Math Games

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.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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.

Demonstrate if a number (up to 100) is even or odd.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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 missing numbers in a given hundred chart or a given sequence.
- Identify errors in a given ordered sequence (i.e., hundred chart).
- Identify errors in a given hundred chart.

Estimate quantities to 100 using referents.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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, one ten and 14 ones 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.
- Represent one unit if shown a pre-grouped model representing ten (e.g., what would one look like if this is ten?).

Demonstrate and explain the effect of adding zero to or subtracting zero from any number.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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).

Relate the number of days to a week and the number of months to a year in a problem-solving context.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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 nonstandard units) used to measure length and mass (weight).
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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.
- 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.

Compare and order objects by length, height, distance around and mass (weight) using nonstandard units, and make statements of comparison.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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.

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
• Students who have achieved this outcome(s) should be able to:
- 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 a given length, that is not a straight line, using non-standard units.

Demonstrate that changing the orientation of an object does not alter the measurements of its attributes.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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 modeling 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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.

Demonstrate an understanding of repeating patterns (three to five elements) by:
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• extending
• comparing
• creating
patterns using manipulatives, diagrams, sounds and actions (numbers to 100)

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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
• Students who have achieved this outcome(s) should be able to:
- 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.