7.N01.04 Explain, using an example, why numbers cannot be divided by 0.
7.N02 Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication, and division of decimals to solve problems (for more than one-digit divisors or more than two-digit multipliers, the use of technology is expected).
7.N02.01 Use estimation to determine the appropriate place value when calculating the sum or difference.
7.N02.10 Solve a given problem involving the multiplication or division of decimal numbers with more than two-digit multipliers or more than one-digit divisors (whole numbers or decimals) with the use of technology.
7.N04 Students will be expected to demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals (with one or two repeating digits) and positive fractions.
7.N04.01 Predict the decimal representation of a given fraction using patterns.
7.N04.02 Match a given set of fractions to their decimal representations.
7.N04.03 Sort a given set of fractions as repeating or terminating decimals.
7.N04.04 Express a given fraction as a terminating or repeating decimal.
7.N04.07 Provide an example where the decimal representation of a fraction is an approximation of its exact value.
7.N05 Students will be expected to demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences).
7.N05.01 Use benchmarks to estimate the sum or difference of positive fractions or mixed numbers.
7.N07 Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals.
7.N07.01 Position proper fractions with like and unlike denominators from a given set on a number line, and explain strategies used to determine order.
7.N07.04 Compare and order the numbers of a given set that includes positive fractions, positive decimals, and/or whole numbers in ascending or descending order and verify the result using a variety of strategies.
7.PR02.03 Sketch the graph from a table of values created for a given linear relation, and describe the patterns found in the graph to draw conclusions (e.g., graph the relationship between n and 2n + 3).
Variables and Equations - Students will be expected to represent algebraic expressions in multiple ways.
7.PR03 Students will be expected to demonstrate an understanding of preservation of equality by: • modelling preservation of equality, concretely, pictorially, and symbolically • applying preservation of equality to solve equations
7.PR03.01 Model the preservation of equality for each of the four operations, using concrete materials and/or pictorial representations; explain the process orally; and record the process symbolically.
7.PR03.02 Write equivalent forms of a given equation by applying the preservation of equality, and verify using concrete materials (e.g., 3b = 12 is equivalent to 3b + 5 = 12 + 5 or 2r = 7 is equivalent to 3(2r) = 3(7).
7.PR06 Students will be expected to model and solve, concretely, pictorially, and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and b are integers.
7.PR06.01 Represent a given problem with a linear equation, and solve the equation using concrete models.
7.PR07 Students will be expected to model and solve, concretely, pictorially, and symbolically, where a, b, and c are whole numbers, problems that can be represented by linear equations of the form: ax + b = c; ax = b; x/a = b, a ≠ 0.
7.PR07.01 Represent a given problem with a linear equation, and solve the equation using concrete models.
Students will be expected to use direct and indirect measurement to solve problems.
7.M01 Students will be expected to demonstrate an understanding of circles by: • describing the relationships among radius, diameter, and circumference • relating circumference to pi • determining the sum of the central angles • constructing circles with a given radius or diameter • solving problems involving the radii, diameters, and circumferences of circles
7.M01.01 Illustrate and explain that the diameter is twice the radius in a given circle.
7.G02.05 Create shapes and designs, and identify the points used to produce the shapes and designs, in any quadrant of a Cartesian plane.
Transformations - Students will be expected to describe and analyze position and motion of objects and shapes.
7.G03 Students will be expected to perform and describe transformations (translations, rotations, or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).
7.G03.01 Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane.
7.G03.02 Describe the horizontal and vertical movement required to move from a given point to another point on a Cartesian plane.
7.G03.03 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, or successive transformations, on a Cartesian plane.
7.G03.04 Draw and describe a 2-D shape and its image, given a combination of transformations.
Data Analysis - Students will be expected to collect, display, and analyze data to solve problems.
7.SP01 Students will be expected to demonstrate an understanding of central tendency and range by: • determining the measures of central tendency (mean, median, mode) and range • determining the most appropriate measures of central tendency to report findings
7.SP01.01 Determine mean, median, and mode for a given set of data, and explain why these values may be the same or different.
7.SP02.03 Identify outliers in a given set of data, and justify whether or not they are to be included in reporting the measures of central tendency.
7.SP02.04 Provide examples of situations in which outliers would and would not be used in reporting the measures of central tendency.
7.SP03 Students will be expected to construct, label, and interpret circle graphs to solve problems.
7.SP03.01 Identify common attributes of circle graphs, such as: • title, label, or legend • the sum of the central angles is 360⁰ • the data is reported as a percent of the total, and the sum of the percents is equal to 100%
7.SP04.02 Provide an example of an event with a probability of 0 or 0% (impossible) and an example of an event with a probability of 1 or 100% (certain).
7.SP05 Students will be expected to identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.
7.SP05.01 Provide an example of two independent events, such as the following, and explain why they are independent. • spinning a four-section spinner and an eight-sided die • tossing a coin and rolling a twelve-sided die • tossing two coins • rolling two dice
7.SP06 Students will be expected to conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or other graphic organizer) and experimental probability of two independent events.
7.SP06.01 Determine the theoretical probability of a given outcome involving two independent events.