
5Grade 5 Standards
Top Mathematicians

The Number System

5.NS.1.1
Students will be expected to represent and partition whole numbers to 1 000 000.
• Performance Indicators
 N01.01 Read a given numeral without using the word 'and.'
 N01.02 Record numerals for numbers expressed orally, concretely, pictorially, or symbolically as expressions, using proper spacing without commas.
 N01.03 Describe the pattern of adjacent place positions moving from right to left.
 N01.04 Explain the meaning of each digit in a given numeral.
 N01.05 Provide examples of large numbers used in print or electronic media.
 N01.06 Express a given numeral in expanded notation.
 N01.07 Write the numeral represented by a given expanded notation.
 N01.08 Compare and order numbers to 1 000 000 in a variety of ways.
 N01.09 Represent a given numeral, 0 to 1 000 000, using a placevalue chart.
 N01.10 Represent a given number, 0 to 1 000 000, in a variety of ways, and explain how they are equivalent.
 N01.11 Represent a given number, 0 to 1 000 000, using expressions.
 N01.12 Read and write given numerals, 0 to 1 000 000, in words. 
5.NS.1.10
Students will be expected to compare and order decimals (to thousandths) by using benchmarks, place value, and equivalent decimals.
• Performance Indicators
 N10.01 Compare and order a given set of decimals by placing them on a number line that contains the benchmarks 0.0, 0.5, and 1.0.
 N10.02 Compare and order a given set of decimals including only tenths using place value.
 N10.03 Compare and order a given set of decimals including only hundredths using place value.
 N10.04 Compare and order a given set of decimals including only thousandths using place value.
 N10.05 Explain what is the same and what is different about 0.2, 0.20, and 0.200.
 N10.06 Compare and order a given set of decimals, including tenths, hundredths, and thousandths, using equivalent decimals. 
5.NS.1.11
Students will be expected to demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).
• Performance Indicators
 N11.01 Predict sums and differences of decimals using estimation strategies.
 N11.02 Use estimation to correct errors of decimal point placements in sums and differences without using paper and pencil.
 N11.03 Explain why keeping track of placevalue positions is important when adding and subtracting decimals.
 N11.04 Solve problems that involve addition and subtraction of decimals, limited to thousandths, using personal strategies. 

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5.NS.1.2
Students will be expected to use estimation strategies, including frontend, frontend adjusted, rounding, and compatible numbers in problemsolving contexts.
• Performance Indicators
 N02.01 Provide a context for when estimation is used to make predictions, check the reasonableness of an answer, and determine approximate answers.
 N02.02 Describe contexts in which overestimating is important.
 N02.03 Determine the approximate solution to a given problem not requiring an exact answer.
 N02.04 Estimate a sum, a difference, a product, or a quotient using an appropriate strategy.
 N02.05 Select and explain an estimation strategy for a given problem. 

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5.NS.1.3
Students will be expected to describe and apply mental mathematics strategies and number properties to recall, with fluency, answers for basic multiplication facts to 81 and related division facts.
• Performance Indicators
 N03.01 Describe the mental mathematics strategy used to determine basic multiplication or division facts.
 N03.02 Explain why multiplying by 0 produces a product of 0 (zero property of multiplication).
 N03.03 Explain why division by 0 is not possible or is undefined (e.g., 8 ÷ 0).
 N03.04 Quickly recall multiplication facts up to 9 × 9 and related division facts. 

5.NS.1.4
Students will be expected to apply mental mathematics strategies for multiplication, including
• multiplying by multiples of 10, 100, and 1000
• halving and doubling
• using the distributive property
• Performance Indicators
 N04.01 Determine the products when one factor is a multiple of 10, 100, or 1000.
 N04.02 Apply halving and doubling when determining a given product (e.g., 32 Ã— 5 is the same as 16 Ã— 10).
 N04.03 Apply the distributive property to determine a given product that involves multiplying factors that are close to multiples of 10 (e.g., 98 Ã— 7 = (100 Ã— 7) â€“ (2 Ã— 7)). 
5.NS.1.5
Students will be expected to demonstrate, with and without concrete materials, an understanding of multiplication (twodigit by twodigit) to solve problems.
• Performance Indicators
 N05.01 Model the multiplication of two twodigit factors, using concrete and visual representations of the area model, and record the process symbolically.
 N05.02 Illustrate partial products in expanded notation for both factors (e.g., For 36 Ã— 42, determine the partial products for (30 + 6) Ã— (40 + 2).).
 N05.03 Represent both twodigit factors in expanded notation to illustrate the distributive property (e.g., To determine the partial products of 36 Ã— 42, record (30 + 6) Ã— (40 + 2) = 30 Ã— 40 + 30 Ã— 2 + 6 Ã— 40 + 6 Ã— 2 = 1200 + 60 + 240 + 12 = 1512.).
 N05.04 Describe a solution procedure for determining the product of two given twodigit factors, using a pictorial representation such as an area model.
 N05.05 Solve a given multiplication problem in context, using personal strategies, and record the process.
 N05.06 Create and solve multiplication story problems, and record the process symbolically.
 N05.07 Determine the product of two given numbers using a personal strategy and record the process symbolically. 
5.NS.1.6
Students will be expected to demonstrate, with and without concrete materials, an understanding of division (threedigit by onedigit), and interpret remainders to solve problems.
• Performance Indicators
 N06.01 Model the division of two given numbers, using concrete or visual representations, and record the process symbolically.
 N06.02 Explain that the interpretation of a remainder depends on the context.
• Ignore the remainder (e.g., making teams of four from 22 people [five teams, but two people are left over]).
• Round the quotient up (e.g., the number of fivepassenger cars required to transport 13 people).
• Express remainders as fractions (e.g., five apples shared by two people).
• Express remainders as decimals (e.g., measurement and money).
 N06.03 Solve a given division problem in context, using personal strategies, and record the process.
 N06.04 Create and solve division story problems, and record the process symbolically.
 N06.05 Determine the quotient of two given numbers using a personal strategy and record the process symbolically. 

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5.NS.1.7
Students will be expected to demonstrate an understanding of fractions by using concrete, pictorial, and symbolic representations to
• create sets of equivalent fractions
• compare and order fractions with like and unlike denominators
• Performance Indicators
 N07.01 Represent a given fraction of one whole, set, linear model, or region using concrete materials.
 N07.02 Create a set of equivalent fractions, and explain, using concrete materials, why there are many equivalent fractions for any given fraction.
 N07.03 Model and explain that equivalent fractions represent the same quantity.
 N07.04 Determine if two given fractions are equivalent, using concrete materials or pictorial representations.
 N07.05 Identify equivalent fractions for a given fraction.
 N07.06 Compare and order two given fractions with unlike denominators by creating equivalent fractions.
 N07.07 Position a given set of fractions with like and unlike denominators on a number line, and explain strategies used to determine the order.
 N07.08 Formulate and verify a personal strategy for developing a set of equivalent fractions. 

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5.NS.1.8
Students will be expected to describe and represent decimals (tenths, hundredths, and thousandths) concretely, pictorially, and symbolically.
• Performance Indicators
 N08.01 Write the decimal for a given concrete or pictorial representation of part of a set, part of a region, or of a unit of measure.
 N08.02 Represent a given decimal using concrete materials or a pictorial representation.
 N08.03 Represent an equivalent tenth, hundredth, or thousandth for a given decimal, using concrete or visual representations.
 N08.04 Express a given tenth as an equivalent hundredth and thousandth.
 N08.05 Express a given hundredth as an equivalent thousandth.
 N08.06 Explain the value of each digit in a given decimal. 

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5.NS.1.9
Students will be expected to relate decimals to fractions and fractions to decimals (to thousandths).
• Performance Indicators
 N09.01 Express, orally and symbolically, a given fraction with a denominator of 10, 100, or 1000 as a decimal.
 N09.02 Read decimals as fractions (e.g., 0.45 is read as zero and fortyfive hundredths).
 N09.03 Express, orally and symbolically, a given decimal in fraction form.
 N09.04 Represent the fractions 1/2 , 1/4 , and 3/4 as decimals using baseten blocks, grids, and number lines.
 N09.05 Express a given pictorial or concrete representation as a fraction or decimal (e.g., 250 shaded squares on a thousandth grid can be expressed as 0.250 or 250/1000).

5.NS.1.1

Measurement and Data

5.MD.1.1
Students will be expected to design and construct different rectangles, given a perimeter or an area or both (whole numbers), and make generalizations.
• Performance Indicators
 M01.01 Draw two or more rectangles for a given perimeter in a problem solving context.
 M01.02 Draw two or more rectangles for a given area in a problemsolving context.
 M01.03 Determine the shape that will result in the greatest area for any given perimeter.
 M01.04 Determine the shape that will result in the least area for any given perimeter.
 M01.05 Provide a reallife context for when it is important to consider the relationship between area and perimeter. 

5.MD.1.2
Students will be expected to demonstrate an understanding of measuring length (mm) by
• selecting and justifying referents for the unit millimetre (mm)
• modelling and describing the relationship between millimetre (mm) and centimetre (cm) units, and between millimetre (mm) and metre (m) units
• Performance Indicators
 M02.01 Provide a referent for one millimetre, and explain the choice.
 M02.02 Provide a referent for one centimetre, and explain the choice.
 M02.03 Provide a referent for one metre, and explain the choice.
 M02.04 Show that 10 millimetres is equivalent to one centimetre, using concrete materials.
 M02.05 Show that 1000 millimetres is equivalent to one metre, using concrete materials.
 M02.06 Provide examples of instances where millimetres are used as the unit of measure.
 M02.07 Estimate and measure length in millimetres, centimetres, and metres. 
5.MD.1.3
Students will be expected to demonstrate an understanding of volume by
• selecting and justifying referents for cubic centimetre (cm^3) or cubic metre (m^3) units
• estimating volume using referents for cubic centimetre (cm^3) or cubic metre (m^3)
• measuring and recording volume (cm^3 or m^3)
• constructing rectangular prisms for a given volume
• Performance Indicators
 M03.01 Identify and explain why the cube is the most efficient unit for measuring volume.
 M03.02 Provide a referent for a cubic centimetre, and explain the choice.
 M03.03 Provide a referent for a cubic metre, and explain the choice.
 M03.04 Determine which standard cubic unit is represented by a given referent.
 M03.05 Estimate the volume of a given 3D object using personal referents.
 M03.06 Determine the volume of a given 3D object using manipulatives, and explain the strategy.
 M03.07 Construct a rectangular prism for a given volume.
 M03.08 Construct more than one rectangular prism for a given volume. 

5.MD.1.4
Students will be expected to demonstrate an understanding of capacity by
• describing the relationship between millilitre (mL) and litre (L) units
• selecting and justifying referents for millilitre (mL) and litre (L) units
• estimating capacity using referents for millilitre (mL) and litre (L)
• measuring and recording capacity (mL or L)
• Performance Indicators
 M04.01 Demonstrate that 1000 millilitres is equivalent to one litre by filling a onelitre container using a combination of smaller containers.
 M04.02 Provide a referent for one litre, and explain the choice.
 M04.03 Provide a referent for one millilitre, and explain the choice.
 M04.04 Determine the capacity unit of a given referent.
 M04.05 Estimate the capacity of a given container using personal referents.
 M04.06 Determine the capacity of a given container using materials that take the shape of the inside of the container (e.g., a liquid, rice, sand, beads), and explain the strategy.

5.MD.1.1

Geometry

5.G.1.1
Students will be expected to describe and provide examples of edges and faces of 3D objects, and sides of 2D shapes that are parallel, intersecting, perpendicular, vertical, and horizontal.
• Performance Indicators
 G01.01 Identify parallel, intersecting, perpendicular, vertical, and horizontal edges and faces on 3D objects.
 G01.02 Identify parallel, intersecting, perpendicular, vertical, and horizontal sides on 2D shapes.
 G01.03 Provide examples from the environment that show parallel, intersecting, perpendicular, vertical, and horizontal line segments.
 G01.04 Find examples of edges, faces, and sides that are parallel, intersecting, perpendicular, vertical, and horizontal in print and electronic media, such as newspapers, magazines, and the Internet.
 G01.05 Draw 2D shapes that have sides that are parallel, intersecting, perpendicular, vertical, or horizontal.
 G01.06 Build 3D objects that have edges and faces that are parallel, intersecting, perpendicular, vertical, or horizontal.
 G01.07 Describe the faces and edges of a given 3D object using terms such as parallel, intersecting, perpendicular, vertical, or horizontal.
 G01.08 Describe the sides of a given 2D shape using terms such as parallel, intersecting, perpendicular, vertical, or horizontal. 
5.G.1.2
Students will be expected to name, identify, and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombi, according to their attributes.
• Performance Indicators
 G02.01 Identify and describe the characteristics of a presorted set of quadrilaterals.
 G02.02 Sort a given set of quadrilaterals, and explain the sorting rule.
 G02.03 Sort a given set of quadrilaterals according to the lengths of the sides.
 G02.04 Sort a given set of quadrilaterals according to whether or not opposite sides are parallel.
 G02.05 Sort a set of quadrilaterals based on properties such as diagonals are congruent, diagonals bisect each other, and opposite angles are equal.
 G02.06 Name and classify quadrilaterals according to their attributes. 
5.G.1.3
Students will be expected to perform a single transformation (translation, rotation, or reflection) of a 2D shape (with and without technology) and draw and describe the image.
• Performance Indicators
 G03.01 Translate a given 2D shape horizontally, vertically, or diagonally, draw the image, and describe the position and orientation of the image.
 G03.02 Rotate a given 2D shape about a vertex, draw the image, and describe the position and orientation of the image.
 G03.03 Reflect a given 2D shape in a line of reflection, draw the image, and describe the position and orientation of the image.
 G03.04 Perform a transformation of a given 2D shape by following instructions.
 G03.05 Draw a 2D shape, translate the shape, and record the translation by describing the direction and magnitude of the movement.
 G03.06 Draw a 2D shape, rotate the shape about a vertex, and describe the direction of the turn (clockwise or counterclockwise) and the fraction of the turn (limited to 1/4, 1/2, 3/4, or full turn).
 G03.07 Draw a 2D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection.
 G03.08 Predict the result of a single transformation of a 2D shape and verify the prediction. 
5.G.1.4
Students will be expected to identify and describe a single transformation, including a translation, rotation, and reflection of 2D shapes.
• Performance Indicators
 G04.01 Provide an example of a translation, rotation, and reflection.
 G04.02 Identify a given single transformation as a translation, rotation, or reflection.
 G04.03 Describe a given rotation about a point of rotation by the direction of the turn (clockwise or counterclockwise).
 G04.04 Describe a given reflection by identifying the line of reflection and the distance of the image from the line of reflection.
 G04.05 Describe a given translation by identifying the direction and magnitude of the movement.
 G04.06 Identify transformations found in everyday pictures, art, or the environment. 
5.G.1.5
Students will be expected to identify right angles.
• Performance Indicators
 G05.01 Provide examples of right angles in the environment.
 G05.02 Sketch right angles without the use of a protractor.
 G05.03 Label a right angle, using a symbol.
 G05.04 Identify angles greater than or less than a right angle. 

5.G.1.1

Patterns and Relations

5.RP.1.1
Students will be expected to determine the pattern rule to make predictions about subsequent terms.
• Performance Indicators
 PR01.01 Extend a given increasing or decreasing pattern, with and without concrete materials, and explain how each term differs from the preceding one.
 PR01.02 Describe, orally or in written form, a given pattern using mathematical language such as one more, one less, or five more.
 PR01.03 Write a mathematical expression to represent a given pattern, such as r + 1, r â€“ 1, r + 5.
 PR01.04 Describe the relationship in a given table or chart using a mathematical expression.
 PR01.05 Determine and explain why a given number is or is not the next term in a pattern.
 PR01.06 Predict subsequent terms in a given pattern.
 PR01.07 Solve a given problem by using a pattern rule to determine subsequent terms.
 PR01.08 Represent a given pattern visually to verify predictions. 

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5.RP.1.2
Students will be expected to solve problems involving singlevariable, onestep equations with whole number coefficients and whole number solutions.
• Performance Indicators
 PR02.01 Explain the purpose of the letter variable in a given addition, subtraction, multiplication, or division equation with one unknown (e.g., 36 Ã· n = 6).
 PR02.02 Express a given pictorial or concrete representation of an equation in symbolic form.
 PR02.03 Express a given problem as an equation where the unknown is represented by a letter variable.
 PR02.04 Create a problem for a given equation with one unknown.
 PR02.05 Solve a given singlevariable equation with the unknown in any of the terms ( n + 2 = 5, 4 + a = 7, 6 = r – 2, 10 = 2c, 15 ÷ r = 3).
 PR02.06 Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially, or symbolically.

5.RP.1.1

Statistics & Probability

5.SP.1.1
Students will be expected to differentiate between firsthand and secondhand data.
• Performance Indicators
 SP01.01 Explain the difference between firsthand and secondhand data.
 SP01.02 Formulate a question that can best be answered using firsthand data and explain why.
 SP01.03 Formulate a question that can best be answered using secondhand data and explain why.
 SP01.04 Find examples of secondhand data in print and electronic media, such as newspapers, magazines, and the Internet. 

5.SP.1.2
Students will be expected to construct and interpret double bar graphs to draw conclusions.
• Performance Indicators
 SP02.01 Determine the attributes (title, axes, intervals, and legend) of double bar graphs by comparing a given set of double bar graphs.
 SP02.02 Represent a given set of data by creating a double bar graph, label the title and axes, and create a legend without the use of technology.
 SP02.03 Draw conclusions from a given double bar graph to answer questions.
 SP02.04 Identify examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines, and the Internet.
 SP02.05 Solve a given problem by constructing and interpreting a double bar graph. 

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5.SP.1.3
Students will be expected to describe the likelihood of a single outcome occurring, using words such as impossible, possible, and certain.
• Performance Indicators
 SP03.01 Identify examples of events from personal contexts that are impossible, possible, or certain.
 SP03.02 Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible, or certain.
 SP03.03 Design and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible, or certain.
 SP03.04 Conduct a given probability experiment a number of times, record the outcomes, and explain the results. 

5.SP.1.4
Students will be expected to compare the likelihood of two possible outcomes occurring, using words such as less likely, equally likely, or more likely.
• Performance Indicators
 SP04.01 Identify outcomes from a given probability experiment that are less likely, equally likely, or more likely to occur than other outcomes.
 SP04.02 Design and conduct a probability experiment in which one outcome is less likely to occur than the other outcome.
 SP04.03 Design and conduct a probability experiment in which one outcome is equally likely to occur as the other outcome.
 SP04.04 Design and conduct a probability experiment in which one outcome is more likely to occur than the other outcome. 

5.SP.1.1