Development and Formalization of Essential Ideas: Thinking with Mathematical Models
Problem
Primary
Purpose
Investigation 1
Introduction
1.1
Bridge Length and
Strength
Graph and interpret ordered
pairs of whole numbers in
the coordinate plane
(situational).
Introduction
1.3
Custom
Construction Parts
Finding Patterns
Investigation 2
Problem
2.1
Modeling Linear
Data Patterns
Introduction
Write an equation with one
operation for a situation.
Primary
Purpose
Prior Knowledge
Introduction
Essential Ideas
When one
variable is
Data about two
dependent
variables from on the other,
real-world
a function
observations or
can model
experiments
the data
can be
pattern.
collected and
Functions
represented in
allow you to
graphs and
answer
tables. These
questions or
representations
make
are useful for
predictions
analyzing
about a
relationships
relationship.
among data.
Linear
relationships
are functions.
Data may
show a
pattern or
association
between
the data.
Essential Ideas
Data may show a
pattern or
association between
the data. Sometimes
you can fit a line to
data, find the
equation of the line,
and measure how
well the line fits the
data pattern. This is
useful for making
predictions about the
points not observed.
Data about two
variables from realworld observations
or experiments can
be collected and
represented in
graphs and tables.
These
representations are
useful for analyzing
relationships among
data, including the
variability of the
data.
Locate an integer on a
number line.
Formalization
2.3
Tree Top Fun
Equations for
Linear Functions
Solve a one-step equation
with fractions by adding or
subtracting the same number
on each side.
Solve a one-step equation
with fractions by multiplying
each side by the reciprocal.
2.2
Up and Down the
Staircase Exploring
Slope
Complete a ratio table and
graph the points on a
coordinate grid.
Name the integer
coordinates of given points.
Bridge Thickness
and Strength
1.2
Prior Knowledge
Formalization
Understand rate as a ratio
and find a unit rate by
dividing whole numbers.
Data may show a pattern or association
between the data. Sometimes you can fit a
line to data, find the equation of the line, and
measure how well the line fits the data
pattern. This is useful for making predictions
about the points not observed.
2.4
Boat Rental
Business Solving
Linear Equations
Practice and
Application
2.5
Amusement Park
or Movies
Intersecting Linear
Models
Investigation 3
Problem
Practice and
Application
Use a ratio (rate) table to find
a percent of a number.
Primary
Purpose
Prior Knowledge
Data may show a pattern or association
between the data. Sometimes you can fit a
line to data, find the equation of the line, and
measure how well the line fits the data
pattern. This is useful for making predictions
about the points not observed.
Essential Idea
3.1
Rectangles with a
Fixed Area
3.2
Distance, Speed and
Time
Introduction
Data about two variables from real-world
observations or experiments can be
collected and represented in graphs and
tables. These representations are useful
for analyzing relationships among data,
including the variability of the data. –
Inverse Variation.
Introduction
3.3
Planning a Field Trip
Finding Individual
Cost
3.4
Introduction
Modeling Data
Patterns
Formalization
Problem
Primary
Purpose
Prior Knowledge
Essential Idea
Investigation 4
4.1
Vitruvian Man
Relating Body
Measurements
Introduction
4.2
Older and Faster
Negative
Correlations
Introduction
4.3
Correlation
Coefficients and
Outliers
Formalization
4.4
Measuring
Variability Standard
Deviation
Formalization
Data may show a pattern or association
between the data.... This is useful for
making predictions about the points not
observed. – Correlation and Standard
Deviation
Data may show a pattern or association
between the data. Sometimes you can fit a
line to data, find the equation of the line,
and measure how well the line fits the
data pattern. This is useful for making
predictions about the points not observed.
Investigation 5
Problem
Primary
Purpose
Prior Knowledge
Essential Idea
5.1
Wood or Steel?
That’s the Question
Introduction
5.2
Politics of Girls and
Boys Analyzing Data
in Two-way Tables
Introduction
5.3
After School Jobs
and Homework
Working Backward:
Setting up a TwoWay Table
Formalization
Categorical data must be analyzed om
different ways than numerical data
including 2-way tables to analyze relative
frequencies.