Computation and Estimation
Focus: Integer Operations and Proportional Reasoning
The student will
a) model addition, subtraction, multiplication, and division of integers. 


Essential Knowledge and Skills 
 Model addition, subtraction, multiplication and division of integers using pictorial representations of concrete manipulatives.

Essential Understandings 
 The sums, differences, products and quotients of integers are either positive, zero, or negative. How can this be demonstrated? This can be demonstrated through the use of patterns and models.


Vertical Articulation 
 SOL 5.18c  model onestep linear
equations using addition/subtraction
 SOL 6.3abc  a) identify/represent integers; b)
order/compare integers; c)
identify/describe absolute value of
integers

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Integers: Addition and Subtraction (PDF)  Modeling addition, subtraction, multiplication, and division of integers (Word)
 Virtual Manipulatives: Glencoe  select options from the menus
 Notes: Modeling Addition and Subtraction of Integers (flipchart)
 Notes: Modeling Addition and Subtraction of Integers (ppt)
 Notes: Modeling Subtraction of Integers with Counters (flipchart)
 Notes: Modeling Subtraction of Integers (flipchart)
 Notes: Modeling Multiplication of Integers (ppt)
 Notes: Modeling Multiplication and Division of Integers with Counters (flipchart)
 Guided Notes: Integers & Human Number Line (doc)
 Notes: Adding Integers with Number Line and Rules (doc)
 Activity: Integer Football (pdf)
 Teacher Notes: Real World Modeling Suggestions (doc)
 VDOE Algebra Readiness Curriculum Companion: Working with Integers (pdf)

Real World Lessons 

Practice 
 Worksheet: Modeling Addition (doc)
 Worksheet: Modeling Integer Operations (doc)
 Worksheet: Modeling Subtraction on a Number Line (doc)

SOL Mini Quiz 
 SOL 7.3a Mini Quiz: Modeling Integers (pdf)  (doc)

Skills 
 Mathematics Assessment Project: E07:Skeleton Tower  Expert  A tower is made of cubes stacked in a particular way. In this task, you must work out a rule for calculating the total number of cubes needed to build towers of different heights.
 Integers: Modeling Integer Operations (doc)
 Integers: Record High Temperatures (doc)

Videos 
 Virtual Nerd: Subtracting Using a Number Line
 Virtual Nerd: Adding Using a Number Line
 Open High School: Multiplying and Dividing Integers
 PH: Representing situations with integers
 PH: Adding integers using a number line

Explore
Learning 
 Adding Real Numbers: Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation.
 Adding and Subtracting Integers: Add and subtract integers on a number line using dynamic arrows.
 Adding and Subtracting Integers with Chips: Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction

Websites 
 Braining Camp: Modeling Integer Multiplication
 NLVM: Modeling Integer Addition
 NLVM: Modeling Integer Subtraction
 Sadlier: Modeling Addition  Color Chips Virtual Manipulative
 Sadlier: Modeling Subtraction  Color Chips Virtual Manipulative
 Learn Alberta: Select Number  Integers

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Working with Integers  The lessons in this section focus on comparing, adding, subtracting, multiplying, and dividing integers as
well as describing the subsets of the real number system. (pdf)

Common Core
Standards 
7.NS.1a 
7.NS.1b 
7.NS.1d 
7.NS.2a 
7.NS.2b 
7.NS.2c 
7.NS.3 
7.EE.3 
