North Thurston Public Schools
Sixth Grade
Math Power Standard 1
Unit Assessment #1 and #3
PS 1 - Estimate products and quotients of fractions and decimals (6.1.C)
Big Idea: Estimating helps us decide if our answers make sense.
Essential Questions: Why do you estimate products and quotients when working with fractions and
decimals?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade)
Terms that May be Used:
Key Concepts
What students need to know

Key Skills
What students need to be able to
do:

Related Standards
approximate, benchmark, estimate, evaluate, integer, justify,
number line, product, quotient, round
Products and quotients can be estimated.
Identify or explain whether estimation or exact calculation is appropriate
in situations involving multiplication and division of non-negative
fractions and decimals
 Estimate in situations involving multiplication and division of nonnegative fractions and decimals
 Use estimation to determine whether a computation result is reasonable
 Describe or explain a strategy used for estimation involving
multiplication and/or division of non-negative fractions and decimals
Compare and order non-negative fractions, decimals, and integers using the
number line, lists, and the symbols =, <, > (6.1.A). Represent
multiplication and division of non-negative fractions and decimals
using area models and the number line, and connect each
representation to the related equation (6.1.B).
Resources
Bits and Pieces II: 3.1, 3.2, 3.3; Bits and Pieces III: 2.1,
2.2, 2.3, 3.1,
Teaching Student Centered Mathematics
 Chapter 3 Pg. 97 - 98
 Chapter 4 Pg. 114 – 116; 124 - 125
North Thurston Public Schools
Sixth Grade
Math Power Standard 2
Unit Assessment #4
PS 2 – Fluently and accurately multiply and divide non-negative fractions and explain the inverse relationship
between multiplication and division with fractions (6.1.D).
Big Idea: With fractions, mixed numbers and whole numbers, there is an inverse relationship between
multiplying and dividing.
Essential Questions: How does multiplying and dividing fractions, and mixed numbers compare to
multiplying and dividing whole numbers?
Key Vocabulary (on WASL)
Terms that May be Used:
numerator, denominator, division, multiple, product
Terms that May be Used with Definitions or Examples:
Quotient
Key Concepts
What students need to know
Key Concepts
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Key Skills
What students need to be able to
do:
Key Skills
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Related Grade Level
Expectations
How mixed numbers and improper fractions relate
Why we convert to improper fractions to multiply
Answer doesn’t follow whole number rules (multiplying can
get smaller and dividing can get bigger)
Dividing is finding how many groups of the divisor fit in the
dividend.
Multiplying means “of”. (2 x 2 = 2 of 2)
Fraction bar = division (numerator divided by the
denominator)
explain or illustrate the meaning of multiplying or dividing
non-negative fractions
select and/or use an appropriate operation to show
understanding of multiplication or division of non-negative
fractions
explain, with words or pictures, why multiplication of
fractions can be done by multiplying denominators
translate a given picture or illustration into an equivalent
symbolic representation of multiplication or division of nonnegative fractions
How to convert mixed numbers to improper fractions and viceversa.
Compare and order non-negative fractions using the number line, lists, and
the symbols =, <, >. Represent multiplication and division of non-
negative fractions using area models and the number line, and
connect each representation to the related equation.
Resources
Bits and Pieces II: 3.4, 3.5 4.3, 4.4
Teaching Student Centered Mathematics
Chapter 3 Pg. 93 – 98 (Multiplication); Pg. 98 – 106 (Division)
North Thurston Public Schools
Grade Six
Math Power Standard 3
Unit Assessment #4
PS 3 - Fluently and accurately multiply and divide non-negative decimals (6.1.F)
Big Idea: Multiplying decimals can be compared to dividing decimals.
Essential Questions: How are multiplying and dividing decimals related?
Key Vocabulary (words in bold
are used in assessments for the first
time at sixth grade)
Key Concepts
What students need to know
Terms that May be Used:

There is an inverse relationship between multiplying and
dividing decimals
Key Skills
What students need to be able to
do:

Understand the inverse relationship between multiplication
and division
Work with different types of rational numbers including whole
numbers and decimal numbers
Related Grade Level
Expectations
Compare and order non-negative decimals using the number line, lists, and
the symbols =, <, >. Represent multiplication and division of non-
hundredths, integer, inverse, tenths, thousandths, whole number

negative decimals using area models and the number line, and
connect each representation to the related equation.
Resources
Bits and Pieces III: 2.4, 3.3, 3.4
Teaching Student Centered Mathematics
 Chapter 6
North Thurston Public Schools
Grade Six
Math Power Standard 4
Unit Assessment #4
PS 4 - Write a mathematical expression or equation with variables to represent information in a table or given
situation (6.2.A)
Big Idea: Tables, expressions, equations, and inequalities represent mathematical relationships.
Essential Questions: How do you use tables, graphs, expressions, equations, and inequalities to determine
a rule?
What does the rule mean?
Key Vocabulary (words in bold
Terms that May be Used:
are used in assessments for the
=, ≠, ≈, <, >, ≤, ≥, axis, distributive property, equation, expression,
first time at sixth grade)
identify, identity property, predict, relationship, rule, variable
Key Concepts
 Rules can be used to describe patterns of two arithmetic
What students need to know
operations.


Key Skills
What students need to be able to
do:
Related Standards
Resources
Tables, graphs, expressions, equations, or inequalities can
represent situations involving two arithmetic operations.
Rules can be used to evaluate expressions.

Identify or write a simple expression, using variables, to represent a
given situation.
 Identify or write a simple equation or simple inequality, with variables,
to represent a given situation, using =, ≠, ≈, <, >, ≤, or ≥.
 Explain the meaning of variables in a formula, expression, equation, or
inequality.
 Identify a situation that corresponds to a given expression, equation, or
inequality.
 Identify or describe a number pattern given in tables, rules, or words.
 Extend a pattern by identifying or supplying missing elements in the
beginning, middle, and/or end and/or describe the pattern or write a rule
with alternating operations between terms.
 Create a pattern that uses the same rule as a given pattern.
 Create a pattern and explain what makes it a pattern.
 Write a simple expression for a given situation and evaluate the
expression given the values for the variables.
 Evaluate an expression or formula given the values for the variables.
Draw a first-quadrant graph in the coordinate plane to represent information
in a table or given situation (6.2.B). Evaluate mathematical expressions
when the value for each variable is given (6.2.C) Solve work problems using
mathematical expressions and equations and verify solutions (6.2.F)
PPS – Algebra Unit: Investigation 1, 2, 3
Teaching Student Centered Mathematics

Chapter 8

Chapter 9

Chapter 10
North Thurston Public Schools
Sixth Grade
Math Power Standard 5
Unit Assessment #4
PS 5 - Solve one-step equations using order of operations and verifying solutions (6.2.E)
Big Idea: Logical patterns exist and are a regular occurrence in mathematics
Essential Questions: How can looking for patterns help us solve every day problems?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade)
Terms that May be Used:
Key Concepts
What students need to know


Order of operations (PEMDAS)
Informal use of inverse operations
Key Skills
What students need to be able to
do:

Identify or write a simple expression, using variables, to represent a
given situation
Identify or write a simple equation or simple inequality, with variables,
to represent a given situation using =, ≠, ≈, <, >, ≤, or ≥
=, ≠, ≈, <, >, ≤, or ≥, equation, expression, function, identify,
inequality, interval, order of operations, relationship, solution,
variable
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
Related Grade Level
Expectations
Resources
Explain the meaning of variables in a formula, expression,
equation, or inequality
Identify a situation that corresponds to a given expression,
equation, or inequality
Solve work problems using mathematical expressions and equations and
verify solutions (6.2.F)
PPS Algebra Unit: Investigations 1, 2, 3
Teaching Student Centered Mathematics
 Chapter 9
North Thurston Public Schools
Sixth Grade
Math Power Standard 6
Unit Assessment #4
PS 6 - Represent percents visually and numerically, and convert between the fractional, decimal, and
percent representations of a number (6.3.C)
Big Idea: Many numbers exist between whole numbers.
A relationship exists between fractions, decimals and percents.
Essential Questions: What relationship exists between fractions, decimals, and percents and how do you
relate them?
How do we use numbers between whole numbers?
Why do we use numbers between whole numbers?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade)
Terms that May be Used:
Key Concepts
What students need to know


The relationship between fractions, decimals, and percents.
Positive non-negative rational numbers (2 ½, 2.5, 250% etc.)
Key Skills
What students need to be able to
do:

Explain when a fraction, decimal or percent of one whole is not the
same as the same fraction, decimal or percent of another whole.
Convert between fractions, improper fractions, mixed numbers,
percents, and/or decimals.
Compare and/or order non-negative proper and improper fractions,
mixed numbers, percents, and decimals on a number line with
illustrations or symbolically.
Explain why one fraction, decimal, or percent is greater than, equal to,
or less then another fraction, decimal, or percent.
=, ≠, ≈, <, >, ≤, or ≥, decimal, denominator, fraction, greatest
common factor, improper fraction, least common multiple, lowest
terms, mixed number, number line, numerator, percent
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

Related Standards
Identify and write ratios as comparisons of part-to-part and part-to-whole
relationships.
Resources
Bits and Pieces III: 4.1, 4.2
Teaching Student Centered Mathematics
 Chapter 3
 Chapter 4
North Thurston Public Schools
Grade Six
Math Power Standard 7
Unit Assessment #4
PS 7 - Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions
(6.3.D)
Big Idea: Decimals can be written as fractions and percents.
Percent means “out of 100”.
Ratios can be written as fractions.
A ratio is a relationship between two units.
Essential Questions: How should ratios be written?
How do you represent part-to-part and part-to-whole and whole-to-whole
relationships?
Key Vocabulary (words in bold
are used in assessments for the first
time at sixth grade)
Terms that May be Used:
Key Concepts
What students need to know

Key Skills
What students need to be able to
do:
conclude, conclusion, per, percent, rate, ratio, scale, support,
unit rate, verify
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Resources
Ratios can be represented in part-to-part, part-to-whole, and
whole-to-whole relationships
A rate is a type of ratio
Identify or write ratios in part/part and part/whole relationships
using objects, pictures, and symbols
Create a ratio equivalent to a given ratio to determine an
unknown value for a dimension or a number of events or
objects.
Identify, demonstrate, or explain percent as 100 equal sized
parts of a set.
Represent equivalent percentages using different objects,
pictures, and/or symbols.
Identify or illustrate the use of percent.
Identify or represent equivalent ratios and/or percents.
Identify or determine a ratio or percent in a given situation.
Explain or show the meaning of a ratio or percent.
Give examples of ratio and/or percents in a situation.
Identify or determine fraction, decimal, or percent equivalents
for common percents such as 90%, 75%, 66% 50%, 33%,
25%, and 10%.
Bits and Pieces III: 4.3, 5.1, 5.2; Comparing and
Scaling: 1.1, 1.2, 1.3, 2.1, 2.2, 2.3 (Blue Book)
Teaching Student Centered Mathematics
 Chapter 6
North Thurston Public Schools
Sixth Grade
Math Power Standard 10
Unit Assessment #4
PS 8 - Determine the probability of a simple event using data collected in an experiment and represent the
probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100 (6.3.F,G)
Big Idea: Probability is the likelihood of an event happening.
Essential Questions: How would you determine the probability of an event happening?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade)
Terms that May be Used:
Key Concepts
What students need to know


Probability can be expressed as a ratio.
There are various ways to determine outcomes of events or situations.
Key Skills
What students need to be able to
do:

Explain why some outcomes are equally likely or more or less
likely to happen than others and how much more or less.
Identify, predict, or determine the probability of an event in a
simple experiment or situation as a ratio, decimal, or percent.
Demonstrate an understanding that probability is a ratio between
and including 0 and 1 or a percent between and including 0% and
100%.
Identify or determine the sample space of simple experiments or
activities.
Translate between representations of probability.
Create a spinner, game, or situation that would produce a given,
fair or unfair, outcome.
Explain why a game is fair or unfair.
complement, event, experiment, justify, outcome, probability
(experimental and theoretical), random, sample space (all possible
outcomes)
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Resources
How Likely Is It?: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4
Teaching Student Centered Mathematics
 Chapter 12
North Thurston Public Schools
Grade Six
Math Power Standard 9
Unit Assessment #4
PS 9 - Determine the perimeter and area of a composite figure that can be divided into triangles, rectangles, and
parts of circles (6.4.B)
Big Idea: Dividing composite figures into individual shapes can help us determine the area and perimeter
of the figures.
Essential Questions: How can formulas be used to determine area and perimeter of composite figures?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade)
Key Concepts
What students need to know
Key Skills
What students need to be able to
do:
Related Grade Level
Expectations
Resources
Terms that May be Used:
acre, area, attribute, centimeter, circumference, circle, compare, diameter,
edge, foot/feet, inch, kilometer, length, meter, mile, millimeter, perimeter, pi
(π), radius/radii, slant height, square unit, unit, yard
 area and perimeter formulas
 composite figures
 area and circumference of circles
 determine whether measurement has been done correctly in a given
situation
 find the perimeter and/or area of a rectangle or right triangle
 determine linear dimensions of a rectangle or right triangle based on a
given perimeter or area
 find the area of a circle using πr²
 find the circumference or a circle using 2πr or πd
 identify or describe circles using geometric properties
Identify the ratio of the circumference to the diameter of a circle as the
constant π, and recognize 22/7 and 3.14 as common approximations of π
(6.3.E). Determine the circumference and area of circles (6.4.A). Describe
and classify polyhedral by their attributes: parallel faces, types of faces,
number of faces, edges, and vertices (6.4.G).
Covering and Surrounding: Investigations 1, 2, 3, 4, 5
Teaching Student Centered Mathematics
 Chapter 7
North Thurston Public Schools
Sixth Grade
Math Power Standard 10
Unit Assessment #4
PS 10 - Determine the surface area and volume of rectangular prisms using appropriate formulas and
explain why the formulas work (6.4.E)
Big Idea: Volume is the space within a three-dimensional rectangular shape expressed in cubic units.
Surface area is the combined area of the outside surfaces of a three-dimensional rectangular
shape expressed in square units.
Essential Questions: What does volume mean and how do you use it?
What is the difference between volume and surface area?
Key Vocabulary (words in bold
are used in assessments for the
first time at sixth grade
Terms that May be Used:
Key Concepts
What students need to know
angle, area, centimeter, compare, construct, cube, cubic unit, degree,
edge, face, foot/feet, inch, kilometer, meter, mile, millimeter, net,
perimeter, polyhedron, prism, pyramid, rectangle, regular
polyhedron, right angle, square unit, surface area, tetrahedron,
three-dimensional, two-dimensional, volume, yard
 Rules to determine volume and surface area of rectangular prisms.
 Importance of the relationship between volume and surface area.
Key Skills
What students need to be able to
do:

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Identify or describe angles in a picture, diagram, or object.
Identify or describe angles by their relationship to a right angle.
Compare the meaning of surface area and volume of a rectangular
prism
Use area or volume to compare rectangles, right triangles, or
rectangular prisms.
Identify the volume for a given rectangular prism from a picture
or model.
Identify examples of surface area and/or volume.
Use surface area and volume to describe a rectangular prism.
Label measurements of a rectangular prism to show understanding
of the relationships among linear dimensions, surface area, and
volume of rectangular prisms and that area is measured in square
units and volume in cubic units.
Related Standards
Determine the surface area of a prism. Describe and sort polyhedra by their
attributes: parallel faces, type of faces, number of faces, edges, and vertices.
Resources
Filling and Wrapping: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3 (Blue
Book)
Teaching Student Centered Mathematics
 Chapter 7
 Chapter 8