Integers

toc

=ACOS Objective 1=


 * Demonstrate computational fluency with addition, subtraction, and multiplication of integers.**
 * Developing algorithms for performing operations on integers.
 * Using inverse properties of addition and of multiplication.

ARMT Possible Points = 5 (MC, GR)
 * Only one operation will be required for each item.
 * Parentheses or the multiplication symbol (*) will be used for multiplication.
 * The multiplication symbol (x) will not be used.
 * Negative integers may be in parentheses.
 * Integers will not exceed four digits in the stem.
 * No word problems/real-life situations will be used.
 * One of the options may be NH, which means "Not Here."

Sample problems from Item Specs

//Integers are also tested through CS 2 (order of operations) and CS 3 (rational numbers). Division of integers is included in the sample test items for CS 3.//

=Prerequisites=


 * Objective 7.1.1:** Identify numbers less than zero by extending the number line.
 * Objective 7.1.2:** Solve problems involving basic operations on whole numbers, including addition and subtraction of seven-digit numbers, multiplication with two-digit multipliers, and division with two-digit divisors.

· Developing algorithms for performing operations on integers Example: determining a systematic set of steps that can be used to subtract integers · Using inverse properties of addition and of multiplication
 * Additional content to be taught:**

=Ideas=

CMP unit "Accentuate the Negative" gives a slow introduction to negative numbers and operations with integers.

Have students walk a number line. I taped paper on the wall on which I had written one number per sheet. This is a great way to show students that adding a negative and subtracting a positive give the same result. They can easily see that walking backwards two steps will put them in the same place as turning around and then walking forward two steps.
 * Teaching Addition and Subtraction of Integers**
 * Start at zero facing the positive numbers.
 * Walk forward for a positive number and backwards for a negative number.
 * Turn around (180º) for subtraction.

//It is good (+) to love (+), and it is bad (-) to hate (-)!//
 * Rules for Multiplying and Dividing Integers**

If you love to love, that is good. (positive x positive = positive) If you love to hate, that is bad. (positive x negative = negative) If you hate to love, that is bad. (negative x positive = negative) If you hate to hate, that is good. (negative x negative = positive)

[|Evaluate Expressions] Students will evaluate expressions using order of operations and add parentheses to get certain outcomes.
 * Interwrite Lesson**

[|Matrix Integers]
 * Games**

=Links=

[|Integer Videos] Teacher Tube has two pages of videos on integers

[|Stand and Deliver] Jaime Escalante explains integers to his students in this movie clip.

[|Interesting Integers] Webquest with handouts

[|Math.com Homework Help] Signed Integers, Adding and Subtracting Integers, Multiplying and Dividing Integers, Properties of Integers First Glance, In Depth, Examples, Workout

[|Mrs. Glosser's Math Goodies] Free Lessons: Introduction to Integers, Adding Integers, Subtracting Integers, Challenge Exercises, Printable Worksheet

[|Amby's Math Resources] Explanation, Practice Exercises with Instant Feedback, and a great story explaining the rule for multiplication

[|Integer Games]

[|Builder Ted] Put numbers in order. Levels 2 and 3 have negative numbers.

[|Mystery Picture Game]

[|Line Jumper] Practice using a number line for addition and subtraction.
 * Fun Brain**

[|MathCar Racing Game] Try to beat the computer by picking the expression that has the largest answer. You can choose the skill level and the operation to practice.

[|Addition with Color Chips] [|Subtraction with Color Chips] Use color chips to illustrate subtraction of integers. [|Circle Zero] A puzzle involving adding positive and negative integers to sum to zero. [|Circle 21] A puzzle involving adding positive and negative integers to sum to twenty one. [|Number Line Bounce] Number line addition and subtraction game.
 * National Library of Virtual Manipulatives**

[|Arithmetic Four] This **game** asks the players to add, subtract, multiply, and divide whole numbers and **integers**. Choose difficulty level, question types, and time limit.

[|Explore Learning Gizmos] Interactive "Gizmo" illustrating addition of integers on a number line. Comes with exploration guide and assessment questions. By subscription, but has Free 30 day trial account.

[|Choose Math Operation Game] Choose the range to include negative numbers in this fun game to get practice in how to add/subtract/multiply/divide integers.

[|Space Coupe to the Rescue] By choosing a positive or negative number, the player controls the vertical position of a spaceship. If the spaceship reaches the same vertical position as a virus pod, the pod is destroyed.

[|Flashcards with Negative Numbers]