Grade 7: Instructional Focus Unit 1-2
Course:
Pre-Algebra
Instructional Focus Unit(s): (7.RP.A.2 a-c not included in deconstruction)
1-2
Domain(s):
Ratios and Proportional Relationships
Cluster(s): (7.RP.A.2 a-c not included in deconstruction)
7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
Standard(s):
7.RP.A.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units.
7.NS.A.2. Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
7.NS.A.3. Solve real-world and mathematical problems involving the four operations with rational numbers.
(Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
7.EE.B.4.a – see note on Focus 1
7.G.A.1 – see note on Focus 1
Verbs
Noun (phrases)
Analyze
Proportional relationships
Use
Real-world and mathematical problems
solve
Unit rates
compute
Ratios of fractions
apply
Ratios of lengths, areas, other quantities
extend
Like or different units
add
Previous understandings of operations with
subtract
fractions
multiply
Rational number (positive according to focus)
divide
Rational number to a decimal
convert
Long division
know
Decimal form
represent
Terminates in 0s
construct
Repeats
reasoning
Four operations with rational numbers (positive)
compare
Numerical and algebraic expressions and
identifying
equations
recognize
Variables
decide
Quantities
identify
Simple equations and inequalities
explain
Px+q=r, p(x+q)=r
observing
Equations
Revised 2/13/13
Kyrene School District
Working Document
Student will be able to:
 Compare fractions to fractions (use of ratios as
fractions)
 Work with proper and improper fractions
 Solve a unit rate with positive rational numbers
 Convert a rational number to a decimal
 Identify which fractions will terminate
 Solve real-world problems
 Translate words to expressions and equations
 Find unit rates with complex fractions
 Connect models – double number lines, tape
diagrams, ratio tables (from grade 6) to division
when finding unit rates
 Solve one-step equations from word problems
 Write equations from real-world unit rate
situations
 Determine if 2 quantities are in a proportional
relationship from a table, graph, verbal
descriptions or equation
 Represent a proportional relationship in a table,
graph, equation
 Interpret the ordered pairs
 Find the constant of proportionality (unit rate)
 Identify the coefficient as the unit rate
 Create tables and graphs of non-proportional
relationships
 Explain how you determine the constant of
proportionality
 Recognize that (1,r) is the unit rate
 Explain (1,r) as the unit rate
Revised 2/13/13
Forms fluently
Sequence of operations
Algebraic solution
Arithmetic solutions
Equivalent ratios in a table
Graphing on a coordinate plane
Graph is a straight line through the origin
Constant of proportionality (unit rate)
Tables
Graphs
Equations
Diagrams
Verbal descriptions
Point (x,y) on the graph
Terms of the situation
Special attention to (0,0) and (1,r) where r is the
unit rate
Student will understand:
 Unit rate
 Difference between terminating and
repeating decimals
 Rational numbers
 Word problems
 Multiplicative reasoning
 Constant of proportionality is the unit
rate
Kyrene School District
Working Document
Revised Learning Goal(s) :
The students will be able to analyze use, and explain proportional relationships to solve real-world and
mathematical problems.
Learning Scale(s):
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:


Make
connection
with other
concepts in
math
Make
connection
with other
content areas.
3
The students will
be able to analyze
use, and explain
proportional
relationships to
solve real-world
and mathematical
problems.
 Explain the unit
rate (constant
of
proportionality)
on tables,
graphs,
equations, and
verbal
descriptions
 Explain the
relationship
between (0,0)
and (1,r) in
terms of the
situation.
 Represent the
proportional
relationship as
an equation
2
The students will
be able to identify
unit rates in tables,
graphs, verbal
descriptions, and
equations to solve
real-world and
mathematical
problems.
 Identify unit
rate (constant
of
proportionality)
on tables,
graphs,
equations, and
verbal
descriptions
 Solve a unit
rate problem
with positive
rational
numbers
1
With help from
the
teacher, the
student has
partial success
with the level 2
and 3 elements.
0
Even with help,
the student has no
success with the
proportional
relationships.
Assessment(s):
Attached
Revised 2/13/13
Kyrene School District
Working Document
Sequencing of Learning Targets:
Connect models – double number lines, tape diagrams, ratio tables (from grade 6) to division when finding
unit rates
Understand Multiplicative reasoning
Solve real-world problems
 Convert a rational number to a decimal
 Understand difference between terminating and repeating decimals
 Identify which fractions will terminate
 Work with proper and improper fractions
 Understand rational numbers
 Translate words to expressions and equations
 Understand word problems
 Solve one-step equations from word problems
 Compare fractions to fractions (use of ratios as fractions)
 Find unit rates with complex fractions
 Find the constant of proportionality (unit rate)
 Solve a unit rate with positive rational numbers
 Understand unit rate
 Understand constant of proportionality is the unit rate
 Explain how you determine the constant of proportionality
 Represent a proportional relationship in a table, graph, equation
 Create tables and graphs of non-proportional relationships
 Determine if 2 quantities are in a proportional relationship from a table, graph, verbal descriptions
or equation
 Interpret the ordered pairs
 Identify the coefficient as the unit rate
 Write equations from real-world unit rate solutions
Revised 2/13/13
Kyrene School District
Working Document