Simplify an algebraic expression by combining like terms

- Represent linear functions using tables, equations, and graphs

MI A.RP.06.08 - Understand that relationships between quantities can be suggested by graphs and tables.

MI A.PA.06.09 - Solve problems involving linear functions whose input values are integers; write the equation; graph the resulting ordered pairs of integers, e.g., given c chairs, the "leg function" is 4c; if you have 5 chairs, how many legs?; if you have 12 legs, how many chairs?

Domain 2 - Algebra (AL) Skill 311 - WP: Determine the variable expression with one operation for a table of paired numbers

Skill 312 - WP: Generate a table of paired numbers based on a variable expression with one operation

Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportionSkill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation

MI 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 equationsMI A.FO.06.11 - Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular contexts and solve.

Domain 2 - Algebra (AL) Skill 341 - Solve a 1-step equation involving whole numbers

Skill 342 - Solve a 1-step linear equation involving integersSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation


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MI 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.MI 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.MI 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, use calculators otherwise, and interpret the results.MI M - Measurement - Convert within measurement systemsMI M.UN.06.01 - Convert between basic units of measurement within a single measurement system, e.g., square inches to square feet.


Skill 435 - Convert between inches, feet, and yards

Skill 436 - Convert between customary units of capacitySkill 437 - Convert within metric units of mass, length, and capacity

- Find volume and surface areaMI M.PS.06.02 - Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets).MI M.TE.06.03 - Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides, using formulas.


Skill 487 - Determine the volume of a rectangular prism

Skill 489 - Determine the surface area of a rectangular prism

MI G - Geometry - Understand and apply basic propertiesMI G.GS.06.01 - Understand and apply basic properties of lines, angles, and triangles, including:MI G.GS.06.01.1 - Understand and apply basic properties of lines, angles, and triangles, including: triangle inequality


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MI G.GS.06.01.2 - Understand and apply basic properties of lines, angles, and triangles, including: relationships of vertical angles, complementary angles, supplementary angles




MI G.GS.06.01.3 - Understand and apply basic properties of lines, angles, and triangles, including: congruence of corresponding and alternate interior angles when parallel lines are cut by a transversal, and that such congruencies imply parallel lines


Skill 445 - Identify angle relationships formed by parallel lines cut by a transversal

MI G.GS.06.01.4 - Understand and apply basic properties of lines, angles, and triangles, including: 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 anglesMI G.GS.06.01.5 - Understand and apply basic properties of lines, angles, and triangles, including: know that the sum of the exterior angles of a convex polygon is 360°.

- Understand the concept of congruence and basic transformationsMI G.GS.06.02 - Understand that for polygons, congruence means corresponding sides and angles have equal measures.MI 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.

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


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

MI D - Data and Probability - Understand the concept of probability and solve problemsMI D.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.


Skill 555 - Determine the probability of a single event

MI 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.




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Agency Tag Set NameMichigan, Math, 2006, Seventh Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Understand derived quantitiesMI N.MR.07.02 - Solve problems involving derived quantities such as density, velocity, and weighted averages. - Understand and solve problems involving rates, ratios, and proportionsMI N.FL.07.03 - Calculate rates of change including speed.MI N.MR.07.04 - Convert ratio quantities between different systems of units, such as feet per second to miles per hour.


Skill 441 - Convert a rate from one unit to another with a change in one unit

Skill 442 - Convert a rate from one unit to another with a change in both units

MI N.FL.07.05 - Solve 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.


Skill 245 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problem

Skill 246 - WP: Determine a unit rate with a whole number valueSkill 249 - WP: Determine a part given a ratio and the whole where the whole is less than 50Skill 250 - WP: Determine the whole given a ratio and a part where the whole is less than 50Skill 251 - Solve a proportion involving whole numbersSkill 252 - WP: Solve a proportionSkill 259 - WP: Determine a unit rate

Skill 260 - WP: Use a unit rate to solve a problemSkill 261 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Skill 262 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50

Skill 263 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50



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Agency Tag Set NameMichigan, Math, 2006, Seventh Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


Skill 264 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50Skill 265 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Skill 266 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50


Skill 440 - WP: Solve a measurement problem involving a proportional relationship

- Recognize irrational numbersMI N.MR.07.06 - Understand the concept of square root and cube root, and estimate using calculators.


Skill 282 - Evaluate the positive square root of a perfect square

Skill 284 - Determine an approximate square root of a number

- Compute with rational numbers

MI N.FL.07.07 - Solve problems involving operations with integers.


Skill 278 - WP: Add and subtract using integersSkill 281 - WP: Multiply or divide integers

MI N.FL.07.08 - Add, subtract, multiply, and divide positive and negative rational numbers fluently.



Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominators


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Skill 192 - Add two decimal numbers of differing places to thousandths

Skill 196 - Subtract two decimal numbers of differing places to thousandthsSkill 201 - Subtract a decimal number from a whole numberSkill 204 - Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths

Skill 205 - Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths

Skill 207 - Multiply a fraction by a fractionSkill 208 - Multiply a mixed number by a whole numberSkill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fractionSkill 212 - Divide a whole number by a fraction resulting in a fractional quotientSkill 214 - Divide a fraction by a whole number resulting in a fractional quotientSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbersSkill 221 - Multiply a decimal number through thousandths by a whole numberSkill 226 - Multiply decimal numbers less than one in hundredths or thousandthsSkill 227 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Skill 228 - Divide a decimal number by 10, 100, or 1,000Skill 229 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places


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Skill 231 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberSkill 233 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Skill 234 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed

Skill 235 - Divide decimal numbersSkill 237 - Divide a decimal number by a decimal number through thousandths, rounded quotient if neededSkill 276 - Add integersSkill 277 - Subtract integersSkill 279 - Multiply integersSkill 280 - Divide integers

MI N.FL.07.09 - Estimate results of computations with rational numbers.


Skill 158 - Estimate the sum of fractions with unlike 1-digit denominatorsSkill 159 - Estimate the difference between fractions with unlike 1-digit denominatorsSkill 160 - Estimate the difference between mixed numbers with unlike denominatorsSkill 191 - Estimate the sum of two decimal numbersSkill 194 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 199 - Estimate the difference of two decimal numbersSkill 200 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 203 - Estimate the difference of a whole number and a decimal number

MI A - Algebra - Understand and apply directly proportional relationships and relate to linear relationships


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MI A.PA.07.01 - Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.MI A.RP.07.02 - Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.

Domain 2 - Algebra (AL) Skill 321 - Determine the graph of a 1-operation linear function

Skill 322 - Determine the graph of a 2-operation linear functionSkill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportionSkill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 353 - Use a 2-variable equation to construct an input-output table

Skill 354 - Use a 2-variable equation to represent a relationship expressed in a tableSkill 357 - Determine the table of values that represents a linear equation with rational coefficients in two variablesSkill 358 - Determine a linear equation in two variables that represents a table of values

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

Domain 2 - Algebra (AL) Skill 367 - WP: Interpret the meaning of the slope of a graphed line

Skill 368 - WP: Interpret the meaning of the y-intercept of a graphed line


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


Skill 352 - WP: Use a 2-variable linear equation to represent a situation

MI A.PA.07.05 - Recognize 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.


- Understand and represent linear functionsMI A.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.

Domain 2 - Algebra (AL) Skill 323 - Determine the slope of a line given its graph or a graph of a line with a given slope

Skill 370 - Determine the slope of a line given two points on the line or the graph of the line

MI 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.


Skill 322 - Determine the graph of a 2-operation linear functionSkill 354 - Use a 2-variable equation to represent a relationship expressed in a tableSkill 358 - Determine a linear equation in two variables that represents a table of valuesSkill 367 - WP: Interpret the meaning of the slope of a graphed line


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Skill 368 - WP: Interpret the meaning of the y-intercept of a graphed line

MI A.FO.07.08 - Find and interpret the x and/or y intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax+b=0 corresponds to the point at which the graph of y=ax+b crosses the x axis.

Domain 2 - Algebra (AL) Skill 369 - Determine the x- or y-intercept of a line given an equation

- Understand and solve problems about inversely proportional relationshipsMI 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.MI 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. - Apply basic properties of real numbers in algebraic contextsMI A.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.

- Combine algebraic expressions and solve equations

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

Domain 2 - Algebra (AL) Skill 375 - Simplify an algebraic expression by combining like terms

Skill 376 - Multiply two monomial algebraic expressions


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MI 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.

Domain 2 - Algebra (AL) Skill 347 - WP: Solve a problem involving a 1-variable, 2-step equation

Skill 359 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

MI G - Geometry - Draw and construct geometric objectsMI G.SR.07.01 - Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specified dimensions.MI 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 informal justifications. - Understand the concept of similar polygons, and solve related problemsMI G.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.MI G.TR.07.04 - Solve problems about similar figures and scale drawings.


Skill 499 - Determine a missing dimension given two similar shapes

Skill 500 - WP: Solve a problem involving similar shapes

MI 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.


Skill 485 - Identify a triangle similarity postulate that justifies a similarity statement


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Skill 486 - Identify similar triangles using triangle similarity postulates or theorems

MI 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.

MI D - Data and Probability - Represent and interpret dataMI D.RE.07.01 - Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-and-whisker plots, and select appropriate representation to address specific questions.


Skill 538 - Answer a question using information from a histogram

Skill 540 - Answer a question using information from a circle graph using percentage calculations

Skill 547 - Use a circle graph to represent percentage dataSkill 548 - Use a histogram to represent data

MI D.AN.07.02 - Create and interpret scatter plots and find line of best fit; use an estimated line of best fit to answer questions about the data.


Skill 539 - Answer a question using information from a scatter plot

Skill 549 - Use a scatter plot to organize data

- Compute statistics about data setsMI D.AN.07.03 - Calculate and interpret relative frequencies and cumulative frequencies for given data sets.MI D.AN.07.04 - Find and interpret the median, quartiles, and interquartile range of a given set of data.


Skill 551 - Determine the median of an odd number of data values

Skill 552 - Determine the median of an even number of data valuesSkill 553 - Determine the median of a set of data given a frequency table


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Agency Tag Set NameMichigan, Math, 2006, Eighth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI N - Number and Operations - Understand real number conceptsMI N.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.MI N.ME.08.02 - Understand meanings for zero and negative integer exponents.


Skill 271 - Evaluate a whole number raised to a negative power

MI 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 repeating = 1/9; 0.3 repeating = 1/3.


Skill 129 - Locate a mixed number on a number line

Skill 182 - Estimate a decimal number from its position on a number line

MI 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., square root of 2, square root of 3, pi, on the number line.


Skill 287 - Approximate the location of a square root on a number line

MI N.FL.08.05 - Estimate and solve problems with square roots and cube roots using calculators.MI N.FL.08.06 - Find square roots of perfect squares and approximate the square roots of non-perfect squares by locating between consecutive integers, e.g., square root of 130 is between 11 and 12.


Skill 282 - Evaluate the positive square root of a perfect square

Skill 283 - Determine the square root of a perfect-square fraction or decimalSkill 285 - Determine both square roots of a perfect square



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Agency Tag Set NameMichigan, Math, 2006, Eighth Grade, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


Skill 286 - Determine the two closest integers to a given square root

- Solve problemsMI N.MR.08.07 - Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase of a quantity x is x + .03x = 1.03x.MI N.MR.08.08 - Solve problems involving percent increases and decreases.


Skill 288 - WP: Determine the percent of decrease applied to a numberSkill 289 - WP: Determine the percent of increase applied to a numberSkill 290 - WP: Determine the result of applying a percent of decrease to a valueSkill 291 - WP: Determine the result of applying a percent of increase to a value

MI N.FL.08.09 - Solve problems involving compounded interest or multiple discounts.MI N.MR.08.10 - Calculate weighted averages such as course grades, consumer price indices, and sports ratings.MI N.FL.08.11 - Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile.


Skill 260 - WP: Use a unit rate to solve a problem

MI A - Algebra - Understand the concept of non-linear functions using basic examplesMI A.RP.08.01 - Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax³); roots (y = the square root of x); and exponentials (y = a to the x power, a > 0); using tables, graphs, and equations.


Skill 322 - Determine the graph of a 2-operation linear functionSkill 353 - Use a 2-variable equation to construct an input-output table


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Skill 357 - Determine the table of values that represents a linear equation with rational coefficients in two variablesSkill 358 - Determine a linear equation in two variables that represents a table of valuesSkill 360 - WP: Use a 2-variable equation with rational coefficients to represent a situation

MI 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.

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

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

- Understand and represent quadratic functionsMI A.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.MI 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. - Recognize, represent, and apply common formulasMI A.FO.08.07 - Recognize and apply the common formulas:MI A.FO.08.07.1 - Recognize and apply the common formulas: (a + b)² = a² + 2 ab + b²


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MI A.FO.08.07.2 - Recognize and apply the common formulas: (a - b)² = a² - 2 ab + b²MI A.FO.08.07.3 - Recognize and apply the common formulas: (a + b) (a - b) = a² - b²; represent geometrically.MI 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.

Domain 2 - Algebra (AL) Skill 402 - Solve a quadratic equation using the square root rule

MI A.FO.08.09 - Solve applied problems involving simple quadratic equations. - Understand solutions and solve equations, simultaneous equations, and linear inequalities

MI A.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).

MI 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.

Domain 2 - Algebra (AL) Skill 373 - Solve a system of linear equations in two variables using any method

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

Domain 2 - Algebra (AL) Skill 328 - Determine the graph of a 2-variable linear inequality

Skill 394 - Solve a 2-step linear inequality in one variableSkill 396 - Determine the graph of the solutions to a 2-step linear inequality in one variable


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Skill 397 - Solve a 1-variable linear inequality with the variable on both sidesSkill 406 - Relate a 1-variable inequality to its graph

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

Domain 2 - Algebra (AL) Skill 374 - WP: Determine a system of linear equations that represents a given situation

Skill 395 - WP: Solve a problem involving a 2-step linear inequality in one variable

MI G - Geometry - Understand and use the Pythagorean TheoremMI G.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.


Skill 502 - Use the Pythagorean theorem to determine a length

Skill 503 - WP: Use the Pythagorean theorem to find a length or a distance

MI 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.

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


Skill 458 - Solve a problem involving the circumference of a circle

Skill 473 - Determine the area of a circleSkill 474 - Solve a problem given the area of a circle

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


Skill 457 - WP: Determine the perimeter or the area of a complex shape

Skill 469 - Determine the area of a complex shape


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MI G.SR.08.05 - Solve applied problems involving areas of triangles, quadrilaterals, and circles.


Skill 467 - WP: Determine the area of a triangle

Skill 468 - WP: Determine a missing dimension given the area and another dimensionSkill 471 - Determine the area of a quadrilateralSkill 473 - Determine the area of a circleSkill 474 - Solve a problem given the area of a circle

- Understand concepts of volume and surface area, and apply formulasMI 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 pi (radius)³) and apply them to solve problems.


Skill 495 - Solve a problem involving the volume of a right pyramid or a right cone

Skill 497 - Determine the volume of a sphere or hemisphere

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


Skill 489 - Determine the surface area of a rectangular prism

Skill 496 - Determine the surface area of a sphere

- Visualize solidsMI G.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.

- Understand and apply concepts of transformation and symmetry

MI G.TR.08.09 - Understand the definition of a dilation from a point in the plane, and relate it to the definition of similar polygons.


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MI G.TR.08.10 - Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems.MI D - Data and Probability - Draw, explain, and justify conclusions based on dataMI D.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.

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

- Understand probability concepts for simple and compound events

MI D.PR.08.03 - Compute relative frequencies from a table of experimental results for a repeated event. Interpret the results using relationship of probability to relative frequency.MI 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.

MI D.PR.08.05 - Find and/or compare the theoretical probability, the experimental probability, and/or the relative frequency of a given event.



Skill 556 - Determine the probability of independent events


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MI 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.


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Agency Tag Set NameMichigan, Math, 2007, Grades: 9-12, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill DescriptionMI 1 - Quantitative Literacy and Logic

MI L1 - Based 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.

MI L1.1 - Number Systems and Number SenseMI L1.1.1 - 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.

MI 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.MI 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.MI 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.

MI L1.1.5 - Justify numerical relationshipsMI L1.1.6 - Explain the importance of the irrational numbers the square root of 2 and the square root of 3 in basic right triangle trigonometry, and the importance of pi because of its role in circle relationships.

MI L1.2 - Representations and Relationships


STAR Math Enterprise Grades 9 - 12

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Agency Tag Set NameMichigan, Math, 2007, Grades: 9-12, Grade Level and High School Content Expectations, State Department of EducationStandard Domain Description Skill Description


MI L1.2.1 - Use mathematical symbols to represent quantitative relationships and situations.

Domain 2 - Algebra (AL) Skill 358 - Determine a linear equation in two variables that represents a table of valuesSkill 360 - WP: Use a 2-variable equation with rational coefficients to represent a situation

MI L1.2.2 - Interpret representations that reflect absolute value relationships in such contexts as error tolerance.MI 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.MI 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.


Skill 549 - Use a scatter plot to organize data

MI L1.2.5 - Read and interpret representations from various technological sources, such as contour or isobar diagrams.MI L1.3 - Counting and Probabilistic ReasoningMI L1.3.1 - Describe, explain, and apply various counting techniques; relate combinations to Pascal's triangle; know when to use each technique.MI L1.3.2 - Define and interpret commonly used expressions of probability.MI L1.3.3 - Recognize and explain common probability misconceptions such as "hot streaks" and "being due."MI L2 - Students 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.MI L2.1 - Calculation Using Real and Complex NumbersMI L2.1.1 - Explain the meaning and uses of weighted averages.


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MI 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.


Skill 268 - Evaluate or represent an expression of a whole number raised to a whole number power

Skill 269 - Evaluate an integer raised to a whole number powerSkill 270 - Evaluate a numerical expression involving integer exponents and/or integer basesSkill 271 - Evaluate a whole number raised to a negative powerSkill 272 - Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbersSkill 275 - Evaluate a whole number raised to a fractional power

MI 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.MI L2.1.4 - Know that the complex number i is one of two solutions to x² = -1.MI L2.1.5 - Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of complex numbers.MI L2.1.7 - Understand the mathematical bases for the differences among voting procedures.MI L2.2 - Sequences and IterationMI L2.2.1 - Find the nth term in arithmetic, geometric, or other simple sequences.MI L2.2.2 - Compute sums of finite arithmetic and geometric sequences.

MI L2.2.3 - Use iterative processes in such examples as computing compound interest or applying approximation procedures.MI L2.2.4 - Compute sums of infinite geometric sequences.


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MI L2.3 - Measurement Units, Calculations, and ScalesMI L2.3.1 - Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly.


Skill 439 - Determine the approximate value of a unit converted between customary and metric measures

MI L2.3.2 - Describe and interpret logarithmic relationships in such contexts as the Richter scale, the pH scale, or decibel measurements; solve applied problems.

MI L2.4 - Understanding ErrorMI L2.4.1 - 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 computation; recognize accumulated error in applied situations.

MI L2.4.2 - Describe and explain round-off error, rounding, and truncating.MI L2.4.3 - Know the meaning of and interpret statistical significance, margin of error, and confidence level.

MI L3 - Students 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.

MI L3.1 - Mathematical Reasoning


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MI L3.1.1 - Distinguish between inductive and deductive reasoning, identifying and providing examples of each.MI L3.1.2 - Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic.MI L3.1.3 - 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.MI L3.2 - Language and Laws of LogicMI L3.2.1 - Know and use the terms of basic logic.MI L3.2.2 - 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.MI L3.2.3 - Use the quantifiers "there exists" and "all" in mathematical and everyday settings and know how to logically negate statements involving them.MI L3.2.4 - 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.

MI L3.3 - ProofMI L3.3.1 - Know the basic structure for the proof of an "if..., then..." statement (assuming the hypothesis and ending with the conclusion) and that proving the contrapositive is equivalent.MI L3.3.2 - Construct proofs by contradiction. Use counterexamples, when appropriate, to disprove a statement.


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MI L3.3.3 - 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.

MI 2 - Algebra and FunctionsMI A1 - Students 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.

MI A1.1 - Construction, Interpretation, and Manipulation of Expressions

MI 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.

Domain 2 - Algebra (AL) Skill 331 - Evaluate a 2-variable expression, with two or three operations, using whole number substitution

Skill 332 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbersSkill 333 - Evaluate a 2-variable expression, with two or three operations, using integer substitution

Skill 355 - Use a 1-variable, 1-step equation to represent a verbal statement

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

Domain 2 - Algebra (AL) Skill 379 - Apply the product of powers property to a monomial algebraic expression

Skill 380 - Apply the power of a power property to a monomial algebraic expression


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Skill 381 - Apply the power of a product property to a monomial algebraic expressionSkill 382 - Apply the quotient of powers property to monomial algebraic expressionsSkill 383 - Apply the power of a quotient property to monomial algebraic expressionsSkill 388 - Simplify a monomial algebraic radical expression

MI A1.1.3 - Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.

Domain 2 - Algebra (AL) Skill 378 - Factor a common term from a binomial expression

Skill 386 - Factor the GCF from a polynomial expressionSkill 387 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)

MI A1.1.4 - Add, subtract, multiply, and simplify polynomials and rational expressions.

Domain 2 - Algebra (AL) Skill 377 - Multiply two binomials

Skill 384 - Add or subtract polynomial expressionsSkill 385 - Multiply two binomials of the form (ax +/- b)(cx +/- d)Skill 389 - Simplify a rational expression involving polynomial termsSkill 390 - Multiply rational expressionsSkill 392 - Add or subtract two rational expressions with unlike polynomial denominators

MI A1.1.5 - Divide a polynomial by a monomial.

Domain 2 - Algebra (AL) Skill 391 - Divide a polynomial expression by a monomial

MI 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.

MI A1.1.7 - Transform trigonometric expressions into equivalent forms using basic identities such as sin² theta + cos² theta = 1 and tan² theta + 1 = sec² theta


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MI A1.2 - Solutions of Equations and InequalitiesMI A1.2.1 - Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.

Domain 2 - Algebra (AL) Skill 345 - Solve a 1-step equation involving rational numbers

Skill 346 - Solve a 2-step equation involving rational numbersSkill 347 - WP: Solve a problem involving a 1-variable, 2-step equationSkill 348 - Solve a 1-variable linear equation with the variable on both sidesSkill 355 - Use a 1-variable, 1-step equation to represent a verbal statementSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation

Skill 359 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operationsSkill 360 - WP: Use a 2-variable equation with rational coefficients to represent a situation

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

MI A1.2.3 - Solve linear and quadratic equations and inequalities including systems of up to three linear equations with three unknowns. Justify steps in the solution, and apply the quadratic formula appropriately.

Domain 2 - Algebra (AL) Skill 342 - Solve a 1-step linear equation involving integers

Skill 343 - Solve a 2-step linear equation involving integersSkill 345 - Solve a 1-step equation involving rational numbersSkill 346 - Solve a 2-step equation involving rational numbersSkill 348 - Solve a 1-variable linear equation with the variable on both sidesSkill 373 - Solve a system of linear equations in two variables using any method


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Skill 394 - Solve a 2-step linear inequality in one variableSkill 397 - Solve a 1-variable linear inequality with the variable on both sidesSkill 400 - Solve a quadratic equation using the quadratic formula

Skill 401 - Solve a quadratic equation by factoringSkill 402 - Solve a quadratic equation using the square root rule

MI A1.2.4 - Solve absolute value equations and inequalities, and justify steps in the solution.

Domain 2 - Algebra (AL) Skill 398 - Solve a 1-variable absolute value inequality

MI A1.2.5 - Solve polynomial equations and equations involving rational expressions, and justify steps in the solution.

Domain 2 - Algebra (AL) Skill 404 - Solve a rational equation involving terms with monomial denominators

Skill 405 - Solve a rational equation involving terms with polynomial denominators

MI A1.2.6 - Solve power equations and equations including radical expressions, justify steps in the solution, and explain how extraneous solutions may arise.

Domain 2 - Algebra (AL) Skill 403 - Solve a radical equation that leads to a quadratic equation

MI A1.2.7 - Solve exponential and logarithmic equations, and justify steps in the solution.MI A1.2.8 - Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution.

Domain 2 - Algebra (AL) Skill 349 - Rewrite an equation to solve for a specified variable

MI A1.2.9 - Know common formulas and apply appropriately in contextual situations.MI A1.2.10 - Use special values of the inverse trigonometric functions to solve trigonometric equations over specific intervals.


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MI A2 - Students 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. Students 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.

MI A2.1 - Definitions, Representations, and Attributes of FunctionsMI A2.1.1 - Determine whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function and identify its domain and range.MI A2.1.2 - Read, interpret, and use function notation and evaluate a function at a value in its domain.

Domain 2 - Algebra (AL) Skill 334 - Evaluate a function written in function notation for a given value

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


Skill 322 - Determine the graph of a 2-operation linear functionSkill 325 - Determine the graph of a linear equation given in slope-intercept, point-slope, or standard formSkill 326 - Determine the graph of a given quadratic functionSkill 357 - Determine the table of values that represents a linear equation with rational coefficients in two variablesSkill 358 - Determine a linear equation in two variables that represents a table of values

MI A2.1.4 - Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined.


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MI A2.1.5 - Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions.

MI A2.1.6 - Identify the zeros of a function, the intervals where the values of a function are positive or negative, and describe the behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.MI A2.1.7 - Identify and interpret the key features of a function from its graph or its formula(e).

Domain 2 - Algebra (AL) Skill 366 - Determine the x- or y-intercept of a line given its graph

Skill 369 - Determine the x- or y-intercept of a line given an equationSkill 370 - Determine the slope of a line given two points on the line or the graph of the lineSkill 372 - Determine the slope of a line given an equation of the line

MI A2.2 - Operations and TransformationsMI A2.2.1 - Combine functions by addition, subtraction, multiplication, and division.MI A2.2.2 - Apply given transformations to basic functions and represent symbolically.MI A2.2.3 - Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs.MI A2.2.4 - If a function has an inverse, find the expression(s) for the inverse.MI 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.MI A2.2.6 - Know and interpret the function notation for inverses and verify that two functions are inverses using composition.MI A2.3 - Representations of Functions


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MI 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.MI A2.3.2 - Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.MI A2.3.3 - Write the general symbolic forms that characterize each family of functions.MI A2.4 - Models of Real-world Situations Using Families of FunctionsMI A2.4.1 - Identify the family of function best suited for modeling a given real-world situation.MI A2.4.2 - Adapt the general symbolic form of a function to one that fits the specification of a given situation by using the information to replace arbitrary constants with numbers.

Domain 2 - Algebra (AL) Skill 362 - Determine an equation of a line given the slope and y-intercept of the line

Skill 364 - Determine an equation for a line given the slope of the line and a point on the line that is not the y-interceptSkill 365 - Determine an equation of a line given two points on the line

MI A2.4.3 - Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.MI A2.4.4 - Use methods of linear programming to represent and solve simple real-life problems.MI A3 - Students study the symbolic and graphical forms of each function family. By recognizing the unique characteristics of each family, they can use them as tools for solving problems or for modeling real-world situations.

MI A3.1 - Lines and Linear Functions


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MI A3.1.1 - Write the symbolic forms of linear functions (standard, point-slope, and slope-intercept) given appropriate information, and convert between forms.

Domain 2 - Algebra (AL) Skill 361 - Determine the slope-intercept form or the standard form of a linear equation

Skill 362 - Determine an equation of a line given the slope and y-intercept of the lineSkill 363 - Determine an equation for a line given a graphSkill 364 - Determine an equation for a line given the slope of the line and a point on the line that is not the y-interceptSkill 365 - Determine an equation of a line given two points on the line

MI A3.1.2 - Graph lines (including those of the form x = h and y = k) given appropriate information.


Skill 322 - Determine the graph of a 2-operation linear functionSkill 324 - Determine the graph of a line using given informationSkill 325 - Determine the graph of a linear equation given in slope-intercept, point-slope, or standard form

MI A3.1.3 - Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.

Domain 2 - Algebra (AL) Skill 369 - Determine the x- or y-intercept of a line given an equation

Skill 372 - Determine the slope of a line given an equation of the line

MI A3.1.4 - 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.MI A3.2 - Exponential and Logarithmic FunctionsMI A3.2.1 - Write the symbolic form and sketch the graph of an exponential function given appropriate information.


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MI A3.2.2 - Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions; recognize the logarithmic function as the inverse of the exponential function.MI A3.2.3 - Apply properties of exponential and logarithmic functions.

MI A3.2.4 - 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.

MI A.3.2.5 - Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.MI A3.3 - Quadratic FunctionsMI A3.3.1 - Write the symbolic form and sketch the graph of a quadratic function given appropriate information.

Domain 2 - Algebra (AL) Skill 326 - Determine the graph of a given quadratic function

MI A3.3.2 - 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.

MI A3.3.3 - Convert quadratic functions from standard to vertex form by completing the square.MI A3.3.4 - Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function.MI A3.3.5 - Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros.

MI A3.4 - Power FunctionsMI A3.4.1 - Write the symbolic form and sketch the graph of power functions.MI A3.4.2 - Express direct and inverse relationships as functions and recognize their characteristics.


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MI A3.4.3 - Analyze the graphs of power functions, noting reflectional or rotational symmetry.MI A3.5 - Polynomial FunctionsMI A3.5.1 - Write the symbolic form and sketch the graph of simple polynomial functions.MI A3.5.2 - Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.MI A3.5.3 - 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.

MI A3.6 - Rational FunctionsMI A3.6.1 - Write the symbolic form and sketch the graph of simple rational functions.MI A3.6.2 - Analyze graphs of simple rational functions and understand the relationship between the zeros of the numerator and denominator and the function's intercepts, asymptotes, and domain.

MI A3.7 - Trigonometric FunctionsMI A3.7.1 - Use the unit circle to define sine and cosine; approximate values of sine and cosine; use sine and cosine to define the remaining trigonometric functions; explain why the trigonometric functions are periodic.

MI A3.7.2 - Use the relationship between degree and radian measures to solve problems.MI A3.7.3 - Use the unit circle to determine the exact values of sine and cosine, for integer multiples of pi/6 and pi/4.MI A3.7.4 - Graph the sine and cosine functions; analyze graphs by noting domain, range, period, amplitude, and location of maxima and minima.


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MI A3.7.5 - 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.MI 3 - Geometry and TrigonometryMI G1 - Students 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.

MI G1.1 - Lines and Angles; Basic Euclidean and Coordinate Geometry

MI G1.1.1 - Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles.




MI 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.


Skill 445 - Identify angle relationships formed by parallel lines cut by a transversal

Skill 506 - Determine the measure of an angle formed by parallel lines and one or more transversals

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


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MI 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.

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


Skill 505 - Determine the midpoint of a line segment given the coordinates of the endpoints

MI G1.1.6 - Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms, axioms, definitions, and theorems.

MI G1.2 - Triangles and Their PropertiesMI G1.2.1 - 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.

MI G1.2.2 - Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.MI G1.2.3 - Know a proof of the Pythagorean Theorem, and use the Pythagorean Theorem and its converse to solve multistep problems.


Skill 513 - Determine a length in a complex figure using the Pythagorean theorem

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


Skill 514 - Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

MI G1.2.5 - Solve multistep problems and construct proofs about the properties of medians, altitudes, perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle. Using a straightedge and compass, construct these lines.


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MI G1.3 - Triangles and Trigonometry

MI G1.3.1 - 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.

MI 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 angle theta using the formula Area = (1/2) absin theta.

MI 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.MI G1.4 - Quadrilaterals and Their PropertiesMI G1.4.1 - Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.


Skill 471 - Determine the area of a quadrilateral

Skill 472 - Determine a length given the area of a quadrilateral

MI G1.4.2 - Solve multistep problems and construct proofs involving quadrilaterals using Euclidean methods or coordinate geometry.

MI G1.4.3 - Describe and justify hierarchical relationships among quadrilaterals.MI G1.4.4 - Prove theorems about the interior and exterior angle sums of a quadrilateral.MI G1.4.5 - Understand the definition of a cyclic quadrillateral and know and use the basic properties of cyclic quadrilaterals.MI G1.5 - Other Polygons and Their Properties


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MI G1.5.1 - Know and use subdivision or circumscription methods to find areas of polygons.MI 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.


Skill 509 - Determine the measure of an angle or the sum of the angles in a polygon

MI G1.6 - Circles and Their PropertiesMI G1.6.1 - Solve multistep problems involving circumference and area of circles.


Skill 474 - Solve a problem given the area of a circle

MI G1.6.2 - Solve problems and justify arguments about chords and lines tangent to circles.


Skill 517 - Determine the length of a line segment, the measure of an angle, or the measure of an arc using a tangent to a circleSkill 518 - Determine a length using a line segment tangent to a circle and the radius that intersects the tangent

MI G1.6.3 - Solve problems and justify arguments about central angles, inscribed angles, and triangles in circles.


Skill 515 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angleSkill 519 - Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arc

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


Skill 476 - Determine the length of the radius or the diameter of a circle given the area of a sector

Skill 477 - WP: Determine a length or an area involving a sector of a circle

Skill 478 - Determine the measure of an arc or an angle given the area of a sector of a circleSkill 515 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angleSkill 516 - Solve a problem involving the length of an arcSkill 519 - Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arc

MI G1.7 - Conic Sections and Their Properties


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

Domain 2 - Algebra (AL) Skill 330 - Relate a graph of an ellipse to its equation

MI G1.7.4 - Know and use the relationship between the vertices and foci in and ellipse, the vertices and foci in a hyperboia, and the directrix and focus in a parabola, interpret these relationships in applied contexts.MI G1.8 - Three- Dimensional FiguresMI G1.8.1 - Solve multi-step problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.


Skill 494 - Determine a length given the surface area of a right cylinder or a right prism that has a rectangle or a right triangle as a base

Skill 495 - Solve a problem involving the volume of a right pyramid or a right cone

MI G1.8.2 - Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

MI G2 - Students 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.MI G2.1 - Relationships Between Area and Volume FormulasMI G2.1.1 - 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.MI G2.1.2 - Know and demonstrate the relationships between the area formulas of various quadrilaterals.


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MI 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).

MI G2.2 - Relationships Between Two-dimensional and Three-dimensional RepresentationsMI G2.2.1 - Identify or sketch a possible three-dimensional figure, given two-dimensional views. Create a two-dimensional representation of a three-dimensional figure.

MI G2.2.2 - Identify or sketch cross sections of three-dimensional figures. Identify or sketch solids formed by revolving two-dimensional figures around lines.

MI G2.3 - Congruence and Similarity

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


Skill 483 - Identify a triangle congruence postulate that justifies a congruence statement

MI G2.3.2 - Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates.MI G2.3.3 - Prove that triangles are similar by using SSS, SAS, and AA conditions for similarity.


Skill 485 - Identify a triangle similarity postulate that justifies a similarity statement

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

MI 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.


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MI G3 - Students 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.

MI G3.1 - Distance-preserving Transformations: IsometriesMI G3.1.1 - Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.MI G3.1.2 - Given two figures that are images of each other under an isometry, find the isometry and describe it completely.MI 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.

MI G3.2 - Shape-preserving Transformations: Dilations and IsometriesMI G3.2.1 - Know the definition of dilation and find the image of a figure under a given dilation.MI G3.2.2 - Given two figures that are images of each other under some dilation, identify the center and magniture of the dilation.MI G3.2.3 - Find the image of a figure under the composition of a dilation and an isometry.MI 4 - Statistics and ProbabilityMI S1 - Students 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.

MI S1.1 - Producing and Interpreting Plots


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MI S1.1.1 - 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.


Skill 537 - Answer a question using information from a double-bar graph

Skill 538 - Answer a question using information from a histogramSkill 546 - Use a double-bar graph to represent dataSkill 548 - Use a histogram to represent data

MI 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.MI S1.2 - Measures of Center and VariationMI S1.2.1 - 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.


Skill 550 - Determine the mean of a set of whole number data

Skill 551 - Determine the median of an odd number of data valuesSkill 552 - Determine the median of an even number of data valuesSkill 553 - Determine the median of a set of data given a frequency table

MI 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.


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MI S1.2.3 - Compute and interpret measures of variation, including percentiles, quartiles, interquartile range, variance, and standard deviation.MI S1.3 - The Normal DistributionMI S1.3.1 - Explain the concept of distribution and the relationship between summary statistics for a data set and parameters of a distribution.MI S1.3.2 - Describe characteristics of the normal distribution, including its shape and the relationships among its mean, median, and mode.

MI 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.

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

MI S2 - Students 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.MI S2.1 - Scatterplots and Correlation

MI S2.1.1 - Construct a scatterplot for a bivariate data set with appropriate labels and scales.MI S2.1.2 - Given a scatterplot, identify patterns, clusters, and outliers. Recognize no correlation, weak correlation, and strong correlation.MI 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.


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MI 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.MI S2.2 - Linear RegressionMI S2.2.1 - For bivariate data that 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.

MI S2.2.2 - Use the equation of the least squares regression line to make appropriate predictions.MI S3 - Students 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.

MI S3.1 - Data Collection and AnalysisMI S3.1.1 - Know the meanings of a sample from a population and a census of a population, and distinguish between sample statistics and population parameters.

MI 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.

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


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

MI 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.

MI 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.MI S3.2.1 - Explain the basic ideas of statistical process control, including recording data from a process over time.MI S3.2.2 - Read and interpret basic control charts; detect patterns and departures from patterns.

MI S4 - Students 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.MI S4.1 - ProbabilityMI S4.1.1 - Understand and construct sample spaces in simple situations.

MI 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.


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


Skill 556 - Determine the probability of independent events

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


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michigan standards alignment kindergarten through grade twelve

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