Math Games

Relate the passage of time to common activities, using nonstandard and standard units (minutes, hours, days, weeks, months, years).
• Select and use a nonstandard unit of measure, such as television shows or pendulum swings, to measure the passage of time, and explain the choice.
• Identify activities that can or cannot be accomplished in minutes, hours, days, weeks, months and years.
• Provide personal referents for minutes and hours.

Relate the number of seconds to a minute, the number of minutes to an hour and the number of days to a month in a problem-solving context.
• Determine the number of days in any given month, using a calendar.
• Solve a given problem involving the number of seconds in a minute, minutes in an hour or days in a given month.
• Create a calendar that includes days of the week, dates and personal events.

Demonstrate an understanding of measuring length (cm, m) by:
• selecting and justifying referents for the units cm and m.
• modelling and describing the relationship between the units cm and m.
• estimating length, using referents.
• measuring and recording length, width and height.
• Provide a personal referent for one centimetre, and explain the choice.
• Provide a personal referent for one metre, and explain the choice.
• Match a given standard unit to a given referent.
• Show that 100 cm is equivalent to 1 m by using concrete materials.
• Estimate the length of an object, using personal referents.
• Determine and record the length and width of a given 2-D shape.
• Determine and record the length, width or height of a given 3-D object.
• Draw a line segment of a given length, using a ruler.
• Sketch a line segment of a given length without using a ruler.

Demonstrate an understanding of measuring mass (g, kg) by:
• selecting and justifying referents for the units g and kg.
• modelling and describing the relationship between the units g and kg.
• estimating mass, using referents.
• measuring and recording mass.
• Provide a personal referent for one gram, and explain the choice.
• Provide a personal referent for one kilogram, and explain the choice.
• Match a given standard unit to a given referent.
• Explain the relationship between 1000 g and 1 kg, using a model.
• Estimate the mass of a given object, using personal referents.
• Determine and record the mass of a given 3-D object.
• Measure, using a scale, and record, using the units g and kg, the mass of given everyday objects.
• Provide examples of 3-D objects that have a mass of approximately 1 g, 100 g and 1 kg.
• Determine the mass of two given similar objects with different masses, and explain the results.
• Determine the mass of an object, change its shape, re-measure its mass, and explain the results.

Demonstrate an understanding of perimeter of regular and irregular shapes by:
• estimating perimeter, using referents for cm or m.
• measuring and recording perimeter (cm, m).
• constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter.
• Measure and record the perimeter of a given regular shape, and explain the strategy used.
• Measure and record the perimeter of a given irregular shape, and explain the strategy used.
• Construct a shape for a given perimeter (cm, m).
• Construct or draw more than one shape for a given perimeter.
• Estimate the perimeter of a given shape (cm, m), using personal referents.

Describe 3-D objects according to the shape of the faces and the number of edges and vertices.
• Identify the faces, edges and vertices of given 3-D objects, including cubes, spheres, cones, cylinders, pyramids and prisms.
• Identify the shape of the faces of a given 3-D object.
• Determine the number of faces, edges and vertices of a given 3-D object.
• Construct a skeleton of a given 3-D object, and describe how the skeleton relates to the 3-D object.
• Sort a given set of 3-D objects according to the number of faces, edges or vertices.

Sort regular and irregular polygons, including:
• triangles according to the number of sides.
• quadrilaterals according to the number of sides.
• pentagons according to the number of sides.
• hexagons according to the number of sides.
• octagons according to the number of sides.
• Classify a given set of regular and irregular polygons according to the number of sides.
• Identify given regular and irregular polygons that have different dimensions.
• Identify given regular and irregular polygons that have different orientations.

Collect first-hand data and organize it using:
• tally marks to answer questions.
• line plots to answer questions.
• charts to answer questions.
• lists to answer questions.
• Record the number of objects in a given set, using tally marks.
• Determine the common attributes of line plots by comparing line plots in a given set.
• Organize a given set of data, using tally marks, line plots, charts or lists.
• Collect and organize data, using tally marks, line plots, charts and lists.
• Answer questions arising from a given line plot, chart or list.
• Answer questions using collected data.

Construct, label and interpret bar graphs to solve problems.
• Determine the common attributes, titles and axes of bar graphs by comparing bar graphs in a given set.
• Create a bar graph, labelling the title and axes, to represent a given set of data.
• Draw conclusions from a given bar graph to solve problems.
• Solve problems by constructing and interpreting a bar graph.

Demonstrate an understanding of increasing patterns by:
• describing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• extending numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• comparing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• creating numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• Describe a given increasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues; e.g., for 42, 44, 46… the pattern rule is start at 42 and add 2 each time.
• Identify the pattern rule of a given increasing pattern, and extend the pattern for the next three terms.
• Identify and explain errors in a given increasing pattern.
• Locate and describe various increasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns.
• Compare numeric patterns of counting by 2s, 5s, 10s, 25s and 100s.
• Create a concrete, pictorial or symbolic representation of an increasing pattern for a given pattern rule.
• Create a concrete, pictorial or symbolic increasing pattern; and describe the relationship, using a pattern rule.
• Solve a given problem, using increasing patterns.
• Identify and describe increasing patterns in the environment.
• Identify and apply a pattern rule to determine missing elements for a given pattern.
• Describe the strategy used to determine missing elements in a given increasing pattern.

Demonstrate an understanding of decreasing patterns by:
• describing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• extending numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• comparing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• creating numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• Describe a given decreasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues.
• Identify the pattern rule of a given decreasing pattern, and extend the pattern for the next three terms.
• Identify and explain errors in a given decreasing pattern.
• Identify and describe various decreasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns.
• Compare decreasing numeric patterns of counting backward by 2s, 5s, 10s, 25s and 100s.
• Create a concrete, pictorial or symbolic decreasing pattern for a given pattern rule.
• Create a concrete, pictorial or symbolic decreasing pattern; and describe the relationship, using a pattern rule.
• Solve a given problem, using decreasing patterns.
• Identify and describe decreasing patterns in the environment.
• Identify and apply a pattern rule to determine missing elements for a given pattern.
• Describe the strategy used to determine missing elements in a given decreasing pattern.

Sort objects or numbers, using one or more than one attribute.
• Classify a given set of numbers according to the number of digits.
• Classify a given set of numbers as odd or even.
• Classify a given set of numbers as fractions or whole numbers.
• Determine the difference between two given pre-sorted sets of objects that have been sorted based on two attributes, and explain a possible sorting rule used to sort them.
• Record the sorting of a set of objects, using tools such as Venn diagrams.
• Sort a given set of objects or numbers in more than one way, and explain how the sorting rules are different.

Solve one-step addition and subtraction equations involving a symbol to represent an unknown number.
• Explain the purpose of the symbol in a given addition or subtraction equation with one unknown; e.g., in the equation 3 + ? = 10, the triangle represents the number that would make the equation true.
• Create an addition or subtraction equation with one unknown to represent a given combining or separating action.
• Provide an alternative symbol for the unknown in a given addition or subtraction equation.
• Solve, using manipulatives, a given addition or subtraction equation with one unknown that represents combining or separating actions.
• Solve a given addition or subtraction equation with one unknown, using a variety of strategies, including guess and test.
• Solve a given addition or subtraction equation when the unknown is on the left or the right side of the equation.
• Explain why the unknown in a given addition or subtraction equation has only one value.

Say the number sequence 0 to 1000 forward and backward by:
• 5s, 10s or 100s, using any starting point.
• 3s, using starting points that are multiples of 3.
• 4s, using starting points that are multiples of 4.
• 25s, using starting points that are multiples of 25.
• Extend a given skip counting sequence by 5s, 10s or 100s, forward and backward, using a given starting point.
• Extend a given skip counting sequence by 3s, forward and backward, starting at a given multiple of 3.
• Extend a given skip counting sequence by 4s, forward and backward, starting at a given multiple of 4.
• Extend a given skip counting sequence by 25s, forward and backward, starting at a given multiple of 25.
• Identify and correct errors and omissions in a given skip counting sequence.
• Determine the value of a given set of coins (nickels, dimes, quarters, loonies) by using skip counting.
• Identify and explain the skip counting pattern for a given number sequence.

Apply mental mathematics strategies and number properties in order to understand and recall basic addition facts and related subtraction facts to 18.
• Describe a mental mathematics strategy that could be used to determine a given basic fact, such as:
- doubles; e.g., for 6 + 8, think 7 + 7.
- doubles plus one; e.g., for 6 + 7, think 6 + 6 + 1.
- doubles take away one; e.g., for 6 + 7, think 7 + 7 – 1.
- doubles plus two; e.g., for 6 + 8, think 6 + 6 + 2.
- doubles take away two; e.g., for 6 + 8, think 8 + 8 – 2.
- making 10; e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4.
- commutative property; e.g., for 3 + 9, think 9 + 3.
- addition for subtraction; e.g., for 13 – 7, think 7 + ? = 13.
• Apply the property of zero to determine a given sum or difference when adding or subtracting zero; e.g., 5 + 0 = 5 and 5 – 0 = 5.
• Provide a rule for determining answers when adding and subtracting zero.
• Apply a mental mathematics strategy to provide a solution to a given basic addition fact up to and including 9 + 9 or a related subtraction fact.
• Demonstrate understanding, recall/memorization and application of addition facts up to and including 9 + 9 and related subtraction facts.

Demonstrate an understanding of multiplication to 5 × 5 by:
• representing and explaining multiplication using equal grouping and arrays.
• creating and solving problems in context that involve multiplication.
• modelling multiplication using concrete and visual representations, and recording the process symbolically.
• relating multiplication to repeated addition.
• relating multiplication to division.
• Identify events from experience that can be described as multiplication.
• Represent a given story problem, using manipulatives or diagrams, and record the problem in a number sentence.
• Represent a given multiplication expression as repeated addition.
• Represent a given repeated addition as multiplication.
• Create and illustrate a story problem for a given number sentence; e.g., 2 × 3 = 6.
• Represent, concretely or pictorially, equal groups for a given number sentence.
• Represent a given multiplication expression, using an array.
• Create an array to model the commutative property of multiplication.
• Relate multiplication to division by using arrays and writing related number sentences.
• Solve a given multiplication problem.
• Demonstrate understanding and recall/memorization of multiplication facts to 5 × 5.

Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 × 5) by:
• representing and explaining division using equal sharing and equal grouping.
• creating and solving problems in context that involve equal sharing and equal grouping.
• modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically.
• relating division to repeated subtraction.
• relating division to multiplication.
• Identify events from experience that can be described as equal sharing.
• Identify events from experience that can be described as equal grouping.
• Illustrate, with counters or a diagram, a given story problem, presented orally, that involves equal sharing; and solve the problem.
• Illustrate, with counters or a diagram, a given story problem, presented orally, that involves equal grouping; and solve the problem.
• Listen to a story problem; represent the numbers, using manipulatives or a sketch; and record the problem with a number sentence.
• Create and illustrate, with counters, a story problem for a given number sentence; e.g., 6 ÷ 3 = 2.
• Represent a given division expression as repeated subtraction.
• Represent a given repeated subtraction as a division expression.
• Relate division to multiplication by using arrays and writing related number sentences.
• Solve a given problem involving division.
• Demonstrate understanding and recall/memorization of division facts related to multiplication facts to 5 × 5.

Demonstrate an understanding of fractions by:
• explaining that a fraction represents a part of a whole.
• describing situations in which fractions are used.
• comparing fractions of the same whole that have like denominators.
• Identify common characteristics of a given set of fractions.
• Describe everyday situations where fractions are used.
• Cut or fold a whole into equal parts, or draw a whole in equal parts; demonstrate that the parts are equal; and name the parts.
• Sort a given set of shaded regions into those that represent equal parts and those that do not, and explain the sorting.
• Represent a given fraction concretely or pictorially.
• Name and record the fraction represented by the shaded and non-shaded parts of a given region.
• Compare given fractions with the same denominator, using models.
• Identify the numerator and denominator for a given fraction.
• Model and explain the meaning of numerator and denominator.

Represent and describe numbers to 1000, concretely, pictorially and symbolically.
• Read a given three-digit numeral without using the word and; e.g., 321 is three hundred twenty-one, NOT three hundred AND twenty-one.
• Read a given number word (0 to 1000).
• Represent a given number as an expression; e.g., 300 – 44 or 20 + 236 for 256.
• Represent a given number, using manipulatives such as base ten materials.
• Represent a given number pictorially.
• Write number words for given multiples of ten to 90.
• Write number words for given multiples of a hundred to 900.

Compare and order numbers to 1000.
• Place a given set of numbers in ascending or descending order, and verify the result by using a hundred chart (e.g., a one hundred chart, a two hundred chart, a three hundred chart), a number line or by making references to place value.
• Create as many different 3-digit numerals as possible, given three different digits. Place the numbers in ascending or descending order.
• Identify and explain errors in a given ordered sequence.
• Identify missing numbers in parts of a given hundred chart.
• Identify errors in a given hundred chart.

Estimate quantities less than 1000, using referents.
• Estimate the number of groups of ten in a given quantity, using 10 as a referent (known quantity).
• Estimate the number of groups of a hundred in a given quantity, using 100 as a referent.
• Estimate a given quantity by comparing it to a referent.
• Select an estimate for a given quantity by choosing among three possible choices.
• Select and justify a referent for determining an estimate for a given quantity.

Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.
• Record, in more than one way, the number represented by given proportional materials (e.g., base-ten materials) and non-proportional materials (e.g., money).
• Represent a given number in different ways, using proportional and non-proportional materials, and explain how the representations are equivalent; e.g., 351 can be represented as three 100s, five 10s and one 1; or two 100s, fifteen 10s and one 1; or three 100s, four 10s and eleven 1s.
• Explain and show, with counters, the meaning of each digit for a given 3-digit numeral with all digits the same; e.g., for the numeral 222, the first digit represents two hundreds (two hundred counters) the second digit represents two tens (twenty counters) and the third digit represents two ones (two counters).
• Explain, using concrete materials, the meaning of zero as a place holder in a given number.

Describe and apply mental mathematics strategies for adding two 2-digit numerals.
• Add two given 2-digit numerals, using a mental mathematics strategy, and explain or illustrate the strategy.
• Explain how to use the "adding from left to right" strategy; e.g., to determine the sum of 23 + 46, think 20 + 40 and 3 + 6.
• Explain how to use the "taking one addend to the nearest multiple of ten and then compensating" strategy; e.g., to determine the sum of 28 + 47, think 30 + 47 – 2 or 50 + 28 – 3.
• Explain how to use the "using doubles" strategy; e.g., to determine the sum of 24 + 26, think 25 + 25; to determine the sum of 25 + 26, think 25 + 25 + 1 or doubles plus 1.
• Apply a mental mathematics strategy for adding two given 2-digit numerals.

Describe and apply mental mathematics strategies for subtracting two 2-digit numerals.
• Subtract two given 2-digit numerals, using a mental mathematics strategy, and explain or model the strategy used.
• Explain how to use the "taking the subtrahend to the nearest multiple of ten and then compensating" strategy; e.g., to determine the difference of 48 – 19, think 48 – 20 + 1.
• Explain how to use the "adding on" strategy; e.g., to determine the difference of 62 – 45, think 45 + 5, then 50 + 12 and then 5 + 12.
• Explain how to use the "using doubles" strategy; e.g., to determine the difference of 24 – 12, think 12 + 12 = 24.
• Apply a mental mathematics strategy for subtracting two given 2-digit numerals.

Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context.
• Estimate the solution for a given problem involving the sum of two 2-digit numerals; e.g., to estimate the sum of 43 + 56, use 40 + 50 (the sum is close to 90).
• Estimate the solution for a given problem involving the difference of two 2-digit numerals; e.g., to estimate the difference of 56 – 23, use 50 – 20 (the difference is close to 30).

Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2- and 3-digit numerals), concretely, pictorially and symbolically, by:
• using personal strategies for adding and subtracting with and without the support of manipulatives.
• creating and solving problems in context that involve addition and subtraction of numbers.
• Model the addition of two or more given numbers, using concrete or visual representations, and record the process symbolically.
• Model the subtraction of two given numbers, using concrete or visual representations, and record the process symbolically.
• Create an addition or subtraction story problem for a given solution.
• Determine the sum of two given numbers, using a personal strategy; e.g., for 326 + 48, record 300 + 60 + 14.
• Determine the difference of two given numbers, using a personal strategy; e.g., for 127 – 38, record 38 + 2 + 80 + 7 or 127 – 20 – 10 – 8.
• Refine personal strategies to increase their efficiency.
• Solve a given problem involving the sum or difference of two given numbers.
• Solve a given problem using the standard/traditional addition algorithm.
• Solve a given problem using the standard/traditional subtraction algorithm.