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    APA Scope and sequence  (6th grade)

     

    1st Nine weeks 

    Number Sense( 10 days)

    ·     Classify rational numbers

    6.2A  classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to

    describe relationships between sets of numbers

    6.2E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where

    b ≠ 0.

    ·     Estimate to Determine Solutions

    5.2C round decimals to tenths or hundredths. (60%)

    5.3A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication,

    or division (52%)

    ·     Whole Number Multiplication and Division

    5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm; (78%)

    5.3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard

    algorithm (90%)

    Integer Operations(15 days)

    ·     Integer operations

    6.2B  identify a number, its opposite, and its absolute value;

    6.3C  represent integer operations with concrete models and connect the actions with the models to standardized algorithms;

    6.3D  add, subtract, multiply, and divide integers fluently

    ·     Properties (embed identity, commutative, & associative within Integers)

    6.7D generate equivalent expressions using the properties of operations: inverse, identity, commutative,

    associative and  distributive properties.

     

    Rational Number Conversions(15 days) 

    ·     Convert between Fraction, Decimal, Percent

    6.2E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b

    where b ≠ 0.

    6.4E  represent ratios and percents with concrete models, fractions, and decimals

    6.4F  represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using

    10 by 10 grids, strip diagrams, number lines, and numbers

    6.4G  generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems

    that involve money

    6.5C use equivalent fractions, decimals, and percents to show equal parts of the same whole.

    ·     Compare and Order Rational Numbers

    5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or

    = (80%)

    6.2C  locate, compare, and order integers and rational numbers using a number line

    6.2D  order a set of rational numbers arising from mathematical and real-world contexts

    ·     Coordinate Plane

    5.8A describe the key attributes of the coordinate plane… (n/a)

    5.8B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane (30%)

    6.11A  graph points in all four quadrants using ordered pairs of rational numbers

     2nd Nine Weeks                                                    
     

    Rational Number – Multiplication and Division (17 days)

    ·     Represent and Solve Multiplication and Division of Fractions

    5.3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and

    pictorial models, including area models (58%)

    5.3J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction

    such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models (58%)

    5.3L divide whole numbers by unit fractions and unit fractions by whole numbers (50%)

    6.3A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

    6.3B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction,

    including values greater than or less than one

    6.3E multiply and divide positive rational numbers fluently

    ·     Represent and Solve Multiplication and Division of Decimals

    5.3D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area

    models (27%)

    5.3E solve for products of decimals to the hundredths, including situations involving money, using strategies based

    on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers

    (74%)

    5.3F represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using

    objects and pictorial models, including area models (60%)

    5.3G solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number

    divisors, using strategies and algorithms, including the standard algorithm (48%)

    6.3A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

    6.3E multiply and divide positive rational numbers fluently

    ·     Order of Operations

    5.4E describe the meaning of parentheses and brackets in a numeric expression (94%)

    5.4F simplify numerical expressions that do not involve exponents, including up to two levels of grouping (77%)

    6.7A generate equivalent numerical expressions using order of operations, including whole number exponents 

    and prime factorization

    3rd Nine Weeks 

     

    Multiple Representations (17 days)

    •    Write equations and inequalities to represent constraints or  conditions in problems including

    relatedto area and volume

    6.9A  write one-variable, one-step equations and inequalities to represent constraints or conditions within problems

    •    Write problem situations given one-variable, one-step equations and inequalities

    6.9C write corresponding real-world problems given one-variable, one-step equations or inequalities

    ·    Multiplicative vs. Additive

          5.4D recognize the difference between additive and multiplicative numerical     patterns given in a table or graph (74%)

    ·      Independent vs Dependent events

    6.6A  identify independent and dependent quantities from tables and graphs

    6.6B  write an equation that represents the relationship between independent and dependent quantities from a table

    •    Represent & compare rules, tables, graphs

    5.4C generate a numerical pattern when given a rule in the form y = ax or y = x + a & graph (49%)

    5.8C  graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical

    and real-world problems, including those generated by number patterns or found in an input-output table (37%)

    5.9B  represent discrete paired data on a scatterplot (n/a)

    6.4A  compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to

    differentiate between additive and multiplicative relationships

    6.6C  represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or

    y = x + b

     

    Proportional Reasoning ( 25 days)

    ·    Examples of rates and ratios

    6.4C give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;

    6.4D give examples of rates as the comparison by division of two quantities having different attributes, including rates as

    quotients;

    ·    Apply ratios and rates to real world scenarios

    6.5A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and

    proportions

    6.4B apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems

    involving

    ratios and rates

    ·    Percent applications

    6.5B solve real-world problems to find the whole given a part and the percent, to find the part given

    thewhole and the percent, and to find the percent given the part and the whole, including the use

    of concrete and pictorial models

    ·    Convert within measurement systems

    5.7A solve problems by calculating conversions within a measurement system, customary or metric (79%)

    6.4H convert units within a measurement system, including the use of proportions and unit rates

    4th Nine Weeks

     

    Graphing and Statistics (12 days)

    ·    Represent and Interpret numerical data within graphs

    5.9A  represent categorical data with bar graphs or frequency tables and numerical data, including data sets of

    measurements in fractions or decimals, with dot plots or stem-and-leaf plots (n/a)

    5.9C  solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf

    plot, or scatterplot (65%)

    6.12A  represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

    6.12B  use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution

    6.13A  interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

    ·    Summarize data with measures of center and graphical summaries

    6.12C  summarize numeric data with numerical summaries, including the mean and median (measures of center)

    and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the

    center, spread, and shape of the data distribution

    6.12D  summarize categorical data with numerical and graphical summaries, including the mode, the percent of

    values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution

    ·    Variability

    6.13B  distinguish between situations that yield data with and without variability

    Geometry and Equations (16 days)

    ·    2D Figures Attributes and Properties

    5.5A classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their

    attributes and properties (54%)

    ·    Triangle relationships

    6.8A  extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship

    between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle

    ·    Model  area formulas

    6.8B  model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

    ·    Determine solutions of perimeter, area, and volume problems

    5.4G  use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the

    special form for a cube (V = l x w x h, V = s x s x s, and V = Bh) (n/a)

    5.4H represent and solve problems related to perimeter and/or area and related to volume (59%)

    5.6A recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a

    three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible (78%)

    5.6B determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers

    times the number of unit cubes in the area of the base (41%)

    6.8D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles

    and volume of right rectangular prisms where dimensions are positive rational numbers

    ·    Model and Solve one variable – one step equations and inequalities using geometric figures

    6.10A  model and solve one-variable, one-step equations and inequalities that represent problems, including

    geometric concept

    ·    Write equations that represent problems related area and volume

    6.8C  write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and

    volume of right rectangular prisms where dimensions are positive rational numbers

    		  
     

    Financial Literacy (5 days)·    

          Defining taxes and income (5.10A, 5.10B)

    ·     Methods of Payment (5.10C, 6.14B, 6.14C)

    ·     Credit History (6.14D, 6.14E, 6.14F)

    ·     Financial Institutions (6.14A)

    ·     Paying for College (6.14G)

    ·     Budgets (5.10D, 5.10E (84%), 5.10F)

    ·     Compare Salaries (6.14H)

    		  

    STAAR Review (5 days)