Mathematics Scope & Sequence 2016-17
Grade 6 Pre-AP
Revised: June 2016
Second Six Weeks (24 Days)
Readiness Standard(s)
6.4G generate equivalent forms of fractions,
decimals, and percents using real-world problems,
including problems that involve money
Supporting Standard(s)
Fractions, Decimals, and Percents
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
6.5C use equivalent fractions, decimals, and
percents to show equal parts of the same whole
6.14E describe the information in a credit report and
how long it is retained
6.14F describe the value of credit reports to
borrowers and to lenders
Represent percents using pictures and models, including 100’s
grid. (6.4E)
Represent benchmark fractions and decimals (0, ½, 1) using 10
by 10 grids, strip diagrams, number lines, and numbers. (6.4F)
Represent benchmark percents such as 1%, 10%, 25%, 33
1/3% using 10 by 10 grids. (6.4F)
Represent multiples of these benchmark values using 10 by 10
grids. (6.4F)
Determine if given fractions, decimals and percents are
equivalent. (6.5C)
Show equal parts of the same whole using equivalent fractions,
decimals, percents. (6.5C)
Apply equivalent fractions, decimals and percents to real-world
examples. (6.5C)
Generate equivalent forms of fractions, decimals, and percents,
using real-world problems, including problems that involve
money and percents less than 1% and greater than 100%.
(6.4G)
Convert between equivalent forms of fractions (with like and
unlike denominators), mixed numbers, proper and improper
fractions, and repeating, terminating and non-terminating
decimals (6.4G).
Evaluate reasonableness of solutions using benchmark
fractions and percents. (6.4F)
Determine a person’s credit worthiness (excellent, good, fair, or
poor) based on a given credit report. (6.14E)
Describe the information in a credit report. (6.14E)
Explain how long the information on a credit report is retained.
(6.14E)
Describe the value of credit reports to borrowers and lenders.
(6.14F)
Textbook Sections: Course 1 - 5.1, 5.2, 5.3
Days
Including, but not limited to…
8-9
Days
Readiness Standard(s)
6.2D order a set of rational numbers arising from
mathematical and real-world contexts
Supporting Standard(s)
6.2B identify a number, its opposite, and its absolute
value
6.2C locate, compare, and order integers and
rational numbers using a number line
6.2E extend representations for division to include
fraction notation such as a/b represents the same
number as a ÷ b where b ≠ 0
6.4F 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
Rational Numbers
6.14G explain various methods to pay for college,
including through savings, grants, scholarships,
student loans, and work-study
7.2A extend previous knowledge of sets and
subsets using a visual representation to describe
relationships between sets of rational numbers
Including, but not limited to…
Identify a number, its opposite and absolute values on a number
line, both horizontal and vertical, including fractions, decimals
and integers. (6.2B)
Read negative numbers as the opposite of its value. Example: 4 could be read as “the opposite of 4” which would be negative
4 (6.2B)
Determine that the sum of a number and its opposite has a
value of zero. (6.2B)
Apply absolute value to everyday life, and understand the
significance of zero. (6.2B)
Connect various forms of fraction notation, including a/b
represents the same number as
a ÷ b where b ≠ 0 to yield a decimal equivalence, including
mixed and improper fractions. (6.2E)
Explain through division, why b ≠ 0 and why a fraction equals 1
when the numerator and denominator are the same. (6.2E)
Classify numbers as whole numbers, integers, and rational
numbers using a visual representation such as a Venn diagram.
(7.2A)
Describe relationships, similarities, and differences between 2
and 3 sets of numbers, using Venn diagrams and other graphic
organizers. (7.2A)
Describe relationships between sets of rational numbers. (7.2A)
Order integers, positive and negative decimals and positive and
negative benchmark fractions or any combination in real world
context such as money, temperatures, distance, and
speed/time, altitude, profit/ loss and deposit/withdrawal. (6.2D)
Compare and order integers, positive and negative decimals,
and positive and negative benchmark fractions or any
combination using a variety of number lines. (6.2C)
Write inequalities with symbols such as <,>, = to represent
relationships between integers and rational numbers. (6.2C)
Locate integers, positive and negative decimals, and positive
and negative benchmark fractions or any combination using a
variety of number lines including vertical and horizontal lines,
integers only marked, fourths marked, halves marked, tenths
marked, missing numbers, negative decimals, etc. (6.2C)
Represent benchmark fractions using 10 by 10 grids, strip
diagrams, number lines, and numbers. (6.4F)
Apply integers to real world situations, including the profit-loss
model. (6.2C)
Compare and contrast the various methods to pay for college,
including through savings, grants, scholarships, student loans,
and work study. (6.14G)
Differentiate between savings, grants, scholarships, student
loans, and work study. (6.14G)
Identify which method of payment for college is described in a
given situation. (6.14G)
Textbook Sections: Course 2 - 1.1, 1.2
First six weeks continued on next page.
5
Days
Including, but not limited to…
Readiness Standard(s)
6.3D add, subtract, multiply, and divide integers
fluently
6.3E multiply and divide positive rational numbers
fluently
6.7A generate equivalent numerical expressions
using order of operations, including whole number
exponents and prime factorization
7.3B apply and extend previous understandings of
operations to solve problems using addition,
subtraction, multiplication, and division of rational
numbers.
Integer Operations
Supporting Standard(s)
6.3C represent integer operations with concrete
models and connect the actions with the models to
standardized algorithms
6.14A compare the features and costs of a checking
account and a debit card offered by different local
financial institutions
6.14C balance a check register that includes
deposits, withdrawals, and transfers
7.3A add, subtract, multiply, and divide rational
numbers fluently
Model integer operations with concrete models, pictorial models,
horizontal and vertical number lines, two color counters, colored
tiles, + and – signs, including operations that have more than 2
integers. (6.3C)
Connect the actions with the models to standardized algorithms
including operations that have more than 2 integers. (6.3C)
Create zero pairs as necessary in both addition and subtraction
models. (6.3C)
Add, subtract, multiply, and divide integers
flexibly, accurately and efficiently. (6.3D)
Recognize and perform the correct order of operations to solve
a problem with multiple operations (6.7A)
Determine and apply appropriate integer operations to realworld problems. (6.3D)
Differentiate between deposits, withdrawals and transfers.
(6.14C)
Balance a register that includes deposits, withdrawals, and
transfers (whole numbers only). (6.14C)
Add and subtract positive and negative decimals flexibly,
accurately and efficiently. (7.3A)
Add and subtract positive and negative decimals using a
number line. (7.3A)
Model multiplication and division of positive decimals using
manipulatives. (6.3E)
Multiply and divide positive and negative decimals using a
number line. (7.3A)
Connect operations with models to standard algorithms. (6.3E)
Estimate to evaluate reasonableness of a solution. (6.3E)
Compare the features and costs of a checking account and a
debit card from different local financial institutions (such as
transaction fees and ATM fees associated with checking
accounts and debit cards). (6.14A)
Determine which local financial institution best suits the needs
of a given situation. (6.14A)
Textbook Sections: Course 2 - 1.3, 1.4, 1.8, 1.9
9-10
Days
Second Six Weeks (25 Days)
Including, but not limited to…
Readiness Standard(s)
6.3E multiply and divide positive rational numbers
fluently
Multiply and divide positive and negative decimals flexibly,
accurately and efficiently. (7.3A)
6.7A generate equivalent numerical expressions
using order of operations including whole number
exponents and prime factorization
Add, subtract, multiply and divide positive and negative
decimals given real-world situations (i.e. temperature,
measurement, and monetary). (7.3B)
7.3B apply and extend previous understandings of
operations to solve problems using addition,
subtraction, multiplication, and division of rational
numbers
Supporting Standard(s)
6.2E extend representations for division to include
fraction notation such as a/b represents the same
number as a ÷ b where b ≠ 0
Rational Number Operations
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
7.3A add, subtract, multiply, and divide rational
numbers fluently
Days
Solve real-world problems involving a combination of adding,
subtracting, multiplying, and dividing decimals. (7.3B)
Evaluate reasonableness of solutions to real-world problems
involving operations with decimals. (7.3B)
Connect fractions with division. For example,
a x 1/b = a ÷ b = a/b. (6.2E)
Add and subtract positive and negative fractions and mixed
numbers using a number line. (7.3A)
Model multiplication and division of positive fractions and mixed
numbers using manipulatives. (6.3E)
Connect operations with models to standard algorithms. (6.3E)
Model the result of dividing by a fraction and multiplying by its
reciprocal using manipulatives. (6.3A)
Model multiplication by fractions greater than and less than one,
using visuals to demonstrate increase or decrease. (6.3B)
Discover the rules/patterns of multiplication by fractions greater
than and less than one. (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. (6.3B)
Multiply and divide negative fractions and mixed numbers using
a number line. (7.3A)
Multiply and divide positive fractions flexibly, accurately and
efficiently. (6.3E)
Make connections between dividing by a fraction and multiplying
by its reciprocal including whole numbers, mixed numbers and
improper fractions. (6.3A)
Solve order of operation problems that contain exponents where
bases are rational numbers. (6.7A)
Solve order of operation problems that contain positive rational
numbers and positive and negative integers. (6.7A)
Evaluate reasonableness of solutions to problems involving
operations with fractions and mixed numbers. (7.3A)
Add, subtract, multiply, and divide positive and negative
fractions and mixed numbers flexibly, accurately and efficiently.
(7.3A)
Add, subtract, multiply and divide positive and negative fractions
and mixed numbers given real-world situations (i.e.
temperature, measurement, and monetary). (7.3B)
Solve mathematic and real-world problems involving a
combination of adding, subtracting, multiplying, and dividing
fractions, mixed numbers, decimals and integers. (7.3B)
Evaluate reasonableness of solutions to real-world problems
involving operations with fractions and mixed numbers. (7.3B)
Textbook Sections: Course 2 - 1.5, 1.6, 1.7, 1.8, 1.9
8-10
Days
Second six weeks continued on next page.
Including, but not limited to…
Algebraic Expressions
Readiness Standard(s)
6.7 A generate equivalent numerical expressions
using order of operations, including whole number
exponents and prime factorization
Write expressions from real world situations. (6.7D)
6.7D generate equivalent expressions using the
properties of operations: inverse, identity,
commutative, associative, and distributive properties
Recognize equivalent expressions using concrete models,
pictures and algebraic sentences. (6.7C)
Differentiate between expressions and equations. (6.7B)
Simplify expressions to show equivalence. (6.7C)
Supporting Standard(s)
6.7B distinguish between expressions and
equations verbally, numerically, and algebraically
6.7C determine if two expressions are equivalent
using concrete models, pictorial models, and
algebraic representations
Simplify expressions using order of operations (6.7A)
Connect operations with models to standard algorithms. (6.7C)
Generate equivalent expressions using the inverse identity,
commutative, associative, and distributive properties. (6.7D)
Simplify expressions using the properties of operations. (6.7D)
Textbook Sections: Course 1: 7.4, 7.5, 7.6, 7.7, 7.8
Readiness Standard(s)
7.11A model and solve one-variable, two-step
equations and inequalities
Algebraic Equations and Inequalities
Supporting Standard(s)
6.7B distinguish between expressions and equations
verbally, numerically, and algebraically
4-5
Days
Including, but not limited to…
Identify and compare expressions and equations verbally,
numerically, and algebraically. (6.7B)
Explain the difference between inequalities and equations.
(7.10A)
Determine whether a given situation requires an equation or
inequality. (7.10A)
7.10A write one-variable, two-step equations and
inequalities to represent constraints or conditions
within problems
Explain why a given value is or is not a reasonable solution to a
given situation. (7.11B)
7.10B represent solutions for one-variable, two-step
equations and inequalities on number lines; and
Write one-step and two-step equations and inequalities from
real-world examples. (7.10A)
7.10C write a corresponding real-world problem
given a one-variable, two-step equation or inequality
Evaluate reasonableness of solution based on constraints or
conditions within real-world problems. (7.10A)
7.11B determine if the given value(s) make(s) onevariable, two-step equations and inequalities true
Solve one-step and two-step equations using models, such as
algebra tiles. (7.11A)
Connect operations with models to standard algorithms. (7.11A)
Solve one-step and two-step equations and inequalities
algebraically. (7.11B)
Record solutions for equations and inequalities on a number
line. (7.10B)
Evaluate reasonable solutions to equations and inequalities.
(7.10B)
Write real-world situations given one-step and two-step
equations and inequalities. (7.10C)
Determine if a given value is a solution to a one-step and twostep equation or inequality. (7.11B)
Textbook Sections: Course 2 - 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7
8-10
Days
Third Six Weeks (29 Days)
Readiness Standard(s)
6.10A model and solve one-variable, one-step
equations and inequalities that represent problems,
including geometric concepts
Triangle Relationships
Supporting Standard(s)
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
7.11C write and solve equations using geometry
concepts, including the sum of the angles in a
triangle, and angle relationships.
Including, but not limited to…
Use knowledge of triangles and their properties to find the sum
of angles of a triangle. (6.8A)
Extend previous knowledge of triangles and their properties to
include the relationship between the lengths of sides and
measures of angles in a triangle. (6.8A)
Explore the properties of triangles using manipulatives. (6.8A)
Determine when three lengths form a triangle. For example, in
Triangle ABC, A+B>C, A+C>B, and B+C>A must all be true.
(6.8A)
Solve one-step equations and inequalities to find missing
angles, including complementary and supplementary, and
missing sides. (6.10A)
Apply the properties of triangles to solve real-world problems.
(6.8A)
Describe real-world situations involving triangle properties.
(6.8A)
Solve two-step equations to answer real world problems
involving geometry concepts. (7.11C)
Write equations that involve geometry concepts, including area,
perimeter, volume, the sum of angles in a triangle, angle
relationships, etc. (7.11C)
Textbook Sections: Course 1: 9.1, 9.2, 9.3, 9.4 Course 2 - 8.1, 8.2, 8.3
Third Six Weeks continued on next page
Days
8-9
Days
Including, but not limited to…
Readiness Standard(s)
6.6C represent a given situation using verbal
descriptions, tables, graphs, and equations in the
form y = kx or y = x + b
6.11A graph points in all four quadrants using
ordered pairs of rational numbers
Supporting Standard(s)
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
Multiple Representations
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
6.14H compare the annual salary of several
occupations requiring various levels of postsecondary education or vocational training and
calculate the effects of the different annual salaries
on lifetime income
Write an equation from a table. (6.6B)
Identify the independent and dependent variables from a table
and equation and relate to real world examples. (6.6B)
Differentiate between additive and multiplicative relationships by
comparing two rules verbally, numerically, graphically and
symbolically. (6.4A)
Compare two rules verbally, numerically with tables and ordered
pairs, graphically, and
symbolically in the form of y=ax or y= x + a. (6.4A)
Create tables that are both horizontal and vertical, with the
independent and dependent variables appropriately labeled.
(6.4A)
Relate the x-axis to the independent variable and the y-axis to
the dependent variable, especially in quadrant 1 graphs. (6.11A)
Graph points in all four quadrants using ordered pairs of rational
numbers. (6.11A)
Identify independent and dependent quantities from tables and
graphs that represent real-world situations. (6.6A)
Explain the terms of an arithmetic sequence, such as “the value
of the expression depends on the number of the term”. (6.6A)
Move fluidly between multiple representations of a situation,
including tables, graphs, equations, and verbal descriptions.
(6.6C)
Solve real world problems using multiple representations of data
within a single context. (6.6C)
Solve real world problems using the 4-Corners Problem Solving
Board. (6.6C)
Compare the annual salary of several occupations requiring
various levels of education. (6.14H)
Calculate the effects of the different annual salaries on a lifetime
income. (6.14H)
Draw conclusions about the effects of higher education. (6.14H)
Compare and contrast post-secondary education to vocational
training. (6.14H)
Textbook Sections: : Course 1: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6
9-11
Days
Readiness Standard(s)
6.4B apply qualitative and quantitative reasoning to
solve prediction and comparison of real-world
problems involving ratios and rates
Including, but not limited to…
Represent ratios with concrete models, pictures, fractions and
decimals. (6.4E)
Identify ratios in various forms (part:part, part:whole,
whole:part). (6.4E)
Supporting Standard(s)
Rates and Ratios
6.4C give examples of ratios as multiplicative
comparisons of two quantities describing the same
attribute
Represent ratios in a table, equation or verbal description.
(6.4E)
Simplify ratios to lowest terms, including whole numbers. (6.4E)
6.4D give examples of rates as the comparison by
division of two quantities having different attributes,
including rates as quotients
Create a unit rate through division. (6.4D)
6.4E represent ratios and percents with concrete
models, fractions, and decimals
Identify the relationships between and within equivalent ratios.
(6.4B)
7.4B calculate unit rates from rates in mathematical
and real-world problems
Give examples of ratios as multiplicative comparisons of two
quantities describing the same attribute. (6.4C)
Generate equivalent forms of ratios. (6.4E)
Create ratio tables and graphs to solve problems. (6.4C)
Give examples of rates as the comparison by division of two
quantities having different attributes, including rates as
quotients. (6.4D)
Compare the characteristics of a ratio to those of a rate. (6.4D)
Determine whether a given real-world situation represents a
ratio or a rate. (6.4D)
Apply qualitative and quantitative reasoning to solve prediction
and comparison of real-world problems to proportional
relationships involving ratios and rates. (6.4B)
Explain the significance of unit rates. (7.4B)
Calculate unit rates in mathematical and real-world problems.
(7.4B)
Textbook Sections: Course 2 - 2.1, 2.2 Course 1 – 4.1, 4.2, 4.3, 4.4, 4.5
9-10
Days
Fourth Six Weeks (33 Days)
Readiness Standard(s)
6.4G generate equivalent forms of fractions,
decimals, and percents using real-world problems,
including problems that involve money
6.5B solve real-world problems to find the whole
given a part and the percent, to find the part given
the whole and the percent, and to find the percent
given the part and the whole, including the use of
concrete and pictorial models
7.4D solve problems involving ratios, rates, and
percents, including multi-step problems involving
percent increase and percent decrease, and
financial literacy problems; and
Supporting Standard(s)
Proportions with Percents
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
7.13A calculate the sales tax for a given purchase
and calculate income tax for earned wages;
7.13B identify the components of a personal budget,
including income; planned savings for college,
retirement, and emergencies; taxes; and fixed and
variable expenses, and calculate what percentage
each category comprises of the total budget;
7.13C create and organize a financial assets and
liabilities record and construct a net worth statement
7.13D use a family budget estimator to determine
the minimum household budget and average hourly
wage needed for a family to meet its basic needs in
the student's city or another large city nearby;
7.13F analyze and compare monetary incentives,
including sales, rebates, and coupons.
Including, but not limited to…
Represent percents using pictures and models, including the
percent bar model and 100’s grid. (6.4E)
Represent benchmark percents and multiples such as 1%, 10%,
25%, 33 1/3% using 10 by 10 grids, strip diagrams, number
lines, and numbers. (6.4F)
Solve problems with fractions, decimals and percents including
problems involving money and percents less than 1% and
greater than 100%. (6.4G)
Solve real-world problems using all three types of application
problems involving percents: finding the whole, finding the part,
or finding the percent including the use of concrete and pictorial
models(6.5B)
Solve problems involving ratios and rates. (7.4D)
Solve problems involving percents, including multi-step
problems involving percent increase and percent decrease.
(7.4D)
Apply knowledge of ratios, rates and percents to financial
literacy problems. (7.4D)
Differentiate and compare between ratios, rates, and part to
whole. (7.4D)
Estimate, calculate, and differentiate the sales tax for a given
purchases and income tax for earned wages.(7.13A)
Identify a variety of factors that should be included in a personal
budget, including income, planned savings for college,
retirement and emergencies, taxes, fixed and variable
expenses. (7.13B)
Calculate the percentage of each category of a total budget,
given different aspects of the budget. (7.13B)
Give examples of expenses that would be included in each
category. (7.13B)
Differentiate between a financial asset and liability and
determine whether a given example is an asset or liability.
(7.13C)
Create and organize a financial assets and liabilities record.
(7.13C)
Explain the various aspects of net worth and create a net worth
statement. (7.13C)
Determine a minimum household budget and average hourly
wage needed for a family to meet its basic needs using a family
budget estimator. (7.13D)
Compare the basic needs of a small town to those of a large
city. (7.13D)
Differentiate between sales, rebates and coupons and calculate
the price of an item after applying a sale, rebate or coupon.
(7.13F)
Compare various offers from different stores to determine which
is the best deal. (7.13F)
Textbook Sections: Course 2 - 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
Fourth Six weeks continued on next page…
Days
8-9
Days
Including, but not limited to…
Readiness Standard(s)
7.4E convert between measurement systems,
including the use of proportions and the use of unit
rates
Supporting Standard(s)
Proportions
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
6.4E represent ratios and percents with concrete
models, fractions, and decimals
6.5A represent mathematical and real-world
problems involving ratios and rates using scale
factors, tables, graphs, and proportions
Represent mathematical and real-world problems involving
ratios and rates using tables. (6.5A)
Describe equivalent ratios using proportions in real world
situations. (6.4E)
Set up and solve proportion problems from a real world verbal
description. (6.4D)
Solve proportional situations using multiplicative reasoning
(rather than cross product algorithms). (6.4C)
Recognize scale factor in proportional relationships. (6.5A)
Make predictions using proportions. (6.4D)
Represent mathematical and real-world problems involving
ratios and rates using proportions, scale factors, and graphs.
(6.5A)
Determine if two quantities are proportional using graphs and
tables. (6.5A)
Convert units within a measurement system, including the use
of proportions and unit rates. (7.4E)
Convert between units within a measurement system, both
customary and metric using proportions. (7.4E)
Solve problems using the conversions and formulas on the
Assessment Reference Materials. (7.4E)
Estimate solutions to real world conversion problems prior to
calculating an exact answer. (7.4E)
Evaluate reasonableness of solutions. (7.4E)
Textbook Sections: Course 2 – 2.3, 2.7
Course 1 –4.1, 4.2, 4.6, 4.7
Fourth Six weeks continued on next page…
8-9
Days
Readiness Standard(s)
Including, but not limited to…
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
Create equivalent expressions by decomposing and rearranging
parts of parallelograms, trapezoids, and triangles. (6.8B)
Area
6.10A model and solve one-variable, one-step equations
and inequalities that represent problems, including
geometric concepts
7.9C determine the area of composite figures containing
combinations of rectangles, squares, parallelograms,
trapezoids, triangles, semicircles, and quarter circles
Connect these expressions to area formulas on the STAAR
Reference Materials sheet. (6.8B)
Write equations that could be used to find the area of
rectangles, parallelograms, trapezoids and triangles where the
dimensions are positive rational numbers. (6.8C)
Solve real world problems involving area. (6.8D)
Solve one-step equations and inequalities to answer real world
problems, including area and perimeter. (6.10A)
9-10
Days
Supporting Standard(s)
Connect models to algebraic formulas. (7.8C)
6.8B model area formulas for parallelograms, trapezoids,
and triangles by decomposing and rearranging parts of
these shapes
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
Calculate the area of composite figures containing combinations
of rectangles, squares, parallelograms, trapezoids, and
triangles. (7.9C)
Identify real world situations that involve composite figures.
(7.9C)
Justify reasonableness of solutions to area problems. (7.9C)
Textbook Sections: Course 1: 9.5, 9.6, 9.7, 9.8, 9.9 Course 2 - 8.5
Including, but not limited to…
Readiness Standard(s)
7.9B Determine the circumference and area of
circles
Explore π =
𝐶
𝑑
(7.5B)
𝐶
7.9C Determine area of composite figures
containing combinations of rectangles, squares,
parallelograms, trapezoids, triangles, semi-circles
and quarter-circles
Circles
Supporting Standard(s)
7.5B describe π as the ratio of the circumference
of a circle to its diameter
7.8C use models to determine the approximate
formulas for the circumference and area of a circle
and connect the models to the actual formulas
Connect combinations of formulas𝜋 = , 𝐶 = 𝜋 d, 𝐶 = 2 𝜋 r.
𝑑
(7.5B)
Collect data from varying sizes of circles to verify that the
circumference is approximately 3.14 times as long as the
diameter (7.5B)
Approximate formulas for the circumference and area of a circle
using models. (7.8C)
Determine the radius and diameter of a given circle. (7.9B)
Determine whether a problem is asking for area or
circumference. (7.9B)
Calculate the circumference and area of a circle given either the
radius or diameter. (7.9B)
Calculate the area of composite figures containing combinations
of rectangles, squares, parallelograms, trapezoids, triangles,
semicircles, and quarter circles. (7.9C)
Apply circumference and area to real-world problem situations.
(7.9B)
Textbook Sections: Course 2: 4.4-8.4, 8.5
This unit is continued in the fifth six weeks.
5
Days
\
Fifth Six Weeks (33 Days)
Days
This unit is continued from the 4th six weeks.
Readiness Standard(s)
7.9B Determine the circumference and area of circles
7.9C Determine area of composite figures containing
combinations of rectangles, squares, parallelograms,
trapezoids, triangles, semi-circles and quarter-circles
Circles
Supporting Standard(s)
7.5B describe π as the ratio of the circumference of a
circle to its diameter
7.8C use models to determine the approximate formulas
for the circumference and area of a circle and connect
the models to the actual formulas
Including, but not limited to…
Explore π =
𝐶
𝑑
(7.5B)
𝐶
Connect combinations of formulas𝜋 = , 𝐶 = 𝜋 d, 𝐶 =
𝑑
2 𝜋 r. (7.5B)
Collect data from varying sizes of circles to verify that the
circumference is approximately 3.14 times as long as the
diameter (7.5B)
Approximate formulas for the circumference and area of a
circle using models. (7.8C)
Determine the radius and diameter of a given circle. (7.9B)
Determine whether a problem is asking for area or
circumference. (7.9B)
Calculate the circumference and area of a circle given either
the radius or diameter. (7.9B)
Calculate the area of composite figures containing
combinations of rectangles, squares, parallelograms,
trapezoids, triangles, semicircles, and quarter circles. (7.9C)
Apply circumference and area to real-world problem
situations. (7.9B)
Textbook Sections: Course 2: 4.4-8.4, 8.5
4
Days
Readiness Standard(s)
Including, but not limited to…
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
Write equations that can be used to find the volume of right rectangular
prisms where the dimensions are positive rational numbers. (6.8C)
6.10A model and solve one-variable, one-step
equations and inequalities that represent problems,
including geometric concepts
Volume
7.8A model the relationship between the volume of
a rectangular prism and a rectangular pyramid
having both congruent bases and heights and
connect that relationship to the formulas;
7.8B explain verbally and symbolically the
relationship between the volume of a triangular
prism and a triangular pyramid having both
congruent bases and heights and connect that
relationship to the formulas; and
7.9A solve problems involving the volume of
rectangular prisms, triangular prisms, rectangular
pyramids, and triangular pyramids
Supporting Standard(s)
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
Solve real world problems involving volume. (6.8D)
Determine whether a problem is referring to area or volume from a
given situation. (6.8C)
Solve one-step equations and inequalities to answer real world problem
volume. (6.10A)
Determine reasonableness of solutions regarding area and volume.
(6.8C)
Find the volume of rectangular prisms, triangular prisms, rectangular
pyramids and triangular pyramids in real world problems. (7.9A)
Determine which formula to use from the Reference Material. (7.9A)
Explain why the formulas for volume use B, the area of the base. (7.9A)
Collect data from varying sizes of rectangular pyramid and rectangular
prism pairs with congruent bases and heights to model the relationship
between their volumes. (7.8A)
10
Days
Describe the similarities and differences between the volume formulas
for a rectangular pyramid and a rectangular prism. (7.8A)
Explain the significance of rectangular pyramids and prisms having
congruent bases and heights. (7.8A)
Collect data from varying sizes of triangular pyramid and triangular
prism pairs with congruent bases and heights to model the relationship
between their volumes. (7.8B)
Describe the similarities and differences between the volume formulas
for a triangular pyramid and a triangular prism. (7.8B)
Explain the significance of triangular pyramids and prisms having
congruent bases and heights. (7.8B)
Connect the relationship between these shapes to their volume
formulas. (7.8B)
Textbook Sections: Course 2 - 8.6, 8.7
District Benchmark
Fifth Six Weeks continued on the next page…
1-2
days
Central Tendencies
Readiness Standard(s)
Including, but not limited to…
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
Determine whether or not a situation has variable data. (6.13B)
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
Find the mean of a list of data by using the numerical method.
(6.12C)
6.13A interpret numeric data summarized in dot
plots, stem-and-leaf plots, histograms, and box plots
7.6G solve problems using data represented in bar
graphs, dot plots, and circle graphs, including partto-whole and part-to-part comparisons and
equivalents;
7.12A compare two groups of numeric data using
comparative dot plots or box plots by comparing
their shapes, centers, and spreads;
Calculate the mean, median, range and interquartile range from
a set of data. (6.12C)
Describe the center, spread and shape of data distribution using
the mean, median, range and interquartile range. (6.12C)
Draw conclusions about numeric data from the center, spread,
and shape of data distribution. (6.12C)
Summarize categorical data with numerical summaries,
including the mode, the percent of values in each category
(relative frequency table). (6.12D)
Summarize categorical data with the graphical summaries,
including the percent bar graph. (6.12D)
9-10
Days
Describe the data distribution using the numerical and graphical
summaries. (6.12D)
Make predictions based on numerical and graphical summaries.
(6.12D)
Justify conclusions drawn from these graphs. (6.13A)
Supporting Standard(s)
Compare the shapes, centers and spreads of dot plots. (7.12A)
6.13B distinguish between situations that yield data
with and without variability
Draw conclusions about two sets of data from these
comparisons. (7.12A)
Solve problems from bar graphs, dot plots and circle graphs
including part-to-whole and part-to-part comparisons and
equivalents. (7.6G)
Draw conclusions from these graphs. (7.6G)
Determine which type of graph best represents a set of data.
(7.6G)
Statistical Representations and
Displays
Textbook Sections: Course 2 - 9.1, 9.2, 9.3, 9.5, 9.6, 9.7
Readiness Standard(s)
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
6.13A interpret numeric data summarized in dot
plots, stem-and-leaf plots, histograms, and box plots
Supporting Standard(s)
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
Including, but not limited to…
Interpret data in dot plots, stem-and-leaf plots, histograms.
(6.13A)
Calculate the mean, median, range and interquartile range from
a set of data. (6.12C)
Draw conclusions about numeric data from a given graph.
(6.12A)
Justify conclusions drawn from these graphs. (6.13A)
Create dot plots, stem-and-leaf plots, and histograms from a set
of data (6.12A)
Analyze a graph to determine the set of numbers that it
represents (6.12A)
Describe the mean, median, mode, range and shape of data
given a graphical representation. (6.12B)
Draw conclusions about numeric data from the center, spread,
and shape of data distribution from a graph. (6.12B)
Textbook Sections: Course 2 - 10.4, 10.5, 10.6, 10.8, 10.9, 10.10
5-7
Days
Sixth Six Weeks (33 Days)
Box Plots
Readiness Standard(s)
Including, but not limited to…
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
Draw conclusions about numeric data from a box plot. (6.12A)
6.13A interpret numeric data summarized in dot
plots, stem-and-leaf plots, histograms, and box
plots
Describe the mean, median, mode, range and shape of data given a
box plot. (6.12B)
7.12A compare two groups of numeric data using
comparative dot plots or box plots by comparing
their shapes, centers, and spreads;
Supporting Standard(s)
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
Days
Create box plots from a set of data (6.12A)
Analyze a graph to determine the set of numbers that it represents
(6.12A)
Draw conclusions about numeric data from the center, spread, and
shape of data distribution from a box plot. (6.12B)
Interpret data in box plots. (6.13A)
5 Days
Justify conclusions drawn from box plots. (6.13A)
Compare the shapes, centers and spreads of dot plots or box plots.
(7.12A)
Draw conclusions about two sets of data from these comparisons.
(7.12A)
Calculate the mean, median, range and interquartile range from a set
of data. (6.12C)
Describe the center, spread and shape of data distribution using the
mean, median, range and interquartile range. (6.12C)
Draw conclusions about numeric data from the center, spread, and
shape of data distribution. (6.12C)
Textbook Sections: Course 1: 10.7
Readiness Standard(s)
Including, but not limited to…
STAAR Short Course
Supporting Standard(s)
10
Days
Sixth Six weeks continued on next page
Including, but not limited to…
Equations and Inequalities with Acceleration
Readiness Standard(s)
6.10A model and solve one-variable,
one-step equations and inequalities that
represent problems including geometric
concepts
7.11A model and solve one-variable,
two-step equations and inequalities
Write two-step equations and inequalities from realworld examples. (7.10A)
Write real-world situations given two-step equations
and inequalities. (7.10C)
Determine if a given value is a solution to a two-step
equation and inequalities. (7.11B)
Supporting Standard(s)
7.10A Write one-variable, two-step
equations and inequalities to represent
constraints or conditions within problems
7.10C Write a corresponding real-world
problem given a one-variable, two-step
equation or inequality
7.11B Determine if the given value(s)
make(s) one-variable, two-step
equations and inequalities true
7.11C Write and solve equations using
geometry concepts, including the sum of
the angles in a triangle, and angle
relationships
Represent two-step equations and inequalities using
algebra tiles. (7.11A)
Connect operations with models to standard
algorithms. (7.11A)
Solve two-step equations and inequalities algebraically
using a variety of rational numbers, including the use of
the distributive property. (7.11A)
Explain why a given value is or is not a reasonable
solution to a given real world situation. (7.11B)
Evaluate reasonable solutions to equations and
inequalities. (7.10B)
Evaluate reasonableness of solution to an equation
based on constraints or conditions within real-world
problems. (7.10A)
Textbook Sections: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 8.1, 8.2, 8.3
Sixth Six weeks continued on next page
5-8
Days
Readiness Standard(s)
Multiple Representations with Acceleration
6.6C represent a given situation using
verbal descriptions, tables, graphs, and
equations in the form y = kx or y = x + b
Supporting Standard(s)
Including, but not limited to…
Move fluidly between multiple representations of a
situation, including tables, graphs, equations, and
verbal descriptions. (6.6C)
Solve real world problems using multiple
representations of data within a single context. (6.6C)
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
Solve real world problems using the 4-Corners Problem
Solving Board. (6.6C)
6.6A identify independent and
dependent quantities from tables and
graphs
Identify the independent and dependent variables from
a table and equation and relate to real world examples
(6.6C).
6.6B write an equation that represents
the relationship between independent
and dependent quantities from a table
Compare two rules verbally, numerically with tables
and ordered pairs, graphically, and symbolically in the
form of y=ax or y=x + a. (6.4A)
Write an equation from a table. (6.6B)
Create tables that are both horizontal and vertical, with
the independent and dependent variables appropriately
labeled. (6.4A)
Identify independent and dependent quantities from
tables and graphs that represent real-world situations.
(6.6A)
Explain the terms of an arithmetic sequence, such as
“the value of the expression depends on the number of
the term”. (6.6A)
Textbook Sections: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6
5-8
Days