• 6th Grade Math
     
    Boy Doing Math HW
         This course promotes mathematical skills through a balance of math computation and problem solving activities which connect to real world experiences.  Students work to achieve mastery in number sense, data and statistical analysis, geometry, algebra, and mathematical reasoning areas.  Students’ skills in numerical operations, measurement, and estimation will be applied throughout the course.
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    6th Grade Math Curriculum

    (created Spring 2013)


    Unit 1: Ratios and Proportional Relationships


    Essential Question - How can you use mathematics to describe and model real-world situations?


    Chapter 1:  Ratios and Rates


    Essential Question:  How do you use equivalent rates in the real world?


    Necessary Background:

    • Multiplication and Division Fact Families

    • Identifying Equivalent Fractions

    • Simplifying Fractions


    Student Learning Objectives:

    • Identify GCF and LCM of given numbers.

    • Use ratios to compare categorical data.

      • Write ratios in various ways, including simplest form.

      • Explain the meaning of ratios used to represent data.

    • Use rates to compare quantities.

      • Write rates as fractions.

      • Convert rates to unit rates.

    • Use scaling to complete ratio and rate tables.

    • Graph ordered pairs based on ratio tables.

    • Use bar diagrams or equations with equivalent ratios to solve ratio and rate problems.



    Chapter 2:  Fractions, Decimals, and Percents


    Essential Question:  When is it better to use a fraction, decimal, or percent?


    Necessary Background:

    • Decimal Place Value

    • Reading and Writing Decimals

    • Identifying Equivalent Fractions

    • Simplifying Fractions


    Student Learning Objectives:

    • Convert between decimals and fractions.

    • Use percents to represent parts of a whole.

    • Convert between fractions, including mixed numbers, and percents.

    • Convert between percents and decimals.

    • Compare and order fractions, decimals, and percents.

    • Estimate the percent of a number.

    • Find the percent of a number.

    • Solve percent problems numerically and with number lines.



    Unit 2:  The Number System


    Essential Question - How can mathematical ideas be represented?


    Chapter 3:  Compute with Multi-Digit Numbers


    Essential Question:  How can estimating be helpful?


    Necessary Background:

    • Adding, Subtracting, Multiplying, and Dividing Multi-Digit Whole Numbers


    Student Learning Objectives:

    • Add and subtract decimals.

    • Estimate products by using rounding.

    • Multiply decimals by whole numbers.

    • Multiply decimals by decimals.

    • Divide multi-digit numbers with three and four digit dividends.

    • Estimate quotients by rounding dividends and divisors.

    • Dividing decimals by whole numbers.

    • Dividing decimals by decimals.



    Chapter 4:  Multiply and Divide Fractions


    Essential Question:  What does it mean to multiply and divide fractions?


    Necessary Background:

    • Writing Whole Numbers as Fractions

    • Converting Between Mixed Numbers and Improper Fractions


    Student Learning Objectives:

    • Round fractions to benchmark numbers - 0, ½, or 1.

    • Estimate fraction products with fractions and whole numbers.

    • Identify the commutative property.

    • Multiply fractions with whole numbers, other fractions, and mixed numbers.

    • Convert measurement units using the customary system.

    • Identify reciprocals of given numbers.

    • Divide fractions, mixed numbers, and whole numbers using models and algorithms.



    Chapter 5:  Integers and the Coordinate Plane


    Essential Question:  How are integers and absolute value used in real world situations?


    Necessary Background:

    • Compare decimals and fractions, with and without a number line.


    Student Learning Objectives:

    • Write integers to represent real world situations.

    • Graph and label integers on a number line.

    • Identify absolute value and the opposite of given integers.

    • Compare signs and magnitude of the numbers to compare and order integers.

    • Divide the numerator by the denominator to write rational numbers as decimals.

    • Use a number line or write in the same form to compare and order rational numbers.

    • Identify the four quadrants on the coordinate plane.

    • Identify points, ordered pairs, and reflections on the coordinate plane.


    Unit 3:  Expressions and Equations


    Essential Question - How can you communicate mathematical ideas effectively?


    Chapter 6:  Expressions


    Essential Question:  How is it helpful to write numbers in different ways?


    Necessary Background:

    • Multiply whole numbers

    • Add and subtract fractions


    Student Learning Objectives:

    • Express numbers using exponents (powers).

    • Write powers as products, by determining the base and the exponent.

    • Perform the order of operations (PEMDAS) by grouping symbols and simplifying inside parentheses first.

    • Replace variables to evaluate algebraic expressions.  

    • Replace variables and follow the order of operations to evaluate multi-step expressions.

    • Describe the situation, choose a variable, and translate the verbal phrase into an algebraic expression.

    • Multiply each addend by the number outside the parentheses to apply the distributive property.

    • Factor an expression by writing numeric or algebraic expressions as products of their factors.

    • Use properties to write an equivalent expression that has no like terms and no parentheses.

    • Use properties to simplify or factor expressions with two variables.



    Chapter 7:  Equations


    Essential Question:  How do you determine if two numbers or expressions are equal?


    Necessary Background:

    • Subtract decimals and fractions.


    Student Learning Objectives:

    • Solve equations by replacing the variable with a value that results in a true sentence.

    • Use the Subtraction Property of Equality to solve addition equations.

    • Use the Addition Property of Equality to solve subtraction equations.

    • Use the Division Property of Equality to solve multiplication equations.

    • Use the Multiplication Property of Equality to solve division equations.



    Chapter 8:  Functions and Inequalities


    Essential Question:  How are symbols (such as <, >, and =) useful?


    Necessary Background:

    • Compare whole numbers

    • Solve one-step equations


    Student Learning Objectives:

    • Compute function tables and find function rules.

    • Extend and describe arithmetic sequences using algebraic expressions.

    • Construct and analyze different verbal, tabular, graphical, and algebraic representations of functions.

    • Solve inequalities by using mental math and the guess-check-revise strategy.

    • Write and graph inequalities.

    • Solve one-step linear inequalities.



    Unit 4:  Geometry


    Essential Question - How can you use different measurements to solve real-life problems?


    Chapter 9:  Area


    Essential Question:  How does measurement help you solve problems in everyday life?


    Necessary Background:

    • Area of a rectangle

    • Multiply by fractions


    Student Learning Objectives:

    • Find the areas and missing dimensions of parallelograms.

    • Find the areas and missing dimensions of triangles.

    • Find the areas of trapezoids.

    • Determine the effects of changing dimensions on perimeter and area.

    • Draw polygons in the coordinate plane and use coordinates to find length.

    • Find the area of composite figures.



    Chapter 10:  Volume and Surface Area


    Essential Question:  How is shape important when measuring a figure?


    Necessary Background:

    • Multiply rational numbers

    • Evaluate numerical expressions


    Student Learning Objectives:

    • Find the volume of rectangular prisms.

    • Find the volume of triangular prisms.

    • Find the surface area of rectangular prisms.

    • Find the surface area of triangular prisms.

    • Find the surface area of pyramids.



    Unit 5:  Statistics and Probability


    Essential Question - Why is learning math important?


    Chapter 11:  Statistical Measures


    Essential Question:  How are the mean, median, and mode helpful in describing data?


    Necessary Background:

    • Add decimals

    • Divide decimals


    Student Learning Objectives:

    • Find the mean of a set of data.

    • Find and interpret the median and mode of a set of data.

    • Find the measures of variation.

    • Find and interpret the mean absolute deviation for a set of data.

    • Choose an appropriate measure of central tendency.



    Chapter 12:  Statistical Displays


    Essential Question:  Why is it important to carefully evaluate graphs?


    Necessary Background:

    • Find the mean and median of a set of data


    Student Learning Objectives:

    • Construct and analyze line plots.

    • Construct and analyze histograms.

    • Display and interpret data in box plots.

    • Describe a data distribution by its center, spread, and overall shape.

    • Draw and interpret line graphs.

    • Select an appropriate display for a data set.