
4Grade 4 Standards
Top Mathematicians

Patterns and Relations

4.PR.1
Identify and describe patterns found in tables and charts, including a multiplication chart.
• Achievement Indicators
 Identify and describe a variety of patterns in a multiplication chart.
 Determine the missing element(s) in a given table or chart.
 Identify 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
Reproduce a pattern shown in a table or chart using concrete materials.
• Achievement Indicators
 Create a concrete representation of a given pattern displayed in a table or chart.
 Explain why the same relationship exists between the pattern in a table and its concrete
representation. 

4.PR.3
Represent and describe patterns and relationships using charts and tables to solve problems.
• Achievement Indicators
 Extend patterns found in a table or chart to solve a given problem.
 Translate the information provided 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.
• Achievement Indicators
 Complete a Carroll diagram by entering given data into correct squares to solve a given problem.
 Determine where new elements belong in a given Carroll diagram.
 Solve a given problem using a 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. 

4.PR.5
Express a given problem as an equation in which a symbol is used to represent an unknown number.
• Achievement Indicators
 Explain the purpose of the symbol, such as a triangle or circle, 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 story problem, represent the problem with an equation and solve the problem concretely, pictorially or symbolically.
 Create a problem in context for a given equation with one unknown. 
4.PR.6
Solve onestep equations involving a symbol to represent an unknown number.
• Achievement Indicators
 Solve a given onestep equation using manipulatives.
 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 symbols to represent the unknown.

4.PR.1

Shape and Space

4.SS.1
Read and record time using digital and analog clocks, including 24hour clocks.
• Achievement Indicators
 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.
 Describe time orally and numerically from a 24hour digital clock.
 Describe time orally as “minutes to” or “minutes after” the hour.
 Explain the meaning of AM and PM, and provide an example of an activity that occurs during the AM and another that occurs during the PM. 

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4.SS.2
Read and record calendar dates in a variety of formats.
• Achievement Indicators
 Write dates in a variety of formats, e.g., yyyy/mm/dd, dd/mm/yyyy, March 21, 2006, 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 by 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.
• Achievement Indicators
 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 rectangular and triangular prisms.
• Achievement Indicators
 Identify and name common attributes of rectangular prisms from given sets of rectangular prisms.
 Identify and name common attributes of triangular prisms from given sets of triangular prisms.
 Sort a given set of rectangular and triangular prisms using the shape of the base.
 Construct and describe a model of rectangular and triangular prisms using materials, such as pattern blocks or modelling clay.
 Construct rectangular prisms from their nets.
 Construct triangular prisms from their nets.
 Identify examples of rectangular and triangular prisms found in the environment. 

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4.SS.5
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.
• Achievement Indicators
 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 a Mira 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.
• Achievement Indicators
 Compare graphs in which different intervals or correspondences are used and explain why the interval or correspondence was used.
 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 which manytoone correspondence is used in print and electronic media, such as newspapers, magazines and the Internet, and describe the correspondence used. 

4.SP.2
Construct and interpret pictographs and bar graphs involving manytoone correspondence to draw conclusions.
• Achievement Indicators
 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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4.SP.1

Number

4.N.1
Represent and describe whole numbers to 10 000, pictorially and symbolically.
• Achievement Indicators
 Read a given fourdigit numeral without using the word “and,” e.g., 5321 is five thousand three hundred twenty one, NOT five thousand three hundred AND twenty one.
 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.
 Describe the meaning of each digit in a given numeral.
 Express a given numeral in expanded notation, e.g., 321 = 300 + 20 + 1.
 Write the numeral represented by a given expanded notation.
 Explain and show the meaning of each digit in a given 4digit numeral 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 (to hundredths).
• Achievement Indicators
 Read decimals as fractions, e.g., 0.5 is zero and five tenths.
 Express orally and in written form a given decimal in fractional form.
 Express orally and in written form a given fraction with a denominator of 10 or 100 as a decimal.
 Express a given pictorial or concrete representation as a fraction or decimal, e.g., 15 shaded squares on a hundred 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 compatible numbers
• estimating sums and differences
• using mental math strategies
to solve problems.
• Achievement Indicators
 Predict sums and differences of decimals using estimation strategies.
 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.
 Estimate a sum or difference using compatible numbers.
 Count back change for a given purchase. 

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4.N.2
Compare and order numbers to 10 000.
• Achievement Indicators
 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. 

4.N.3
Demonstrate an understanding of addition of numbers with answers to 10 000 and their corresponding subtractions (limited to 3 and 4digit numerals) by:
• using personal strategies for adding and subtracting
• estimating sums and differences
• solving problems involving addition and subtraction.
• Achievement Indicators
 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.
 Solve problems that involve addition and subtraction of more than 2 numbers. 

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4.N.4
Explain the properties of 0 and 1 for multiplication, and the property of 1 for division.
• Achievement Indicators
 Explain the property for determining the answer when multiplying numbers by one.
 Explain the property for determining the answer when multiplying numbers by zero.
 Explain the property for determining the answer when dividing numbers by one. 

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4.N.5
Describe and apply mental mathematics strategies, such as:
• skip counting from a known fact
• using doubling or halving
• using doubling or halving and adding or subtracting one more group
• using patterns in the 9s facts
• using repeated doubling
to determine basic multiplication facts to 9 × 9 and related division facts.
• Achievement Indicators
 Provide examples for applying mental mathematics strategies:
• 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
• use ten facts 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. 
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.
• Achievement Indicators
 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.
 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. 

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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.
• Achievement Indicators
(It is not intended that remainders be expressed as decimals or fractions.)
 Solve a given division problem without a remainder using arrays or base ten materials.
 Solve a given division problem with a remainder using arrays or base ten materials.
 Solve a given division problem using a personal strategy and record the process.
 Create and solve a word problem involving a 1 or 2digit dividend.
 Estimate a quotient using a personal strategy, e.g., 86 ÷ 4 is close to 80 ÷ 4 or close to 80 ÷ 5. 

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4.N.8
Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial 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.
• Achievement Indicators
 Represent a given fraction using concrete materials.
 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.
 Represent a given fraction pictorially by shading parts of a given set.
 Represent a given fraction pictorially by shading parts of a given whole.
 Explain how denominators can be used to compare two given unit fractions with numerator 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 cloudberries is not equivalent to half of sixteen cloudberries.
 Provide an example of a fraction that represents part of a set and a fraction that represents part of a whole from everyday contexts. 

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4.N.9
Describe and represent decimals (tenths and hundredths) concretely, pictorially and symbolically.
• Achievement Indicators
 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 hundredths, e.g., 0.9 is equivalent to 0.90 or 9 dimes is equivalent to 90 pennies. 

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4.N.1