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Math 6 - Scope and Sequence
6.1 Areas Current Unit
In this unit, students learn to find areas of polygons by decomposing, rearranging, and composing shapes. They learn to understand and use the terms “base” and “height,” and find areas of parallelograms and triangles. Students approximate areas of non-polygonal regions by polygonal regions. They represent polyhedra with nets and find their surface areas
6.2 Ratios, Rates, and Percentages
In this unit, students learn to understand and use the terms “ratio,” “rate,” “equivalent ratios,” “per,” “at this rate,” “constant speed,” “constant rate,” “unit rate,” “speed,” “pace,” “percent,” and “percentage.” They recognize when two ratios are or are not equivalent and that equivalent ratios have equal unit rates.
6.3 Fractions and Decimals
In the first half of this unit, students examine how the relative sizes of numerator and denominator affect the size of their quotient when numerator or denominator (or both) is a fraction.
In the second half of this unit, students compute sums, differences, products, and quotients of multi-digit whole numbers and decimals, using efficient algorithms. They use calculations with whole numbers and decimals to solve problems set in real-world contexts.
6.4 Expressions and Equations
In this unit, students learn to understand and use the terms “variable,” “coefficient,” “solution,” “equivalent expressions,” “exponent,” “independent variable,” and “dependent variable.” They begin to write coefficients next to variables without a multiplication symbol, e.g., 10x rather than 10•x, and note that x is 1•x. They learn other situations in which the multiplication symbol can be omitted, e.g., 6•(3+2) can be written as 6(3+2).
6.5 Proportional Relationships
In this unit, students learn to understand and use the terms “proportional,” “constant of proportionality,” and “proportional relationship,” and recognize when a relationship is or is not proportional. They represent proportional relationships with tables, equations, and graphs. Students use these terms and representations in reasoning about situations that involve constant speed, unit pricing, and measurement conversions. Then, special focus is given to circumference and area of circles as examples of proportional and non-proportional relationships, respectively. Students informally derive the formulas for circumference and area of a circle and are introduced to the value 𝜋.
6.6 Percentage Increase and Decrease
In this unit, students use ratios, scale factors, unit rates (also called constants of proportionality), and proportional relationships to solve multi-step, real-world problems that involve fractions and percentages. They learn to understand and use the terms “repeating decimal,” “terminating decimal,” “percent increase,” “percent decrease,” “percent error,” and “measurement error.” They represent amounts and corresponding percent rates with double number line diagrams and tables. They use these terms and representations in reasoning about situations involving sales taxes, tips, markdowns, markups, sales commissions, interest, depreciation, and scaling a picture.
6.7 Rational Numbers
In this unit, students interpret signed numbers in contexts (e.g., temperature, elevation, deposit and withdrawal, position, direction, speed and velocity, percent change) together with their sums, differences, products, and quotients. (“Signed numbers” include all rational numbers, written as decimals or in the form a/b) They understand and use the terms “positive number,” “negative number,” “rational number,” “opposite,” “sign,” “absolute value,” “less than,” “greater than,” and the corresponding symbols. They plot points with signed rational number coordinates on the number line, and recognize and use the connection between relative position of two points on the number line and inequalities involving the coordinates of the points. They understand and use absolute value notation, understanding that the absolute value of a number as its distance from zero on the number line.
Students use tables and number line diagrams to represent sums and differences of signed numbers or changes in quantities represented by signed numbers such as temperature or elevation, becoming more fluent in writing different numerical addition and subtraction equations that express the same relationship. They compute sums and differences of signed numbers. Students plot pairs of signed number coordinates in the plane, understanding the relationship between the signs of a pair of coordinates and the quadrant of the corresponding point, and use coordinates to calculate horizontal and vertical distances between two points. They view situations in which objects are traveling at constant speed (familiar from previous units) as proportional relationships.
6.8 Data Sets and Distributions
Students are introduced to dot plots and histograms as ways of visualizing data and distributions. They informally describe the distributions using center and spread before more formally computing mean, median, mean absolute deviation, and interquartile range as ways of quantifying the center and variability. Then, students consider what they can do when they do not have access to all of the necessary data. Ways to get samples, why using random processes is important, and how information from samples can be variable are all introduced.
6.9 Putting It All Together
In this unit, students use concepts and skills from previous units to solve additional problems.
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