
5th grade preap 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 realworld problems involving addition, subtraction, multiplication,
or division (52%)
· Whole Number Multiplication and Division
5.3B multiply with fluency a threedigit number by a twodigit number using the standard algorithm; (78%)
5.3C solve with proficiency for quotients of up to a fourdigit dividend by a twodigit 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 realworld 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 realworld 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 placevalue 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 fourdigit dividends and twodigit whole number divisors, using
objects and pictorial models, including area models (60%)
5.3G solve for quotients of decimals to the hundredths, up to fourdigit dividends and twodigit 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 onevariable, onestep equations and inequalities to represent constraints or conditions within problems
• Write problem situations given onevariable, onestep equations and inequalities
6.9C write corresponding realworld problems given onevariable, onestep 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 realworld problems, including those generated by number patterns or found in an inputoutput 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 realworld 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 realworld problems
involving
ratios and rates
· Percent applications
6.5B solve realworld 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 stemandleaf plots (n/a)
5.9C solve one and twostep problems using data from a frequency table, dot plot, bar graph, stemandleaf
plot, or scatterplot (65%)
6.12A represent numeric data graphically, including dot plots, stemandleaf 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, stemandleaf 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 twodimensional 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
threedimensional 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 onevariable, onestep 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)