6th Grade Scope and Sequence 2012
6th Grade 1st Six Weeks
Student Expectations
Unpacked
Unit 1
Lesson 1, 2
6.2D, 6.1C
6.2 Number, operation, and quantitative
reasoning. The student adds, subtracts,
multiplies and divides to solve problems
and justify solutions.
D. estimate and round to approximate
reasonable results and to solve problems
where exact answers are not required
Concept - Estimation
Concept - Reasonableness
6.2D1.S - Estimate approximate reasonable
results
6.2D2.S - Round to approximate
reasonable results
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
C. use integers to represent real-life
situations
6.1C1.S - Use integers to represent real-life
situations
Suggestions for unit
1. Problem solving model
2. Scaffolding Problems
3. Ability grouping (hands on /
creating problems)
4. peer tutoring (inside/outside
circle)
Leading Questions and
talking questions
1. Why are there processes
involved when dealing with
problem solving?
2. What are the differences
between the different
processes?
6th Grade Scope and Sequence 2012
Unit 2
Lesson 3, 4, 5
6.1 D, E, F 6.1A
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
D. Write prime factorizations using
exponents
Concept - Factor
6.1D1.K - Prime
6.1D2.K - Base
6.1D3.K - Exponent
6.1D4.S - Write prime factorizations using
exponents
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
E. Identify factors of a positive integer,
common factors, and the greatest common
factor of a set of positive integers.
Concept - Factor
6.1E1.K - Factors
6.1E2.K - Multiples
6.1E3.S - Identify factors of a positive
integer
6.1E4.S - Identify common factors
6.1E5.S - Identify the greatest common
factor of a set of positive integers
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
F. Identify multiples of a positive integer and
common multiples and the least common
multiple of a set of positive integers.
6.1E1.S - Identify multiples of a positive
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
A. compare and order non-negative rational
numbers
C - Rational number
6.1A1.K - Positive number
6.1A2.K - Negative number
6.1A3.S - Compare non-negative rational
numbers
6.1A4.S - Order non- negative rational
numbers
integer
6.1E2.S - Identify common multiples
6.1E3.S - Identify the least common
multiple of a set of positive integers
1. Introduce simple factors, and
multiples
2. Introduce finding common
numbers
3. Focus on vocabulary and
understanding the difference
between multiples and factors.
4. Mini lesson and practice of
exponents
5. Prime factorization tree farm,
with practice.
6. Rotations around the
classroom with the three
different SE’s
7. Factors, multiples and primes
collage in the hallway.
1. Explain why it is important
for you to understand what
factors are.
2. Describe the patterns you
find when a numbers have
common factors.
3. Explain why it is important
for you to understand what
factors are.
4. Describe the patterns you
find when a numbers have
common factors.
5. Explain how factors help you
find prime factorization.
6.Why is it important that you
know your prime numbers?
6th Grade Scope and Sequence 2012
Unit 3
Lesson 6, 7
6.2C
6.2 Number, operation, and quantitative
reasoning. The student adds, subtracts,
multiplies and divides to solve problems
and justify solutions.
C. Use multiplication and division of whole
numbers to solve problems including
situations involving equivalent ratios and
rates
Concept - Ratio
Concept - Rate
6.2C1.S - Use multiplication of whole
numbers to solve problems involving
equivalent ratios
6.2C2.S - Use division of whole numbers to
solve problems involving equivalent ratios
6.2C3.S - Use multiplication of whole
numbers to solve problems involving rates
6.2C4.S - Use division of whole numbers to
solve problems involving rates
Unit 4
Lesson 8, 9, 10, 11
6.10A,D
6.10 Probability and statistics. The
student uses statistical representations
to analyze data.
A. Select and use an appropriate
representation for presenting and displaying
different graphical representations of the
same data including line plot, line graph,
bar graph, and stem and leaf plot.
6.10A1.S - Represent a like set of data as a
line plot
6.10A2.S - Represent a like set of data as a
line graph
6.10A3.S - Represent a like set of data as a
bar graph
6.10A4.S - Represent a like set of data as a
stem and leaf plot
6.10 Probability and statistics. The
student uses statistical representations
to analyze data.
D. solve problems by collecting, organizing,
displaying, and interpreting data
6.10D1.S - Solve problems by collecting
data
6.10D2.S - Solve problems by organizing
data
6.10D3.S - Solve problems by displaying
data
6.10D4.S - Solve problems by interpreting
data
1. Finding key words in a word
problem, and determine what
operation it means to perform.
2. Practice making different
word problems using these key
words.
3. Solving multiple problems by
being able to identify what
operation you use to solve the
problem.
4. Push the students into
solving 6th grade level problems
involving ratios and
proportions.
1. Describe the patterns you
find when multiplying.
2. Explain how multiplying and
dividing are similar.
3. What key words describe
multiplying, dividing, adding,
and subtracting
4. Construct problems using the
key words to form math
problems.
5. Describe what the problem is
asking you.
6. How do you know when to
multiply and when to divide?
7. What are others ways I could
solve this same problem, which
one is my favorite and why?
1. Introduce the students to the
different types of graphs, have
them make some on their own,
and analyze others that are
already made.
2. Have the students compare
the differences between the
different graphs.
3. Conduct the “Great Graph
Contest”
1. What types of data do you
use within this graph.
2. Describe and compare the
visualization of this graph to
other graphs.
3. What is found in the data that
you can compare it to other
parts of this graph?
4. What is the purpose of this
graph?
6th Grade Scope and Sequence 2012
Unit 5
Lesson 12, 13, 14
6.9A,B 6.10D
6.9 Probability and statistics. The
student uses experimental and
theoretical probability to make
predictions.
A. construct sample spaces using lists and
tree diagrams
Concept - Sample space
6.9A1.S - Construct sample spaces using
lists
6.9A2.S - Construct sample spaces using
tree diagrams
6.9 Probability and statistics. The
student uses experimental and
theoretical probability to make
predictions.
B. find the probabilities of a simple event
and its complement and describe the
relationship between the two
Concept - Probability
6.9B1.S - Find the probabilities of a simple
event
6.9B2.S - Find the probability of the
compliment of a simple event
6.9B3.S - Describe the relationship between
a simple event and its complement
6.10 Probability and statistics. The
student uses statistical representations
to analyze data.
D. solve problems by collecting, organizing,
displaying, and interpreting data
6.10D1.S - Solve problems by collecting
data
6.10D2.S - Solve problems by organizing
data
6.10D3.S - Solve problems by displaying
data
6.10D4.S - Solve problems by interpreting
data
Unit 6
Lesson 15
6.2E , 6.10B
6.2 Number, operation, and quantitative
reasoning. The student adds, subtracts,
multiplies and divides to solve problems
and justify solutions.
E. Use order of operations to simplify whole
number expressions (without exponents) in
problem solving situations.
6.2E1.S - Use order of operations to
simplify whole number expressions (without
exponents) in problem solving situations.
6.10 Probability and statistics. The
student uses statistical representations
to analyze data.
B. Identify mean (using concrete objects
and pictorial models), median, mode, and
range of a set of data
Concept - Measures of central tendencies
6.10B1.S - Identify mean (using concrete
objects and pictorial models) of a set of
data
6.10B2.S - Identify the mode of a set of
data
6.10B3.S - Identify the median of a set of
data
6.10B4.S - Identify the range of a set of
data
1. Use the 3 for E slides to
question students into
understanding the problems.
2. Have students make lists and
tree diagrams, and compare the
two.
3. Have students draw out
pictures of simple events and
represent a visualization of
what the question is asking
them to find, and what it is not
asking them to find.
1. Describe what this problem
is asking you to find.
2. Describe what other objects
that are in this problem.
3. How are making a list and
making a diagram different?
4. How are making a list and
drawing a diagram the same?
5. What represents each part of
the circle?
6. Describe the percent of the
circle graphs what the question
is asking, and what percent it is
not asking for.
1. Connect order of operations
to real life.
2. Start with very simple twostep problems and build up to
more complex.
3. Peer tutoring
(inside/outside)
4. Make 10, solve 10, do 10
1. Is there a specific order in
life?
2. What makes something more
important than the other?
3. How do you determine what
operation to do first?
6th Grade Scope and Sequence 2012
Unit 7
Lesson 16, 17
6.7A
6.7 Geometry and spatial reasoning.
The student uses coordinate geometry
to identify location in two dimensions.
The student is expected to locate and
name points on a coordinate plane using
ordered pairs of non-negative rational
numbers.
Concept - Ordered pairs of numbers
Concept - Coordinate plane
Concept - Two dimensional
6.7A1.K - X Axis
6.7A2.K - Y Axis
6.7A3.K - Origin
6.7A4.S - Locate points on a coordinate
plane using ordered pairs of non-negative
rational numbers
6.7A5.S - Name points on a coordinate
plane using ordered pairs of non-negative
rational numbers
Unit 8
Lesson 18, 19, 20
6.6A,B
6.6 Geometry and spatial reasoning.
The student uses geometric vocabulary
to describe angles, polygons, and
circles.
A. use angle measurements to classify
angles as acute, obtuse, or right
Concept - Angle
6.6A1.K - Acute angle
6.6A2.K - Obtuse angle
6.6A3.K - Right angle
6.6A4.S - Use angle measurements to
classify an angle as acute
6.6A5.S - Use angle measurements to
classify an angle as obtuse
6.6A6.S - Use angle measurements to
classify an angle as right
6.6 Geometry and spatial reasoning.
The student uses geometric vocabulary
to describe angles, polygons, and
circles.
B. Identify relationships involving angles in
triangles and quadrilaterals
Concept- Triangle
Concept - Quadrilateral
6.6B1.S - Identify relationships involving
angles in triangles
6.6B2.S - Identify relationships involving
angles in quadrilaterals
1. Call points out to students to
make a design.
2. Allow students to create their
own design.
3. Practice having students plot
points that do not have whole
number coordinate points.
1. Why is it important to plot
your points in the right order?
2. Why is it important to label
your Axis’?
3. What could happen if you
plot the point in the wrong
order?
4. How would you plot a point
that does not have a whole
number point?
1. Have students make many
different shapes with
construction paper.
2. Have the students measure
and label the shapes with the
use of the protractor.
3. Major vocabulary
enrichment.
4. Have students find the
missing interior angle with the
use of a protractor and then
without a protractor.
1. Why would different shapes
have different names?
2. What patterns do you find in
the names of different shapes?
3. What makes differences
between the different
quadrilaterals?
4. Why would you name a
triangle by it’s angles
5. Identify the different parts of
a protractor
6. How do you determine which
measurement to use?
7. What numbers do you use for
finding a missing angle?
8. What process would you
need to go through to find a
missing angle?
6th Grade Scope and Sequence 2012
Unit 9
Lesson 21, 22, 23, 24
6.1B, 6.2A,B
6.1 Number, operation, and quantitative
reasoning. The student represents and
uses rational numbers in a variety of
equivalent forms.
B. generate equivalent forms of rational
numbers including whole numbers,
fractions, and decimals
Concept - Equivalence
6.1B1.S - Generate equivalent forms of
rational numbers - whole numbers
6.1B2.S - Generate equivalent forms of
rational numbers - fractions
6.1B3.S - Generate equivalent forms of
rational numbers – decimals
6.2 Number, operation, and quantitative
reasoning. The student adds, subtracts,
multiplies and divides to solve problems
and justify solutions.
A. Model addition and subtraction situations
involving fractions with objects, pictures,
words, and numbers
6.2A1.S - Model addition situations
involving fractions with objects
6.2A2.S - Model addition situations
involving fractions with pictures
6.2A3.S - Model addition situations
involving fractions with words
6.2A4.S - Model addition situations
involving fractions with numbers
6.2A5.S - Model subtraction situations
involving fractions with objects
6.2A6.S - Model subtraction situations
involving fractions with pictures
6.2A7.S - Model subtraction situations
involving fractions with words
6.2A8.S - Model subtraction situations
involving fractions with numbers
6.2 Number, operation, and quantitative
reasoning. The student adds, subtracts,
multiplies and divides to solve problems
and justify solutions.
B. Use addition and subtraction to solve
problems involving fractions and decimals
Concept - Decimal
Concept - Fraction
6.2B1.S - Use addition to solve problems
involving fractions
6.2B2.S - Use addition to solve problems
involving decimals
6.2B3.S - Use subtraction to solve problems
involving fractions
6.2B4.S - Use subtraction to solve problems
involving decimals
1. Students will review and
expand from their background
knowledge of fractions.
2. Students will connect
fractions, decimals and
percents with mixed numbers
and improper fractions.
3. Students will show mastery
when they are able to make a
word problem involving the
correct use of fractions.
1. What do fractions, percents
and decimals have in common?
2. What makes them the same?
3. What makes fractions
equivalent?
4. How can you make a visual
representation of equivalent
fractions.
5. Describe the process
involved in adding and
subtracting fractions.
6. How can you use GCF and
LCM to help you find common
denominators?
6th Grade Scope and Sequence 2012
Unit 10
Lessons 25 and 26
6.3A,B,C
6.3 Patterns, relationships, and
algebraic thinking. The student solves
problems involving proportional
relationships.
A. Use ratios to describe proportional
situations
Concept - Ratio
Concept - Proportion
6.3A1.S - Use ratios to describe
proportional situations
6.3 Patterns, relationships, and
algebraic thinking. The student solves
problems involving proportional
relationships.
B. Represent ratios and percents with
concrete models, fractions, and decimals
6.3B1.S - Represent ratios with concrete
models
6.3B2.S - Represent ratios with fractions
6.3B3.S - Represent ratios with decimals
6.3B4.S - Represent percents with concrete
models
6.3B5.S - Represent percents with fractions
6.3B6.S - Represent percents with decimals
6.3 Patterns, relationships, and
algebraic thinking. The student solves
problems involving proportional
relationships.
C. Use ratios to make predictions in
proportional situations
6.3C1.S - Use ratios to make predictions in
proportional situations
1. Connect problems to the
students where they can relate.
2. Use models and colors for
students to understand
connections between ratios.
3. Use tables, and proportions,
equivalent fractions and
multiplication and division to
solve the word problems.
4. Project on traveling.
1. Can you visualize the
problem.
2. Describe what a ratio, rate or
proportion means in real life,
and come up with an event
where you would need to use
them.
3. Explain how rates,
proportions and ratios are
connected to GCF, LCM and
equivalent fractions.
6th Grade Scope and Sequence 2012
Unit 11
Lessons 27 and 28
6.4A,B
6.4 Patterns, relationships, and
algebraic thinking. The student uses
letters as variables in mathematical
expressions to describe how one
quantity changes when a related
quantity changes.
A. use tables and symbols to represent and
describe proportional and other
relationships such as those involving
conversions, arithmetic sequences,
perimeter, and area.
6.4A1.S - Use tables to represent Proportional and
other relationships involving conversions
6.4A2.S - Use tables to represent Proportional and
other relationships involving arithmetic sequences
6.4A3.S - Use tables to represent Proportional and
other relationships involving perimeter
6.4A4.S - Use tables to represent Proportional and
other relationships involving area
6.4A5.S - Use symbols to represent Proportional
and other relationships involving conversions
6.4A6.S - Use symbols to represent Proportional
and other relationships involving arithmetic
sequences
6.4A7.S - Use symbols to represent Proportional
and other relationships involving perimeter
6.4A8.S - Use symbols to represent Proportional
and other relationships involving area
6.4A9.S - Use tables to describe Proportional and
other relationships involving conversions
6.4A10.S - Use tables to describe Proportional and
other relationships involving arithmetic sequences
6.4A11.S - Use tables to describe Proportional and
other relationships involving perimeter
6.4A12.S - Use tables to describe Proportional and
other relationships involving area
6.4A13.S - Use symbols to describe Proportional
and other relationships involving conversions
6.4A14.S - Use symbols to describe Proportional
and other relationships involving arithmetic
sequences
6.4A15.S - Use symbols to describe Proportional
and other relationships involving perimeter
6.4A16.S - Use symbols to describe Proportional
and other relationships involving area
6.4 Patterns, relationships, and
algebraic thinking. The student uses
letters as variables in mathematical
expressions to describe how one
quantity changes when a related
quantity changes.
B. Use tables of data to generate formulas
to representing relationships involving
perimeter, area , volume of a rectangular
prism, etc.
Concept - Formula
Concept - Variable
6.4B1.S - Generate formulas from a table of
data to represent relationships involving
perimeter
6.4B2.S - Generate formulas from a table of
data to represent relationships involving
area
6.4B3.S - Generate formulas from a table of
data to represent relationships involving
volume of a rectangular prism
1. Connect to solving equations,
and making tables from solving
ratios.
2. Use lots of pre-made
questions for students to prove
correct or incorrect.
3. Connect to order of
operations to solve the
equations involved in the
sequences.
4. Warm-up of area and
perimeter of shapes, so they
can connect the tables to the
formulas found on the formula
chart.
1. What is the pattern that you
see?
2. What are the orders you need
to follow when solving
equations involved in
sequences?
6th Grade Scope and Sequence 2012
Unit 12
Lesson 29
6.5A
1. Use problems to question the
students on the understanding
of the problem.
1. Explain why it is a certain
operation between the
numbers.
2. What would be another way
to solve that exact same
problem?
1. Have students measure
shapes to find the relationship
between radius, diameter and
circumference.
2. Have students build a model
to represent radius, diameter
and circumference that they
can use on their test.
3. Build vocabulary
1. What relationships do you
see between radius, perimeter
and diameter?
2. What process and inverse
operations do you need to go
through to convert between
radius, diameter, and
circumference?
6.5 Patterns, relationships, and
algebraic thinking. The student uses
letters to represent an unknown in an
equation. The student is expected to
formulate equations from problem
situations described by linear
relationships.
Concept - Unknown
Concept - Equation
6.5A1.S - Use letters to represent unknown
6.5A2.S - Formulate an equation from a
problem situation described by a linear
relationship.
Unit 13
Lesson 30
6.6C
6.6 Geometry and spatial reasoning.
The student uses geometric vocabulary
to describe angles, polygons, and
circles.
C. describe the relationship between radius,
diameter, and circumference of a circle.
6.6C1.K - Radius
6.6C2.K - Diameter
6.6C3.K - Circumference
6.6C4.S - Describe the relationship
between radius, diameter, circumference
6th Grade Scope and Sequence 2012
Unit 14
Lessons 31, 32, 33, and 34
6.8A,B,D
6.8 Measurement. The student solves
application problems involving
estimation and measurement of length,
area, time, temperature, volume, weight,
and angles.
A. estimate measurements and evaluate
reasonableness of results
Concept - Measurement
6.8A1.S - Estimate measurements
(including circumference)
6.8A2.S - Evaluate estimations as to
reasonableness
1. Show the relationship
between the area of a triangle
and a rectangle.
2. Bouncy bounce technique for
converting between time.
3. Connection to the formula
chart, and use models to show
volume.
4. Connection to fractions and
ratios when teaching
conversions between the same
measurement system.
6.8 Measurement. The student solves
application problems involving
estimation and measurement of length,
area, time, temperature, volume, weight,
and angles.
B. select and use appropriate units, tools, or
formulas to measure and to solve problems
involving length (including perimeter), area,
time, temperature, capacity,and weight
6.8B1.S - Select and use appropriate units to
measure length (including perimeter)
6.8B2.S - Select and use appropriate units to
measure area
6.8B3.S - Select and use appropriate units to
measure time
6.8B4.S - Select and use appropriate units to
measure temperature
6.8B5.S - Select and use appropriate units to
measure volume
6.8B6.S - Select and use appropriate units to
measure weight
6.8B7.S - Select and use appropriate tools to
measure length (including perimeter)
6.8B8.S - Select and use appropriate tools to
measure area
6.8B9.S - Select and use appropriate tools to
measure time
6.8B10.S - Select and use appropriate tools to
measure temperature
6.8B11.S - Select and use appropriate tools to
measure volume
6.8B12.S - Select and use appropriate tools to
measure weight
6.8B13.S - Select and use appropriate formulas to
measure length (including perimeter)
6.8B14.S - Select and use appropriate formulas to
measure area
6.8B15.S - Select and use appropriate formulas to
measure time
6.8B16.S - Select and use appropriate formulas to
measure temperature
6.8B17.S - Select and use appropriate formulas to
measure volume
6.8B18.S - Select and use appropriate formulas to
measure weight
Unit 15, 16, 17
Lessons 35, 36, and 37
7.1B, 7.5B, 7.7A
1. Utilize the excitement the
students have to move to the
middle school to introduce
them into 7th grade topics.
1. Connect the formula table to
the area and perimeter of
objects
2. Why is adding or subtracting
time different than regular
subtraction or addition rules?