Math Games

Demonstrate an understanding of place value, including numbers that are:
• greater than one million
• less than one thousandth.

• Achievement Indicators:
- 6N1.1 Explain how the pattern of the place value system, i.e., the repetition of ones, tens and hundreds within each period, makes it possible to read and write numerals for numbers of any magnitude.
- 6N1.2 Provide examples of where large and small numbers are used; e.g., media, science, medicine, technology.

Solve problems involving whole numbers and decimal numbers.
• Achievement Indicators:
- 6N2.1 Identify which operation is necessary to solve a given problem, and solve it.
- 6N2.2 Estimate the solution to, and solve, a given problem.
- 6N2.3 Determine the reasonableness of an answer.
- 6N2.4 Determine whether the use of technology is appropriate to solve a given problem, and explain why.
- 6N2.5 Use technology when appropriate to solve a given problem.

Demonstrate an understanding of factors and multiples by:
• determining multiples and factors of numbers less than 100
• identifying prime and composite numbers
• solving problems using multiples and factors.

• Achievement Indicators:
- 6N3.1 Determine all the whole number factors of a given number, using arrays.
- 6N3.2 Identify the factors for a given number, and explain the strategy used; e.g., concrete or visual representations, repeated division by prime numbers or factor trees.
- 6N3.3 Solve a given problem involving factors or multiples.
- 6N3.4 Identify multiples and factors for a given number, and explain the strategy used to identify them.
- 6N3.5 Provide an example of a prime number, and explain why it is a prime number.
- 6N3.6 Provide an example of a composite number, and explain why it is a composite number.
- 6N3.7 Sort a given set of numbers as prime and composite.
- 6N3.8 Explain why 0 and 1 are neither prime nor composite.

Relate improper fractions to mixed numbers.
• Achievement Indicators:
- 6N4.1 Demonstrate, using models, that a given improper fraction represents a number greater than 1.
- 6N4.2 Translate a given improper fraction between concrete, pictorial and symbolic forms.
- 6N4.3 Express improper fractions as mixed numbers.
- 6N4.4 Translate a given mixed number between concrete, pictorial and symbolic forms.
- 6N4.5 Express mixed numbers as improper fractions.
- 6N4.6 Place a given set of fractions, including mixed numbers and improper fractions, on a number line, and explain strategies used to determine position.

Demonstrate an understanding of ratio, concretely, pictorially and symbolically.
• Achievement Indicators:
- 6N5.1 Write a ratio from a given concrete or pictorial representation.
- 6N5.2 Express a given ratio in multiple forms, such as 3:5, or 3 to 5.
- 6N5.3 Explain the part/whole and part/part ratios of a set; e.g., for a group of 3 girls and 5 boys, explain the ratios 3:5, 3:8 and 5:8.
- 6N5.4 Provide a concrete or pictorial representation for a given ratio.
- 6N5.5 Identify and describe ratios from real-life contexts, and record them symbolically.
- 6N5.6 Demonstrate an understanding of equivalent ratios.
- 6N5.7 Solve a given problem involving ratio.

Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically.
• Achievement Indicators:
- 6N6.1 Explain that “percent” means “out of 100.”
- 6N6.2 Explain that percent is a ratio out of 100.
- 6N6.3 Use concrete materials and pictorial representations to illustrate a given percent.
- 6N6.4 Record the percent displayed in a given concrete or pictorial representation.
- 6N6.5 Identify and describe percents from real-life contexts, and record them symbolically.
- 6N6.6 Express a given percent as a fraction and a decimal.
- 6N6.7 Solve a given problem involving percents.

Demonstrate an understanding of integers, concretely, pictorially and symbolically.
• Achievement Indicators:
- 6N7.1 Extend a given number line by adding numbers less than zero, and explain the pattern on each side of zero.
- 6N7.2 Describe contexts in which integers are used; e.g., on a thermometer.
- 6N7.3 Place given integers on a number line, and explain how integers are ordered.
- 6N7.4 Order given integers in ascending or descending order.
- 6N7.5 Compare two integers; represent their relationship using the symbols <, > and =; and verify the relationship, using a number line.

Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural number divisors).
• Achievement Indicators:
- 6N8.1 Predict products and quotients of decimals, using estimation strategies.
- 6N8.2 Solve a given problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9.
- 6N8.3 Place the decimal point in a product, using estimation; e.g., for 15.205 m × 4, think 15 m × 4, so the product is greater than 60 m.
- 6N8.4 Correct errors of decimal point placement in a given product or quotient without using paper and pencil.
- 6N8.5 Place the decimal point in a quotient, using estimation; e.g., for $26.83 ÷ 4, think $24 ÷ 4, so the quotient is greater than $6.

Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).
• Achievement Indicators:
- 6N9.1 Explain, using examples, why there is a need to have a standardized order of operations.
- 6N9.2 Apply the order of operations to solve multistep problems with and without technology; e.g., a computer, a calculator.

Create, label and interpret line graphs to draw conclusions.
• Achievement Indicators:
- 6SP1.1 Determine the common attributes (title, axes and intervals) of line graphs by comparing a given set of line graphs.
- 6SP1.2 Determine whether a given set of data can be represented by a line graph (continuous data) or a series of points (discrete data), and explain why.
- 6SP1.3 Create a line graph from a given table of values or a given set of data.
- 6SP1.4 Interpret a given line graph to draw conclusions.

Select, justify and use appropriate methods of collecting data, including:
• questionnaires
• experiments
• databases
• electronic media.

• Achievement Indicators:
- 6SP2.1 Design and administer a questionnaire for collecting data to answer a given question, and record the results.
- 6SP2.2 Explain when it is appropriate to use a database as a source of data.
- 6SP2.3 Gather data for a given question by using electronic media, including selecting data from databases.
- 6SP2.4 Answer a given question by performing an experiment, recording the results and drawing a conclusion.
- 6SP2.5 Select a method for collecting data to answer a given question, and justify the choice.

Graph collected data, and analyze the graph to solve problems.
• Achievement Indicators:
- 6SP3.1 Determine an appropriate type of graph for displaying a set of collected data, and justify the choice of graph.
- 6SP3.2 Solve a given problem by graphing data and interpreting the resulting graph.

Demonstrate an understanding of probability by:
• identifying all possible outcomes of a probability experiment
• differentiating between experimental and theoretical probability
• determining the theoretical probability of outcomes in a probability experiment
• determining the experimental probability of outcomes in a probability experiment
• comparing experimental results with the theoretical probability for an experiment.

• Achievement Indicators:
- 6SP4.1 List the possible outcomes of a probability experiment, such as:
• tossing a coin
• rolling a die with a given number of sides
• spinning a spinner with a given number of sectors.
- 6SP4.2 Determine the theoretical probability of an outcome occurring for a given probability experiment.
- 6SP4.3 Predict the probability of a given outcome occurring for a given probability experiment by using theoretical probability.
- 6SP4.4 Distinguish between theoretical probability and experimental probability, and explain the differences.
- 6SP4.5 Conduct a probability experiment, with or without technology, and compare the experimental results with the theoretical probability.
- 6SP4.6 Explain that as the number of trials in a probability experiment increases, the experimental probability approaches theoretical probability of a particular outcome.

Demonstrate an understanding of the relationships within tables of values to solve problems.
• Achievement Indicators:
- 6PR1.1 Create a concrete or pictorial representation of the relationship shown in a table of values.
- 6PR1.2 Describe the pattern within each column of a given table of values.
- 6PR1.3 State, using mathematical language, the relationship in a given table of values.
- 6PR1.4 Predict the value of an unknown term, using the relationship in a table of values, and verify the prediction.
- 6PR1.5 Formulate a rule to describe the relationship between two columns of numbers in a table of values.
- 6PR1.6 Generate values in one column of a table of values, given values in the other column and a pattern rule.
- 6PR1.7 Create a table of values to record and reveal a pattern to solve a given problem.
- 6PR1.8 Identify missing elements in a given table of values.
- 6PR1.9 Identify errors in a given table of values.

Represent and describe patterns and relationships, using graphs and tables.
• Achievement Indicators:
- 6PR2.1 Create a table of values from a given pattern or a given graph.
- 6PR2.2 Translate a pattern to a table of values, and graph the table of values (limited to linear graphs with discrete elements).
- 6PR2.3 Describe, using everyday language, orally or in writing, the relationship shown on a graph.

Represent generalizations arising from number relationships, using equations with letter variables.
• Achievement Indicators:
- 6PR3.1 Describe the relationship in a given table, using a mathematical expression.
- 6PR3.2 Represent a pattern rule, using a simple mathematical expression such as 4d or 2n + 1.
- 6PR3.3 Write and explain the formula for finding the perimeter of any given rectangle.
- 6PR3.4 Develop and justify equations using letter variables that illustrate the commutative property of addition and multiplication; e.g., a + b = b + a or a × b = b × a.
- 6PR3.5 Write and explain the formula for finding the area of any given rectangle.

Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.
• Achievement Indicators:
- 6PR4.1 Model the preservation of equality for addition, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
- 6PR4.2 Model the preservation of equality for subtraction, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
- 6PR4.3 Model the preservation of equality for multiplication, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
- 6PR4.4 Model the preservation of equality for division, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
- 6PR4.5 Write equivalent forms of a given equation by applying the preservation of equality and verify using concrete materials, e.g., 3b = 12 is the same as 3b + 5 = 12 + 5 or 2r = 7 is the same as 3(2r) = 3(7).

Demonstrate an understanding of angles by:
• identifying examples of angles in the environment
• classifying angles according to their measure
• estimating the measure of angles, using 45°, 90° and 180° as reference angles
• determining angle measures in degrees
• drawing and labelling angles when the measure is specified.

• Achievement Indicators:
- 6SS1.1 Provide examples of angles found in the environment.
- 6SS12 Classify a given set of angles according to their measure; e.g., acute, right, obtuse, straight, reflex.
- 6SS1.3 Estimate the measure of an angle, using 45°, 90° and 180° as reference angles.
- 6SS1.4 Sketch 45°, 90° and 180° angles without the use of a protractor, and describe the relationship among them.
- 6SS1.5 Measure, using a protractor, given angles in various positions.
- 6SS1.6 Draw and label a specified angle in various positions, using a protractor

Demonstrate that the sum of interior angles is:
• 180° in a triangle
• 360° in a quadrilateral.

• Achievement Indicators:
- 6SS2.1 Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles.
- 6SS2.2 Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals.

Develop and apply a formula for determining the:
• perimeter of polygons
• area of rectangles
• volume of right rectangular prisms.

• Achievement Indicators:
- 6SS3.1 Explain, using models, how the perimeter of any polygon can be determined.
- 6SS3.2 Generalize a rule (formula) for determining the perimeter of polygons, including rectangles and squares.
- 6SS3.3 Solve a given problem involving the perimeter of polygons, the area of rectangles and/or the volume of right rectangular prisms.
- 6SS3.4 Explain, using models, how the area of any rectangle can be determined.
- 6SS3.5 Generalize a rule (formula) for determining the area of rectangles.
- 6SS3.6 Explain, using models, how the volume of any right rectangular prism can be determined.
- 6SS3.7 Generalize a rule (formula) for determining the volume of right rectangular prisms.

Construct and compare triangles, including:
• scalene
• isosceles
• equilateral
• right
• obtuse
• acute
in different orientations.

• Achievement Indicators:
- 6SS4.1 Identify the characteristics of a given set of triangles according to their sides and/or their interior angles.
- 6SS4.2 Sort a given set of triangles, and explain the sorting rule.
- 6SS4.3 Draw a specified triangle; e.g., scalene.
- 6SS4.4 Replicate a given triangle and show that the two are congruent.

Describe and compare the sides and angles of regular and irregular polygons.
• Achievement Indicators:
- 6SS5.1 Sort a given set of 2-D shapes into polygons and non-polygons, and explain the sorting rule.
- 6SS5.2 Demonstrate that the sides of a given regular polygon are of the same length and that the angles of a regular polygon are of the same measure.
- 6SS5.3 Sort a given set of polygons as regular or irregular, and justify the sorting.
- 6SS5.4 Identify and describe regular and irregular polygons in the environment.
- 6SS5.5 Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing.
- 6SS5.6 Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by measuring.

Perform a combination of translations, rotations and / or reflections on a single 2-D shape, with and without technology, and draw and describe the image.
• Achievement Indicators:
- 6SS6.1 Model a given set of successive translations, successive rotations or successive reflections of a 2-D shape.
- 6SS6.2 Draw and describe a 2-D shape and its image, given a combination of transformations.
- 6SS6.3 Describe the transformations performed on a 2-D shape to produce a given image.
- 6SS6.4 Demonstrate that a 2-D shape and its transformation image are congruent.
- 6SS6.5 Model a given combination of two different types of transformations of a 2-D shape.
- 6SS6.6 Model a given set of successive transformations (translations, rotations and/or reflections) of a 2-D shape.
- 6SS6.7 Perform and record one or more transformations of a 2-D shape that will result in a given image.

Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.
• Achievement Indicators:
- 6SS7.1 Analyze a given design created by transforming one or more 2-D shapes, and identify the original shape(s) and the transformations used to create the design.
- 6SS7.2 Create a design using one or more 2-D shapes, and describe the transformations used.

Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.
• Achievement Indicators:
- 6SS8.1 Label the axes of the first quadrant of a Cartesian plane, and identify the origin.
- 6SS8.2 Plot a point in the first quadrant of a Cartesian plane, given its ordered pair.
- 6SS8.3 Match points in the first quadrant of a Cartesian plane with their corresponding ordered pair.
- 6SS8.4 Plot points in the first quadrant of a Cartesian plane with intervals of 1, 2, 5 or 10 on its axes, given whole number ordered pairs.
- 6SS8.5 Draw shapes or designs, given ordered pairs, in the first quadrant of a Cartesian plane.
- 6SS8.6 Draw shapes or designs in the first quadrant of a Cartesian plane, and identify the points used to produce them.
- 6SS8.7 Determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane.

Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).
• Achievement Indicators:
- 6SS9.1 Identify the coordinates of the vertices of a given 2-D shape (limited to the first quadrant of a Cartesian plane).
- 6SS9.2 Perform a transformation on a given 2-D shape, and identify the coordinates of the vertices of the image (limited to the first quadrant).
- 6SS9.3 Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation (limited to the first quadrant).