Math Games

6.N.1

Demonstrate an understanding of place value for numbers: • greater than one million • less than one thousandth. • Achievement Indicators - Explain how the pattern of the place value system, e.g., the repetition of ones, tens and hundreds, makes it possible to read and write numerals for numbers of any magnitude. - Provide examples of where large numbers and small decimals are used, e.g., media, science, medicine, technology.

6.N.2

Solve problems involving large numbers, using technology. • Achievement Indicators - Identify which operation is necessary to solve a given problem and solve it. - Determine the reasonableness of an answer. - Estimate the solution and solve a given problem.

6.N.3

Demonstrate an understanding of factors and multiples by: • determining multiples and factors of numbers less than 100 • identifying prime and composite numbers • solving problems involving multiples. • Achievement Indicators - Identify multiples for a given number and explain the strategy used to identify them. - Determine all the whole number factors of a given number using arrays. - 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. - Provide an example of a prime number and explain why it is a prime number. - Provide an example of a composite number and explain why it is a composite number. - Sort a given set of numbers as prime and composite. - Solve a given problem involving factors or multiples. - Explain why 0 and 1 are neither prime nor composite.

6.N.4

Relate improper fractions to mixed numbers. • Achievement Indicators - Demonstrate using models that a given improper fraction represents a number greater than 1. - Express improper fractions as mixed numbers. - Express mixed numbers as improper fractions. - Place a given set of fractions, including mixed numbers and improper fractions, on a number line and explain strategies used to determine position.

6.N.5

Demonstrate an understanding of ratio, concretely, pictorially and symbolically. • Achievement Indicators - Provide a concrete or pictorial representation for a given ratio. - Write a ratio from a given concrete or pictorial representation. - Express a given ratio in multiple forms, such as 3:5, 3/5 , or 3 to 5. - Identify and describe ratios from real-life contexts and record them symbolically. - 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. - Solve a given problem involving ratio.

6.N.6

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

6.N.7

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

6.N.8

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

6.N.9

Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers). • Achievement Indicators - Demonstrate and explain with examples why there is a need to have a standardized order of operations. - Apply the order of operations to solve multi-step problems with or without technology, e.g., computer, calculator.

6.SP.1

Create, label and interpret line graphs to draw conclusions. • Achievement Indicators - Determine the common attributes (title, axes and intervals) of line graphs by comparing a given set of line graphs. - 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. - Create a line graph from a given table of values or set of data. - Interpret a given line graph to draw conclusions.

6.SP.2

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

6.SP.3

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

6.SP.4

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 - 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. - Determine the theoretical probability of an outcome occurring for a given probability experiment. - Predict the probability of a given outcome occurring for a given probability experiment by using theoretical probability. - Conduct a probability experiment, with or without technology, and compare the experimental results to the theoretical probability. - Explain that as the number of trials in a probability experiment increases, the experimental probability approaches theoretical probability of a particular outcome. - Distinguish between theoretical probability and experimental probability, and explain the differences.

6.SS.1

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 - Provide examples of angles found in the environment. - Classify a given set of angles according to their measure, e.g., acute, right, obtuse, straight, reflex. - Sketch 45°, 90° and 180° angles without the use of a protractor, and describe the relationship among them. - Estimate the measure of an angle using 45°, 90° and 180° as reference angles. - Measure, using a protractor, given angles in various orientations. - Draw and label a specified angle in various orientations using a protractor. - Describe the measure of an angle as the measure of rotation of one of its sides. - Describe the measure of angles as the measure of an interior angle of a polygon.

6.SS.2

Demonstrate that the sum of interior angles is: • 180° in a triangle • 360° in a quadrilateral. • Achievement Indicators - Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles. - Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals.

6.SS.3

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

6.SS.4

Construct and compare triangles, including: • scalene • isosceles • equilateral • right • obtuse • acute in different orientations. • Achievement Indicators - Sort a given set of triangles according to the length of the sides. - Sort a given set of triangles according to the measures of the interior angles. - Identify the characteristics of a given set of triangles according to their sides and/or their interior angles. - Sort a given set of triangles and explain the sorting rule. - Draw a specified triangle, e.g., scalene. - Replicate a given triangle in a different orientation and show that the two are congruent.

6.SS.5

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

6.SS.6

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

6.SS.7

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

6.SS.8

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

6.SS.9

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 - Identify the coordinates of the vertices of a given 2-D shape (limited to the first quadrant of a Cartesian plane). - Perform a transformation on a given 2-D shape and identify the coordinates of the vertices of the image (limited to the first quadrant). - 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 first quadrant).

6.PR.1

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

6.PR.2

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

6.PR.3

Represent generalizations arising from number relationships using equations with letter variables. • Achievement Indicators - Write and explain the formula for finding the perimeter of any given rectangle. - Write and explain the formula for finding the area of any given rectangle. - 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. - Describe the relationship in a given table using a mathematical expression. - Represent a pattern rule using a simple mathematical expression, such as 4 d or 2n + 1.

6.PR.4

Demonstrate and explain the meaning of preservation of equality concretely, pictorially and symbolically. • Achievement Indicators - Model the preservation of equality for addition using concrete materials, such as a balance or using pictorial representations and orally explain the process. - Model the preservation of equality for subtraction using concrete materials, such as a balance or using pictorial representations and orally explain the process. - Model the preservation of equality for multiplication using concrete materials, such as a balance or using pictorial representations and orally explain the process. - Model the preservation of equality for division using concrete materials, such as a balance or using pictorial representations and orally explain the process. - 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).