
4Grade 4 Standards
Top Mathematicians

Patterns and Relations

4.PR.1
Identify and describe patterns found in tables and charts.
• Identify and describe a variety of patterns in a multiplication chart.
• Determine the missing element(s) in a given table or chart.
• Identify the error(s) in a given table or chart.
• Describe the pattern found in a given table or chart. 

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4.PR.2
Translate among different representations of a pattern, such as a table, a chart or concrete materials.
• Create a concrete representation of a given pattern displayed in a table or chart.
• Create a table or chart from a given concrete representation of a pattern. 

4.PR.3
Represent, describe and extend patterns and relationships, using charts and tables, to solve problems.
• Translate the information in a given problem into a table or chart.
• Identify and extend the patterns in a table or chart to solve a given problem. 

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4.PR.4
Identify and explain mathematical relationships, using charts and diagrams, to solve problems.
• Complete a given Carroll diagram to solve a problem.
• Determine where new elements belong in a given Carroll diagram.
• Identify a sorting rule for a given Venn diagram.
• Describe the relationship shown in a given Venn diagram when the circles intersect, when one circle is contained in the other and when the circles are separate.
• Determine where new elements belong in a given Venn diagram.
• Solve a given problem by using a chart or diagram to identify mathematical relationships. 

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4.PR.5
Express a given problem as an equation in which a symbol is used to represent an unknown number.
• Explain the purpose of the symbol in a given addition, subtraction, multiplication or division equation with one unknown; e.g., 36 ÷ __ = 6.
• Express a given pictorial or concrete representation of an equation in symbolic form.
• Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically.
• Create a problem for a given equation with one unknown. 

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4.PR.6
Solve onestep equations involving a symbol to represent an unknown number.
• Represent and solve a given onestep equation concretely, pictorially or symbolically.
• Solve a given onestep equation, using guess and test.
• Describe, orally, the meaning of a given onestep equation with one unknown.
• Solve a given equation when the unknown is on the left or right side of the equation.
• Represent and solve a given addition or subtraction problem involving a "partpartwhole" or comparison context, using a symbol to represent the unknown.
• Represent and solve a given multiplication or division problem involving equal grouping or partitioning (equal sharing), using a symbol to represent the unknown.

4.PR.1

Number

4.N.1
Represent and describe whole numbers to 10 000, pictorially and symbolically.
• Read a given fourdigit numeral without using the word and; e.g., 5321 is five thousand three hundred twentyone, NOT five thousand three hundred AND twentyone.
• Write a given numeral, using proper spacing without commas; e.g., 4567 or 4 567, 10 000.
• Write a given numeral 0–10 000 in words.
• Represent a given numeral, using a place value chart or diagrams.
• Express a given numeral in expanded notation; e.g., 321 = 300 + 20 + 1.
• Write the numeral represented by a given expanded notation.
• Explain the meaning of each digit in a given 4digit numeral, including numerals with all digits the same; e.g., for the numeral 2222, the first digit represents two thousands, the second digit two hundreds, the third digit two tens and the fourth digit two ones. 

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4.N.10
Relate decimals to fractions and fractions to decimals (to hundredths).
• Express, orally and in written form, a given fraction with a denominator of 10 or 100 as a decimal.
• Read decimals as fractions; e.g., 0.5 is zero and five tenths.
• Express, orally and in written form, a given decimal in fraction form.
• Express a given pictorial or concrete representation as a fraction or decimal; e.g., 15 shaded squares on a hundredth grid can be expressed as 0.15 or 15/100.
• Express, orally and in written form, the decimal equivalent for a given fraction; e.g., 50/100 can be expressed as 0.50. 
4.N.11
Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by:
• using personal strategies to determine sums and differences to solve problems.
• estimating sums and differences to solve problems.
• using mental mathematics strategies to solve problems.
• Predict sums and differences of decimals, using estimation strategies.
• Determine the sum or difference of two given decimal numbers, using a mental mathematics strategy, and explain the strategy.
• Refine personal strategies to increase their efficiency.
• Solve problems, including money problems, which involve addition and subtraction of decimals, limited to hundredths.
• Determine the approximate solution of a given problem not requiring an exact answer. 

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4.N.2
Compare and order numbers to 10 000.
• Order a given set of numbers in ascending or descending order, and explain the order by making references to place value.
• Create and order three different 4digit numerals.
• Identify the missing numbers in an ordered sequence or on a number line.
• Identify incorrectly placed numbers in an ordered sequence or on a number line. 

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4.N.3
Demonstrate an understanding of addition of numbers with answers to 10 000 and their corresponding subtractions (limited to 3 and 4 digit numerals) by:
• using personal strategies for adding and subtracting.
• estimating sums and differences.
• solving problems involving addition and subtraction.
• Explain how to keep track of digits that have the same place value when adding numbers, limited to 3 and 4digit numerals.
• Explain how to keep track of digits that have the same place value when subtracting numbers, limited to 3 and 4digit numerals.
• Describe a situation in which an estimate rather than an exact answer is sufficient.
• Estimate sums and differences, using different strategies; e.g., frontend estimation and compensation.
• Refine personal strategies to increase their efficiency.
• Solve problems that involve addition and subtraction of more than 2 numbers.
• Solve a given problem using the standard/traditional addition algorithm.
• Solve a given problem using the standard/traditional subtraction algorithm. 

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4.N.4
Apply the properties of 0 and 1 for multiplication and the property of 1 for division.
• Determine the answer to a given question involving the multiplication of a number by 1, and explain the answer.
• Determine the answer to a given question involving the multiplication of a number by 0, and explain the answer.
• Determine the answer to a given question involving the division of a number by 1, and explain the answer. 
4.N.5
Describe and apply mental mathematics strategies to determine basic multiplication facts to 9 × 9 and related division facts.
• Provide examples for applying mental mathematics strategies:
 skip counting from a known fact; e.g., for 3 × 6, think 3 × 5 = 15 plus 3 = 18.
 doubling; e.g., for 4 × 3, think 2 × 3 = 6 and 4 × 3 = 6 + 6.
 doubling and adding one more group; e.g., for 3 × 7, think 2 × 7 = 14 and 14 + 7 = 21.
 patterns when multiplying by 9; e.g., for 9 × 6, think 10 × 6 = 60, and 60 – 6 = 54; for 7 × 9, think 7 × 10 = 70, and 70 – 7 = 63.
 halving; e.g., if 4 × 6 is equal to 24, then 2 × 6 is equal to 12.
 relating division to multiplication; e.g., for 64 ÷ 8, think 8 × ? = 64.
 repeated doubling; e.g., for 4 × 6, think 2 × 6 = 12 and 2 × 12 = 24.
• Demonstrate understanding and application of strategies for multiplication and related division facts to 9 × 9.
• Demonstrate recall/memorization of multiplication and related division facts to 7 × 7. 
4.N.6
Demonstrate an understanding of multiplication (2 or 3digit by 1digit) to solve problems by:
• using personal strategies for multiplication with and without concrete materials.
• using arrays to represent multiplication.
• connecting concrete representations to symbolic representations.
• estimating products.
• applying the distributive property.
• Model a given multiplication problem, using the distributive property; e.g., 8 × 365 = (8 × 300) + (8 × 60) + (8 × 5).
• Use concrete materials, such as base ten blocks or their pictorial representations, to represent multiplication; and record the process symbolically.
• Create and solve a multiplication problem that is limited to 2 or 3digits by 1digit, and record the process.
• Refine personal strategies to increase their efficiency.
• Estimate a product, using a personal strategy; e.g., 2 × 243 is close to or a little more than 2 × 200, or close to or a little less than 2 × 250.
• Model and solve a given multiplication problem, using an array, and record the process.
• Solve a given multiplication problem, and record the process.
• Solve a given problem using the standard/traditional multiplication algorithm. 

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4.N.7
Demonstrate an understanding of division (1digit divisor and up to 2digit dividend) to solve problems by:
• using personal strategies for dividing with and without concrete materials.
• estimating quotients.
• relating division to multiplication.
• Solve a given division problem without a remainder, using arrays or base ten materials, and connect this process to the symbolic representation.
• Solve a given division problem with a remainder, using arrays or base ten materials, and connect this process to the symbolic representation.
• Solve a given division problem, using a personal strategy, and record the process.
• Refine personal strategies to increase their efficiency.
• Create and solve a division problem involving a 1 or 2digit dividend, and record the process.
• Estimate a quotient, using a personal strategy; e.g., 86 ÷ 4 is close to 80 ÷ 4 or close to 80 ÷ 5.
• Solve a given division problem by relating division to multiplication; e.g., for 100 ÷ 4, we know that 4 × 25 = 100, so 100 ÷ 4 = 25.
• Solve a given problem using the standard/traditional division algorithm. 

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4.N.8
Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to:
• name and record fractions for the parts of a whole or a set.
• compare and order fractions.
• model and explain that for different wholes, two identical fractions may not represent the same quantity.
• provide examples of where fractions are used.
• Represent a given fraction, using a region, object or set.
• Identify a fraction from its given concrete representation.
• Name and record the shaded and nonshaded parts of a given set.
• Name and record the shaded and nonshaded parts of a given whole region, object or set.
• Represent a given fraction pictorially by shading parts of a given set.
• Represent a given fraction pictorially by shading parts of a given whole region, object or set.
• Explain how denominators can be used to compare two given unit fractions with a numerator of 1.
• Order a given set of fractions that have the same numerator, and explain the ordering.
• Order a given set of fractions that have the same denominator, and explain the ordering.
• Identify which of the benchmarks 0, 1/2 or 1 is closer to a given fraction.
• Name fractions between two given benchmarks on a number line.
• Order a given set of fractions by placing them on a number line with given benchmarks.
• Provide examples of when two identical fractions may not represent the same quantity; e.g., half of a large apple is not equivalent to half of a small apple, half of ten Saskatoon berries is not equivalent to half of sixteen Saskatoon berries.
• Provide, from everyday contexts, an example of a fraction that represents part of a set and an example of a fraction that represents part of a whole. 

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4.N.9
Represent and describe decimals (tenths and hundredths), concretely, pictorially and symbolically.
• Write the decimal for a given concrete or pictorial representation of part of a set, part of a region or part of a unit of measure.
• Represent a given decimal, using concrete materials or a pictorial representation.
• Explain the meaning of each digit in a given decimal with all digits the same.
• Represent a given decimal, using money values (dimes and pennies).
• Record a given money value, using decimals.
• Provide examples of everyday contexts in which tenths and hundredths are used.
• Model, using manipulatives or pictures, that a given tenth can be expressed as a hundredth; e.g., 0.9 is equivalent to 0.90, or 9 dimes is equivalent to 90 pennies. 

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4.N.1

Shape and Space

4.SS.1
Read and record time, using digital and analog clocks, including 24hour clocks.
• State the number of hours in a day.
• Express the time orally and numerically from a 12hour analog clock.
• Express the time orally and numerically from a 24hour analog clock.
• Express the time orally and numerically from a 12hour digital clock.
• Express time orally and numerically from a 24hour digital clock.
• Describe time orally as "minutes to" or "minutes after" the hour.
• Explain the meaning of a.m. and p.m., and provide an example of an activity that occurs during the a.m., and another that occurs during the p.m. 

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4.SS.2
Read and record calendar dates in a variety of formats.
• Write dates in a variety of formats; e.g., yyyy/mm/dd, dd/mm/yyyy, March 21, 2007, dd/mm/yy.
• Relate dates written in the format yyyy/mm/dd to dates on a calendar.
• Identify possible interpretations of a given date; e.g., 06/03/04. 

4.SS.3
Demonstrate an understanding of area of regular and irregular 2D shapes by:
• recognizing that area is measured in square units.
• selecting and justifying referents for the units cm² or m².
• estimating area, using referents for cm² or m².
• determining and recording area (cm² or m²).
• constructing different rectangles for a given area (cm² or m²) in order to demonstrate that many different rectangles may have the same area.
• Describe area as the measure of surface recorded in square units.
• Identify and explain why the square is the most efficient unit for measuring area.
• Provide a referent for a square centimetre, and explain the choice.
• Provide a referent for a square metre, and explain the choice.
• Determine which standard square unit is represented by a given referent.
• Estimate the area of a given 2D shape, using personal referents.
• Determine the area of a regular 2D shape, and explain the strategy.
• Determine the area of an irregular 2D shape, and explain the strategy.
• Construct a rectangle for a given area.
• Demonstrate that many rectangles are possible for a given area by drawing at least two different rectangles for the same given area. 

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4.SS.4
Describe and construct right rectangular and right triangular prisms.
• Identify and name common attributes of right rectangular prisms from given sets of right rectangular prisms.
• Identify and name common attributes of right triangular prisms from given sets of right triangular prisms.
• Sort a given set of right rectangular and right triangular prisms, using the shape of the base.
• Construct and describe a model of a right rectangular and a right triangular prism, using materials such as pattern blocks or modelling clay.
• Construct right rectangular prisms from their nets.
• Construct right triangular prisms from their nets.
• Identify examples of right rectangular and right triangular prisms found in the environment. 

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4.SS.5
Demonstrate an understanding of congruency, concretely and pictorially.
• Determine if two given 2D shapes are congruent, and explain the strategy used.
• Create a shape that is congruent to a given 2D shape.
• Identify congruent 2D shapes from a given set of shapes shown in different orientations.
• Identify corresponding vertices and sides of two given congruent shapes. 

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4.SS.6
Demonstrate an understanding of line symmetry by:
• identifying symmetrical 2D shapes.
• creating symmetrical 2D shapes.
• drawing one or more lines of symmetry in a 2D shape.
• Identify the characteristics of given symmetrical and nonsymmetrical 2D shapes.
• Sort a given set of 2D shapes as symmetrical and nonsymmetrical.
• Complete a symmetrical 2D shape, given half the shape and its line of symmetry.
• Identify lines of symmetry of a given set of 2D shapes, and explain why each shape is symmetrical.
• Determine whether or not a given 2D shape is symmetrical by using an image reflector or by folding and superimposing.
• Create a symmetrical shape with and without manipulatives.
• Provide examples of symmetrical shapes found in the environment, and identify the line(s) of symmetry.
• Sort a given set of 2D shapes as those that have no lines of symmetry, one line of symmetry or more than one line of symmetry.

4.SS.1

Statistics & Probability

4.SP.1
Demonstrate an understanding of manytoone correspondence.
• Compare graphs in which the same data has been displayed using onetoone and manytoone correspondences, and explain how they are the same and different.
• Explain why manytoone correspondence is sometimes used rather than onetoone correspondence.
• Find examples of graphs in print and electronic media, such as newspapers, magazines and the Internet, in which manytoone correspondence is used; and describe the correspondence used. 

4.SP.2
Construct and interpret pictographs and bar graphs involving manytoone correspondence to draw conclusions.
• Identify an interval and correspondence for displaying a given set of data in a graph, and justify the choice.
• Create and label (with categories, title and legend) a pictograph to display a given set of data, using manytoone correspondence, and justify the choice of correspondence used.
• Create and label (with axes and title) a bar graph to display a given set of data, using manytoone correspondence, and justify the choice of interval used.
• Answer a given question, using a given graph in which data is displayed using manytoone correspondence. 

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