EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Number and numeration

1.1.1

 

Understand the concepts and symbolic representations of mixed numbers, proper and improper fractions, and decimals.  W

 

EXAMPLES

 

EX         Represent mixed numbers, proper and improper fractions, and decimals using words, pictures, models, and/or numbers.

EX         Make a model when given a symbolic representation or write a fraction or decimal when given a number line, picture, or model.

EX         Explain how the value of a fraction changes in relationship to the size of the whole. 

EX         Explain the value for a given digit and/or show how to read and write decimals to at least the thousandths place. 

EX         Represent improper fractions as mixed numbers and mixed numbers as improper fractions. 

 

Understand the concept and symbolic representations of integers as the set of natural numbers, their additive inverses, and 0.  W

 

EXAMPLES

 

EX         Explain or illustrate integer values using words, pictures, models, and symbols. 

EX         Explain the meaning of integers and gives examples.

EX         Locate the additive inverse of a given integer on a number line.

 

Understand the concept and symbolic representation of fractions, decimals, and integers.  W

 

 

EXAMPLES

 

EX         Explain the meaning of fractions, decimals, and integers and give examples.

EX         Convert between equivalent forms of fractions, decimals, or percents.

EX         Explain or demonstrate that fractions may have multiple equivalent representations.

EX         Explain or demonstrate that decimals may have multiple equivalent representations.

 

Understand the concept and symbolic representation of rational numbers.  W

 

 

 

EXAMPLES

 

EX         Explain the meaning of integers raised to whole number exponents and provide examples. 

EX         Explain the meaning of an integer squared and provide examples.

EX         Explain the meaning of square root of a whole number and provide examples.

 

Understand and use scientific notation.  W

 

 

 

 

EXAMPLES

 

EX         Explain the meaning of scientific notation using words, pictures, symbols, or numbers. 

EX         Express and/or use equivalents among fractions, decimals, percents, integers, positive integer exponents, square roots, and/or numbers written in scientific notation.

EX         Read and translate numbers represented in scientific notation from calculators and other technology, texts, tables, and charts.

EX         Use scientific notation in a given situation.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Number and numeration

1.1.2

 

Understand the relative values of non‑negative fractions or decimals.  W

 

 

EXAMPLES

 

EX         Order decimals, proper and improper fractions, and/or mixed numbers with denominators 2, 3, 4, 5, 6, 10, 12, and/or 15 using symbolic representations, number lines, or pictures.

EX         Identify and/or explain the relationship among equivalent decimals and fractions.

EX         Explain why one fraction is greater than, less than, or equal to another fraction. 

EX         Explain why one decimal is greater than, less than, or equal to another decimal. 

EX         Show how factors and multiples can be used to name equivalent fractions. 

 

Understand the relative values of integers and non‑negative fractions, decimals, and percents.  W

 

EXAMPLES

 

EX         Order different representations of fractions, decimals, and/or percents.

EX         Show and determine equivalence between non‑negative integers, fractions, decimals, and percents using words, pictures, models, and symbols. 

EX         Order integers, fractions, decimals, and/or percents and explain why one number is greater than, less than, or equal to another. 

EX         Explain when a fraction, decimal, or percent of one whole is not the same as the same fraction, decimal, or percent of a different whole.

 

Understand the relative values of decimals, fractions, or integers.  W

 

 

EXAMPLES

 

EX         Order decimals, fractions, and/or percents and explains why one number is greater than, less than, or equal to another number.

EX         Order decimals, fractions and/or integers based on a picture of a real world model, locations on a number line, or symbolic representation.

EX         Explain why one integer, fraction, decimal, or percent is greater than, less than, or equal to another given number.

 

Understand the relative values of rational numbers.  W

 

 

 

EXAMPLES

 

EX         Order rational numbers including integers, whole number powers, and square roots, and explain why one rational number is greater than, equal to, or less than another.

EX         Order rational numbers including integers, whole number powers, and square roots based on a picture of a real world model, locations on a number line, or symbolic representation.

EX         Explain why one given rational number including integers, whole‑number powers, and square roots is greater than, equal to, or less than another rational number.

 

 

Maintain Skills

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Number and numeration

1.1.3

 

Understand and apply the concept of divisibility including primes, composites, factors, and multiples.  W

 

 

EXAMPLES

 

EX         Use the concepts of odd and even numbers to check for divisibility.

EX         Illustrate prime or composite numbers by creating a physical model.

EX         Identify prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite. 

EX         Explain how to find the least common multiple (LCM) and greatest common factor (GCF) of two numbers. 

EX         Use factors, multiples, and prime and composite numbers in a variety of situations.

EX         Factor a number into its prime factorization or into factor pairs.

EX         Explain or show whether one number is a factor of another number.

EX         Explain or demonstrate why a number is prime or composite.

 

Understand and use properties of addition and multiplication on non‑negative decimals and fractions.  W

 

 

EXAMPLES

 

EX         Illustrate and explain the commutative, associative, and identity properties of addition and multiplication and the zero property of multiplication on non‑negative decimals and fractions.

EX         Use addition and multiplication properties to assist in computations.

EX         Determine whether a computation is reasonable based on application of the commutative, associative, and identity properties of addition and/or multiplication. 

Understand and use the inverse property of addition on integers (W) and the inverse property of multiplication on non‑negative decimals or fractions. 

 

EXAMPLES

 

EX         Use the inverse relationship between multiplication and division to simplify computations.

EX         Use the inverse properties of addition and multiplication to simplify computations and explain why they work with integers, fractions, and decimals.

EX         Use, represent, or evaluate an application of the commutative, associative, and/or identity properties of addition on non‑negative decimals or fractions.

EX         Use, represent, or evaluate an application of the commutative associative, identity, and/or zero properties of multiplication on non‑negative decimals or fractions.

 

Understand and use the distributive property and the properties of addition and multiplication on rational numbers.  W

 

EXAMPLES

 

EX         Demonstrate the distributive property of multiplication over addition using an area model or picture. 

EX         Use the distributive property to simplify expressions that include integers.

EX         Use the distributive property to factor expressions.

EX         Represent or evaluate the application of the addition and multiplication properties on rational numbers including integers.

EX         Use the addition and multiplication properties, including the distributive property, to assist with computations.

 

 

Maintain Skills

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Number and numeration

1.1.4

 

 

Understand the concepts of ratio and percent.  W

 

 

 

EXAMPLES

 

EX         Write or show and explain ratios in part/part and part/whole relationships using words, objects, pictures, models, and/or symbols.

EX         Represent equivalent ratios using objects, pictures, or symbols. 

EX         Represent equivalent percentages using objects, pictures, and symbols. 

EX         Express or represent percent as a ratio based on 100 equal size parts of a set.

EX         Explain ratio and percents and give examples of each.  

EX         Create a ratio equivalent to a given ratio to determine an unknown value for a dimension or a number of events or objects.

 

Understand the concept of direct proportion.  W

 

 

 

EXAMPLES

 

EX         Explain or illustrate the meaning of a ratio, percent or proportion. 

EX         Express proportional relationships using objects, pictures, and symbols. 

EX         Complete or write a proportion for a given situation. 

EX         Predict a future situation using direct proportion

EX         Represent equivalent ratios and/or percents using pictures, diagrams, or symbols.

EX         Determine or use a ratio, percent, or proportion in a given situation.

 

Apply the concepts of ratio, percent, and direct proportion.  W

 

 

EXAMPLES

 

EX         Determine an unknown value for a dimension or a number of events or objects using ratio or proportion.

EX         Determine an unknown value for a dimension or a number of events or objects using percents.

EX         Select and use the most advantageous representation of ratios or percents in a given situation.

EX         Determine a ratio or percent in a given situation.

 

Understand the concept of inverse proportion and apply direct and inverse proportion.  W

 

EXAMPLES

 

EX         Explain, illustrate, or describe examples of inverse proportion. 

EX         Determine whether a real‑world problem involves direct or inverse proportion.

EX         Use direct or inverse proportion to determine an unknown number of objects or an unknown value in a given situation.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Computation

1.1.5

 

Understand the meaning of addition and subtraction of non‑negative decimals and fractions.  W

 

 

EXAMPLES

 

EX         Represent addition and subtraction of fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10. 

EX         Represent or explain addition and subtraction of non‑negative decimals through thousandths using words, pictures, models, or numbers.

EX         Explain a strategy for adding and subtracting fractions.

EX         Select and/or use an appropriate operation(s) to show understanding of addition and subtraction of non‑negative decimals and/or fractions.

EX         Explain the relationship between addition and subtraction of non‑negative decimals and fractions.

EX         Translate a picture or illustration into an equivalent symbolic representation of addition and subtraction of non‑negative fractions and decimals.

Understand the meaning of multiplication and division of non‑negative decimals and fractions.  W

 

 

EXAMPLES

 

EX         Explain or show the meaning of multiplying and dividing non‑negative fractions and decimals using words, pictures, or models.

EX         Explain the effect of multiplying a whole number by a decimal number.  

EX         Explain why multiplication of fractions involves multiplying denominators.

EX         Demonstrate how multiplication and division with decimals affects place value.

EX         Explain remainders of a division problem in a given situation.

EX         Translate a picture or illustration into an equivalent symbolic representation of multiplication and division of non‑negative fractions and decimals.

EX         Select and/or use an appropriate operation to show understanding of addition, subtraction, multiplication, or division of non‑negative rational numbers.

Understand the meaning of addition and subtraction of integers.  W

 

 

 

EXAMPLES

 

EX         Explain or show the meaning of addition and subtraction of integers using words, pictures, or real‑world models.

EX         Translate a symbolic addition or subtraction of integers into a real‑life situation.  

EX         Show addition and subtraction of integers using technology.

EX         Translate a given picture or illustration representing addition or subtraction of integers into an equivalent symbolic representation.

EX         Explain why multiplication of fractions involves multiplying denominators while addition of fractions requires finding common denominators. 

EX         Select and/or use an appropriate operation to show understanding of addition and subtraction of integers.

 

Understand the meaning of addition, subtraction, multiplication, division, powers, and square roots on rational numbers.  W

 

EXAMPLES

 

EX         Explain the meaning of multiplication and division of integers including remainders using words, pictures, or models. 

EX         Explain the meaning of taking whole number powers of integers or square roots of whole numbers using words, pictures, or models.

EX         Represent a situation involving multiplication or division of integers, whole number powers of integers, or square roots of whole numbers. 

EX         Explain how the result of dividing a rational number by a fraction between 0 and 1 is different from the result of dividing the same number by a fraction greater than 1.

EX         Translate a given situation, picture, or illustration into a numeric expression or equation involving decimals, fractions, integers, whole number powers, and square roots of whole numbers.

EX         Select and/or use an appropriate operation to show understanding of whole number powers and square roots.

EX         Convert between equivalent forms of rational numbers including whole number powers and square roots of perfect squares.

 

Compute using scientific notation.  W

 

 

 

 

EXAMPLES

 

EX         Compute using scientific notation. 

EX         Use scientific notation to simplify a calculation. 

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Computation

1.1.6

 

Apply strategies or uses computational procedures to add and subtract non‑negative decimals and like‑denominator fractions.

 

 

 

EXAMPLES

 

EX         Add and subtract non‑negative decimals and like‑denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and/or 15.

EX         Find sums or differences of decimals or like‑denominator fractions in given situations.  

EX         Calculate sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths.

EX         Calculate difference of numbers with decimals to thousandths.

 

Apply strategies or uses computational procedures to add and subtract non‑negative decimals and fractions.  W

 

 

 

 

EXAMPLES

 

EX         Find the sums or differences of non‑negative fractions or decimals.

EX         Find sums or differences of decimals or fractions in real‑world situations.

EX         Use the least common multiple and the greatest common factor of whole numbers to simplify or compute with fractions.  

EX         Calculate sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths.

EX         Calculate difference between numbers with decimals to thousandths.

EX         Complete multiple‑step computations requiring addition and/or subtraction.

Apply strategies or uses computational procedures using order of operations to add, subtract, multiply, and divide non‑negative decimals and fractions.  W

 

 

EXAMPLES

 

EX         Find the product or quotient using non‑negative decimals and fractions.

EX         Use multiplication and division in real world situations involving non‑negative rational numbers. 

EX         Multiply non‑negative decimals and fractions.

EX         Divide non‑negative decimal numbers by non‑negative decimal numbers to the hundredths place.

EX         Compute with non‑negative rational numbers using order of operations.

EX         Interpret and apply the concept of remainder in a given situation.

EX         Complete multi‑step calculations requiring two or more operations with non‑negative decimals and fractions.

 

Apply strategies or uses computational procedures using order of operations and addition, subtraction, multiplication, division, powers, and square roots on rational numbers.  W

 

EXAMPLES

 

EX         Compute with rational numbers using order of operations.

EX         Compute using whole number powers and/or square roots of perfect squares.

EX         Interpret and apply the concept of remainder in a given situation.

EX         Complete multi‑step computations using two or more different operations with rational numbers.

 

 

Complete multi‑step computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots.  W

 

EXAMPLES

 

EX         Calculate using order of operations on rational numbers.

EX         Use properties to reorder and rearrange expressions to compute more efficiently. 

EX         Apply strategies to complete multi‑step computations fluently.

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Computation

1.1.7

 

Apply strategies and uses tools appropriate to tasks involving addition and subtraction of non‑negative decimals or like‑denominator fractions.

 

 

EXAMPLES

 

EX         Select and use appropriate tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. 

EX         Explain why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation.

EX         Describe strategies for mentally adding or subtracting non‑negative decimals and/or like‑denominator fractions. 

Apply strategies and uses tools appropriate to tasks involving addition and subtraction of non‑negative decimals and fractions.

 

 

EXAMPLES

 

EX         Select and use appropriate strategies and tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. 

EX         Explain why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation.

EX         Describe strategies for mentally adding and/or subtracting non‑negative decimals and fractions.

Apply strategies and uses tools to complete tasks involving addition and subtraction of integers and the four basic operations on non‑negative decimals and fractions.

 

EXAMPLES

 

EX         Select and use appropriate strategies and tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. 

EX         Explain why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation.

EX         Describe strategies for mentally adding and/or subtracting integers and multiplying and/or dividing non‑negative decimals and fractions.

 

Apply strategies and uses tools to complete tasks involving computation of rational numbers.

 

 

 

EXAMPLES

 

EX         Select and justify appropriate strategies and tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. 

EX         Explain why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation.

EX         Describe strategies for mental computation with integers using powers and square roots.

 

 

Maintain Skills

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.1:  Understand and apply concepts and procedures from number sense.

GLE

5

6

7

8

9/10

Estimation

1.1.8

 

Apply estimation strategies involving addition and subtraction of non‑negative decimals and like‑denominator fractions to predict results or determine reasonableness of answers.  W

 

 

EXAMPLES

 

EX         Explain when an estimation or exact answer is or is not appropriate.

EX         Use a variety of estimation strategies to predict an answer prior to computation

EX         Use estimation to verify the reasonableness of calculated results.

EX         Compute to check the reasonableness of estimated answers for a given situation.

EX         Explain an appropriate adjustment when an estimate and a computation do not agree.

EX         Explain or describe a strategy used for estimation involving addition and subtraction of non‑negative decimals and like‑denominator fractions.

 

 

Apply estimation strategies involving addition and subtraction of non‑negative decimals and fractions to predict results or determine reasonableness of answers.  W

 

 

 

EXAMPLES

 

EX         Explain whether estimation or exact calculation is appropriate in situations involving addition and subtraction of non‑negative decimals and fractions.

EX         Use a variety of estimation strategies prior to computation to predict an answer. 

EX         Use estimation to verify the reasonableness of calculated results.

EX         Compute to check the reasonableness of estimated answers for a given situation.

EX         Explain an appropriate adjustment when an estimate and a computation do not agree.

EX         Explain or describe a strategy for estimation involving addition and subtraction of non‑negative decimals and fractions.

 

Apply estimation strategies involving addition and subtraction of integers and the four basic operations on non‑negative decimals and fractions to predict results or determine reasonableness of answers.  W

 

EXAMPLES

 

EX         Determine and explain when an approximation, estimation, or exact computation is appropriate and selects or illustrates a real‑life situation where estimation is sufficient.   

EX         Use estimation strategies to predict an answer prior to operations on non‑negative rational numbers. 

EX         Use estimation to verify the reasonableness of calculated results.

EX         Compute to check the reasonableness of estimated answers for a given situation.

EX         Explain an appropriate adjustment when an estimate and a computation do not agree.

EX         Explain or describe a strategy for estimation involving computation with non‑negative decimals and fractions.

 

Apply estimation strategies involving computation of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict results or determine reasonableness of answers.  W

 

EXAMPLES

 

EX         Select, explain, and justify situations involving rational numbers where estimates are sufficient and others for which an exact value is required. 

EX         Use a variety of estimation strategies to predict results prior to computation.

EX         Use a variety of estimation strategies to verify the reasonableness of calculated results.

EX         Compute to check the reasonableness of estimated answers for a given situation.

EX         Explain an appropriate adjustment when an estimate and a computation do not agree.

EX         Explain or describe a strategy for estimation involving computation with decimals, fractions, and integers, using +, -, x, ÷, powers, and square roots.

 

Apply estimation strategies in situations involving multi‑step computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers.  W

 

EXAMPLES

 

EX         Select, explain, and justify situations involving rational numbers where estimates are sufficient and others for which an exact value is required. 

EX         Use a variety of estimation strategies to predict or to verify the reasonableness of calculated results. 

EX         Describe a strategy used for estimation using multi‑step computations.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Attributes, units, and systems

1.2.1

 

Understand the concept of angle measurement.  W

 

 

 

 

 

 

 

EXAMPLES

 

EX         Identify or describe angles in pictures, diagrams, illustrations and in the environment. 

EX         Sort, classify, and label angles as equal to, less than, or greater than 90°. 

EX         Describe angles in shapes and figures as equal to, less than, or greater than 90°.

EX         Explain and provide examples of how angles are formed.

 

Understand the concepts of surface area and volume of rectangular prisms.  W

 

 

 

 

 

 

EXAMPLES

 

EX         Represent the volume for given rectangular prisms using pictures or models. 

EX         Describe and provide examples of surface area and volume.

EX         Explain and give examples of how area and surface area are related.

EX         Describe the relationship between surface area and volume of a rectangular prism.

EX         Label measurements of rectangular prisms to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms.

 

Understand how changes in one linear dimension affect other linear measurements and area of rectangles, triangles, and circles.  W

 

 

 

 

EXAMPLES

 

EX         Determine and/or describe the impact on the perimeter, circumference, and/or area of a rectangle, triangle, and/or circle caused by a change in one dimension.

EX         Determine and/or describe the impact on one dimension caused by a change in perimeter, circumference and/or area of a rectangle, triangle, and/or circle.

Understand how a change in one linear dimension affects surface area and volume of rectangular prisms and cylinders and how changes in two linear dimensions affect perimeter and area of rectangles.  W

 

EXAMPLES

 

EX         Determine and/or describe the impact that a change in one dimension has on volume and surface area in right cylinders and rectangular prisms. 

EX         Determine and/or describe a change in a linear dimension given a change in volume and/or surface area of rectangular prisms and cylinders.

EX         Determine and/or describe the impact on perimeter and/or area of a rectangle caused by a change in two dimensions.

 

Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume.  W

 

 

 

EXAMPLES

 

EX         Determine and/or describe the impact of a change in two linear dimensions on perimeter, area, surface area, and/or volume.

EX         Describe how changes in one or more linear dimensions affect perimeter, area, and/or volume in real world situations.

EX         Determine the change in one or more linear dimensions given a change in perimeter, area, surface area, and/or volume.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Attributes, units, and systems

1.2.2

 

Understand the concept of degree as a unit of measurement for angles.  W

 

EXAMPLES

 

EX         Explain how degrees are used as measures of angles.

EX         Describe an angle in relation to a 90° angle. 

EX         Sort, classify, and label angles as approximately 30°, 45°, 60°, 90°, or 180°.

EX         Draw angles with approximate measures of 30°, 45°, 60°, 90°, and 180°.

EX         Identify or describe angles with approximate measures of 30°, 45°, 60°, 90°, or 180° with or without a protractor.

 

Understand the differences between area (square) units and volume (cubic) units.  W

 

EXAMPLES

 

EX         Select appropriate units for area and volume in given situations. 

EX         Explain why volume is measured in cubic units. 

EX         Explain how the selected unit of length affects the size of cubic units.

EX         Explain why area is measured in square units and volume is measured in cubic units.

 

Maintain Skills

 

Understand and use rate, slope, and other derived units of measurement.  W

 

EXAMPLES

 

EX         Explain the concept of a rate or slope in a given situation. 

EX         Explain how division of measurements produces a derived unit of measurement.

EX         Calculate a rate of change or slope in a situation.

EX         Use unit analysis to find equivalent rates.

EX         Use rate to determine a measured outcome and labels units.

 

Maintain Skills

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Attributes, units, and systems

1.2.3

 

Understand how measurement units of capacity, mass, and length are organized in the metric system.  W

 

 

EXAMPLES

 

EX         Explain and cite examples of the metric system units for capacity, mass, and length.

EX         Explain or show the relationship between units in the metric system for capacity, mass, or length.

EX         Convert between units in the metric system:

·       Length – millimeter, centimeter, meter, kilometer

·       Capacity – milliliter, liter

·       Mass – gram, kilogram

 

 

Maintain Skills

 

Understand how the unit of measure affects the precision of measurement.  W

 

 

 

EXAMPLES

 

EX         Identify, describe, or explain how the unit selected for a situation can affect the precision of the measurement.

EX         Explain why measurement systems have different size units and how that allows for different levels of precision.

EX         Convert between units within a system to demonstrate understanding of the precision required.

Explain why different situations require different levels of precision.  W

 

 

 

EXAMPLES

 

EX         Describe or explain why different situations require different levels of precision.

EX         Compare situations that require different levels of precision.

EX         Select and describe an appropriate unit of measure for the precision needed in a given situation.

EX         Convert between units in a measurement system to demonstrate understanding of the precision required. 

 

Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision.  W

 

EXAMPLES

 

EX         Convert within a system while maintaining the same level of precision.

EX         Use procedures to convert derived units of measure.

EX         Explain why different situations require different levels of precision.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Procedures and estimation

1.2.4

 

Use a systematic procedure to measure and describe the area of rectangles or triangles.  W

 

 

EXAMPLES

 

Suggested Procedure:

¾  Identify the attribute to measure.

¾  Select an appropriate unit to measure the attribute identified.

¾  Select a tool that matches the unit chosen.

¾  Use the selected tool to determine the number of units.

¾  Report or record the number of units and a label.

 

EX         Select and describe the appropriate units and/or tools for measuring length, perimeter, and/or area.

EX         Demonstrate a procedure for measuring the area of a rectangle or right triangle.

EX         Use procedures to measure length, perimeter, and/or area.

EX         Measure the area in figures composed of rectangles and triangles.

EX         Determine whether an area measurement has been done correctly.

 

Use a systematic procedure to measure and describe the volume of rectangular prisms.  W

 

EXAMPLES

 

Suggested Procedure:

¾  Identify the attribute to measure.

¾  Select an appropriate unit to measure the attribute identified. 

¾  Select a tool that matches the unit chosen.

¾  Use the selected tool to determine the number of units.

¾  Report or record the number of units and a label.

 

EX         Select and describe the appropriate units and/or tools for measuring length, area, and/or volume.

EX         Measure the volume of rectangular prisms using manipulatives or pictures and counts the number of units as part of the measurement procedure.

EX         Determine whether measurement has been done correctly.

 

Understand and use a systematic procedure to measure and describe angles.  W

 

EXAMPLES

 

Suggested Procedure:

¾  Identify the attribute to measure.

¾  Select an appropriate unit to measure the attribute identified.

¾  Select a tool that matches the unit chosen.

¾  Use the selected tool to determine the number of units.

¾  Report or record the number of units and a label.

 

EX         Measure angles in assorted shapes and figures using the suggested procedure.

EX         Select and describe the appropriate units and/or tools for measuring angles.

EX         Use a protractor to draw angles accurate to within 3°.

EX         Determine whether measurement has been done correctly.

 

 

Maintain Skills

 

 

Maintain Skills

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Procedures and estimation

1.2.5

 

Use formulas to determine perimeter and area of rectangles and right triangles.  W

 

 

 

EXAMPLES

 

EX         Explain how to find the perimeter or area of any rectangle using a rule. 

EX         Explain and use formulas to calculate the perimeter or area of a rectangle and labels units. 

EX         Explain and use a formula to determine or calculate the area of a right triangle and labels units. 

EX         Determine and label right triangles and all rectangles with whole number dimensions and a given perimeter or area.

EX         Explain why formulas are used to find area and/or perimeter.

 

Maintain Skills

 

Use formulas to determine measurements related to circles, triangles, and rectangular prisms.  W

 

 

EXAMPLES

 

EX         Use formulas to determine and label missing measurements for circles, including radius, diameter, circumference, and area, in given situations.

EX         Use formulas to determine and label missing measurements for rectangular prisms, including length, width, height, volume, and surface area, in given situations.

EX         Use formulas to determine and label missing measurements for triangles, including base, height, perimeter, and area, in given situations.

EX         Demonstrate or explain how to use a formula for finding the area and circumference of a circle.

EX         Calculate and label dimensions of rectangular prisms with given volumes and/or surface areas.

EX         Determine the surface area of a rectangular prism.

 

Use formulas, including the Pythagorean Theorem, to determine measurements related to triangles, rectangular prisms, and right cylinders.  W

 

EXAMPLES

 

EX         Explain how to use a formula to calculate and label the surface area and volume of a prism or cylinder. 

EX         Use the Pythagorean Theorem to determine and label a missing dimension of a right triangle or prism. 

EX         Determine and label surface areas of right cylinders and right prisms.

EX         Determine and label dimensions of a triangle, prism, or cylinder based on a given perimeter, circumference, area, and/or volume.

 

Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids.  W

 

 

EXAMPLES

 

EX         Use formulas to determine and label the volume of a compound figure.

EX         Use formulas to determine and label the surface area of a compound figure.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.2:  Understand and apply concepts and procedures from measurement.

GLE

5

6

7

8

9/10

Procedures and estimation

1.2.6

 

Understand and apply strategies to obtain reasonable estimates of angle measurements and areas of rectangles and right triangles.  W

 

 

EXAMPLES

 

EX         Describe situations in which estimated measurements are appropriate.

EX         Estimate and label areas of rectangles and right triangles.

EX         Explain an appropriate process for estimating perimeter or area of a rectangle or right triangle or an angle measurement. 

EX         Use estimation to determine reasonableness of an angle or area measurement.

EX         Determine whether an angle is closest to 30°, 45°, 60°, 90°, or 180°.

EX         Draw angles with measurements that are approximately 30o, 45o, 60o, 90o, or 180o.

 

Understand and apply strategies to obtain reasonable estimates of volume using manipulatives and/or drawings.  W

 

 

 

EXAMPLES

 

EX         Describe situations in which estimated measures are sufficient.

EX         Estimate and label volume or capacity.

EX         Use estimation to determine reasonableness of a volume of a rectangular prism.  

EX         Describe a procedure to find a reasonable estimate of volume or capacity.   

EX         Explain why estimation would be used rather than a direct measurement.

 

Understand and apply strategies to obtain a reasonable estimate of measurements related to circles, right triangles, and surface area of rectangular prisms.  W

 

EXAMPLES

 

EX         Describe situations in which estimated measures are sufficient. 

EX         Estimate and label circle, right triangle, and rectangular prism measurements.

EX         Use common approximations of pi to estimate and label the circumference and the area of circles.

EX         Use or describe a process to find a reasonable estimate of measurements.

EX         Explain why estimation or precise measurement is appropriate in a given situation. 

 

Apply strategies to obtain reasonable estimates of surface area and volume of right cylinders and rectangular prisms, and the lengths of sides of right triangles.  W

 

EXAMPLES

 

EX         Describe situations in which estimated measures are sufficient.

EX         Use estimation to determine and label volume and surface area for right cylinders and right prisms and explain why an approximation is appropriate.

EX         Use estimation strategies to determine and label the approximate length of the third side of a right triangle given the lengths of two sides.

EX         Use estimation strategies to determine and labels the approximate distance or height in a situation using similar triangles or the Pythagorean Theorem. 

EX         Describe a procedure that would obtain an estimated measurement.

EX         Explain why estimation would be used rather than a direct measurement.

 

Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision.  W

 

 

EXAMPLES

 

EX         Determine when approximate measurements are sufficient and estimate a reasonable measurement at an appropriate level of precision. 

EX         Estimate quantities using derived units of measure.

EX         Estimate derived units of measure.

EX         Select and use a procedure to find a reasonable estimate for and label the volumes of prisms and cylinders.

EX         Estimate conversions between yards and meters and quarts and liters.

EX         Describe a procedure that would be an appropriate way to estimate a measurement.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.3:  Understand and apply concepts and procedures from geometric sense.

GLE

5

6

7

8

9/10

Properties and relationships

1.3.1

 

Understand the attributes of angles and polygons.  W

 

 

 

 

EXAMPLES

 

EX         Explain the difference between a regular and irregular polygon.

EX         Describe a 2‑dimensional shape and/or figure using properties including number of sides, number of vertices, and types of angles.

EX         Draw a simple 2‑dimensional shape and/or figure having given characteristics including number of sides, number of vertices, types of angle(s), and/or congruence.

EX         Use and/or explain mathematical conventions used to label vertices, line segments, and angles.

 

Understand the properties of circles and rectangular prisms.  W

 

 

 

EXAMPLES

 

EX         Describe circles or rectangular prisms using geometric properties.

EX         Draw a figure given properties that describe a circle or rectangular prism.

EX         Explain lines of symmetry for 2‑dimensional figures including circles.

EX         Describe the relationship between the diameter and the radius of a circle. 

Understand the concept of similarity and its relationship to congruence.  W

 

 

 

EXAMPLES

 

EX         Identify or describe congruence in figures.

EX         Explain how two figures are similar and/or congruent using definitions or real‑world examples.

EX         Produce a sample scale drawing and explains how it is an example of similarity.   

EX         Use mathematical conventions to label vertices, line segments, and angles.

 

 

Understand properties of cylinders, cones, and pyramids.  W

 

 

 

EXAMPLES

 

EX         Identify or describe cylinders, cones, or pyramids.

EX         Classify and label cylinders, cones, or pyramids.

EX         Draw nets of cylinders, prisms, and pyramids.

EX         Identify and label rays, lines, end points, line segments, vertices, and angles in three‑dimensional shapes and figures.

 

Understand the properties of and the relationships among 1‑dimensional, 2‑dimensional, and 3‑dimensional shapes and figures.  W

 

EXAMPLES

 

EX         Make and test conjectures about 2‑dimensional and 3‑dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models.

EX         Use the relationship between similar figures to determine the scale factor.

EX         Match or draw a 3‑dimensional figure that could be formed by folding a given net.

 

EALR 1:  The student understands and applies the concepts and procedures of mathematics.

COMPONENT 1.3:  Understand and apply concepts and procedures from geometric sense.

GLE

5

6

7

8