numbersandoperations order lesson objective · forrelease6.0.3 8/12/15 lesson objective...

For Release 6.0.3 8/12/15

Lesson Objective

1 Numerals and Counting to 10

Count up to 10 objects in a given set using verbal names and one-‐to-‐one correspondence. Use numbers and pictures to describe how many objects in a set. Understand the concept of 0. Order numbers from 0 to 10.

2 Counting with One-‐to-‐One Correspondence

Count up to ten objects in a given set using verbal names and one-‐to-‐one correspondence. Use numbers and pictures to describe how many objects are in a set.

3 Counting Objects in a Set

Create a set of concrete materials to represent quantities. Recognize "how many" in a small group of objects. Use numbers and pictures to describe how many objects are in a set.

4 Counting to 20 Count how many objects in a given set. Create a set of a given size. Recognize the numerals from 11 to 20.

5 Counting On Count on from a number other than one. Recognize the numerals from 0 to 20.

6 One More Create sets of objects with one more. Identify numbers that come after other numbers in a number line.

7 One Less Create sets of objects with one fewer. Identify numbers that come before other numbers in a number line.

8 Counting by 10s Group objects in sets of ten. Count orally to 100 by 10s using concrete materials and a hundreds chart.

9 Comparing Sets

Use one-‐to-‐one correspondence to compare equal and unequal sets with up to ten objects in each. Compare two or more sets with up to ten objects in each one and identify which set is equal to, more than, or less than the other.

10 Using a Number Line to Add and Subtract

Use a number line to demonstrate how to count up and count back from a given number. Count forward to add 1 and 2. Count backward to subtract 1 and 2.

11 Ordinal Numbers* Use ordinal numbers to indicate position.

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12 Counting and Ordering to 20

Establish one-‐to-‐one correspondence by moving, touching, or pointing to objects. Connect number words and numerals to the quantities they represent. Read numerals to 20. Count forward and backward by one. Order whole numbers to 20.


Establish one-‐to-‐one correspondence by moving, touching, or pointing to objects. Connect number words and numerals to the quantities they represent. Read numerals to 30. Count forward and backward by one. Order whole numbers to 30.


Establish one-‐to-‐one correspondence by moving, touching, or pointing to objects. Connect number words and numerals to the quantities they represent. Read numerals to 100. Count forward and backward by one. Order whole numbers to 100 or more using concrete materials, drawings.

15 Counting On: 1 to 100Identify the number that comes after any number from 0 to 100. Count forward by one beginning with any number less than 100.

16 Counting Back: 100 to 1Identify the number that comes after before any number from 0 to 100. Count backward by one beginning with any number less than 100. Order numbers from 100 to 1.

17 Comparing Numbers to 100 Using Symbols

Compare and order two-‐digit numbers. Compare numbers using the greater than symbol, less than symbol, and equals sign.

18 Grouping into Tens and Ones

Count and group up to 100 objects into tens and ones. Use numerals to represent numbers to 100 in terms of tens and ones. Use base-‐ten models to represent two-‐digit numbers and to relate the grouping to the corresponding written numeral. Write two-‐digit numbers in standard and expanded form.

19 Regrouping Tens As Ones Use base-‐ten models to regroup tens or ones. Create equivalent representations of two-‐digit numbers.

20 Adding a Two-‐Digit Number and a One-‐Digit Number

Find the sum of a two-‐digit number plus a one-‐digit number. Use a number line to add a two-‐digit number and a one digit number. Estimate the sum of a two-‐digit number plus a one-‐digit number. Solve addition problems.

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21 Adding a Two-‐Digit Number and a Multiple of 10

Find the sum of a two-‐digit number plus ten or a multiple of ten. Use a hundreds chart to add two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

22 Adding Two-‐Digit Numbers

Find the sum of two-‐digit numbers. Use base-‐ten models to add two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

23 Subtracting 10 from a Two-‐Digit Number

Find the difference between a two-‐digit number and ten or twenty. Use a hundreds chart to subtract two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

24 Subtracting Two-‐Digit Numbers

Find the difference of two-‐digit numbers. Use base-‐ten models to subtract two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

25 Ordinal Numbers: 1st Through 10th*

Use ordinal numbers to indicate position. Identify objects that are between others in a line. Recognize that position is related to a point of view.

26 Fraction of a Set: Halves and Fourths*

Represent fractions (1/2 and 1/4) as parts of a set using concrete materials and drawings. Relate fractions to sharing equally and dividing into equal parts.

27 Counting Backward*Experience counting backwards using pictures. Count backwards by 1 starting with any number up to and including 10.

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28 Place Value: Hundreds, Tens, and Ones

Use base-‐ten models to represent three-‐digit numbers and to relate the grouping to the corresponding written numeral. Identify the value of the digits in three-‐digit numbers. Know place value patterns using zero as a place holder. Write three-‐digit numbers in standard and expanded form.

29 Place Value to 1,000

Know the value of each place is ten times that of the place to the right. Know the value of any given digit in whole numbers to hundreds. Write and understand expanded forms of numbers.

30 Place Value and Writing Numbers in Standard Form

Know the value of each place is ten times that of the place to the right. Know the value of any given digit in whole numbers to thousands. Write and understand expanded forms of numbers. Write numbers in standard form using the comma as a place holder.

31 Comparing and Ordering Three-‐Digit Numbers

Compare and order three-‐digit numbers. Compare numbers using the greater than symbol and less than symbol. Determine the order of three non-‐consecutive numbers less than 1,000.

32 Comparing and Ordering Numbers to 1,000

Compare and order numbers up to a thousand using number lines. Compare and order numbers using a place-‐value chart. Compare numbers using the greater than symbol and the less than symbol.

33 Add or Subtract 10 or 100Mentally add 10 or 100 to a given number 100-‐900. Mentally subtract 10 or 100 from a given number 100-‐900.

34 Mental Addition of Two-‐Digit and One-‐Digit Numbers

Find the sum of a two-‐digit number plus a one-‐digit number. Recognize that the order of addends does not affect the sum. Develop mental math addition strategies. Solve addition problems.

35 Two-‐Digit Sums and Estimation

Find the sum of two-‐digit numbers. Estimate the sum of two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

36 Two-‐Digit Sums with Base-‐Ten Models

Find the sum of two-‐digit numbers. Estimate the sum of two-‐digit numbers. Use base-‐ten models and the standard algorithm to add two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

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37 Adding Three-‐Digit Numbers

Use a number line and rounding to estimate the results of whole-‐number computations. Find the sum of two 3-‐digit numbers, using base-‐ten blocks, a place-‐value chart, and the standard algorithm. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations. Solve real-‐world problems with addition.

38 Add Up to Four Two-‐Digit Numbers

Apply strategies based on place value and properties of operations to add up to four two-‐digit numbers.

39 Subtracting a One-‐Digit Number from a Two-‐Digit Number

Find the difference of a two-‐digit number minus a one-‐digit number. Use tens frames and concrete objects to subtract. Develop mental math subtraction strategies. Solve subtraction problems.

40 Subtracting Two-‐Digit Numbers and Estimating Differences

Find the difference between 2 two-‐digit numbers. Estimate the difference between two-‐digit numbers. Use base-‐ten models to subtract two-‐digit numbers. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

41 Subtracting Two-‐Digit Numbers

Find the difference between 2 two-‐digit numbers. Estimate the difference between 2 two-‐digit numbers. Use base-‐ten models and the standard algorithm to subtract 2-‐digit numbers. Develop and use estimation strategies.

42 Subtracting Three-‐Digit Numbers

Solve real-‐world problems using subtraction. Estimate the results of whole-‐number computations. Find the difference of two 3-‐digit numbers, using base-‐ten blocks, a place-‐value chart, and the standard algorithm. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations.

43 Number Words 0-‐10* Read and write number words from 0 -‐ 10.44 Number Words 0-‐20* Read and write number words from 10 -‐ 20.45 Number Words 0-‐120* Read and write number words from 1 -‐ 120.

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46 Use Place Value to Round Numbers

Round two-‐ and three-‐digit numbers to the nearest 10.

Round three-‐digit numbers to the nearest 100.

47 Add and subtract within 1000

Use a variety of strategies to fluently add within 1000.

Use a variety of strategies to fluently subtract within 1000.

Estimate to determine if an answer is reasonable.

48 Multiply Multiples of 10 Multiply ten by a one-‐digit number. Multiply a multiple of ten by a one-‐digit number.

49 Understand What a Fraction Is

Understand that a fraction is a whole divided into some number of equal parts.Understand and recognize the parts of a fraction.Understand that unit fractions are the building blocks of fractions in the same way that 1 is the building block of whole numbers.

50 Understand Fractions on a Number Line

Understand that fractions are numbers on a number line. Understand how to use number lines to count and identify fractional parts. Represent fractions on a number line that are less than, equal to, or greater than one.

51 Find Equivalent Fractions

Use fraction models and number lines to identify and create equivalent fractions, including those that are greater to or equal to one whole.

Express whole numbers as fractions.

Identify fractions that are equivalent to whole numbers.

52 Fractions: Part of a Whole in Real-‐World Problems

Represent fractions (halves, fourths, and thirds) as parts of a whole using concrete materials and drawings. Compare fractions in real-‐life situations using concrete materials or drawings. Use visual fraction models to find fractional parts of whole numbers.

53 Fraction of a Whole: Denominators Through 12

Identify and name fractions as parts of a whole using models, pictures, and drawings. Read, write, and identify fractions with denominators including 2, 3, 4, 5, 6, 8, 10, and 12.

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54 Understand Place Value

Identify the value of a digit based on its location in the number.Demonstrate how moving from one place-‐value position to the next changes the value by a multiple of ten.Use standard form, word form, and expanded form to read and write multi-‐digit whole numbers.

55 Compare and Order Whole Numbers Using Number Lines

Compare and order large numbers using number lines. Compare and order large numbers using a place-‐value chart. Express the relationship between two whole numbers, using equality or inequality symbols.

56 Rounding to the Nearest 10, 100, or 1,000 Round numbers to the nearest 10, 100, and 1,000.

57 Adding Multi-‐Digit NumbersEstimate the sum of two or more multi-‐digit numbers. Find the sum of two or more multi-‐digit numbers. Check addition by using the commutative property of addition.

58 Subtracting Multi-‐Digit Numbers

Solve real-‐world problems with subtraction. Use tables and graphs to solve problems. Subtract multi-‐digit numbers by counting up. Estimate differences using rounding. Subtract multi-‐digit numbers with regrouping. Check the difference by addition.

59 Multiplying Two-‐Digit Numbers by One-‐Digit Numbers

Estimate the product of a two-‐digit number by a one-‐digit number. Find the product of a two-‐digit number by a one-‐digit number using array models and the partial products method.

60 Relating Division to Multiplication

Solve division problems having divisors of one-‐digit and dividends not exceeding two digits, with or without remainders. Understand the relationship between multiplication and division.

61 Divide Whole Numbers

Divide up to four-‐digit dividends by one-‐digit divisors, with remainders.

Use equations, rectangular arrays, and area models to illustrate and explain calculations.

Interpret the remainder in a division word problem.

62 Equivalent Fractions

Understand why a fraction a/b is equivalent to a fraction (n x a)/(n x b).

Recognize and generate equivalent fractions.

Fourth Grade

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63 Understand Adding and Subtracting Fractions

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way. Use fraction models to add and subtract fractions with like denominators.

64 Understand Mixed Numbers

Use fraction models, number lines, and equations to decompose a fraction greater than one into the sum of a whole number and a fraction smaller than one.

Use mixed number notation.

Replace a mixed number with an equivalent fraction using addition.

Add and subtract mixed numbers with like denominators.

65 Add and Subtract Fractions

Solve word problems involving addition and subtraction of fractions and mixed numbers referring to the same whole and having like denominators.

Use fraction models, number lines, and equations to represent the word problems.

66 Understand Fraction Multiplication Multiply a fraction by a whole number.

67 Fractions as Tenths and Hundredths

Rewrite a fraction that has a denominator of 10 as an equivalent fraction with a denominator of 100.

Add two fractions with denominators of 10 or 100.

68 Renaming Fractions As Decimals

Rename fractions and mixed numbers as decimals to the hundredths. Rename decimals as fractions. Read, write, and identify decimal numbers. Understand decimal place value to the hundredths.

69 Comparing and Ordering Decimal Numbers

Use language and symbols (greater than symbol, less than symbol, and equals sign) to compare relative size of decimal numbers in the context of money. Translate problem situations into diagrams and models using decimal notation in the context of money.Compare and order decimal numbers from greatest to least and least to greatest in the context of money.

70 Dividing Whole Numbers Solve whole-‐number division problems using estimation and algorithms.

Fourth Grade

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71 Fractional Part of a Set: Denominators Through 12

Identify and name fractions as parts of a set using models, pictures, and drawings. Read, write and identify fractions with denominators including 2, 3, 4, 5, 6, 8, 10, 12. Use a visual fraction model to find fractional parts of whole numbers.

72 Comparing and Ordering Numbers to 100,000

Compare and order numbers up to a hundred thousand on a number line. Compare and order numbers using a place-‐value chart. Express the relationship between two whole numbers using inequality signs.

73 Fraction of a Set: Halves, Thirds, Fourth, Eighths

Identify and name fractions as parts of a set using models, pictures, and drawings. Read, write, and identify fractions with denominators including 2, 3, 4, and 8. Use visual fraction models to find fractional parts of whole numbers.

74 Decimal Notation Using Money

Read, write, and identify decimal notation in the context of money. Translate problem situations into diagrams and models, using decimal notation in the context of money. Understand decimal place value to the hundredths.

75 Comparing and Ordering Two Unlike Fractions

Use models to understand the relative size of commonly used fractions with unlike denominators and/or numerators. Use language and symbols (greater than symbol, less than symbol, and equals sign) to compare the relative size of two fractions.

76 Comparing and Ordering Three Unlike Fractions

Use models to understand the relative size of commonly used fractions with unlike denominators and/or numerators. Use language and symbols (greater than symbol, less than symbol, and equals sign) to compare the relative size of two fractions. Order fractions with unlike denominators and/or numerators from least to greatest and greatest to least.

77 Review Multiplying Two-‐Digit Numbers by One-‐Digit Numbers

Find the product of two-‐digit numbers by one-‐digit numbers using various strategies.

78 Finding the Least Common Denominator

Find a common denominator for two fractions with different denominators. Compare and order two fractions with different denominators.

Fourth Grade

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79 Add and Subtract FractionsFind the sum of fractions with unlike denominators.

Find the difference of fractions with unlikedenominators.

80 Add and Subtract Fractions in Word Problems

Solve word problems involving addition and subtraction of fractions referring to the same whole and having unlike denominators.

Estimate the reasonableness of solutions to word problems involving addition and subtraction of fractions referring to the same whole.

81 Fractions as Division

Understand that the fraction a/b = a Ã·∙ b.

Solve word problems involving division of whole numbers where the quotient is a fraction or mixed number.

Estimate between what two whole numbers a fraction greater than 1 is.

82 Understand Products of Fractions

Understand what multiplying by a fraction means.

Use visual fraction models to multiply a whole number by a fraction.

Use visual fraction models to multiply a fraction by a fraction.

83 Understand Multiplication as Scaling

Understand that multiplying a number times a fraction greater than 1 results in a product greater than the original number.

Understand that multiplying a number times a fraction less than 1 results in a product less than the original number.

Fifth Grade

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84 Understand Division with Unit Fractions

Understand situations that involve dividing a unit fraction by a whole number and situations that involve dividing a whole number by a unit fraction.

Apply understanding of division to find the quotient of a unit fraction divided by a whole number using a visual model.

Apply understanding of division to find the quotient of a whole number divided by a unit fraction using a visual model.

85 Divide Unit Fractions in Word Problems

Represent and solve real-‐world problems involving division of unit fractions by whole numbers using visual fraction models and equations.

Represent and solve real-‐world problems involving division of a whole number by unit fractions using visual fraction models and equations.

86 Understand Place Value

Recognize that in a multi-‐digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Identify place values through thousandths.

87Multiplication and Division of Decimals by Positive Powers of Ten

Use place value concepts to mentally multiply whole numbers and decimals by 10, 100, 1000, etc. Use place value concepts to mentally divide whole numbers and decimals by 10, 100, 1000, etc.

88 Read and Write Decimals

Read decimals to the thousandths place using base ten, number names, and expanded form.

Write decimals to the thousandths place using base ten, number names, and expanded form.

89 Compare and Order Decimal Numbers with Number Lines

Compare and order decimals using number lines and place-‐value charts. Express the relationship between two decimal numbers, using equality or inequality symbols. Compare money amounts and other real-‐world quantities using decimal notation.

90 Round decimalsUse benchmark numbers to round decimals.

Explain why a number is rounded to a given place value.

Fifth Grade

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91 Multiplying by Two-‐Digit Numbers

Use arrays to model multiplication problems. Predict the relative size of products. Multiply multi-‐digit numbers using the partial products and vertical multiplication methods.

92 Division of Whole Numbers

Fluently divide multi-‐digit numbers (4-‐digit by 2-‐digit), using the partial quotients method.Use rounding to estimate the quotient before dividing.Check answer with multiplication.

93 Add and Subtract Decimals

• Add decimals to hundredths.• Subtract decimals to hundredths.• Use models to show how to add and subtract decimals to hundredths.

94 Adding and Subtracting Unlike Fractions

Find a common denominator for fractions that have unlike denominators. Calculate the sum of fractions with unlike denominators. Calculate the difference of fractions with unlike denominators.

95 Rewriting Mixed Numbers and Fractions Greater than 1

Rewrite fractions greater than 1 as mixed numbers. Rewrite mixed numbers as fractions greater than 1.

96 Dividing Fractions Divide fractions and mixed numbers using visual models and algorithms.

97 Adding and Subtracting Decimals With Money

Solve addition and subtraction problems of decimals with money using real-‐world problems. Add decimals using money notation. Subtract decimals using money notation. Estimate the sum by rounding to the nearest dollar. Estimate the difference by rounding to the nearest dollar. Check subtraction using addition.

98 Multiplying a Whole Number and a Fraction

Model the product of a whole number and a fraction and the product of two fractions with area and number line models.

99 Multiplying FractionsCalculate the product of two fractions. Calculate the product of fractions and mixed numbers. Calculate the product of mixed numbers and whole numbers.

Fifth Grade

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100 Division of Fractions

Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

101 Four-‐Digit Dividends

Use long division to solve division problems with four-‐digit dividends by two-‐digit divisors. Check division by multiplying and adding the remainder. Predict the relative size of quotients.

102 Fluently add and subtract decimals

• Fluently add and subtract multi-‐digit decimals using place value strategies including the standard algorithm.• Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

103 Multiplication of DecimalsEstimate products of decimal numbers. Multiply multi-‐digit decimal numbers up to the thousandths.

104 Division of Whole Numbers and Decimals

Divide whole numbers with decimal quotients.Divide decimals by whole numbers.

105 Division of Decimals Divide whole numbers by decimals.Divide decimals by decimals.

106 Prime Factors

Determine the prime factors of all numbers through 100.Write the numbers as the product of their prime factors.Find the greatest common factor of two whole numbers less than or equal to 100.Find the least common multiple of two whole numbers less than or equal to 12.

107 Rational Numbers and Absolute Value

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Understand a rational number as a point on the number line.Understand ordering and absolute value of rational numbers.

108 Coordinate Plane and Absolute Value

Graph points in all four quadrants of the coordinate plane.Find distances between points with the same first coordinate or the same second coordinate, using coordinates and absolute value.Name a point given the distance to a given point.

Sixth Grade

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109 Addition and Subtraction of Positive and Negative Integers

Add and subtract positive and negative integers. Apply properties of addition as a strategy to add and subtract integers.

110 Multiplication and Division of Positive and Negative Integers

Multiply positive and negative integers. Divide positive and negative integers.

111 Expressing Fractions as Decimals Convert a rational number to a decimal using long division.

112 Multiplication and Division of Rational Numbers

Add and subtract positive and negative rational numbers. Use mental computations and estimation to check the reasonableness of an answer.

113 Addition and Subtraction of Rational Numbers

Add and subtract positive and negative rational numbers. Use mental computations and estimation to check the reasonableness of an answer.

114 Percents and Fractions* Change percents to fractions. Change fractions to percents.

115 Percents and Decimals* Change percents to decimals. Change decimals to percents.

116 Percent Concepts* Understand the meaning of percent.

Seventh Grade

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117 Estimating and Calculating Percents*

Use real-‐world situations to estimate percent. Use real-‐world situations to calculate percent of a number.

118 Properties of Integer Exponents Discover and apply the properties of integer exponents.

119 Square Roots and Cube Roots

Evaluate square roots of perfect squares less than or equal to 225. Evaluate cube roots of perfect cubes less than or equal to 125. Use symbolic notation to solve equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Understand that an equation of the form x^2 = p has two solutions, where p is a positive rational number.

120 Rational and Irrational NumbersIdentify real numbers as rational or irrational. Write rational numbers as fractions given their decimal expansions.

121 Approximating Irrational Numbers

Estimate square roots to the nearest hundredth. Compare and order rational and irrational numbers using a number line.

122 Scientific Notation

Write numbers as the product of a single digit and an integer power of ten. Write numbers expressed with scientific notation in standard notation. Compare the size of quantities written in scientific notation.

Eighth Grade

*Additional content that can be assigned as an Extra Lesson but is not part of the automated iReady lesson sequence.

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Lesson Objective

1 Identifying Two-‐Dimensional Shapes

Identify, name, and describe shapes, including circles, squares, rectangles, triangles, hexagons, and trapezoids, in contextual settings. Recognize similarities and differences between shapes.

2 Comparing Two-‐Dimensional Shapes

Recognize similarities and differences between shapes, including circles, squares, rectangles, triangles, hexagons, and trapezoids. Compare and sort shapes using a variety of attributes such as shape, size, and position.

3 Identifying Three-‐Dimensional Shapes

Associate solid three-‐dimensional figures with familiar objects. See the relationship between solid three-‐dimensional figures and two-‐dimensional plane shapes. Compare and contrast attributes of three-‐dimensional figures (roll, slide, stack). Follow directions to move three-‐dimensional objects in relation to another such as over, under, next to, on top of, below, behind, and between.

4 Spatial Relationships Identify spatial relationships including in and out, above and below, over and under, on top, behind, and between.

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5 Decomposing Two-‐Dimensional Shapes

Compose and decompose plane shapes, including making predictions about them. Build an understanding of part-‐whole relationships and properties of shapes.

6 Classifying Plane Shapes by Attributes

Identify attributes of plane shapes, including triangles, rectangles, squares, hexagons, and circles. Compare and contrast attributes of plane shapes, including number of sides and relative size.

7 Attributes of Three-‐Dimensional Shapes

Identify and compare attributes (vertices, faces, and curves) of three-‐dimensional figures, including cubes, rectangular solids, triangular solids, triangular prisms, and cylinders. Use informal and formal language to describe geometric shapes.

8 Concepts of Fractions in Two-‐Dimensional Shapes

Compose and decompose two-‐dimensional shapes to develop foundations of the concept of fractions. Predict results of combining and dividing two-‐dimensional shapes.

9 Fraction Concepts: Part of a Whole*

Develop concepts of a whole, parts, and parts that make up a whole. Make a connection between the fractional parts of real objects and the names for those parts: half, halves, fourth, and fourths.

Lesson Objective

10 Recognize and Draw Shapes

Identify triangles, quadrilaterals, pentagons, and hexagons based on the number of sides and angles they have.

Draw a shape based on specific attributes.

11 Concepts of Area in Two-‐Dimensional Shapes

Compose and decompose two-‐dimensional shapes to develop foundations for the concept of area. Compare areas of different shapes.

12 Fraction of a Whole: Halves and Fourths

Represent fractions (1/2, 1/4, 3/4) as parts of a whole using concrete materials and drawings. Relate fractions to sharing equally and dividing into equal parts.

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13 Classifying Polygons

Classify two-‐dimensional shapes according to their properties. Develop definitions of classes of shapes such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and regular polygons.

14 Divide Shapes Into Parts with Equal Areas

• Partition a shape into equal areas.

• Express the area of an equal part as a unit fraction of the area of the whole shape.

• Partition the same shape in different ways.

15 Locations on a Grid*

Understand and use the compass directions north, south, east and west. Follow multiple-‐step directions to reach a location successfully. Compose specific multiple-‐step directions.

Lesson Objective

16 Lines and AnglesIdentify lines, line segments, and rays. Define lines as parallel and perpendicular. Classify angles as straight, right, acute, and obtuse.

17 Classifying Angles Understand and identify types of lines and angles.

18 Quadrilaterals

Describe and identify different types of irregular and regular quadrilaterals, including: squares, rectangles, parallelograms, rhombuses, and trapezoids. Compare and contrast attributes of quadrilaterals.

19 Classifying TrianglesDescribe and identify different types of triangles, including: isosceles, equilateral, right, scalene, acute, and obtuse. Compare and contrast attributes of triangles.

20 Concepts of SymmetryIdentify one or more lines of symmetry in two-‐dimensional shapes. Recognize and create two-‐dimensional shapes that have lines of symmetry.

21 Line Symmetry Identify lines of symmetry in two-‐dimensional shapes. Use pattern blocks to make symmetrical designs.

22 Rotational Symmetry* Identify and describe rotational symmetry in two-‐dimensional shapes and designs.

Third

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Fourth Grade

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23 Classify Two-‐Dimensional Figures

Understand that attributes belonging to a category of two-‐dimensional figures also belong to all subcategories of that category. Classify two-‐dimensional figures in a hierarchy based on properties.

24 Analyze Patterns and Relationships

Generate a numeric sequence given a rule. Identify apparent relationships between corresponding terms of two sequences.Graph ordered pairs on a coordinate plane.

25 Two-‐Dimensional Models of Three-‐Dimensional Shapes*

Relate two-‐dimensional shapes to three-‐dimensional shapes. Recognize volume as an attribute of three-‐dimensional space. Build three-‐dimensional objects from two-‐dimensional representations or views. Draw two-‐dimensional representations or views in a grid from three-‐dimensional shapes.

Fifth Grade

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26 Polygons in the Coordinate Plane

Draw polygons in the coordinate plane, given coordinates for the vertices.

Use coordinates to find the length of a side, joining two points with the same first coordinate or the same second coordinate.

Apply these techniques in the context of solving real-‐world and mathematical problems.

27 Concepts of Area and Perimeter Find the area of rectangles, squares, and right triangles.Analyze the differences between perimeter and area.

28 Area of Parallelograms, Quadrilaterals, and Polygons

Discover the formula for the area of parallelograms, triangles, and trapezoids

Find the area of parallelograms, triangles, and trapezoids

Find the area of special quadrilaterals and complex polygons by composing and decomposing into simpler polygons.

29 Nets and Surface Area

Identify or draw 2D nets made up of rectangles and triangles that represent 3D objects.

Use nets of three-‐dimensional figures to find the surface area of rectangular and triangular prisms and pyramids.

Apply knowledge of nets of three-‐dimensional figures to solve real-‐world and mathematical problems involving spatial representation and surface area.

30 Volume with Fractional Length

Find the volume of a right rectangular prism with fractional edge lengths by filling the prism with unit cubes of the appropriate unit fraction edge lengths.

Apply the formulas V = lwh or V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-‐world and mathematical problems.

Sixth Grade

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31 Nets*

Relate two-‐dimensional shapes to three-‐dimensional shapes. Identify which geometric solids can be made from given nets. Create nets for common geometric solids.

32 Plotting Ordered Pairs*

Locate and plot ordered pairs on a coordinate grid. Use the point of origin as a point of reference. Understand and use positive and negative integers to identify points in all four quadrants.

33 Review Plotting Ordered Pairs*

Locate and plot ordered pairs on a coordinate grid. Use the point of origin as a point of reference. Understand and use positive and negative integers to identify points in all four quadrants.

Sixth Grade

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34 Scale Drawings

Given a model and a scale, find the side lengths of the real image as well as the area. Reproduce a scale drawing at a different scale. Given the side lengths of the model and the real image, calculate the scale.

35 Construction of Triangles

Construct triangles from three measures of angles or sides. Recognize when the given measures form a unique triangle. Recognize when the given measures cannot be used to form a triangle.

36 Problem Solving with Angles

Identify complementary, supplementary, adjacent and vertical angles. Use the relationship between angles to set up and solve a simple equation for an unknown angle in a figure.

37 Area and Circumference of a Circle

Understand the relationship between circumference and area of a circle. Use the formulas for area and circumference of a circle to solve problems.

38 Area of Composed Figures

Find the area of two-‐dimensional objects composed of triangles and quadrilaterals.

Apply formulas to solve real-‐world mathematical problems.

39 Surface Area of Composed Figures

Find the surface area of three-‐dimensional objects composed of cubes and right prisms. Apply formulas to solve real-‐world mathematical problems.

40 Volume of Composed FiguresFind the volume of three-‐dimensional shapes composed of cubes and right prisms. Apply formulas to solve real-‐world problems.

41 Cross-‐sections of Prism and Pyramids

Describe the intersection of a plane and a right rectangular prism. Describe the intersection of a plane and a right rectangular pyramid. Intersections may be parallel, perpendicular or neither to the base(s).

42 Circles* Model and identify radius, diameter, center, circumference, and chord.

43 Understanding Circumference*Identify the circumference of a circular object. Understand and use the formula for the circumference of a circle.

Seventh Grade

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44 Properties of Translations and Reflections

Describe the effect of translations on two-‐dimensional figures using coordinates. Describe the effect of reflections on two-‐dimensional figures using coordinates. Describe a sequence of reflections and translations that demonstrates the congruence between two figures in a coordinate plane.

45 Properties of Rotations

Describe the effect of rotations on two-‐dimensional figures using coordinates. Describe a sequence of reflections, translations and rotations that demonstrates the congruence between two figures in a coordinate plane.

46 Properties of Dilations

Describe the effect of dilations on two-‐dimensional figures using coordinates. Determine if two two-‐dimensional figures are similar. Describe the sequence of rotations, reflections, translations, and dilations that demonstrates similarity between two figures in a coordinate plane.

47 Geometric Properties involving Angles

Given two parallel lines cut by a transversal

a. identify alternate interior angles and know that they are congruent

b. identify alternate exterior angles and know that they are congruent

c. identify corresponding angles and know that they are congruent

d. Identify linear pairs and know that the sum of the angles is 180 degrees

Eighth Grade

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48 Angle Sums Properties

Make a conjecture about the sum of the interior angles of a triangle.

Use parallel lines and alternate interior angles to confirm the sum of the interior angles of a triangle. Make a conjecture about the relationship between an exterior angle of a triangle and its two non-‐adjacent interior angles. Use parallel lines and alternate interior angles to confirm the relationship between an exterior angle of a triangle and its two non-‐adjacent interior angles.

49 The Pythagorean Theorem

Show and explain an informal proof of the Pythagorean Theorem. Understand the converse of the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions.

50 Applications of the Pythagorean Theorem

Use absolute value to find the distance between two points in the coordinate plane with the same x-‐coordinates or the same y-‐coordinates. Use the Pythagorean Theorem to find the distance between two points that have different x-‐coordinates and different y-‐coordinates. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions.

51 Volume of Cylinders, Cones, and Spheres.

Understand the formula for the volume of a cylinder by comparing it to the volume of a prism. Understand the formula for the volume of a cone by comparing it to the volume of a cylinder. Understand the formula for the volume of a sphere by comparing it to the volume of a cylinder. Use the formulas for the volumes of cones, cylinders, and spheres to solve real-‐world and mathematical problems.

52 Transformations: Slides and Turns*

Recognize and apply translations or slides, and rotations or turns. Predict and describe the results of translations or slides, and rotations or turns.

53 Transformations: Flips, Slides, and Turns*

Recognize and apply reflections or flips, translations or slides, and rotations or turns. Predict and describe the results of reflections or flips, translations or slides, and rotations or turns.

Eighth Grade

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Eighth Grade

54 Tessellations* Create tessellations in order to explore pattern and shape combinations.


25


Lesson Objective

1 Measuring Time

Demonstrate an understanding of time using digital and analog clocks at hour and half-‐hour intervals. Measure elapsed time to the hour or half-‐hour. Know appropriate tools (clocks and calendar) for measuring time, days, weeks, months.

2 Time Concepts

Describe concepts of time (e.g., before or after). Estimate and measure the time of day as day or night; morning, afternoon, or evening. Know which of two daily activities takes more or less time. Identify the time (to the nearest hour) of everyday events (e.g., lunch time is 12 o'clock; bedtime is 8 o'clock at night).

Lesson Objective

3 Picture Graphs Organize, represent, and interpret data with up to three categories.

4 Elapsed Time Determine what time it will be after a given number of hours.

5 Telling Time to 5 Minutes Tell time to five-‐minute intervals.

Lesson Objective6 Telling Time to 15 Minutes ll time to fifteen-‐minute intervals.

7 Estimating Time: Choosing Units Estimate how long an everyday activity takes (minutes, hours, or days).

8 Inches, Feet, and Yards Decide which is the best unit of measurement to measure length (inches, feet or yards).

9 Using a Ruler: Inches Measure length in inches using a ruler. Add partial lengths to find the total length.

10 Length: Using a Benchmark for Inches

Measure length in inches using a benchmark (eraser, paper clip).

11 Centimeters and Meters Decide the best unit of measurement to measure length (centimeters or meters).

12 Using a Ruler: Centimeters Measure length in centimeters using a ruler.

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Lesson ObjectiveMeasurement and Data

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13 Understand Measurement with Different Units

Understand how the number of units used to measure is related to the size of the units used.

14 Compare Lengths Measure to determine how much longer or shorter one object is than another

15 Solve Problems Involving Length

Use addition and subtraction to solve word problems involving lengths.

Use models, including a number line, to solve word problems involving lengths.

16 Line plot and measuring length Measure lengths and make a line plot to show the measurements.

17 Picture Graphs and Bar Graphs Construct and interpret frequency tables, bar graphs, and picture graphs.

18 Coin Values

Know and compare money values, including the quarter, half-‐dollar, and dollar. Recognize the relative value of a penny, nickel, dime, and quarter, and show how different combinations can have the same or equal value. Determine the value of a group of coins, including pennies, nickels, dimes, and quarters, by skip counting.

19 Counting Coin Values*

Count and compare bills and coins using mixed counting to one dollar or more. Know and use decimal notation and the dollar and cent symbols for money. Solve problems using combinations of coins and bills.

20 Clocks and Calendars* Select an appropriate tool (clock or calendar) to measure time.

21 Reading Fahrenheit Thermometers* Read temperature with Fahrenheit thermometers.

22 Reading Celsius Thermometers* Read temperature with Celsius thermometers.

23 Meters and Kilometers* Decide which is the best unit of measurement for measuring length (meters or kilometers).

24 Ounces and Pounds* Decide which is the best unit of measurement (ounces or pounds).

25 Measuring Weight with a Scale*Measure the weight of objects using a virtual scale (pounds). Measure the weight of objects using virtual balance and a non-‐standard unit (apples).

Second

Grade

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26 Pennies, Nickels, and Dimes*

Know and compare the values of a penny (1 cent), a nickel (5 cents), and a dime (10 cents). Understand the concept of comparison (more/less/same) according to value. Identify the difference between heads and tails on a coin.

27 Measuring Length in Inches with a Ruler*

Measure length with standard and non-‐standard units (pennies and inches).

28 Length: Using a Benchmark for Centimeters*

Measure length in centimeters using a benchmark (paper clip, golf tee).

29 Estimating Length* Decide whether an estimate or an exact measurement is needed.

30 Line Plots* Construct and interpret line plots.

31 Counting Money in Bills and Coins*

Identify bills and coins. Know the value of bills and coins. Count bills and coins. Write money with the dollar sign.

32 Telling Time to the Minute Tell time to the minute.

33 Solve Problems About Time

Measure time intervals in minutes using clock models and number lines.Solve word problems involving addition of time intervals in minutes.Solve word problems involving subtraction of time intervals in minutes.

Second

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34 Finding Elapsed Time to Solve Problems Use elapsed time to solve real-‐world problems.

35 Solve Problems About Liquid Volume

Understand the relative sizes of a liter and a milliliter.Use unit size to measure and estimate liquid volume.Solve one-‐step word problems involving liquid volume.

36 Solve Problems about MassUnderstand mass and measure mass using grams and kilograms.Solve one-‐step word problems involving mass.

37 Scaled Pictographs and Bar Graphs

Construct scaled picture graphs given a frequency table. Construct scaled bar graphs given a frequency table. Construct a frequency table from a bar or picture graph.

38 Interpreting Bar Graphs and Pictographs

Construct and interpret frequency tables, scaled bar graphs, and pictographs. Compare data and draw conclusions.

39 Measure Length and Plot Data on Line Plots

• Use a ruler to measure objects to the nearest ½ inch.• Use a ruler to measure objects to the nearest ¼ inch.• Display measurement data in a line plot.

40 Using a Ruler: Centimeters or Inches Use a ruler to measure length.

41 Understand Area

Recognize area as an attribute of plane figures.Understand how to measure area by covering a shape with unit squares and counting the squares.Find the area of shapes using unit squares (non-‐standard units, square inch, square foot).

42 Add and Multiply to Find Area

Understand that multiplying side lengths of a rectangle provides the same results as tiling it and counting the units.Multiply side lengths to find areas of rectangles with whole-‐number side lengths in the context of solving real world and mathematical problems.Decompose rectilinear shapes formed by rectangles to find the area.Use the distributive property to find the area of combined rectangles.

43 Connect Area and Perimeter

Understand the difference between perimeter and area.Use side lengths to find the perimeter of a shape.Find an unknown side length given the perimeter of a shape.

Third

Grade

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44 Double-‐Bar Graphs Construct and interpret double-‐bar graphs. Compare data and draw conclusions.

45 Months of the Year* Know the order of the 12 months of the year.46 Reading Dates* Find a given date in a calendar (month/day/year).

47 Reading Days of the Week* Read a calendar and identify the month, the day of the week, and the date.

48 Elapsed Time to the Minute* Determine the duration of intervals of time.49 Estimating Time: Minutes* Decide if the estimated time is reasonable.

50 Fahrenheit Temperature* Associate the weather with temperature using Fahrenheit units.

51 Celsius Temperature* Associate the weather with temperature using Celsius units.

52 Using a Balance Scale: Pounds* Find out how much objects weigh in pounds and ounces using a balance scale.

53 Comparing Weight in Pounds* Compare the weight of two objects by estimation and decide which weighs more.

54 Using a Balance Scale: Ounces* Measure weight in ounces using a benchmark (spoon).

55 Equivalent Capacity: Cups and Pints*

Use the equivalence of cups and pints to make the amount of liquid equal.

56 Equivalent Capacity: Cups, Pints, Quarts, Gallons*

Use the equivalence of cups, pints, gallons, and quarts to make the amount of liquid equal using a conversion chart.

57 Liters and Milliliters* Choose the more appropriate unit to measure liquid in a container (liters or milliliters).

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58 Solve Word Problems Involving Measurement

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.Use the four operations to solve word problems involving distances, liquid volumes, and weights and masses of objects, including problems involving simple fractions or decimals.Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

59 Making Change Calculate the correct change from a purchase.

60 Express Measurements in Larger Units

• Convert measurements from a larger unit to a smaller unit within the same system.

• Create a conversion table showing equivalent measurements within the same system.

61 Understanding Area and Surface Area

Understand area. Apply formulas for the area of a rectangle, square, parallelogram, and triangle. Find the area of an irregular polygon.

62 Understanding PerimeterUnderstand the steps needed to obtain the measurement of perimeter. Add the measurement of each side of a shape to obtain the perimeter.

63 Add and Subtract Angle Measures

Recognize that an angle is a geometric shape measured in degrees. Identify angle measures and show that angles can be put together to form larger angles and broken up into two or more smaller angles.Use addition and subtraction to find unknown angle measures

64 Using a Protractor Measure angles using a protractor.

65 Interpreting Line PlotsConstruct line plots to display a data set of measurements in fractions of a unit. Read and analyze line plots.

66 Temperature: Fahrenheit and Celsius*

Estimate approximate temperatures in Celsius and Fahrenheit. Read a thermometer to the nearest degree. Understand the difference between Celsius and Fahrenheit scales.

67 Cups, Pints, Quarts, and Gallons* Know the equivalences of cups, pints, quarts, and gallons.

Fourth Grade

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68 Understanding Volume*Identify and determine the volume of a rectangular prism. Understand the formula for volume of a rectangular prism and when to use it.

69 Comparing Feet, Yards, and Miles*

Decide which is the best unit of measurement for measuring length (feet, yards, or miles).

Lesson Objective

70 Solve Word Problems Involving Conversions

Solve multi-‐step real world problems that require expressing measurements in larger or smaller units within a measurement system.

71 Line plots with fractions

Make a line plot to display a data set of measurements in fractions of a unit.Add, subtract, multiply, and divide fractions to solve problems that contain fraction data sets presented in line plots.

72 Understand and Measure Volume

Understand the concept of volume as an attribute of solid figures. Find the volume of right rectangular prisms with whole number edge lengths by counting unit cubes. Understand that a unit cube can be different sizes depending on which unit of measurement the cube represents.Find the volume of a rectangular prism with whole-‐ number side lengths using addition and multiplication.

73 Find Volume of Rectangular Prisms Using Formulas

Solve real world problems involving volumes of right rectangular prisms by multiplying the height by the area of the base or using the formula V = l x w x h. Use addition to find volumes of solid figures composed of two non-‐overlapping right rectangular prisms.

74 Review Volume*Identify and determine the volume of a rectangular prism. Understand the formula for volume of a rectangular prism and when to use it.

75 Maps and Scales*Understand and apply the use of the compass rose on a map. Understand and apply the use of scale on a map. Understand and apply the use of math legends.

76 Line Graphs and Double-‐Line Graphs*

Construct and interpret line graphs and double-‐line graphs.


Fifth Grade

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Fifth Grade

77 Adding and Subtracting Decimals to Solve Problems*

Determine the operation needed to solve real-‐world problems involving addition and subtraction of decimals. Use problem-‐solving strategies to solve real-‐world problems involving addition and subtraction of decimals.

Lesson Objective

78 Understanding Statistics

• Understand that data generated from statistical questions will vary.

• Identify the difference between a statistical and non-‐statistical question.

• Understand that data distribution can be viewed by its center, spread, and overall shape

79 Box Plots

Display numerical data in a box plot.

Describe what kinds of inferences can be drawn from a box plot.

Find, use, and interpret median and the interquartile range.

80 Dot Plots

Display numerical data in dot plots.

Describe what kinds of inferences can be drawn from a dot plot.

Describe overall pattern of data in a dot plot.

81 Histograms

Display numerical data on a histogram.

Describe what kinds of inferences can be drawn from a histogram.

Describe the overall pattern of data in a histogram.

82 Choosing Data Displays Understand what types of data are best displayed in a dot plot, histogram, or box plot.

Sixth Grade


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83 Random Samples Recognize when a sample is representative of a population.

84 Making Statistical Inferences Use data from a sample(s) to make inferences about the population.

85 Using Mean and Mean Absolute Deviation to Compare Data

Calculate the mean absolute deviation of a set of data. Compare the means of two populations with similar variability using their mean absolute deviations. Visually compare the means of two populations with similar variability by using their dot plots. Calculate the difference in means of two populations and determine if it is likely that the difference is the result of chance.

86 Using Measures of Center and Variability to Compare Data

Visually compare the medians of two samples by using their boxplots. Compare the medians of two samples using their quartiles. Calculate the difference in medians of two samples and determine if it is meaningful.

87 Probability Concepts

Explain why the probability of an event cannot be greater than 1. Explain why events that are likely to occur have probabilities close to 1, unlikely to occur have probabilities near 0, etc. Evaluate probabilities to determine how likely an event is to occur.

88 Experimental Probability

Approximate the probability of a chance event occurring by observing its behavior in the long run. Predict the approximate relative frequency of a chance event, given the probability of the event occurring.

89 Probability ModelsCreate a probability model, given a table of data, a description of an event, or a diagram. Compare probability models to data collected through observation.

90 Probability of Compound Events Find probabilities of compound events using organized lists, tables and tree diagrams.

91 Simulations of Compound Events Design and use a simulation to observe frequencies of compound events.

92 Combinations*

List the possible combinations or outcomes. Use a tree diagram to find possible outcomes. Use the Counting Principle to calculate the number of combinations or outcomes.

Seventh Grade

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93 Scatter Plots

Construct a scatterplot using two sets of quantitative data. Identify clusters and outliers in a scatterplot. Determine if there is a linear or non-‐linear association in a scatterplot. Determine if a linear association is positive or negative in a scatterplot.

94 Linear ModelsUse a straight line to model a relationship between two quantitative variables. Informally evaluate the fit of the line by judging the closeness of data points to the line.

92 Problem Solving with Linear Models

Interpret the slope and intercepts of a given equation of a linear model to solve problems.

Eighth Grade


35


Lesson Objective

1 Complements of 10 Find complements of 10. Understand that the number ten can be represented in a variety of equivalent forms.

2 Joining Sets to Add

Demonstrate and describe the effect of putting together sets of objects. Solve combining and joining addition problems. Use the term "plus" and the plus (addition) symbol to describe addition problems. Use the term "equal" to describe equal sets and to recognize the equals sign.

3 Taking Away to Subtract

Solve "take away" subtraction problems. Use the term "minus" and the minus (subtraction) symbol to describe subtraction situations. Use the term "equal" to describe equal sets and to recognize the equals symbol. Write number sentences for subtraction situations.

4 Acting Out Addition and Subtraction

Act out number stories using objects and pictures. Count forward to add 1 and 2. Count backward to subtract 1 and 2.

5 Identifying Patterns

Identify, duplicate and extend, or follow simple pictorial, rhythmic and symbolic linear patterns. Tell what comes next in a linear pattern. Find the missing element of a linear pattern. Identify the repeating part of a linear pattern.

6 Addition Number Sentences

Understand the meaning of addition. Build number sentences to represent addition problems. Recognize that the order of addends does not affect the sum. Solve addition problems.

7 Counting On to Solve Addition Problems

Solve addition problems using "counting on". Recognize that the order of addends does not affect the sum.

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Lesson ObjectiveAlgebra and Algebraic Thinking

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8 Addition FactsCombine sets to form a set of equivalent size. Use number sentences to describe addition situations. Identify missing addends.

9 Addition Facts for 10 Use number sentences to describe addition situations. Find the combinations of 10. Identify missing addends.

10 Addition Facts: Doubles Identify doubles addition facts. Solve addition problems using doubles.

11 Subtraction Concepts: Separation

Understand the meaning of subtraction in separation situations. Build number sentences to represent subtraction problems and solve them. Solve problems using subtraction. Check the solution using addition.

12 Subtraction Concepts: Part-‐Part-‐Whole

Understand the meaning of subtraction in part-‐part-‐whole situations. Build number sentences to represent subtraction problems. Solve problems using subtraction. Check the solution using addition.

13 Subtraction Concepts: Comparison

Understand the meaning of subtraction in comparison situations. Build number sentences to represent subtraction problems. Solve problems using subtraction.

14 Counting Back to Subtract 1, 2, or 3

Solve basic subtraction facts using concrete objects and a number line and the strategy of counting back. Count back to subtract 1, 2 or 3. Use number sentences to describe subtraction situations.

15 Using Length to Represent Subtraction

Solve basic subtraction facts using concrete objects and the concept of length. Use number sentences to describe subtraction situations involving comparisons of length. Solve number sentences to find the difference.

16 Addition and Subtraction Fact Families

Practice basic addition and subtraction facts. Know the related facts that represent the inverse relationship between addition and subtraction. Complete addition and subtraction fact families.

17 Counting by 2s* Group objects in sets of two. Count orally to 20 by 2s using a chart and concrete materials.

18 Counting On to Add* Recognize, describe, and extend patterns.

19 Counting Back to Subtract*

Understand the meanings of addition. Build number sentences to represent addition problems. Solve addition problems using "counting on". Recognize that the order of addends does not affect the sum.

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20 Adding Three Numbers*Develop strategies for adding three numbers. Solve addition problems with three sets. Use number sentences to describe addition situations.

21 Describing and Extending Patterns* Recognize, describe, and extend patterns.

22 Odd and Even NumbersDemonstrate the difference between odd and even numbers using concrete objects or drawings. Recognize odd and even numbers up to 100.

23 Addition Facts: Doubles Plus One or Minus One

Identify and use doubles to find sums. Decompose numbers into pairs of addends. Identify and use "double plus" and "double minus" strategies to find sums.

Lesson Objective

24 Addition Facts: Using Sums of 10Identify and use combinations of ten to find sums. Decompose numbers into pairs of addends. Identify and use the "make ten" strategy to find sums.

25 Adding Three or More NumbersAdd three or more numbers. Decompose a number into three or more addends. Solve problems by decomposing numbers.

26 Subtraction in Separation Situations

Understand the meaning of subtraction in separation situations. Build number sentences to represent subtraction problems and solve them. Solve problems using subtraction. Check the solution using addition.

27 Subtraction in Part-‐Part-‐Whole Situations

Understand the meaning of subtraction in part-‐part-‐whole situations. Build number sentences to represent subtraction problems and solve them. Solve problems using subtraction. Check the solution using addition.

28 Subtraction in Comparison Situations

Understand the meaning of subtraction in comparison situations. Build number sentences to represent subtraction problems and solve them. Solve problems using subtraction.

29 Subtraction Facts: Counting Back

Solve basic subtraction facts using concrete objects and a hundreds chart and the thinking strategy of counting back. Count back to subtract 1, 2, or 3. Use number sentences to describe subtraction situations.

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30 Subtraction Facts: Counting Up

Solve subtraction facts using counting up. Use number sentences to describe subtraction situations. Know the related facts that represent the inverse relationship between addition and subtraction.

31 Review Addition and Subtraction Fact Families

Practice basic addition and subtraction facts. Know the related facts that represent the inverse relationship between addition and subtraction. Complete addition/subtraction fact families.

32 Relating Addition and Subtraction Facts

Practice basic addition and subtraction facts. Know the related facts that represent the inverse relationship between addition and subtraction. Complete addition and subtraction fact families.

33 Grouping Objects by 2s or 5s to 100

Count a group of objects by 2s, by 5s, and by 10s to 100. Count a set of objects by grouping in tens, fives, and ones. Count on from ten and decade numbers. Estimate how many groups of five or ten are in a given number of objects less than 100.

34 Add Using Arrays

-‐Interpret an array up to 5 rows with 5 items in each row.

-‐Calculate the number of items in a array using repeated addition and skip-‐counting.

-‐Write an equation to express the total number of items in an array.

35 Money Problems: Addition and Subtraction

Select and use appropriate operations to solve problems involving money. Solve real-‐world problems involving addition and subtraction. Use addition and subtraction fact strategies to solve problems.

36 Solve Two-‐Step Problems

-‐Use addition and subtraction to solve two-‐step problems.

-‐Use drawings and/or equations with a symbol for the unknown number to represent two-‐step problems.

37 Numerical Patterns and Relationships

Use function machines and input-‐output tables to interpret mathematical relationships. Apply the appropriate rule to complete an input-‐output table. Determine how a change in one variable relates to a change in a second variable.

Second

Grade

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38 Counting by 5s* Group objects in sets of five. Count orally to 100 by 5s using a chart and concrete materials.

39 Subtracting to Solve Real-‐World Problems*

Solve real-‐world problems using subtraction. Estimate the results of whole-‐number computations. Find the difference of two 3-‐digit numbers using the standard algorithm. Develop and use strategies to judge the reasonableness of the results of whole-‐number computations. Use addition to check the difference.

40 Problem Solving and Number Sense*

Understand the effects of addition and subtraction on whole numbers. Solve number problems by selecting the proper operation.

41 Understand Multiplication, Part 1

-‐Understand that the symbol x means "groups of," and problems such as 5 x 7 refer to 5 groups of 7.

-‐Interpret a multiplication problem situation using pictures, objects, words, numbers, and equations.

42 Understand Multiplication, Part 2

-‐Understand that the symbol x means "groups of," and problems such as 5 x 7 refer to 5 groups of 7. -‐Interpret a multiplication problem situation using arrays and equations.

-‐Understand that numbers can be multiplied in any order and the product will be the same (commutative property of multiplication).

Lesson Objective

Third

Grade

43 Use Order and Grouping to Multiply

-‐Understand that numbers can be multiplied in any order and the product will be the same.

-‐Understand that three or more factors in a problem can be grouped in different ways and the product will be the same.

-‐Apply properties of operations as strategies to multiply

Algebra and Algebraic Thinking

Second

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44 Understand Division, Part 1

Understand the relationship between multiplication and division. Recognize and write division sentences, including those involving quotients with remainders. Find a quotient using the concept of sharing equal groups. Use multiplication to check division.

45 Understand Division, Part 2

Understand division as separating a total into equal groups and finding the number of groups.

Understand and use the relationship of multiplication and division.

Describe stories or contexts for division expressions, such as 24 x 4.

Represent and solve division problems.

46 Using Fact Families to Solve Division Problems

Use fact families to find missing numbers in basic division facts.

47 Multiplication and Division Fact Families

-‐ Use drawings and symbols to represent and solve a multiplicative comparison problem.

-‐ Use an equation to solve for the unknown in a multiplicative comparison problem.

48 Multiplication Fact ReviewDemonstrate the meaning of multiplication using arrays, the multiplication fact table, and area. Solve multiplication basic facts.

49 Solve One-‐Step Word Problems Using Multiplication and Division

-‐Identify the elements and the relationship between them in a multiplication or division word problem.

-‐Solve multiplication and division word problems involving equal groups and using strategies such as arrays, numbers lines or pictures.

50 Money Problems: Addition, Subtraction, Multiplication

Select and use appropriate operations to solve two-‐step and multi-‐step problems involving money. Solve real-‐world problems involving addition, subtraction, and multiplication. Use addition, subtraction, and multiplication fact strategies to solve problems.

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Grade

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51 Solve Two-‐Step Word Problems Using the Four Operations

-‐Determine operations needed to solve two-‐step word problems.

-‐Model two-‐step problems with four operations using a variety of representations, including equations with a variable.

-‐Solve two-‐step problems with four operations.

-‐Assess the reasonableness of answers.

52 Understand Patterns

-‐ Use number properties to find and explain patterns.

-‐ Use knowledge of even and odd numbers to find and explain patterns.

53 Multiplication Concepts: Equal Groups*

Recognize equal groups in multiplication. Understand multiplication as the total of equal groups. Recognize and write multiplication sentences.

54 Multiplication Sentences and Equal Groups*

Recognize equal groups in multiplication. Understand multiplication as the total of equal groups. Recognize and write multiplication sentences.

55 Division Concepts: Sharing Equal Groups*

Find a quotient using the concept of sharing equal groups. Recognize and write division sentences. Identify a remainder in a division problem.

56 Multiplication Concepts: Arrays*

Recognize and write multiplication sentences. Represent multiplication using objects in a rectangular array. Recognize that the order of two factors does not affect their product. Build knowledge of multiplication facts.

57 Multiplication Concepts: Skip Counting*

Solve multiplication problems using skip counting on a number line. Know multiplication facts having 3, 4, and 5 as factors.

58 Using Area for Multiplication: Facts for 3, 4, and 5*

Solve multiplication problems using area. Write multiplication sentences and find the product. Know multiplication facts having 3, 4, and 5 as factors.

59 Using Area for Multiplication: Facts for 6, 7, and 8*

Solve multiplication problems using area and the strategy of 'breaking up' factors (distributive property). Know multiplication facts having 6, 7, and 8 as factors.

60 Division Concepts: Area and Facts for 3, 4, and 5*

Solve division problems using a hundreds chart and area. Know division facts having 3, 4, and 5 as divisors. Check the solution of division problems using multiplication.

Third

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61 Division Concepts: Area and Facts for 6, 7, and 8*

Solve division problems using a hundreds chart and area. Know division facts having 6, 7, 8, and 9 as divisors. Check the solution of division problems using multiplication.

62 Equations and Numerical Relationships*

Express mathematical relationships using equations. Solve equations or find the missing number using related facts.

63 Understand Multiplication

-‐ Solve word problems that indicate a multiplicative comparison.

-‐ Write an equation to represent a multiplicative comparison indicated by a word problem

64 Multiplication and Division in Word Problems

-‐ Use drawings and symbols to represent and solve a multiplicative comparison problem.

-‐ Use an equation to solve for the unknown in a multiplicative comparison problem.

Lesson Objective65 Finding Factors Identify and name factors of a given number.66 Finding Multiples Identify and name multiples of a given number.67 Prime and Composite Numbers Identify prime and composite numbers.

68 Solve Multi-‐Step Problems Solve multi-‐step word problems. Use estimation strategies to make sure the answer makes sense

69 Number and Shape Patterns

• Use rules to generate or extend a number or shape pattern.•Analyze and describe features in number and shape patterns

70 Properties of Multiplication* Learn and use the properties of multiplication: zero and identity; commutative, associative, and distributive.

71 Divisibility Rules* Understand and apply the rules of divisibility for 2, 3, 5, 9, and 10.

72 Identifying Factors* Use a model and knowledge of multiplication facts to determine the factors of whole numbers through 100.

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Grade

Fourth Grade

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73 Identifying Multiples*Identify multiples of whole numbers with products to 60. Use tables and charts to determine multiples of whole numbers 1 through 10.

74 Write and Evaluate Expressions

-‐Evaluate expressions containing parentheses.

-‐Write numerical expressions containing parentheses.

-‐Interpret numerical expressions without evaluating them.

75 Writing Function RulesUse function tables to interpret mathematical relationships. Express functions as equations using the variables x and y.

Lesson Objective

76 Applying a Function Rule to Complete a Table

Use function tables to interpret mathematical relationships. Apply the appropriate rule to complete a function table. Determine how a change in one variable relates to a change in a second variable.

77 Prime Factorization* Express a whole number as a product of its prime factors.

78 Review Divisibility Rules* Understand and apply the rules of divisibility for 2, 3, 4, 5, 6, 9, and 10.

79 Describing Numerical Relationships*

Use pictures, models, tables, and number sentences to interpret mathematical relationships. Apply the appropriate rule to complete a chart. Determine how a change in one variable relates to a change in a second variable.

80 Concept of Ratio

Understand the concept of a ratio.Use ratio language to describe a ratio relationship between two quantities.Recognize a:b and a/b as alternative notations for ratios. Write a ratio equivalent to a given ratio.

81 Concept of RateUnderstand the concept of a unit rate Use rate language in the context of a ratio relationship.Solve rate and unit rate problems.

Fourth Grade

Order

Fifth Grade

Algebra and Algebraic Thinking

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Order

82 Concept of PercentFind a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part and the percent.

83 Problem Solving with Ratio and Percent

Use ratio to solve real-‐world and mathematical problems.Use percent to solve real-‐world and mathematical problems.

84 Numerical Expressions and Order of Operations

Read and write expressions that describe situations as well as operations. Read and write numerical expressions involving whole-‐number exponents. Apply algebraic order of operations to evaluate numerical expressions involving multiple operations.Use standard terms (sum, term, product, factor, quotient, coefficient) to describe numerical expressions.

85 Algebraic Expressions

Write and evaluate algebraic expressions involving whole-‐number exponents.

Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate algebraic expressions.

86 Equivalent ExpressionsApply the properties of operations to generate equivalent expressions. Identify when two expressions are equivalent.

87 Solving Equations

Solve simple one-‐step equations by using inverse operations and the properties of equality. Use substitution to determine whether a given number makes an equation true.

88 Using Equations to Solve Problems

Solve real-‐world and mathematical problems by writing and solving equations of the form x + p = q, x -‐ p = q, and px = q for cases in which p, q, and x are all nonnegative rational numbers.

Sixth Grade

45



Order

89 Solving Inequalities

Use substitution to determine whether a given number in a specified set makes an inequality true.Write an inequality of the form x > c, x >= c, x < c, or x <= c to represent a real-‐world or mathematical problem.Represent solutions of inequalities on a number line diagram.Recognize that inequalities of the form x > c, x >= c, x < c, or x <= c have infinitely many solutions.

90 Relationships Between Variables in Equations

Write equations using variables to represent two quantities in a real-‐world problem that change in relationship to one another.Analyze the relationship between the dependent and independent variables, using graphs and tables, and relate these to the equation.

91 Using a Function Table

Use pictures, models, tables, and equations to interpret mathematical relationships. Apply the appropriate rule to complete a function table to determine how a change in one variable relates to a change in a second variable.

92 Ratio Concepts*Use a ratio to compare quantities. Use multiplication to find equivalent ratios. Use division to find equivalent ratios.

93 Proportions* Solve proportions using cross-‐products.

94 Finding the Greatest Common Factor*

Find the common factors of two numbers. Determine the greatest common factor of two numbers.

95 Equations and Inequalities*

Demonstrate an understanding of the concept of a variable. Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given. Know and understand that equals added to equals are equal. Know and understand that equals multiplied by equals are equal.

96 Problem Solving with Rational Numbers

Solve multi-‐step real-‐world problems by finding the sums, products and/or quotients of rational numbers in any form (fractions, decimals and/or percentages). Use mental computations and estimation to check the reasonableness of an answer.

97 Ratios involving Complex Fractions

Simplify complex fractions. Determine unit rates associated with ratios of fractions.

Sixth Grade

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Order

98 Recognizing Proportional Relationships

Recognize proportional relationships between quantities using tables or graphs in the coordinate plane. Identify the constant of proportionality (unit rate) in a proportional relationship in tables, graphs and/or equations.

99 Equations for Proportional Relationships

Represent a proportional relationship as a linear equation. Explain what a point on the graph of a proportional relationship means in context of the situation.

100 Problem Solving with Proportional Relationships

Use proportional relationships to solve multistep percent problems, including percent increase and percent decrease.

101 Linear Expressions

Use the distributive property to expand linear expressions with rational coefficients. Use the GCF of two terms to factor a linear expression with rational coefficients. Simplify a linear expression by combining like terms, as well as using the associative, commutative, and distributive properties.

102 Problem Solving with Equations

Solve single-‐variable linear equations with rational coefficients. Use variables to represent quantities in a real-‐world or mathematical problem, and construct simple equations to solve the problem.

103 Problem Solving with Inequalities

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

104 Concept of a Function

Understand that a function is a rule that assigns to each input exactly one output. Identify whether a relationship is a function or not, from a graph, equation or table of values.

105 Linear Functions Determine if a function is linear or non-‐linear. Interpret the equation y = mx + b as defining a linear function.

Seventh Grade

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Order

106 Linear Functions, Rate of Change and Initial Value

Determine and interpret the rate of change from the description of a relationship, two coordinates from a table, or two coordinates from a graph. Determine and interpret the initial value from the description of a relationship, a table of values, or a graph.

107 Properties of Functions Compare properties of two functions each represented in a different way.

108 Using a Graph to Analyze a Functional Relationship

Sketch a graph of a function from a verbal description. Describe qualitatively the functional relationship between two quantities by analyzing a graph.

109 Representing Proportional Relationships

Interpret the unit rate of a proportional relationship as the slope of its graph. Understand that the y-‐intercept is zero for proportional relationships. Compare two different proportional relationships represented in different ways.

110 Linear Equations and Slope

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-‐vertical line. Understand that slope is a rate of change and the y-‐intercept is an initial value. Use the slope and y-‐intercept to derive an equation for a linear function. Identify the slope and y-‐intercept from an equation or graph. Relate/match an equation of the form y = mx + b to the corresponding line in the coordinate plane.

111 Solving Linear Equations

Solve linear equations with integer coefficients in one variable with one solution, infinitely many solutions, or no solutions. Use properties and the order of operations to collect like terms and simplify a linear equation.

112 Solving Linear Equations with Rational Coefficients

Solve linear equations with rational coefficients in one variable with one solution, infinitely many solutions, or no solutions. Use properties and the order of operations to collect like terms and simplify a linear equation.

113 Systems of Linear Equations Solve systems of linear equations by graphing the equations.

114 Solving Systems of Linear Equations Algebraically

Estimate solutions to systems of linear equations by graphing the equations. Solve systems of equations in two variables algebraically using substitution (rational solutions).


Eighth Grade

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numbersandoperations order lesson objective · forrelease6.0.3 8/12/15 lesson objective...

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