Unit 1, Review – Transitioning from Previous Mathematics
Instructional Resources: Grade 6: Scott Foresman
Concepts
(and related skills)
Transitioning from previous mathematics to
Sixth Grade Mathematics
•
•
•
•
Understand the relationship between
decimals, fractions and percents and
demonstrate on a number line
Interpret percents as part of a hundred
Determine the prime factors of all numbers
through 50 and write the products of their
prime factors by using exponents to show
multiples of a factor
Add, subtract and perform simple
multiplication and division of fractions and
decimals
Textbook Connections
Vocabulary
Factor
Prime factor
Decimal
Percent
Product
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Unit 1, Concept 2 – Rational Numbers: How to connect Properties and Applications
Instructional Resources: Grade 6: Scott Foresman
Standards:
NS 1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line
Concepts
(and related skills)
Understand the multiplicative identity
property and understand relationships
(including equivalence) among decimals,
fractions, and percents
• Compare and order positive and negative
fractions
• Place positive and negative fractions, mixed
numbers, and decimals on a number line
• Convert numbers from one form to an
equivalent form (fractions, decimals, mixed
numbers, and percents)
• Use the multiplicative identity property to find
equivalent values
Textbook Connections
Vocabulary
Lessons
1.2 – Comparing & Ordering Decimals
4.8 – Comparing & Ordering Fractions and
Mixed Numbers
6.1 – Comparing and Ordering Positive and
Negative Numbers
Multiplicative identity property
Least common denominator
Least common multiple
Improper fraction
Mixed number
Number line
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Unit 1, Concept 3 – Rational Numbers: How to connect Properties and Applications
Instructional Resources: Grade 6: Scott Foresman
Standards:
NS 2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular
operation was used for a given situation.
NS 2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations
NS 2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems
with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
Concepts
(and related skills)
Understand the basic arithmetic operations
(+,–,x,÷) on fractions, and the relationships
among these operations
• Find LCM and GCF of whole numbers
• Add and subtract positive fractions and mixed
numbers with unlike denominators
• Multiply and divide positive fractions and
mixed numbers
Textbook Connections
Vocabulary
Lessons
4.4 – Greatest Common Factor
4.6 – Least Common Multiple
5.2 – Estimating Sums and Differences
5.4 – Adding and Subtracting with Unlike
Denominators
5.5 – Solving Addition and Subtraction
Equations
5.7 – Multiplying Fractions and Mixed Numbers
5.8 – Dividing Fractions and Mixed Numbers
5.10 – Solving Equations using Fractions
5-11 – Using Fractions and Mixed Numbers
Greatest common factor
Prime factorization
Composite
Simplest form
Factor
Multiple
Divisor
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Unit 2, Concept 1 – Algebraic Thinking and Proportional Reasoning
Instructional Resources: Grade 6: Scott Foresman
Standards:
NS 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that
use positive and negative integers and combinations of these operations.
Concepts
(and related skills)
Understand variables and expressions as
symbolic representations of numerical values
• Add, subtract, multiply and divide using
integers
• Evaluate expressions using order of operations
and commutative, associative, and distributive
properties
• Write verbal expressions using symbolic
representations, and vice versa
• Translate between verbal expressions and
symbolic representations
Textbook Connections
Vocabulary
Lessons
6.2 – Adding Integers
6.3 – Subtracting Integers
6.5 – Multiplying Integers
6.6 – Dividing Integers
6.7 – Expressions with Integers
6.8 – Equations with Integers
6.9 – Write an Equation
6.10 – Using Integers
Integer
Inverse property of addition
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Unit 2, Concept 2 – Algebraic Thinking and Proportional Reasoning
Instructional Resources: Grade 6: Scott Foresman
Standards:
AF 1.1 Write and solve one-step linear equations in one variable
AF 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
AF 1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and
justify each step in the process.
AF 1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.
Concepts
Understand equations
• Use integers and properties of equality to
solve one-step equations
Textbook Connections
Vocabulary
Lessons
1.2 – Comparing and Ordering Decimals
2.7 – Solving Multiplication and Division
Equations
5.5 – Solving Addition and Subtraction
Equations
5.10 – Solving Equations and Fractions
5.11 – Using Fractions and Mixed Numbers
6.4 – Translating Expressions
6.7 – Expressions with Integers
6.8 – Equations with Integers
6.9 – Write an Equation
9-6 – Solving Percent Problems Using Equations
10.1 – Equations with More Than One
Operations
Expression
Equation
Subtraction property of equality
Division property of equality
Multiplication of equality
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Unit 2, Concept 3 – Algebraic Thinking and Proportional Reasoning
Instructional Resources: Grade 6: Scott Foresman
Standards:
AF 2.2
AF2.3
NS 1.2
NS 1.3
Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity
Solve problems involving rates, average speed, distance, and time.
Interpret and use ratios in different contexts to show the relative sizes of two quantities, using appropriate notations
Use proportions to solve problems. Use cross-multiplication as a method for solving such problems, understanding it as
the multiplication of both sides of an equation by a multiplicative inverse.
NS 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
Concepts
(and related skills)
Understand and use ratios, proportions,
percents and rates
• Write ratios in different ways (1to 5, 1/5, 1:5)
• Calculate unit rates
• Convert one unit of measurement to another
• Interpret and use ratios in different contexts
• Solve percentage problems
Textbook Connections
Vocabulary
Lessons
8.5 – Rates
8.1 – Ratios and Equivalent Ratios
8.2 – Proportions
8.3 – Solving Proportions Using Cross Products
8.8 – Similar Figures
8.10 - Using Maps
9.3 – Finding a Percent of a Number
9.7 - Write an Equation
9.8 – Finding Sales Tax
9-10 –Using the Interest Formula
Unit rate
Ratio
Proportion
Cross multiplication
Similar polygons
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Unit 3, Concept 1 – Statistics Data and Probability
Instructional Resources: Grade 6: Scott Foresman
Standards:
SDAP 2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it
makes sense to use a sample.
SDAP 2.2 Identify different ways of selecting a sample and which method makes a sample more representative for a
population.
SDAP 2.4 Identify data that represent sampling errors and explain why the sample might be biased.
Concepts
(and related skills)
Understand and use methods for selecting a
representative sample of a population
• Describe, identify and implement sampling
methods
• Represent data in multiple ways
Textbook Connections
Lessons
3.5 – Understanding Sampling
3.6 – Sampling Methods – Interpreting Surveys
3.8 – Analyzing Statistical Results
3.9 – Representing a Point of View
Vocabulary
Population
Sample
Biased sample
Random
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Unit 3, Concept 2 – Statistics Data and Probability
Instructional Resources: Grade 6: Scott Foresman
Standards:
SDAP 1.1 Compute the range, mean, median, and mode of data sets.
SDAP 1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.
SDAP 1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given
context
SDAP 2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results
obtained and why the way in which the results were displayed might have influenced the conclusions reached.
SDAP 2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
Concepts
(and related skills)
Understand the factors that influence the
validity and interpretation of data
• Calculate range, mean, median, and mode
• Recognize outliers and their effect on
measures of central tendency
• Discuss the factors affecting the validity of
claims
Textbook Connections
Vocabulary
Lessons
3.1 – Mean, Median, Mode and Range
3.2 – Data with Outliers
3.8 – Analyzing Statistical Results
3.9 – Representing a Point of View
Measure of central tendency
Median
Mode
Histogram
Box-and whisker plot
Range
Coordinate plane
Scatter plot
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Unit 3, Concept 3 – Statistics Data and Probability
Instructional Resources: Grade 6: Scott Foresman
Standards:
SDAP 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and
verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 – P is the
probability of an event not occurring.
Concepts
(and related skills)
Understand that the probability of an event
is between 0 and 1
• Calculate theoretical and experimental
probabilities
• Represent probabilities as ratios, decimals,
and percents
• Calculate the probability of an event not
occurring
• Use probability to make predictions
Textbook Connections
Vocabulary
Lessons
11.1 – Probability
11.2 – Representing Probability
11.3 – Adding Probabilities
Event
Probability of an event
Independent events
Dependent events
Tree diagram
42
Unit 3, Concept 4 – Statistics Data and Probability
Instructional Resources: Grade 6: Scott Foresman
Standards:
SDAP 3.1 Represent all possible outcomes for compound events in an organized way and express the theoretical probability of
each outcome.
SDAP 3.5 Understand the difference between independent and dependent events.
Concepts
(and related skills)
Understand the difference between
dependent and independent events
• Represent all outcomes for a compound
event in multiple ways
• Identify events as dependent and
independent
• Calculate probability for independent events
Textbook Connections
Vocabulary
Lessons
11.5 – Counting Methods
11.6 – Permutations and Combinations
11.9 – Dependent Events
Disjoint events
Tree diagram
43
Unit 4, Concept 1 – Plane and Solid Shapes
Instructional Resources: Grade 6: Scott Foresman
Standards:
MG 1.1 Understand the concept of a constant such as Π; know the formulas for the circumference and area of a circle.
MG 1.2 Know the common estimates of Π and use these values to estimate and calculate the circumference and the area of circles;
compare with actual measurements.
Concepts
(and related skills)
Understand that the ratio of the
circumference to the diameter is the same
for any circle (i.e. the constant π)
• Know the common estimates of π
• Use formulas to calculate the circumference
and area of a circle
Textbook Connections
Vocabulary
Lessons
12.5 - Circumference
12.6 - Area of a Circle
Circle
Radius
Diameter
Circumference
50
Unit 4, Concept 2 – Plane and Solid Shapes
Instructional Resources: Grade 6: Scott Foresman
Standards:
MG 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
MG 2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve
problems involving an unknown angle.
AF 3.1 Use variables in expressions describing geometric quantities.
AF3.2 Express in symbolic form simple relationships arising from geometry
Concepts
(and related skills)
Understand the properties of twodimensional figures
• Identify special angle pairs
• Solve problems using the properties of
special angle pairs and the sum of the angles
of a triangle
• Classify triangles and quadrilaterals
• Calculate area and perimeter
• Solve problems using the properties of
special angles
Textbook Connections
Vocabulary
Lessons
7.5 – Classifying and Measuring Angles
7.6 - Angle Pairs
7.7 – Triangles
7.8 - Quadrilaterals
12.1 – Perimeter
12.2 – Area of Quadrilaterals
12.3 – Area of Triangles
Vertical angles
Complementary angles
Supplementary angles
Adjacent angles
Right angle
Acute angle
Obtuse angle
Parallelogram
Rectangle
51
Unit 4, Concept 3 – Plane and Solid Shapes
Instructional Resources: Grade 6: Scott Foresman
Standards:
MG 1.3 Know and use the formulas for the volume of triangular prisms and cylinders; compare these formulas and explain the
similarity between them and the formula for the volume of a rectangular solid.
Concepts
(and related skills)
Understand the properties of threedimensional figures
• Calculate the volumes of prisms and
cylinders
Textbook Connections
Vocabulary
Lessons
12.9 – Volume of a Rectangular Prism
12.10 – Volume of a Triangular Prism and
Cylinders
Prism
Bases
Right prism
Circular cylinder
Surface area
Lateral surface
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