Math Games

Predict an element in a repeating pattern using a variety of strategies.
• Identify the core of a repeating pattern.
• Describe and extend a pattern with two attributes.
• Explain the rule used to create a repeating non-numerical pattern.
• Predict an element in a repeating pattern using a variety of strategies.
• Predict an element of a repeating pattern, and extend the pattern to verify the prediction.

Demonstrate an understanding of increasing patterns by
• describing
• reproducing
• extending
• creating
patterns using manipulatives, diagrams, sounds, and actions (numbers to 100).

• Identify and describe increasing patterns in a variety of contexts (e.g., hundred chart, number line, addition tables, calendar, a tiling pattern, or drawings).
• Represent an increasing pattern concretely and pictorially.
• Identify errors in an increasing pattern.
• Explain the rule used to create an increasing pattern.
• Create an increasing pattern and explain the pattern rule.
• Represent an increasing pattern using another mode (e.g., colour to shape).
• Solve a problem using increasing patterns.
• Identify and describe increasing patterns in the environment (e.g., house/room numbers, flower petals, book pages, calendar, pine cones, leap years).
• Determine missing elements in a concrete, pictorial, or symbolic increasing pattern, and explain the reasoning.

Demonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0 to 100).
• Determine whether two quantities of the same object (same shape and mass) are equal by using a balance scale.
• Construct and draw two unequal sets using the same object (same shape and mass), and explain the reasoning.
• Demonstrate how to change two sets, equal in number, to create inequality.
• Choose from three or more 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 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.
• Model inequalities using a variety of concrete representations, and record symbolically.

Say the number sequence from 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 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.
• Count by 2s starting from 1 or from any odd number.
• Identify and correct errors and omissions in a skip-counting sequence.
• Count a sum of money with pennies, nickels, or dimes (to 100¢).
• Count quantity using groups of 2s, 5s, or 10s and counting on.

Apply mental mathematics strategies, including
• using doubles
• making 10
• using one more, one less
• using two more, two less
• building on a known double
• using addition for subtraction to develop recall of basic addition facts to 18 and related subtraction facts.

• Explain the mental mathematics strategy that could be used to determine an addition or subtraction fact, such as
- using doubles (e.g., for 4 + 6, think 5 + 5)
- using doubles plus one (e.g., for 4 + 5, think 4 + 4 + 1)
- using doubles take away one (e.g., for 4 + 5, think 5 + 5 – 1)
- using doubles plus two (e.g., for 4 + 6, think 4 + 4 + 2)
- using doubles take away two (e.g., for 4 + 6, think 6 + 6 – 2)
- making 10 (e.g., for 7 + 5, think 7 + 3 + 2)
- building on a known double (e.g., 6 + 6 = 12, so 6 + 7 = 12 + 1 = 13)
- using addition for subtraction (e.g., for 7 – 3, think 3 + ? = 7)
• Use and describe a personal strategy for determining a sum to 18 and the
corresponding subtraction.

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

Describe order or relative position using ordinal numbers.
• Indicate the position of an object in a sequence by using ordinal numbers.
• Compare the relative position of an object in two different sequences.

Represent and describe numbers to 100, concretely, pictorially, and symbolically.
• Represent a number using concrete materials, such as ten frames and base-10 materials.
• Represent a number using coins (pennies, nickels, dimes, and quarters).
• Represent a number using tallies.
• Represent a number pictorially.
• Represent a number using expressions (e.g., 24 + 6, 15 + 15, 40 – 10).
• Read a number (0–100) in symbolic or word form.
• Record a number (0–20) in words.
• Determine compatible number pairs for 20 or 50.

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

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

Illustrate, concretely and pictorially, the meaning of place value for numbers to 100.
• Explain and show with counters the meaning of each digit for a 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 set using groups of 10s and 1s, and record the result as a 2-digit numeral under the headings of 10s and 1s.
• Describe a 2-digit numeral in at least two ways (e.g., 24 as two tens and four ones, twenty and four, two groups of ten and four left over, and twenty-four ones).
• Illustrate using 10 frames and diagrams that a numeral consists of a certain number of groups of 10 and a certain number of 1s.
• Illustrate using proportional base-10 materials that a 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 number and explain why the sum is the same as the addend.
• Subtract zero from a number and explain why the difference is the same as the 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
• explaining that the order in which numbers are added 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 solution.
• Solve a problem involving a missing addend, and describe the strategy used.
• Solve a problem involving a missing minuend or subtrahend, and describe the strategy used.
• Match a number sentence to a missing addend problem.
• Match a number sentence to a missing subtrahend or minuend problem.
• Add a set of numbers in two different ways, and explain that the sum is the same (e.g., 2 + 5 + 3 + 8 = 2 + 3 + 5 + 8 or 5 + 3 + 8 + 2).

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.
• State that there are seven days in a week and twelve months in a year.
• Determine whether a 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 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 non-standard units) used to measure length and mass (weight).
• Explain why one of two non-standard units may be a better choice for measuring the length of an object.
• Explain why one of two non-standard units may be a better choice for measuring the mass of an object.
• Select a non-standard unit for measuring the length or mass of an object, and explain why it was chosen.
• Estimate the number of non-standard units needed for a 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 non-standard units, and make statements of comparison.
• Estimate, measure, and record the length, height, distance around, or mass (weight) of an object using non-standard 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 non-standard 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 non-standard units required to measure the length of an object using a single copy or multiple copies of the same unit of measure.
• Estimate and measure an object using multiple copies of a non-standard unit and using a single copy of the same unit many times, and explain the results.
• Estimate and measure, using non-standard units, a length that is not a straight line.
• Create different rulers, using non-standard units of measure, and use these rulers to measure length.

Demonstrate that changing the orientation of an object does not alter the measurements of its attributes.
• Measure an 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 pre-sorted sets, and explain the sorting rule.
• Identify and name two common attributes of items within a sorted group.
• Sort a set of 2-D shapes (regular and irregular) according to two attributes, and explain the sorting rule.
• Sort a 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
• prisms
• pyramids

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

Describe, compare, and construct 2-D shapes, including
• triangles
• squares
• rectangles
• circles

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

Identify 2-D shapes as parts of 3-D objects in the environment.
• Compare and match a 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 3-D object.

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