Math Games

Students will be expected to read and record time using digital and analog clocks, including 24-hour clocks.
• Performance Indicators
- M01.01 State the number of hours in a day.
- M01.02 Express the time orally and numerically from a 12-hour analog clock.
- M01.03 Express the time orally and numerically from a 24-hour analog clock.
- M01.04 Express the time orally and numerically from a 12-hour digital clock.
- M01.05 Express time orally and numerically from a 24-hour digital clock.
- M01.06 Describe time orally as “minutes toâ€

Students will be expected to read and record calendar dates in a variety of formats.
• Performance Indicators
- M02.01 Write dates in a variety of formats (e.g., yyyy/mm/dd, dd/mm/yyyy, March 21, 2014, dd/mm/yy).
- M02.02 Relate dates written in the format yyyy/mm/dd to dates on a calendar.
- M02.03 Identify possible interpretations of a given date (e.g., 06/03/04).

Students will be expected to demonstrate an understanding of area of regular and irregular 2-D shapes by
• recognizing that area is measured in square units
• selecting and justifying referents for the units square centimetre (cm²) or square metre (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

• Performance Indicators
- M03.01 Describe area as the measure of surface recorded in square units.
- M03.02 Identify and explain why the square is the most efficient unit for measuring area.
- M03.03 Provide a referent for a square centimetre, and explain the choice.
- M03.04 Provide a referent for a square metre, and explain the choice.
- M03.05 Determine which standard square unit is represented by a given referent.
- M03.06 Estimate the area of a given 2-D shape using personal referents.
- M03.07 Determine the area of a regular 2-D shape, and explain the strategy.
- M03.08 Determine the area of an irregular 2-D shape, and explain the strategy.
- M03.09 Construct a rectangle for a given area.
- M03.10 Demonstrate that many rectangles are possible for a given area by drawing at least two different rectangles for the same given area.

Students will be expected to demonstrate an understanding of many-to-one correspondence.
• Performance Indicators
- SP01.01 Compare graphs in which the same data has been displayed using one-to-one and many-toone correspondences, and explain how they are the same and different.
- SP01.02 Explain why many-to-one correspondence is sometimes used rather than one-to-one correspondence.
- SP01.03 Find examples of graphs in print and electronic media, such as newspapers, magazines, and the Internet, in which many-to-one correspondence is used; and describe the correspondence used.

Students will be expected to construct and interpret pictographs and bar graphs involving manyto-one correspondence to draw conclusions.
• Performance Indicators
- SP02.01 Identify an interval and correspondence for displaying a given set of data in a graph, and justify the choice.
- SP02.02 Create and label (with categories, title, and legend) a pictograph to display a given set of data, using many-to-one correspondence, and justify the choice of correspondence used.
- SP02.03 Create and label (with axes and title) a bar graph to display a given set of data, using many-toone correspondence, and justify the choice of interval used.
- SP02.04 Answer a given question, using a given graph in which data is displayed using many-to-one correspondence.

Students will be expected to represent and partition whole numbers to 10 000.
• Performance Indicators
- N01.01 Read a given four-digit numeral without using the word “and.â€

Students will be expected to relate decimals to fractions and fractions to decimals (to hundredths).
• Performance Indicators
- N10.01 Express, orally and symbolically, a given fraction with a denominator of 10 or 100 as a decimal.
- N10.02 Read decimals as fractions (e.g., 0.5 is zero and five tenths).
- N10.03 Express, orally and symbolically, a given decimal in fraction form.
- N10.04 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 ).
- N10.05 Express, orally and symbolically, the decimal equivalent for a given fraction (e.g., 50/100 can be expressed as 0.50).

Students will be expected to demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by
• estimating sums and differences
• using mental mathematics strategies to solve problems
• using personal strategies to determine sums and differences

• Performance Indicators
- N11.01 Predict sums and differences of decimals, using estimation strategies.
- N11.02 Solve problems, including money problems, that involve addition and subtraction of decimals (limited to hundredths), using personal strategies.
- N11.03 Ask students to determine which problems do not require an exact solution.
- N11.04 Determine the approximate solution of a given problem not requiring an exact answer.
- N11.05 Count back change for a given purchase.
- N11.06 Determine an exact solution using mental computation strategies.

Students will be expected to compare and order numbers to 10 000.
• Performance Indicators
- N02.01 Order a given set of numbers in ascending or descending order, and explain the order by making references to place value.
- N02.02 Create and order three different four-digit numerals.
- N02.03 Identify the missing numbers in an ordered sequence and on a number line.
- N02.04 Identify incorrectly placed numbers in an ordered sequence and on a number line.
- N02.05 Place numbers in relative order on an open number line.
- N02.06 Place numbers on a number line containing benchmark numbers for the purpose of comparison.
- N02.07 Compare numbers based on a variety of methods

Students will be expected to demonstrate an understanding of addition and subtraction of numbers with answers to 10 000 (limited to three- and four-digit numerals) by
• using personal strategies for adding and subtracting
• estimating sums and differences
• solving problems involving addition and subtraction

• Performance Indicators
- N03.01 Represent concretely, pictorially, and symbolically the addition and subtraction of whole numbers, limited to three and four-digit numerals.
- N03.02 Determine the sum of two given numbers, limited to three and four-digit numerals, using a personal strategy, and record the process symbolically.
- N03.03 Determine the difference of two given numbers, limited to three- and four-digit numerals, using a personal strategy, and record the process symbolically.
- N03.04 Describe a situation in which an estimate rather than an exact answer is sufficient.
- N03.05 Estimate sums and differences using different strategies.
- N03.06 Create and solve problems that involve addition and subtraction of two or more numbers, limited to three- and four-digit numerals.
- N03.07 Explain mental mathematics strategies that could be used to determine a sum or difference.
- N03.08 Determine a sum or difference of one, two, and three-digit numerals efficiently, using mental mathematics strategies.

Students will be expected to apply and explain the properties of 0 and 1 for multiplication and the property of 1 for division.
• Performance Indicators
- N04.01 Determine the answer to a given question involving the multiplication of a number by 1, and explain the answer using the property of 1 in multiplication.
- N04.02 Determine the answer to a given question involving the multiplication of a number by 0, and explain the answer using the property of 0 in multiplication.
- N04.03 Determine the answer to a given question involving the division of a number by 1, and explain the answer using the property of 1 in division.

Students will be expected to describe and apply mental mathematics strategies, to recall basic multiplication facts to 9 × 9, and to determine related division facts.
• Performance Indicators
- N05.01 Describe the mental mathematics strategy used to determine basic multiplication or division facts.
- N05.02 Use and describe a personal strategy for determining the multiplication facts.
- N05.03 Use and describe a personal strategy for determining the division facts.
- N05.04 Quickly recall basic multiplication facts up to 9 ×9.

Students will be expected to demonstrate an understanding of multiplication (one-, two-, or three-digit by one-digit numerals) 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

• Performance Indicators
- N06.01 Model a given multiplication problem, using the distributive property (e.g., 8 × 365 = (8 × 300) + (8 × 60) + (8 × 5)).
- N06.02 Model the multiplication of two given numbers, limited to one-, two-, or three-digit by onedigit numerals, using concrete or visual representations, and record the process symbolically.
- N06.03 Create and solve multiplication story problems, limited to one-, two-, or three-digit by onedigit numerals, and record the process symbolically.
- N06.04 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).
- N06.05 Model and solve a given multiplication problem using an array, and record the process.
- N06.06 Determine the product of two given numbers using a personal strategy, and record the process symbolically.

Students will be expected to demonstrate an understanding of division (one-digit divisor and up to two-digit dividend) to solve problems by
• using personal strategies for dividing, with and without concrete materials
• estimating quotients
• relating division to multiplication

• Performance Indicators
- N07.01 Model the division of two given numbers without a remainder, limited to a one-digit divisor and up to a two-digit dividend, using concrete or visual representations, and record the process pictorially and symbolically.
- N07.02 Model the division of two given numbers with a remainder, limited to a one-digit divisor and up to a two-digit dividend, using concrete or visual representations, and record the process pictorially and symbolically. (It is not intended that remainders be expressed as decimals or fractions.)
- N07.03 Solve a given division problem, using a personal strategy, and record the process symbolically.
- N07.04 Create and solve division word problems involving a one- or two-digit dividend, and record the process pictorially and symbolically.
- N07.05 Estimate a quotient using a personal strategy (e.g., 86 ÷ 4 is close to 80 ÷ 4 or close to 80 ÷ 5).
- N07.06 Solve a given division problem by relating division to multiplication (e.g., for 80 ÷ 4, we know that 4 × 20 = 80, so 80 ÷ 4 = 20).

Students will be expected to demonstrate an understanding of fractions less than or equal to 1 by using concrete, pictorial, and symbolic representations to
• name and record fractions for the parts of one 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

• Performance Indicators
- N08.01 Represent a given fraction of one whole object, region, or a set using concrete materials.
- N08.02 Identify a fraction from its given concrete representation.
- N08.03 Name and record the shaded and non-shaded parts of a given whole object, region, or set.
- N08.04 Represent a given fraction pictorially by shading parts of a given whole object, region, or set.
- N08.05 Explain how denominators can be used to compare two given unit fractions with a numerator of 1.
- N08.06 Order a given set of fractions that have the same numerator, and explain the ordering.
- N08.07 Order a given set of fractions that have the same denominator, and explain the ordering.
- N08.08 Identify which of the benchmarks 0, 1/2, or 1 is closer to a given fraction.
- N08.09 Name fractions between two given benchmarks on a number line.
- N08.10 Order a given set of fractions by placing them on a number line with given benchmarks.
- N08.11 Provide examples of instances when two identical fractions may not represent the same quantity.
- N08.12 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 one whole.

Students will be expected to describe and represent decimals (tenths and hundredths) concretely, pictorially, and symbolically.
• Performance Indicators
- N09.01 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.
- N09.02 Represent a given decimal using concrete materials or a pictorial representation.
- N09.03 Explain the meaning of each digit in a given decimal.
- N09.04 Represent a given decimal using money values (dimes and pennies).
- N09.05 Record a given money value using decimals.
- N09.06 Provide examples of everyday contexts in which tenths and hundredths are used.
- N09.07 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).
- N09.08 Read decimal numbers correctly.

Students will be expected to describe and construct rectangular and triangular prisms.
• Performance Indicators
- G01.01 Identify and name common attributes of rectangular prisms from given sets of rectangular prisms.
- G01.02 Identify and name common attributes of triangular prisms from given sets of triangular prisms.
- G01.03 Sort a given set of right rectangular and triangular prisms, using the shape of the base.
- G01.04 Construct and describe a model of a rectangular and a triangular prism, using materials such as pattern blocks or modelling clay.
- G01.05 Construct rectangular prisms from their nets.
- G01.06 Construct triangular prisms from their nets.
- G01.07 Identify examples of rectangular and triangular prisms found in the environment.

Students will be expected to demonstrate an understanding of congruency, concretely and pictorially.
• Performance Indicators
- G02.01 Determine if two given 2-D shapes are congruent, and explain the strategy used.
- G02.02 Create a shape that is congruent to a given 2-D shape, and explain why the two shapes are congruent.
- G02.03 Identify congruent 2-D shapes from a given set of shapes shown in different positions in space.

Students will be expected to demonstrate an understanding of line symmetry by
• identifying symmetrical 2-D shapes
• creating symmetrical 2-D shapes
• drawing one or more lines of symmetry in a 2-D shape

• Performance Indicators
- G03.01 Identify the characteristics of given symmetrical and non-symmetrical 2-D shapes.
- G03.02 Sort a given set of 2-D shapes as symmetrical and non-symmetrical.
- G03.03 Complete a symmetrical 2-D shape, given one-half the shape and its line of symmetry, and explain the process.
- G03.04 Identify lines of symmetry of a given set of 2-D shapes, and explain why each shape is symmetrical.
- G03.05 Determine whether or not a given 2-D shape is symmetrical by using an image reflector or by folding and superimposing.
- G03.06 Create a symmetrical shape with and without manipulatives and explain the process.
- G03.07 Provide examples of symmetrical shapes found in the environment, and identify the line(s) of symmetry.
- G03.08 Sort a given set of 2-D shapes as those that have no lines of symmetry, one line of symmetry, or more than one line of symmetry.
- G03.09 Explain connections between congruence and symmetry using 2-D shapes.

Students will be expected to identify and describe patterns found in tables and charts, including a multiplication chart.
• Performance Indicators
- PR01.01 Identify and describe a variety of patterns in a multiplication chart.
- PR01.02 Determine the missing element(s) in a given table or chart.
- PR01.03 Identify the error(s) in a given table or chart.
- PR01.04 Describe the pattern found in a given table or chart

Students will be expected to translate among different representations of a pattern (a table, a chart, or concrete materials).
• Performance Indicators
- PR02.01 Create a table or chart from a given concrete representation of a pattern.
- PR02.02 Create a concrete representation of a given pattern displayed in a table or chart.
- PR02.03 Translate between pictorial, contextual, and concrete representations of a pattern.
- PR02.04 Explain why the same relationship exists between the pattern in a table and its concrete representation.

Students will be expected to represent, describe, and extend patterns and relationships, using charts and tables, to solve problems.
• Performance Indicators
- PR03.01 Translate the information in a given problem into a table or chart.
- PR03.02 Identify, describe, and extend the patterns in a table or chart to solve a given problem.

Students will be expected to identify and explain mathematical relationships, using charts and diagrams, to solve problems.
• Performance Indicators
- PR04.01 Complete a given Carroll diagram to solve a problem.
- PR04.02 Determine where new elements belong is a given Carroll diagram.
- PR04.03 Solve a given problem using a Carroll diagram.
- PR04.04 Identify a sorting rule for a given Venn diagram.
- PR04.05 Describe the relationship shown in a given Venn diagram when the circles overlap, when one circle is contained in the other, and when the circles are separate.
- PR04.06 Determine where new elements belong in a given Venn diagram.
- PR04.07 Solve a given problem by using a chart or diagram to identify mathematical relationships.

Students will be expected to express a given problem as an equation in which a symbol is used to represent an unknown number.
• Performance Indicators
- PR05.01 Explain the purpose of the symbol in a given addition, subtraction, multiplication, or division equation with one unknown (e.g., 36 ÷ ? = 6).
- PR05.02 Express a given pictorial or concrete representation of an equation in symbolic form.
- PR05.03 Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially, and/or symbolically.
- PR05.04 Create a problem in context for a given equation with one unknown.

Students will be expected to solve one-step equations involving a symbol to represent an unknown number.
• Performance Indicators
- PR06.01 Represent and solve a given one-step equation concretely, pictorially, or symbolically.
- PR06.02 Solve a given one-step equation using guess and test.
- PR06.03 Describe, orally, the meaning of a given one-step equation with one unknown.
- PR06.04 Solve a given equation when the unknown is on the left or right side of the equation.
- PR06.05 Represent and solve a given addition or subtraction problem involving a “part-part-wholeâ€