Development and Formalization of Essential Ideas: Accentuate the Negative
Problem
Investigation 1
1.1
Playing Math Fever
Using Positive and
Negative Numbers
1.2
Extending the
Number Line
Prior Knowledge
Introduction
Introduction
From Sauna to
Snowbank Using a
Number Line
1.4
Problem
2.1
Extending Addition
to Rational
Numbers
Compare and order two decimals
to thousandths using the
meanings of the place values.
Introduction
Extending
Subtraction to
Rational Numbers
Primary
Purpose
Prior Knowledge
Introduction
Apply the Commutative
Properties of addition and
multiplication.
2.3
The “+/-“
Connection
2.4
Fact Families
Introduction
Formalization
Formalization
Rational numbers can be compared, ordered
and located on a number line. They can also be
used to indicate a distance between points on
a number line. Number lines are useful models
for solving problems with rational numbers.
Models facilitate understanding the meaning
of addition, subtraction, multiplication, and
division of positive and negative numbers, and
improve understanding of the standard
algorithms for these operations.
Introduction
2.2
Essential Idea
Mathematical sentences, with or without
variables, can model real-world problems,
Sometimes rewriting a problem using a
different operation can be helpful in
finding the solution.
1.3
In the Chips Using a
Chip Model
Investigation 2
Primary
Purpose
Essential Ideas
Models facilitate
understanding the
meaning of addition
and subtraction, and
improve
understanding of the
standard algorithms
for these operations.
Properties of
operations extend to
all rational numbers
and understanding
these properties is
helpful in solving
problems.
Problem
Primary
Purpose
Prior Knowledge
3.1
Multiplication
Patterns with
Integers
Investigation 3
3.2
Multiplication of
Rational Numbers
Mathematical sentences, with or without
variables, can model real-world problems.
– Multiplication and Division
Introduction
Formalization
Essential Idea
Multiply two one-digit
decimals.
Use models to divide a decimal
by a whole number.
3.3
Division of Rational
Numbers
Interpret a fraction as division
of the numerator by the
denominator and use a/b = a +
b to solve problems.
Formalization
Use a common denominator
less than the product of the
unlike denominators to add
two fractions.
Models facilitate understanding the meaning
of multiplication, and division of positive and
negative numbers, and improve understanding
of the standard algorithms for these
operations.
Use the product of the unlike
denominators as a common
denominator to subtract two
fractions.
3.4
Playing the Integer
Product Game
Investigation 4
Problem
4.1
Order of Operations
4.2
The Distributive
Property
4.3
What Operations
are Needed?
Practice &
Application
Primary
Purpose
Prior Knowledge
Essential Idea
Use the Distributive Property
of multiplication over addition
to factor.
Properties of operations extend to all rational
numbers and understanding these properties
is helpful in solving problems.
Formalization
Formalization
Order fractions by changing to
a common denominator.
Formalization
Mathematical sentences, with or without
variables, can model real-world problems,
Sometimes rewriting a problem using a
different operation can be helpful in
finding the solution.