Math Games

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.

• Achievement Indicators:
- 2N1.1 Extend a given skip counting sequence (by 2s, 5s or 10s) forward and backward.
- 2N1.2 Skip count by 10s given any number from 1 to 9 as a starting point.
- 2N1.3 Count by 2s starting from 1 or from any odd number.
- 2N1.4 Identify and correct errors and omissions in a given skip counting sequence.
- 2N1.5 Count a given sum of money with pennies, nickels or dimes (to 100 cents).
- 2N1.6 Count quantity, using groups of 2s, 5s or 10s and counting on.

Apply mental mathematics strategies for the basic addition and related subtraction facts to 18.
• Achievement Indicators:
- 2N10.1 Explain or demonstrate the mental mathematics strategy that could be used to determine a basic fact, such as:
• Using one more, two more; e.g. for 6 + 2 start at 6 and count on 2, so 6, 7, 8.
• Using one less, two less; e.g., for 6 – 2, start at 6 and count back 2, so 6, 5, 4
• Making 10; e.g., for 7 + 5, think 7 + 3 + 2
• Using doubles; e.g., 4 + 6, think 5 + 5
• Using doubles plus one, plus two; e.g., 4 + 5, think 4 + 4 + 1
• Using doubles subtract one, subtract two; e.g., for 4 + 5, think 5 + 5 – 1
• Using addition to subtract; e.g., for 7 – 3, think 3 + ? = 7
- 2N10.2 Use and describe a mental mathematics strategy for determining a sum to 18 and the corresponding subtraction.
- 2N10.3 Refine mental math strategies to increase their efficiency.

Demonstrate if a number (up to 100) is even or odd.
• Achievement Indicators:
- 2N2.1 Determine if a given number is even or odd by using concrete materials or pictorial representations.
- 2N2.2 Identify even and odd numbers in a given sequence, such as in a hundred chart.
- 2N2.3 Sort a given set of numbers into even and odd.

Describe order or relative position, using ordinal numbers (up to tenth).
• Achievement Indicators:
- 2N3.1 Indicate a position of a specific object in a sequence by using ordinal numbers up to tenth.
- 2N3.2 Compare the ordinal position of a specific object in two different given sequences.

Represent and describe numbers to 100, concretely, pictorially and symbolically.
• Achievement Indicators:
- 2N4.1 Represent a given number, using concrete materials such as ten-frames and base ten materials.
- 2N4.2 Represent a given number, using tallies.
- 2N4.3 Represent a given number pictorially and symbolically.
- 2N4.4 Read a given number (0 – 100) in symbolic or word form.
- 2N4.5 Record a given number (0 – 20) in words.
- 2N4.6 Represent a given number, using coins (pennies, nickels, dimes and quarters).
- 2N4.7 Represent a given number, using expressions; e.g., 24 + 6, 15 + 15, 40 – 10.

Compare and order numbers up to 100.
• Achievement Indicators:
- 2N5.1Order 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.
- 2N5.2 Identify and explain errors in a given ordered sequence.
- 2N5.3 Identify missing numbers in a given hundred chart.
- 2N5.4 Identify errors in a given hundred chart.

Estimate quantities to 100, using referents.
• Achievement Indicators:
- 2N6.1 Estimate a given quantity by comparing it to a referent (known quantity).
- 2N6.2 Estimate the number of groups of ten in a given quantity, using 10 as a referent.
- 2N6.3 Select between two possible estimates for a given quantity, and explain the choice.

Illustrate, concretely and pictorially, the meaning of place value for numbers to 100.
• Achievement Indicators:
- 2N7.1 Explain and show with counters the meaning of each digit for a given two-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).
- 2N7.2 Count the number of objects in a given set, using groups of 10s and 1s, and record the result as a twodigit numeral under the headings 10s and 1s.
- 2N7.3 Describe a given two-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.
- 2N7.4 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.
- 2N7.5 Illustrate, using base ten materials, that a given numeral consists of a certain number of tens and a certain number of ones.
- 2N7.6 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.
• Achievement Indicators:
- 2N8.1 Add zero to a given number, and explain why the sum is the same as the addend.
- 2N8.2 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 one- and two-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 (commutative property)
• explaining that the order in which numbers are subtracted may affect the difference.

• Achievement Indicators:
- 2N9.1 Model addition and subtraction, using concrete materials or visual representations, and record the process symbolically.
- 2N9.2 Solve a given problem, using horizontal and vertical forms.
- 2N9.3 Add a given set of numbers in two different ways, and explain why the sum is the same; e.g., 2 + 5 + 3 + 8 = (2 + 3) + 5 + 8 or 5 + 3 + (8 + 2).
- 2N9.4 Create an addition or a subtraction number sentence and a story problem for a given solution.
- 2N9.5 Solve a given problem involving a missing addend, and describe the strategy used.
- 2N9.6 Match a number sentence to a given missing addend problem.
- 2N9.7 Solve a given problem involving a missing minuend or subtrahend, and describe the strategy used.
- 2N9.8 Match a number sentence to a given missing subtrahend or minuend problem.
- 2N9.9 Refine personal strategies to increase their efficiency.

Relate the number of days to a week and the number of months to a year in a problem-solving context.
• Achievement Indicators:
- 2SS1.1 Read a date on a calendar.
- 2SS1.2 Name and order the days of the week.
- 2SS1.3 Identify the day of the week and the month of the year for an identified calendar date.
- 2SS1.4 Communicate that there are seven days in a week and twelve months in a year.
- 2SS1.5 Determine whether a given set of days is more or less than a week.
- 2SS1.6 Identify yesterday’s/tomorrow’s date.
- 2SS1.7 Identify the month that comes before and the month that comes after a given month.
- 2SS1.8 Name and order the months of the year.
- 2SS1.9 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 non-standard units) used to measure length and mass.
• Achievement Indicators:
- 2SS2.1 Explain why one of two given non-standard units may be a better choice for measuring the length of an object.
- 2SS2.2 Select a non-standard unit for measuring the length or mass of an object, and explain why it was chosen.
- 2SS2.3 Estimate the number of non-standard units needed for a given measurement task.
- 2SS2.4 Explain why the number of units of a measurement will vary depending upon the unit of measure used.
- 2SS2.5 Explain why one of two given non-standard units may be a better choice for measuring the mass of an object.

Compare and order objects by length, height, distance around and mass, using non-standard units, and make statements of comparison.
• Achievement Indicators:
- 2SS3.1 Estimate, measure and record the length, height, distance around, or mass of a given object, using non-standard units.
- 2SS3.2 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).

• Achievement Indicators:
- 2SS4.1 Explain why overlapping or leaving gaps does not result in accurate measures.
- 2SS4.2 Count the number of non-standard units required to measure the length of a given object, using a single copy or multiple copies of a unit.
- 2SS4.3 Estimate and measure a given object, using multiple copies of a non-standard unit and using a single copy of the same unit many times, and explain the results.
- 2SS4.4 Estimate and measure, using non-standard 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.
• Achievement Indicators:
- 2SS5.1 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.
• Achievement Indicators:
- 2SS6.1 Determine the differences between two given pre-sorted sets, and explain the sorting rule.
- 2SS6.2 Identify and name two common attributes of items within a given sorted group.
- 2SS6.3 Sort a given set of 2-D shapes (regular and irregular), according to two attributes, and explain the sorting rule.
- 2SS6.4 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
• prisms.

• Achievement Indicators:
- 2SS7.1 Sort a given set of 3-D objects, and explain the sorting rule.
- 2SS7.2 Identify common attributes of cubes, spheres, cones, cylinders, pyramids, and prisms from given sets of the same 3-D objects.
- 2SS7.3 Identify and describe given 3-D objects with different dimensions.
- 2SS7.4 Identify and describe given 3-D objects with different orientations.
- 2SS7.5 Identify examples of cubes, spheres, cones, cylinders and pyramids found in the environment.
- 2SS7.6 Create and describe a representation of a given 3-D object, using materials such as modelling clay.

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

• Achievement Indicators:
- 2SS8.1 Identify common attributes of triangles, squares, rectangles and circles from given sets of the same 2-D shapes.
- 2SS8.2 Identify given 2-D shapes with different dimensions.
- 2SS8.3 Identify given 2-D shapes with different orientations.
- 2SS8.4 Create a model to represent a given 2-D shape.
- 2SS8.5 Create a pictorial representation of a given 2-D shape.

Identify 2-D shapes as parts of 3-D objects in the environment.
• Achievement Indicators:
- 2SS9.1 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.
- 2SS9.2 Name the 2-D faces of a given 3-D object.

Demonstrate an understanding of repeating patterns (three to five elements) by:
• describing
• extending
• comparing
• creating
patterns using manipulatives, diagrams, sounds and actions.

• Achievement Indicators:
- 2PR1.1 Identify the core of a given repeating pattern.
- 2PR1.2 Describe and extend a given double attribute pattern.
- 2PR1.3 Explain the rule used to create a given repeating nonnumerical pattern.
- 2PR1.4 Compare two given repeating patterns, and describe how they are alike/different.
- 2PR1.5 Create a repeating pattern where the core has three to five elements.
- 2PR1.6 Predict an element in a given repeating pattern, using a variety of strategies.
- 2PR1.7 Predict an element of a given 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).

• Achievement Indicators:
- 2PR2.1 Identify and describe increasing patterns in a variety of given contexts; e.g., hundred chart, number line, addition tables, calendar, tiling pattern or drawings.
- 2PR2.2 Explain the rule used to create a given increasing pattern.
- 2PR2.3 Identify and describe increasing patterns in the environment; e.g., house/room numbers, book pages, calendar, pine cones, leap years.
- 2PR2.4 Determine missing elements in a given concrete, pictorial or symbolic increasing pattern, and explain the reasoning.
- 2PR2.5 Represent a given increasing pattern, concretely and pictorially.
- 2PR2.6 Create an increasing pattern, and explain the pattern rule.
- 2PR2.7 Represent a given increasing pattern, using another mode; e.g., colour to shape.
- 2PR2.8 Solve a given problem, using increasing patterns.
- 2PR2.9 Identify errors in a given increasing pattern.

Demonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0-100).
• Achievement Indicators:
- 2PR3.1 Determine whether two given quantities of the same object (same shape and mass) are equal by using a balance scale.
- 2PR3.2 Construct and draw two unequal sets, using the same object (same shape and mass), and explain the reasoning.
- 2PR3.3 Demonstrate how to change two given sets, equal in number, to create inequality.
- 2PR3.4 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.
• Achievement Indicators:
- 2PR4.1 Determine whether two sides of a given number sentence are equal (=) or not equal (≠). Write the appropriate symbol and justify the answer.
- 2PR4.2 Model equalities, using a variety of concrete representations, and record the equality symbolically.
- 2PR4.3 Model inequalities, using a variety of concrete representations, and record the inequality symbolically

Gather and record data about self and others to answer questions.
• Achievement Indicators:
- 2SP1.1 Formulate a question that can be answered by gathering information about self and others.
- 2SP1.2 Organize data as it is collected, using concrete objects, tallies, check marks, charts or lists.
- 2SP1.3 Answer questions, using collected data.

Construct and interpret concrete graphs and pictographs to solve problems.
• Achievement Indicators:
- 2SP2.1 Determine the common attributes of concrete graphs by comparing a given set of concrete graphs.
- 2SP2.2 Answer questions pertaining to a given concrete graph or pictograph.
- 2SP2.3 Determine the common attributes of pictographs by comparing a given set of pictographs.
- 2SP2.4 Create a concrete graph to display a given set of data, and draw conclusions.
- 2SP2.5 Create a pictograph to represent a given set of data, using one-to-one correspondence.
- 2SP2.6 Solve a given problem by constructing and interpreting a concrete graph or pictograph.