Math Games

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

• Achievement Indicators
- Describe a given repeating pattern containing two to four elements in its core.
- Identify errors in a given repeating pattern.
- Identify the missing element(s) in a given repeating pattern.
- Create and describe a repeating pattern using a variety of manipulatives, musical instruments and actions.
- Reproduce and extend a given repeating pattern using manipulatives, diagrams, sounds and actions.
- Identify and describe a repeating pattern in the environment, e.g., classroom, outdoors, using everyday language.
- Identify repeating events, e.g., days of the week, birthdays, seasons.

Translate repeating patterns from one representation to another.
• Achievement Indicators
- Represent a given repeating pattern using another mode, e.g., actions to sound, colour to shape, ABC ABC to blue yellow green blue yellow green.
- Describe a given repeating pattern using a letter code, e.g., ABC ABC…

Describe equality as a balance and inequality as an imbalance, concretely and pictorially (0 to 20).
• Achievement Indicators
- Construct two equal sets using the same objects (same shape and mass) and demonstrate their equality of number using a balance scale.
- Construct two unequal sets using the same objects (same shape and mass) and demonstrate their inequality of number using a balance scale.
- Determine if two given concrete sets are equal or unequal and explain the process used.

Record equalities using the equal symbol.
• Achievement Indicators
- Represent a given equality using manipulatives or pictures.
- Represent a given pictorial or concrete equality in symbolic form.
- Provide examples of equalities where the given sum or difference is on either the left or right side of the equal symbol (=).
- Record different representations of the same quantity (0 to 20) as equalities.

Say the number sequence, 0 to 100, by:
• 1s forward and backward between any two given numbers
• 2s to 20, forward starting at 0
• 5s and 10s to 100, forward starting at 0.

• Achievement Indicators
- Recite forward by 1s the number sequence between two given numbers (0 to 100).
- Recite backward by 1s the number sequence between two given numbers.
- Record a given numeral (0 to 100) symbolically when it is presented orally.
- Read a given numeral (0 to 100) when it is presented symbolically.
- Skip count by 2s to 20 starting at 0.
- Skip count by 5s to 100 starting at 0.
- Skip count forward by 10s to 100 starting at 0.
- Identify and correct errors and omissions in a given number sequence.

Describe and use mental mathematics strategies (memorization not intended), such as:
• counting on and counting back
• making 10
• doubles
• using addition to subtract
to determine the basic addition facts to 18 and related subtraction facts.

• Achievement Indicators
(It is not intended that students recall the basic facts but become familiar with strategies to mentally determine sums and differences.)
- Use and describe a personal strategy for determining a given sum.
- Use and describe a personal strategy for determining a given difference.
- Write the related subtraction fact for a given addition fact.
- Write the related addition fact for a given subtraction fact.

Recognize, at a glance, and name familiar arrangements of 1 to 10 objects or dots.
• Achievement Indicators
- Look briefly at a given familiar arrangement of objects or dots and identify the number represented without counting.
- Look briefly at a given familiar arrangement and identify how many objects there are without counting.
- Identify the number represented by a given arrangement of objects or dots on a ten frame.

Demonstrate an understanding of counting by:
• indicating that the last number said identifies “how many”
• showing that any set has only one count
• using the counting on strategy
• using parts or equal groups to count sets.

• Achievement Indicators
- Answer the question, “How many are in the set?” using the last number counted in a given set.
- Identify and correct counting errors in a given counting sequence.
- Show that the count of the number of objects in a given set does not change regardless of the order in which the objects are counted.
- Count the number of objects in a given set, rearrange the objects, predict the new count and recount to verify the prediction.
- Determine the total number of objects in a given set, starting from a known quantity and counting on.
- Count quantity using groups of 2s, 5s or 10s and counting on.

Represent and describe numbers to 20 concretely, pictorially and symbolically.
• Achievement Indicators
- Represent a given number up to 20 using a variety of manipulatives, including ten frames and base ten materials.
- Read given number words to 20.
- Partition any given quantity up to 20 into 2 parts and identify the number of objects in each part.
- Model a given number using two different objects, e.g., 10 desks represents the same number as 10 pencils.
- Place given numerals on a number line with benchmarks 0, 5, 10 and 20.

Compare sets containing up to 20 elements to solve problems using:
• referents
• one-to-one correspondence.

• Achievement Indicators
- Build a set equal to a given set that contains up to 20 elements.
- Build a set that has more, fewer or as many elements as a given set.
- Build several sets of different objects that have the same given number of elements in the set.
- Compare two given sets using one-to-one correspondence and describe them using comparative words, such as more, fewer or as many.
- Compare a set to a given referent using comparative language.
- Solve a given story problem (pictures and words) that involves the comparison of two quantities.

Estimate quantities to 20 by using referents.
• Achievement Indicators
- Estimate a given quantity by comparing it to a given referent (known quantity).
- Select an estimate for a given quantity by choosing between at least two possible choices and explain the choice.

Demonstrate, concretely and pictorially, how a given number can be represented by a variety of equal groups with and without singles.
• Achievement Indicators
- Represent a given number in a variety of equal groups with and without singles, e.g., 17 can be represented by 8 groups of 2 and one single, 5 groups of 3 and two singles, 4 groups of 4 and one single, and 3 groups of 5 and two singles.
- Recognize that for a given number of counters, no matter how they are grouped, the total number of counters does not change.
- Group a set of given counters into equal groups in more than one way.

Identify the number, up to 20, that is one more, two more, one less and two less than a given number.
• Achievement Indicators
- Name the number that is one more, two more, one less or two less than a given number, up to 20.
- Represent a number on a ten frame that is one more, two more, one less or two less than a given number.

Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially and symbolically by:
• using familiar and mathematical language to describe additive and subtractive actions from their experience
• creating and solving problems in context that involve addition and subtraction
• modelling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically.

• Achievement Indicators
- Act out a given story problem presented orally or through shared reading.
- Indicate if the scenario in a given story problem represents additive or subtractive action.
- Represent the numbers and actions presented in a given story problem by using manipulatives, and record them using sketches and/or number sentences.
- Create a story problem for addition that connects to student experience and simulate the action with counters.
- Create a story problem for subtraction that connects to student experience and simulate the action with counters.
- Create a word problem for a given number sentence.
- Represent a given story problem pictorially or symbolically to show the additive or subtractive action and solve the problem.

Demonstrate an understanding of measurement as a process of comparing by:
• identifying attributes that can be compared
• ordering objects
• making statements of comparison
• filling, covering or matching.

• Achievement Indicators
- Identify common attributes, such as length (height), mass (weight), volume (capacity) and area, that could be used to compare a given set of two objects.
- Compare two given objects and identify the attributes used to compare.
- Determine which of two or more given objects is longest/shortest by matching and explain the reasoning.
- Determine which of two or more given objects is heaviest/lightest by comparing and explain the reasoning.
- Determine which of two or more given objects holds the most/least by filling and explain the reasoning.
- Determine which of two or more given objects has the greatest/least area by covering and explain the reasoning.

Sort 3-D objects and 2-D shapes using one attribute, and explain the sorting rule.
• Achievement Indicators
- Sort a given set of familiar 3-D objects or 2-D shapes using a given sorting rule.
- Sort a given set of familiar 3-D objects using a single attribute determined by the student and explain the sorting rule.
- Sort a given set of 2-D shapes using a single attribute determined by the student and explain the sorting rule.
- Determine the difference between two given pre-sorted sets of familiar 3-D objects or 2-D shapes and explain a possible sorting rule used to sort them.

Replicate composite 2-D shapes and 3-D objects.
• Achievement Indicators
- Select 2-D shapes from a given set of 2-D shapes to reproduce a given composite 2-D shape.
- Select 3-D objects from a given set of 3-D objects to reproduce a given composite 3-D object.
- Predict and select the 2-D shapes used to produce a composite 2-D shape, and verify by deconstructing the composite shape.
- Predict and select the 3-D objects used to produce a composite 3-D object, and verify by deconstructing the composite object.

Compare 2-D shapes to parts of 3-D objects in the environment.
• Achievement Indicators
- Identify 3-D objects in the environment that have parts similar to a given 2-D shape.