Math Games

Gather and record data about self and others to answer questions.
• Formulate a question that can be answered by gathering information about self and others.
• Organize data as it is collected, using concrete objects, tallies, check marks, charts or lists.
• Answer questions, using collected data.

Construct and interpret concrete graphs and pictographs to solve problems.
• Determine the common attributes of concrete graphs by comparing a given set of concrete graphs.
• Determine the common attributes of pictographs by comparing a given set of pictographs.
• Answer questions pertaining to a given concrete graph or pictograph.
• Create a concrete graph to display a given set of data, and draw conclusions.
• Create a pictograph to represent a given set of data, using one-to-one correspondence.
• Solve a given problem by constructing and interpreting a concrete graph or pictograph.

Relate the number of days to a week and the number of months to a year in a problem-solving context.
• Read a date on a calendar.
• Name and order the days of the week.
• Identify the day of the week and the month of the year for an identified calendar date.
• Communicate that there are seven days in a week and twelve months in a year.
• Determine whether a given set of days is more or less than a week.
• Identify yesterday's/tomorrow's date.
• Identify the month that comes before and the month that comes after a given month.
• Name and order the months of the year.
• Solve a given problem involving time that is limited to the number of days in a week and the number of months in a year.

Relate the size of a unit of measure to the number of units (limited to nonstandard units) used to measure length and mass (weight).
• Explain why one of two given nonstandard units may be a better choice for measuring the length of an object.
• Explain why one of two given nonstandard units may be a better choice for measuring the mass (weight) of an object.
• Select a nonstandard unit for measuring the length or mass (weight) of an object, and explain why it was chosen.
• Estimate the number of nonstandard units needed for a given measurement task.
• Explain why the number of units of a measurement will vary depending upon the unit of measure used.

Compare and order objects by length, height, distance around and mass (weight), using nonstandard units, and make statements of comparison.
• Estimate, measure and record the length, height, distance around or mass (weight) of a given object, using nonstandard units.
• Compare and order the measure of two or more objects in ascending or descending order, and explain the method of ordering.

Measure length to the nearest nonstandard unit by:
• using multiple copies of a unit.
• using a single copy of a unit (iteration process).
• Explain why overlapping or leaving gaps does not result in accurate measures.
• Count the number of nonstandard units required to measure the length of a given object, using a single copy or multiple copies of a unit.
• Estimate and measure a given object, using multiple copies of a nonstandard unit and using a single copy of the same unit many times, and explain the results.
• Estimate and measure, using nonstandard units, a given length that is not a straight line.

Demonstrate that changing the orientation of an object does not alter the measurements of its attributes.
• Measure a given object, change the orientation, re-measure, and explain the results.

Sort 2-D shapes and 3-D objects, using two attributes, and explain the sorting rule.
• Determine the differences between two given pre-sorted sets, and explain the sorting rule.
• Identify and name two common attributes of items within a given sorted group.
• Sort a given set of 2-D shapes (regular and irregular), according to two attributes, and explain the sorting rule.
• Sort a given set of 3-D objects, according to two attributes, and explain the sorting rule.

Describe, compare and construct 3-D objects, including:
• cubes.
• spheres.
• cones.
• cylinders.
• pyramids.
• Sort a given set of 3-D objects, and explain the sorting rule.
• Identify common attributes of cubes, spheres, cones, cylinders and pyramids from given sets of the same 3-D objects.
• Identify and describe given 3-D objects with different dimensions.
• Identify and describe given 3-D objects with different orientations.
• Create and describe a representation of a given 3-D object, using materials such as modelling clay.
• Identify examples of cubes, spheres, cones, cylinders and pyramids found in the environment.

Describe, compare and construct 2-D shapes, including:
• triangles.
• squares.
• rectangles.
• circles.
• Sort a given set of 2-D shapes, and explain the sorting rule.
• Identify common attributes of triangles, squares, rectangles and circles from given sets of the same 2-D shapes.
• Identify given 2-D shapes with different dimensions.
• Identify given 2-D shapes with different orientations.
• Create a model to represent a given 2-D shape.
• Create a pictorial representation of a given 2-D shape.

Identify 2-D shapes as parts of 3-D objects in the environment.
• Compare and match a given 2-D shape, such as a triangle, square, rectangle or circle, to the faces of 3-D objects in the environment.
• Name the 2-D faces of a given 3-D object.

Demonstrate an understanding of repeating patterns (three to five elements) by:
• describing patterns using manipulatives, diagrams, sounds and actions.
• extending patterns using manipulatives, diagrams, sounds and actions.
• comparing patterns using manipulatives, diagrams, sounds and actions.
• creating patterns using manipulatives, diagrams, sounds and actions.
• Identify the core of a given repeating pattern.
• Describe and extend a given double attribute pattern.
• Explain the rule used to create a given repeating non-numerical pattern.
• Predict an element in a given repeating pattern, using a variety of strategies.
• Predict an element of a given repeating pattern, and extend the pattern to verify the prediction.
• Compare two given repeating patterns, and describe how they are alike/different.
• Create a repeating pattern where the core has three to five elements.

Demonstrate an understanding of increasing patterns by:
• describing numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• reproducing numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• extending numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• creating numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
• Identify and describe increasing patterns in a variety of given contexts; e.g., hundred chart, number line, addition tables, calendar, tiling pattern or drawings.
• Represent the relationship in a given increasing pattern, concretely and pictorially.
• Identify errors in a given increasing pattern.
• Explain the rule used to create a given increasing pattern.
• Create an increasing pattern, and explain the pattern rule.
• Represent a given increasing pattern, using another mode; e.g., colour to shape.
• Solve a given problem, using increasing patterns.
• Identify and describe increasing patterns in the environment; e.g., house/room numbers, book pages, calendar, pine cones, leap years.
• Determine missing elements in a given concrete, pictorial or symbolic increasing pattern, and explain the reasoning.

Sort a set of objects, using two attributes, and explain the sorting rule.
• Determine the differences between two given pre-sorted sets, and explain the sorting rule.
• Identify and name two common attributes of items within a given sorted group.
• Choose two attributes to sort a given set of objects, sort the set, and explain the sorting rule.

Demonstrate and explain the meaning of equality and inequality, concretely and pictorially.
• Determine whether two given quantities of the same object (same shape and mass) are equal by using a balance.
• Construct and draw two unequal sets, using the same object (same shape and mass), and explain the reasoning.
• Demonstrate how to change two given sets, equal in number, to create inequality.
• Choose from three or more given sets the one that does not have a quantity equal to the others, and explain why.

Record equalities and inequalities symbolically, using the equal symbol or the not equal symbol.
• Determine whether two sides of a given number sentence are equal (=) or not equal (≠). Write the appropriate symbol and justify the answer.
• Model equalities, using a variety of concrete representations, and record the equalities symbolically.
• Model inequalities, using a variety of concrete representations, and record the inequalities symbolically.

Say the number sequence 0 to 100 by:
• 2s, 5s and 10s, forward and backward, using starting points that are multiples of 2, 5 and 10 respectively.
• 10s, using starting points from 1 to 9.
• 2s, starting from 1.
• Extend a given skip counting sequence (by 2s, 5s or 10s) forward and backward.
• Skip count by 10s, given any number from 1 to 9 as a starting point.
• Identify and correct errors and omissions in a given skip counting sequence.
• Count a given sum of money with pennies, nickels or dimes (to 100¢).
• Count quantity, using groups of 2, 5 or 10 and counting on.

Apply mental mathematics strategies for basic addition facts and related subtraction facts to 18.
• Explain or demonstrate the mental mathematics strategy that could be used to determine a basic fact, such as:
- doubles; e.g., for 4 + 6, think 5 + 5.
- doubles plus one; e.g., for 4 + 5, think 4 + 4 + 1.
- doubles take away one; e.g., for 4 + 5, think 5 + 5 – 1.
- doubles plus two; e.g., for 4 + 6, think 4 + 4 + 2.
- doubles take away two; e.g., for 4 + 6, think 6 + 6 – 2.
- making 10; e.g., for 7 + 5, think 7 + 3 + 2.
- one more; e.g., for 7 + 1, think one more than 7.
- one less; e.g., for 9 – 1, think one less than 9.
- two more; e.g., for 6 + 2, think two more than 6.
- two less; e.g., for 11 – 2, think two less than 11.
- building on a known double; e.g., 6 + 6 = 12, so 6 + 7 = 12 + 1 = 13.
- addition for subtraction; e.g., for 7 – 3, think 3 + ? = 7.
• Use and describe a mental mathematics strategy for determining a sum to 18 and the related subtraction facts.
• Refine mental mathematics strategies to increase their efficiency.
• Demonstrate understanding and application of strategies for addition facts up to and including 9 + 9 and related subtraction facts.
• Demonstrate recall/memorization of addition facts up to and including 5 + 5 and related subtraction facts.

Demonstrate if a number (up to 100) is even or odd.
• Use concrete materials or pictorial representations to determine if a given number is even or odd.
• Identify even and odd numbers in a given sequence, such as in a hundred chart.
• Sort a given set of numbers into even and odd.

Describe order or relative position, using ordinal numbers (up to tenth).
• Indicate a position of a specific object in a sequence by using ordinal numbers up to tenth.
• Compare the ordinal position of a specific object in two different given sequences.

Represent and describe numbers to 100, concretely, pictorially and symbolically.
• Represent a given number, using concrete materials such as ten frames and base ten materials.
• Represent a given number, using coins (pennies, nickels, dimes and quarters).
• Represent a given number, using tallies.
• Represent a given number pictorially.
• Represent a given number, using expressions; e.g., 24 + 6, 15 + 15, 40 – 10.
• Read a given number (0–100) in symbolic or word form.
• Record a given number (0–20) in words.

Compare and order numbers up to 100.
• Order a given set of numbers in ascending or descending order, and verify the result, using a hundred chart, number line, ten frames or by making references to place value.
• Identify and explain errors in a given ordered sequence.
• Identify missing numbers in a given hundred chart.
• Identify errors in a given hundred chart.

Estimate quantities to 100, using referents.
• Estimate a given quantity by comparing it to a referent (known quantity).
• Estimate the number of groups of ten in a given quantity, using 10 as a referent.
• Select between two possible estimates for a given quantity, and explain the choice.

Illustrate, concretely and pictorially, the meaning of place value for numerals to 100.
• Explain and show with counters the meaning of each digit for a given 2-digit numeral with both digits the same; e.g., for the numeral 22, the first digit represents two tens (twenty counters) and the second digit represents two ones (two counters).
• Count the number of objects in a given set, using groups of 10s and 1s, and record the result as a 2-digit numeral under the headings 10s and 1s.
• Describe a given 2-digit numeral in at least two ways; e.g., 24 as two 10s and four 1s, twenty and four, two groups of ten and four left over, and twenty-four ones.
• Illustrate, using ten frames and diagrams, that a given numeral consists of a certain number of groups of ten and a certain number of ones.
• Illustrate, using base 10 materials, that a given numeral consists of a certain number of tens and a certain number of ones.
• Explain why the value of a digit depends on its placement within a numeral.

Demonstrate and explain the effect of adding zero to, or subtracting zero from, any number.
• Add zero to a given number, and explain why the sum is the same as the given number.
• Subtract zero from a given number, and explain why the difference is the same as the given number.

Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by:
• using personal strategies for adding and subtracting with and without the support of manipulatives.
• creating and solving problems that involve addition and subtraction.
• using the commutative property of addition (the order in which numbers are added does not affect the sum).
• using the associative property of addition (grouping a set of numbers in different ways does not affect the sum).
• explaining that the order in which numbers are subtracted may affect the difference.
• Model addition and subtraction, using concrete materials or visual representations, and record the process symbolically.
• Create an addition or a subtraction number sentence and a story problem for a given solution.
• Solve a given problem involving a missing addend, and describe the strategy used.
• Solve a given problem involving a missing minuend or subtrahend, and describe the strategy used.
• Refine personal strategies to increase their efficiency.
• Match a number sentence to a given missing addend problem.
• Match a number sentence to a given missing subtrahend or minuend problem.
• Explain or demonstrate why 5 + 6 = 6 + 5.
• Add a given set of numbers, using the associative property of addition, and explain why the sum is the same; e.g., 2 + 5 + 3 + 8 = (2 + 3) + 5 + 8 or 5 + 3 + (8 + 2).
• Solve a given problem, using horizontal and vertical formats.
• Solve a given problem using the standard/traditional addition algorithm.
• Solve a given problem using the standard/traditional subtraction algorithm.