Mathematics Standards - Grades K-5


1	ROYALTON PUBLIC SCHOOLS Mathematics Standards KINDERGARTEN		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
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3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark
4	Topic 1: Sorting & Classifying	Topic 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Counting & Representation K-3	Understand the relationship between quantities and whole numbers up to 31.	K.1.1.1	Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence.
5	Topic 2: Position & Location	Topic 2 Proficiency Scale				K.1.1.2	Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes.
6	Topic 3: Patterns	Topic 3 Proficiency Scale				K.1.1.3	Count, with and without objects, forward and backward to at least 20.
7	Topic 4: Zero to Five	Topic 4 Proficiency Scale				K.1.1.4	Find a number that is 1 more or 1 less than a given number.
8	Topic 5: Six to Ten	Topic 5 Proficiency Scale				K.1.1.5	Compare and order whole numbers, with and without objects, from 0 to 20.
9	Topic 6: Comparing Numbers	Topic 6 Proficiency Scale		Whole Number: Operations K-5	Use objects and pictures to represent situations involving combining and separating.	K.1.2.1	Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.
10	Topic 7: Geometry	Topic 7 Proficiency Scale		Whole Number: Operations K-5		K.1.2.2	Compose and decompose numbers up to 10 with objects and pictures.
11	Topic 8: Fractions and Ordinals	Topic 8 Proficiency Scale	ALGEBRA	Algebra: Relationships & Functions K-HS	Recognize, create, complete and extend patterns.	K.2.1.1	Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ●,●●,●●●.
12	Topic 9: Measurement	Topic 9 Proficiency Scale	GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Recognize and sort basic two- and three-dimensional shapes; use them to model real-world objects.	K.3.1.1	Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres.
13	Topic 10: Addition	Topic 10 Proficiency Scale				K.3.1.2	Sort objects using characteristics such as shape, size, color and thickness.
14	Topic 11: Subtraction	Topic 11 Proficiency Scale				K.3.1.3	Use basic shapes and spatial reasoning to model objects in the real-world.
15	Topic 12: Large Numbers	Topic 12 Proficiency Scale		Geometry: Measurement K-HS	Compare and order objects according to location and measurable attributes.	K.3.2.1	Use words to compare objects according to length, size, weight and position.
16	Topic 13: Money	Topic 13 Proficiency Scale		Geometry: Measurement K-HS		K.3.2.2	Order 2 or 3 objects using measurable attributes, such as length and weight.
17	Topic 14: Time	Topic 14 Proficiency Scale
18	Topic 15: Calendar	Topic 15 Proficiency Scale
19	Topic 16: Graphing	Topic 16 Proficiency Scale


1	ROYALTON PUBLIC SCHOOLS Mathematics Standards 1ST GRADE		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
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3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark

4	Unit 1: Numbers to 12	Unit 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Counting & Representation K-3	Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones.	1.1.1.1	Use place value to describe whole numbers between 10 and 100 in terms of tens and ones.
5	Unit 2: Comparing and Ordering Numbers	Unit 2Proficiency Scale				1.1.1.2	Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.
6	Unit 3: Understanding Addition	Unit 3 Proficiency Scale				1.1.1.3	Count, with and without objects, forward and backward from any given number up to 120.
7	Unit 4: Understanding Subtraction	Unit 4 Proficiency Scale				1.1.1.4	Find a number that is 10 more or 10 less than a given number.
8	Unit 5: Five and Ten Frame Relationships	Unit 5 Proficiency Scale				1.1.1.5	Compare and order whole numbers up to 120.
9	Unit 6: Addition	Unit 6 Proficiency Scale				1.1.1.6	Use words to describe the relative size of numbers.
10	Unit 7: Subtraction	Unit 7 Proficiency Scale				1.1.1.7	Use counting and comparison skills to create and analyze bar graphs and tally charts.
11	Unit 8: Geometry	Unit 8 Proficiency Scale		Whole Number: Operations K-5	Use a variety of models and strategies to solve addition and subtraction problems in real-world and mathematical contexts.	1.1.2.1	Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.
12	Unit 9: Patterns	Unit 9 Proficiency Scale				1.1.2.2	Compose and decompose numbers up to 12 with an emphasis on making ten.
13	Unit 10: Counting and Number Patterns	Unit 10 Proficiency Scale				1.1.2.3	Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s.
14	Unit 11: Tens and Ones	Unit 11 Proficiency Scale	ALGEBRA	Algebra: Relationships & Functions K-HS	Recognize and create patterns; use rules to describe patterns.	1.2.1.1	Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns.
15	Unit 12: Comparing and Ordering Numbers to 100	Unit 12 Proficiency Scale		Algebra: Equations and Inequalities 1-HS	Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.	1.2.2.1	Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.
16	Unit 13: Money	Unit 13 Proficiency Scale				1.2.2.2	Determine if equations involving addition and subtraction are true.
17	Unit 14: Measurement	Unit 14 Proficiency Scale				1.2.2.3	Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as:
18	Unit 15: Telling Time	Unit 15 Proficiency Scale				1.2.2.4	Use addition or subtraction basic facts to represent a given problem situation using a number sentence.
19	Unit 16: Addition Facts to 18	Unit 16 Proficiency Scale	GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Describe characteristics of basic shapes. Use basic shapes to compose and decompose other objects in various contexts.	1.3.1.1	Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres.
20	Unit 17: Subtraction Facts to 18	Unit 17 Proficiency Scale		Geometry: Shapes K-5		1.3.1.2	Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders.
21	Unit 18: Data and Graphs			Geometry: Measurement K-HS	Use basic concepts of measurement in real-world and mathematical situations involving length, time and money.	1.3.2.1	Measure the length of an object in terms of multiple copies of another object.
22						1.3.2.2	Tell time to the hour and half-hour.
23						1.3.2.3	Identify pennies, nickels and dimes; find the value of a group of these coins, up to one dollar.


1	ROYALTON PUBLIC SCHOOLS Mathematics Standards 2ND GRADE		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
2	2020-2021 Scope and Sequence
3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark
4	Unit 1: Place Value Numbers to 100	Unit 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Counting & Representation K-3	Compare and represent whole numbers up to 1000 with an emphasis on place value and equality.	2.1.1.1	Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.
5	Unit 2: Addition Strategies	Unit 2 Proficiency Scale				2.1.1.2	Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds.
6	Unit 3: Subtraction Strategies	Unit 3 Proficiency Scale				2.1.1.3	Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number.
7	Unit 4: Understanding Addition and Subtraction	Unit 4 Proficiency Scale				2.1.1.4	Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100.
8	Unit 5: Counting Money	Unit 5 Proficiency Scale				2.1.1.5	Compare and order whole numbers up to 1000.
9	Unit 6: Two-Digit Addition	Unit 6 Proficiency Scale		Whole Number: Operations K-5	Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems.	2.1.2.1	Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts.
10	Unit 7: Geometry	Unit 7 Proficiency Scale				2.1.2.2	Demonstrate fluency with basic addition facts and related subtraction facts.
11	Unit 8: Two-Digit Subtraction	Unit 8 Proficiency Scale				2.1.2.3	Estimate sums and differences up to 100.
12	Unit 9: Rounding and Estimating Two-Digit Numbers	Unit 9 Proficiency Scale				2.1.2.4	Use mental strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences.
13	Unit 10: Graphing and Probability	Unit 10 Proficiency Scale				2.1.2.5	Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100.
14	Unit 11: Measurement	Unit 11 Proficiency Scale				2.1.2.6	Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts.
15	Unit 12: Time	Unit 12 Proficiency Scale	ALGEBRA	Algebra: Relationships & Functions K-HS	Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.	2.2.1.1	Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts.
16	Unit 13: Numbers and Patterns to 1,000	Unit 13 Proficiency Scale		Algebra: Equations and Inequalities 1-HS	Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.	2.2.2.1	Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences.
17	Unit 14: Three-Digit Addition and Subtraction	Unit 14 Proficiency Scale		Algebra: Equations and Inequalities 1-HS		2.2.2.2	Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true.
18	Unit 15: Patterns and Algebra	Unit 15 Proficiency Scale	GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Identify, describe and compare basic shapes according to their geometric attributes.	2.3.1.1	Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).
19	Unit 16: Fractions	Unit 16 Proficiency Scale		Geometry: Shapes K-5		2.3.1.2	Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres.
20	Unit 17: Multiplication	Unit 17 Proficiency Scale		Geometry: Measurement K-HS	Understand length as a measurable attribute; use tools to measure length.	2.3.2.1	Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.
21	Unit 18: Division	Unit 18 Proficiency Scale				2.3.2.2	Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch.
22	Unit 19: Capacity	Unit 19 Proficiency Scale			Use time and money in real-world and mathematical situations.	2.3.3.1	Tell time to the quarter-hour and distinguish between a.m. and p.m.
23	Unit 20: Perimeter and Area	Unit 20 Proficiency Scale				2.3.3.2	Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount.


1	ROYALTON PUBLIC SCHOOLS Mathematics Standards 3RD GRADE		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
2	2020-2021 Scope and Sequence
3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark
4	Unit 1: Numeration	Unit 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Counting & Representation K-3	Compare and represent whole numbers up to 100,000 with an emphasis on place value and equality.	3.1.1.1	Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.
5	Unit 2: Adding Whole Numbers	Unit 2 Proficiency Scale				3.1.1.2	Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones.
6	Unit 3: Subtraction	Unit 3 Proficiency Scale				3.1.1.3	Find 10,000 more or 10,000 less than a given five-digit number. Find 1000 more or 1000 less than a given four- or five-digit. Find 100 more or 100 less than a given four- or five-digit number.
7	Unit 4: Multiplication	Unit 4 Proficiency Scale				3.1.1.4	Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences.
8	Unit 5: Division	Unit 5 Proficiency Scale				3.1.1.5	Compare and order whole numbers up to 100,000.
9	Unit 6: Patterns and Relationships	Unit 6 Proficiency Scale		Whole Number: Operations K-5	Add and subtract multi-digit whole numbers; represent multiplication and division in various ways; solve real-world and mathematical problems using arithmetic.	3.1.2.1	Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.
10	Unit 7: Solids and Shapes	Unit 7 Proficiency Scale				3.1.2.2	Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.
11	Unit 8: Understanding Fractions	Unit 8 Proficiency Scale				3.1.2.3	Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
12	Unit 9: Time and Temperature	Unit 9 Proficiency Scale				3.1.2.4	Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems.
13	Unit 10: Data, Graphs, & Probability	Unit 10 Proficiency Scale				3.1.2.5	Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties.
14				Fractions & Decimals: Representations and Relationships 3-8	Understand meanings and uses of fractions in real-world and mathematical situations.	3.1.3.1	Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line.
15						3.1.3.2	Understand that the size of a fractional part is relative to the size of the whole.
16						3.1.3.3	Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.
17			ALGEBRA	Algebra: Relationships & Functions K-HS	Use single-operation input-output rules to represent patterns and relationships and to solve real-world and mathematical problems.	3.2.1.1	Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts.
18				Algebra: Equations and Inequalities 1-HS	Use number sentences involving multiplication and division basic facts and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.	3.2.2.1	Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences.
19				Algebra: Equations and Inequalities 1-HS		3.2.2.2	Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.
20			GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Use geometric attributes to describe and create shapes in various contexts.	3.3.1.1	Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids.
21				Geometry: Shapes K-5		3.3.1.2	Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons.
22				Geometry: Measurement K-HS	Understand perimeter as a measurable attribute of real-world and mathematical objects. Use various tools to measure distances.	3.3.2.1	Use half units when measuring distances.
23						3.3.2.2	Find the perimeter of a polygon by adding the lengths of the sides.
24						3.3.2.3	Measure distances around objects.
25					Use time, money and temperature to solve real-world and mathematical problems.	3.3.3.1	Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.
26						3.3.3.2	Know relationships among units of time.
27						3.3.3.3	Make change up to one dollar in several different ways, including with as few coins as possible.
28						3.3.3.4	Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.
29			DATA ANALYSIS & PROBABILITY	Data Analysis 3-5, 7-HS	Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays.	3.4.1.1	Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.


1	ROYALTON PUBLIC SCHOOLS Mathematics Standards 4TH GRADE		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
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3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark
4	Unit 1: Numeration	Unit 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Operations K-5	Demonstrate mastery of multiplication and division basic facts; multiply multi-digit numbers; solve real-world and mathematical problems using arithmetic.	4.1.1.1	Demonstrate fluency with multiplication and division facts.
5	Unit 2: Adding and Subtracting	Unit 2 Proficiency Scale				4.1.1.2	Use an understanding of place value to multiply a number by 10, 100 and 1000.
6	Unit 3: Multiplication	Unit 3 Proficiency Scale				4.1.1.3	Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.
7	Unit 4: Division	Unit 4 Proficiency Scale				4.1.1.4	Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results.
8	Unit 5: Geometry	Unit 5 Proficiency Scale				4.1.1.5	Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
9	Unit 6: Measurement	Unit 6 Proficiency Scale				4.1.1.6	Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.
10	Unit 7: Fractions	Unit 7 Proficiency Scale		Fractions & Decimals: Representations and Relationships 3-8	Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.	4.1.2.1	Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.
11	Unit 8: Decimals	Unit 8 Proficiency Scale				4.1.2.2	Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions.
12	Unit 9: Algebra	Unit 9 Proficiency Scale				4.1.2.3	Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.
13	Unit 10: Data Graphing	Unit 10 Proficiency Scale				4.1.2.4	Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths.
14						4.1.2.5	Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.
15						4.1.2.6	Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths.
16						4.1.2.7	Round decimals to the nearest tenth.
17			ALGEBRA	Algebra: Relationships & Functions K-HS	Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.	4.2.1.1	Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table.
18				Algebra: Equations and Inequalities 1-HS	Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.	4.2.2.1	Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences.
19				Algebra: Equations and Inequalities 1-HS		4.2.2.2	Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true.
20			GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Name, describe, classify and sketch polygons.	4.3.1.1	Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts.
21				Geometry: Shapes K-5	Name, describe, classify and sketch polygons.	4.3.1.2	Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.
22				Geometry: Measurement K-HS	Understand angle and area as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and areas.	4.3.2.1	Measure angles in geometric figures and real-world objects with a protractor or angle ruler.
23						4.3.2.2	Compare angles according to size. Classify angles as acute, right and obtuse.
24						4.3.2.3	Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns.
25						4.3.2.4	Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.
26				Euclidean Geometry and Reasoning 4, 6-HS	Use translations, reflections and rotations to establish congruency and understand symmetries.	4.3.3.1	Apply translations (slides) to figures.
27						4.3.3.2	Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry.
28						4.3.3.3	Apply rotations (turns) of 90˚ clockwise or counterclockwise.
29						4.3.3.4	Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent.
30			DATA ANALYSIS & PROBABILITY	Data Analysis 3-5, 7-HS	Collect, organize, display and interpret data, including data collected over a period of time and data represented by fractions and decimals.	4.4.1.1	Use tables, bar graphs, timelines, and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.


1	ROYALTON PUBLIC SCHOOLS 5TH GRADE Mathematics Standards		The Minnesota Academic Standards in Mathematics are organized by grade level into four content strands: 1) Number and Operation 2) Algebra 3) Geometry and Measurement 4) Data Analysis and Probability. Each strand has one or more standards, and the benchmarks for each standard are designated by a code. Highlighted cells are a Royalton Elementary Priority Standard.
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3	Curriculum Course/Unit/Lesson	Assessment (Evidence of Mastery)	Strand	Sub Strand	Standard	Code	Benchmark

4	Unit 1: Numeration	Unit 1 Proficiency Scale	NUMBER & OPERATIONS	Whole Number: Operations K-5	Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.	5.1.1.1	Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
5	Unit 2: Adding and Subtracting Whole Numbers and Decimals	Unit 2 Proficiency Scale				5.1.1.2	Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
6	Unit 3: Multiplying Whole Numbers	Unit 3 Proficiency Scale				5.1.1.3	Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
7	Unit 4: Dividing By 1-Digit Numbers	Unit 4 Proficiency Scale				5.1.1.4	Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
8	Unit 5: Dividing By 2-Digit Numbers	Unit 5 Proficiency Scale		Fractions & Decimals: Representations and Relationships 3-8	Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.	5.1.2.1	Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.
9	Unit 6: Variables and Expressions	Unit 6 Proficiency Scale				5.1.2.2	Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.
10	Unit 7: Multiplying and Dividing Decimals	Unit 7 Proficiency Scale				5.1.2.3	Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
11	Unit 8: Shapes	Unit 8 Proficiency Scale				5.1.2.4	Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
12	Unit 9: Fractions and Decimals	Unit 9 Proficiency Scale				5.1.2.5	Round numbers to the nearest 0.1, 0.01 and 0.001.
13	Unit 10: Adding and Subtracting Fractions and Mixed Numbers	Unit 10 Proficiency Scale		Fractions & Decimals: Operations 5-7	Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.	5.1.3.1	Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
14	Unit 11: Multiply Fractions and Mixed Numbers	Unit 11 Proficiency Scale				5.1.3.2	Model addition and subtraction of fractions and decimals using a variety of representations.
15	Unit 12: Perimeter and Area	Unit 12 Proficiency Scale				5.1.3.3	Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
16	Unit 13: Solids	Unit 13 Proficiency Scale				5.1.3.4	Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
17	Unit 14: Measurement, Units, Time, and Temperature	Unit 14 Proficiency Scale	ALGEBRA	Algebra: Relationships & Functions K-HS	Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real-world and mathematical problems.	5.2.1.1	Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
18	Unit 15: Solving and Writing Equations and Inequalities	Unit 15 Proficiency Scale		Algebra: Relationships & Functions K-HS		5.2.1.2	Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
19	Unit 16: Ratio and Percent	Unit 16 Proficiency Scale		Algebra: Expressions 5-HS	Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.	5.2.2.1	Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.
20	Unit 17: Equations and Graphs	Unit 17 Proficiency Scale		Algebra: Equations and Inequalities 1-HS	Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.	5.2.3.1	Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
21	Unit 18: Graphs and Data	Unt 18 Proficiency Scale				5.2.3.2	Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
22	Unit 19: Transformations, Congruence, and Symmetry	Unit 19 Proficiency Scale				5.2.3.3	Evaluate expressions and solve equations involving variables when values for the variables are given.
23	Unit 20: Probability	Unit 20 Proficiency Sale	GEOMETERY & MEASURMENT	Geometry: Shapes K-5	Describe, classify, and draw representations of three-dimensional figures.	5.3.1.1	Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
24				Geometry: Shapes K-5		5.3.1.2	Recognize and draw a net for a three-dimensional figure.
25				Geometry: Measurement K-HS	Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.	5.3.2.1	Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
26						5.3.2.2	Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms.
27						5.3.2.3	Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.
28						5.3.2.4	Develop and use the formulas V = ℓwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
29			DATA ANALYSIS & PROBABILITY	Data Analysis 3-5, 7-HS	Display and interpret data; determine mean, median and range.	5.4.1.1	Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data.
30			DATA ANALYSIS & PROBABILITY	Data Analysis 3-5, 7-HS		5.4.1.2	Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.