Grade 6 

Mathematics is learned through questions that arise while solving well-constructed problems.  Our students begin with problems, they use strategies to solve the problems, and they learn the necessary mathematics along the way.  Many classroom investigations are designed so that students will collaboratively or individually discover the mathematical properties.  The properties are then discussed in class, summarized, and become part of the students’ mathematical knowledge to be applied to future problems.

The discovery of the mathematics is an essential part of the development of each student’s confidence as a mathematician.  Knowledge that is gained through inquiry is more likely to be remembered for the long term.  Teachers and parents work together to promote this discovery of math through investigation, problem solving, and reasoning.  Our goal is for students to understand that mathematics makes sense.

Unit 2: Introducing Ratios (Mid-October - November)

In Unit 2, In this unit, students learn to understand and use the terms “ratio,” “rate,” “equivalent ratios,” “per,” “at this rate,” “constant speed,” and “constant rate,” and to recognize when two ratios are or are not equivalent. They represent ratios as expressions, and represent equivalent ratios with double number line diagrams, tape diagrams, and tables. They use these terms and representations in reasoning about situations involving color mixtures, recipes, unit pricing, and constant speed. students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.  Students will uncover the understanding that the interpretation of the relationship of two quantities as a ratio facilitates problem solving.

Common Core State Standards:  6.RP.A.1, 6.RP.A.2, 6.RP.A.3(a-d)

Unit 4: Dividing Fractions (Early December - Mid-January)

In 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. They acquire the understanding that dividing by ab has the same outcome as multiplying by b, then by 1a. They compute quotients of fractions. They solve problems involving lengths and areas of figures with fractional side lengths and extend the formula for the volume of a right rectangular prism to prisms with fractional edge lengths and use it to solve problems. They use tape diagrams, equations, and expressions to represent situations involving partitive or quotitive interpretations of division with fractions. Given a multiplication or division equation or expression with fractions, they describe a situation that it could represent. They use tape diagrams and equations in reasoning about situations that involve multiplication and division of fractions.

Common Core State Standards:   6.NS.A.1, 6.G.A.1, 6.G.A.2,

Unit 6: Expressions and Equations (February to Mid-March)

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 6(3+2). They work with expressions that have positive whole-number exponents and whole-number, fraction, or variable bases, using properties of exponents strategically to evaluate these expressions, given a value for the variable. They find solutions for linear equations in one variable and simple equations that include exponents, e.g., 2x=32 and 100=x2. They use these terms and representations (including expressions with two variables) in reasoning about real-world and geometrical situations, understanding that some values of variables may not make sense in a given context. They represent collections of equivalent ratios as equations and use and make connections between tables, graphs, and linear equations that represent the same relationships.

Common Core State Standards:   6.NS.B.3, 6.EE.A.2, 6.RP.A.3b, 6.EE.B.5-7,6.EE.C.9,

Unit 8: Data Sets and Distributions (Late April - May)

Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.  Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students will understand that the analysis of data answers research questions.

Common Core State Standards:  6.SP.A.1, 6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5(a-d)