Introduction to Integers An ADE Mathematics Lesson Days 6-10
Author ADE Content Specialists Grade Level 5th Grade Duration Five days
Aligns To Connects To Mathematics: Mathematics: Strand 1: Number and Operations Strand 1: Number and Operations Concept 1: Number Sense Concept 1: Number Sense PO 3. Locate integers on a number line. PO 6. Express or interpret positive and negative numbers in context. Strand 5: Structure and Logic Concept 2: Logic, Reasoning, Problem Strand 5: Structure and Logic Solving, and Proof Concept 2: Logic, Reasoning, Problem PO 1. Analyze a problem situation to determine Solving, and Proof the question(s) to be answered. PO 4. Determine whether a problem to be PO 3. Select and use one or more strategies to solved is similar to previously solved problems, efficiently solve the problem and justify the and identify possible strategies for solving the selection. problem. PO 5. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.
Overview Integers are an extension of whole numbers. They include whole numbers (positive integers and zero) and their opposites (negative integers). They can be located on a number line and placed in order.
Purpose This lesson will help prepare you to solve problems with integers, specifically those with negative integers.
Materials • Integer worksheets • Ruler • Number line worksheets
Objectives Students will: • Locate integers on a number line. • Order integers.
Arizona Department of Education 1 Mathematics Grade 5 Days 6-10
Lesson Components
Prerequisite Skills: In previous grades, you have been working with whole numbers.
Vocabulary: integer, positive integer, negative integer
Session 1 (5 days) 1. Students locate integers on a number line and order integers.
Assessment There is one assessment that will help pinpoint misconceptions about integers before moving on to more complex problems that involve integers.
Arizona Department of Education 2 Mathematics Grade 5 Days 6-10 Locate Integers on a Number Line Session 1
Integers are the set of real numbers consisting of the whole numbers and their opposites { … -2, -1, 0, 1, 2 … }. The sign indicates the direction that the number is from 0 and the number indicates the size of the integer. Negative numbers are to the left of zero while positive numbers are to the right of 0. For example, -2 is 2 units to the left of 0. 2 is 2 units to the right of 0. It is important to remember that the distance can be either to the right or to the left of 0.
Example 1: On the number line below, describe the location of -4.
-5 0 5 -4 is located 4 units to the left of zero.
Example 2: On the number line below, describe the location of -2.
-5 0 5 -2 is located 2 units to the left of zero.
Example 3: On the number line below, describe the location of 3.
-5 0 5 3 is located 3 units to the right of zero.
Example 4: On the number line below, describe the location of 5.
-5 0 5 5 is located 5 units to the right of zero.
Example 5: On the number line below, describe the location of -1.
-5 0 5 -1 is located 1 unit to the left of zero.
Arizona Department of Education 3 Mathematics Grade 5 Days 6-10 In each example above, place a mark indicating where the number is located on the number line.
Example 1: On the number line below, describe the location of -4.
-5 0 5
-4 is located 4 units to the left of zero
Example 2: On the number line below, describe the location of -2.
-5 0 5 -2 is located 2 units to the left of zero
Example 3: On the number line below, describe the location of 3.
-5 0 5 3 is located 3 units to the right of zero
Example 4: On the number line below, describe the location of 5.
-5 0 5 5 is located 5 units to the right of zero
Example 5: On the number line below, describe the location of -1.
-5 0 5 -1 is located 1 unit to the left of zero
Arizona Department of Education 4 Mathematics Grade 5 Days 6-10 In the following examples, describe the location of the integer and place a mark indicating where the integer is on the number line.
Problem 1: Describe and draw the location of -3 on the number line below.
-5 0 5
Problem 2: Describe and draw the location of -5 on the number line below.
-5 0 5
Problem 3: Describe and draw the location of 2 on the number line below.
-5 0 5
Problem 4: Describe and draw the location of 4 on the number line below.
-5 0 5
Problem 5: Describe and draw the location of 0 on the number line below.
-5 0 5
In your own words, how would you describe and draw the location of an integer from -5 to 5 on a number line?
Arizona Department of Education 5 Mathematics Grade 5 Days 6-10 We can compare integers by looking at their placement on a number line. Smaller numbers are always to the left on the number line. Larger numbers are to the right on the number line.
Look at the number line below:
-5 -4 -3 -2 -1 0 1 2 3 4 5
-2 is to the left of 5 so -2 is smaller than 5. We write -2 < 5.
-3 is to the left of 0 so -3 is smaller than 0. We write -3 < 0.
5 is the right of 3 so 5 is larger than 3. We write 5 > 3.
1 is to the right of -5 so 1 is larger than -5. We write 1 > -5.
Complete the following sentences to make a true statement. Choose < or > to fill in the last blank.
-5 -4 -3 -2 -1 0 1 2 3 4 5
-3 is to the ______of 2 so -3 is ______than 2. -3 ______2
-2 is to the ______of 0 so -2 is ______than 0. -2 ______0
4 is to the ______of 1 so 4 is ______than 1. 4 ______1
5 is to the ______of -1 so 5 is ______than -1. 5 ______-1
0 is to the ______of -2 so 0 is ______than -2. 0 ______-2
-4 is to the ______of -3 so -4 is ______than -3. -4 ______-3
1 is to the ______of 4 so 1 is ______than 4. 1 ______4
Arizona Department of Education 6 Mathematics Grade 5 Days 6-10 We say that -2 and 2 are opposites because they have exactly the same size but they are in opposite directions from 0 on a number line. -2 is 2 units to left of 0 and 2 is 2 units to the right of 0 on a number line. We do not say that the number 0 has an opposite since it is the starting point from which we say the direction of an integer.
What is the opposite of -3?
What is the opposite of -5?
What is the opposite of 2?
What is the opposite of 4?
What is the opposite of -1?
What is the opposite of 6?
What is the opposite of -7?
What is the opposite of 10?
Arizona Department of Education 7 Mathematics Grade 5 Days 6-10
Complete the following table by inserting the proper words and symbols.
Is to the Is < or > Right or Smaller left? or larger?
Ex: 5 left 10 5 smaller 10 5 < 10
-6 -2 -6 2 -6 2
5 7 5 7 5 7
-8 1 -8 1 -8 1
10 -10 10 -10 10 -10
-4 6 -4 6 -4 6
3 -7 3 -7 3 -7
0 -6 0 -6 0 -6
8 0 8 0 8 0
Arizona Department of Education 8 Mathematics Grade 5 Days 6-10 To compare more than one integer, place them in order from the smallest to the largest or from the largest to the smallest. The problem will usually indicate whether the numbers are to be placed from smallest to largest or vice versa.
Example 1: Place the numbers -3, 5, and 0 in order from the smallest to the largest.
The answer is -3, 0, 5 because -3 is to the left of 0 on the number line and 0 is to the left of 5 on the number line.
Example 2: Place the numbers -6, 8, -1 in order from the smallest to the largest.
The answer is -6, -1, 8 because -6 is to the left of -1 on the number line and -1 is to the left of 8 on the number line.
Example 3: Place the numbers 5, -3, 0 in order from the largest to the smallest.
The answer is 5, 0, -3 because 5 is to the right of 0 on the number line and 0 is to the right of - 3 on the number line.
You could also say that the answer is 5, 0, -3 because -3 is to the left of 0 on the number line and 0 is to the left of 5 on the
A third way to solve the problem is to place the numbers on a number line and then look at their positions.
-5 0 5
5, 0, -3
Example 4: Place the numbers 4, 0, -5 in order from the smallest to the largest.
The answer is -5, 0, 4 because -5 is to the left of 0 on the number line and 0 is to the left of 4 on the number line.
You could also say that the answer is -5, 0, 4 because 4 is to the right of 0 on the number line and 0 is to the right of 4 on the number line.
A third way to solve the problem is to place the numbers on a number line and then look at their positions.
-5 0 5
-5, 0, 4
Arizona Department of Education 9 Mathematics Grade 5 Days 6-10 Place the following sets of numbers in order from the smallest to the largest. Explain your reasoning.
1. -5, 2, -3
2. 0, 6, -1
3. 10, -3, 2
4. -4, -9, -1
5. 3, 8, 0
Arizona Department of Education 10 Mathematics Grade 5 Days 6-10 Locate Integers on a Number Line Assessment 1
1. Describe and draw the location of -3 on the number line below.
-5 0 5
2. Describe and draw the location of 4 on the number line below.
-5 0 5
3. Place the numbers 3, -5, -1 in order from the largest to the smallest.
-5 0 5
4. Place the numbers -2, 4, -4 in order from the smallest to the largest.
-5 0 5
5. Complete the following chart:
Integer Opposite
-10
-5
7
2
-3
Arizona Department of Education 11 Mathematics Grade 5 Days 6-10 Extensions 1. Express or interpret positive and negative integers in context such as spending and earning money, rising and falling temperatures, stock market gains and losses, or gaining and losing yards in a football game.
2. Compare two numbers on a number line using an applet like the one provided at http://www.webmath.com/k8numlinecomp.html
Sources 2008 AZ Mathematics Standards 2006 NCTM Curriculum Focal Points 2000 NCTM Principles and Standards 2008 The Final Report of the National Mathematics Advisory Panel
Arizona Department of Education 12 Mathematics Grade 5 Days 6-10