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
- 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 2s, 5s or 10s and counting on.

Apply mental mathematics strategies, such as:
• using doubles
• making 10
• one more, one less
• two more, two less
• building on a known double
• addition for subtraction
to determine basic addition facts to 18 and related subtraction facts.

• Achievement Indicators
- Explain 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
• building on a known double, e.g., 6 + 6 = 12, so 6 + 7 = 12 + 1 = 13
• addition to 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.
• Achievement Indicators
- 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).
• Achievement Indicators
- 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.
• Achievement Indicators
- 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.
• Achievement Indicators
- 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 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.
• Achievement Indicators
- 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.
• Achievement Indicators
- 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 of 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 proportional 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.
• Achievement Indicators
- Add zero to a given number and explain why the sum is the same as the addend.
- 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
• 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.

• Achievement Indicators
- 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.
- Match a number sentence to a given missing addend problem.
- Match a number sentence to a given missing subtrahend or minuend problem.
- 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).

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

• Achievement Indicators
- 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.

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

• Achievement Indicators
- Identify and describe increasing patterns in a variety of given contexts, e.g., hundred chart,number line, addition tables, calendar, a tiling pattern or drawings.
- Represent 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, flower petals, book pages, calendar, pine cones, leap years.
- Determine missing elements in a given 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).
• Achievement Indicators
- Determine whether two given 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 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.
• Achievement Indicators
- 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 equality.
- Model inequalities using a variety of concrete representations and record the inequality.

Relate the number of days to a week and the number of months to a year in a problem-solving context.
• Achievement Indicators
- 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 which 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).
• Achievement Indicators
- Explain why one of two given non-standard units may be a better choice for measuring the length of an object.
- Explain why one of two given 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 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.
• Achievement Indicators
- Estimate, measure and record the length, height, distance around or mass (weight) of a given 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).

• Achievement Indicators
- 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 a given object using a single copy or multiple copies of a unit.
- 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.
- 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
- 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
- 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.

• Achievement Indicators
- 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.

• Achievement Indicators
- 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 type of 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.
• Achievement Indicators
- 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.

Gather and record data about self and others to answer questions.
• Achievement Indicators
- 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.
• Achievement Indicators
- 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.