# Observation 1. Observation 2. What is the sign of the answer to the problem L3 Q L11?

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1 Name Date Number Sense: Integers Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review, if necessary). Read each screen carefully. Look for new terms, definitions, and concepts. Observations The Observations illustrate number sense concepts relating to the set of integers. Scroll through the Observations using " (! to review, if necessary). Read each screen carefully. When you come to a Write an Observation screen, stop and write the answers to the questions on your worksheet. Observation 1 How far apart are the bird and the fish? Should your answer be positive or negative? Write an explanation for your answers here. Observation 2 What is the sign of the answer to the problem L3 Q L11? In your own words, state the rules for multiplying and dividing signed numbers (shown in the grids on the next screens). Topics in Algebra Texas Instruments Student Worksheet 1-1

3 Name Date Activities (continued) Integer Smash 1. Highlight a level (bronze = least difficult; gold = most difficult), and press b to select it. Scoring: You get two attempts to solve each problem. You earn 2 points for a correct answer on the first try, 1 point for a correct answer on the second try. You can earn up to 10 points. 2. For bronze or silver levels only, press á+â, ánâ, á â, or á â to select the operation you want to practice. 3. Enter the missing number (press Ì for negative numbers) and press b. If the answer is incorrect on the second attempt, the correct answer is displayed; press any key to resume play. As you play the activity, write each number sentence and solution. Show your work here. 4. What level and operation (bronze and silver only) did you play? 5. What was your score? Topics in Algebra Texas Instruments Student Worksheet 1-3

4 Name Date ³ Try-It!é on Your TI.83 Plus or TI.73 Learn to use the subtraction key (¹), the negation key (Ì), and the absolute value function (abs(). Use the negation and the subtraction keys to calculate M5 N M4. To Do This Press Display (TI.83 Plus shown) 1. Exit the Topics in Algebra 1 application and clear the Home screen. 2. Calculate M5 N M4. Note: The negation key (Ì) and the subtraction key (¹) are different. y l áexitâ : Ì 5 ¹ Ì 4 Í Enter M5 N M3 Q M2, first without using parentheses and then using parentheses. To Do This Press Display (TI.83 Plus shown) 1. Calculate M5 N M3 Q M2. Note: On the TI-73, notice the difference between the x variable key (I) and the multiplication key (M). Ì 5 ¹ Ì 3 M Ì2 Í 2. Calculate M5 N (M3 Q M2). Ì 5 ¹ D Ì 3 M Ì 2 E Í 3. Calculate (M5 N M3) Q M2. D Ì 5 ¹ Ì 3 E M Ì 2 Í The graphing calculator uses the Order of Operations rules, which say that multiplication and division are performed from left to right, and then addition and subtraction are performed from left to right. Notice that multiplication was calculated before subtraction in the expression M5 N M3 Q M2. Notice that the expression M5 N (M3 Q M2) has the same answer. The graphing calculator performs operations inside the parentheses before operations outside the parentheses. Notice that the expression (M5 N M3) Q M2 has a different answer than the expressions M5 N M3 Q M2 and M5 N (M3 Q M2). 1-4 Student Worksheet 2004 Texas Instruments Topics in Algebra 1

5 Name Date ³ Try-It!é on Your TI.83 Plus or TI.73 (continued) Use the absolute value (abs() function on the graphing calculator to find the absolute value of M12. To Do This Press Display (TI.83 Plus shown) 1. Find the absolute value of M12, which is written as M12. 1 " Note: The 1 NUM menu varies slightly from the TI-73 to the TI-83 Plus. 2. Select the absolute value (abs() function. It is copied to the Home screen. 1:abs( 3. Calculate the result. a 12 E Í Additional problems Calculate the following problems by hand, then check your answers using the graphing calculator. Remember to use the Order of Operations rules. 1. M4 + M12 Q M10 = 2. 4 Q M8 M10 Q 2 = 3. M30 M5 6 = 4. M12 +M28 = 5. M4 Q M8 N M10 Q 2 = 6. M M3 N 14 N M10 = Topics in Algebra Texas Instruments Student Worksheet 1-5

6 Number Sense: Integers Teacher Notes Objectives To illustrate the set of integers in a Venn diagram. To give an overview of the following definitions: the sign of a number, numbers of opposite sign, and absolute value. To give illustrations of the sets of positive and negative integers, and zero. To review ordering and the additive inverse property. To show examples of addition, subtraction, multiplication, and division of integers. Math Highlights This section begins with a Venn diagram and follows with an illustration of the use of integers on the Fahrenheit and Celsius scales. The temperature equivalencies shown are integer values. Students are reminded that the absolute value operation is defined as the distance of the number from zero. Examples of addition, subtraction, multiplication, and division operations are given. A number line model is used for addition and subtraction. Subtraction uses the add-the-opposite rule. Common Student Errors Students may have trouble identifying rules, such as the add-the-opposite rule for subtraction. Note: The number line model for addition and subtraction is shown on the graphing calculator when the Topics in Algebra 1 application is installed. Following are some activities to help students construct the rules for multiplication and division. These activities are not part of the Topics in Algebra 1 application. Pattern Development for Multiplication and Division Investigation 1: What is the product of a positive and negative number? Begin by writing the product of two positive numbers, for example, 3 Q 3 = 9. Keep decreasing the second term by 1 to create the sequence of multiplication values shown to the right. Notice the values on the right side of the number sentences decrease by 3. Observation: The product of a positive and negative number is negative. 3 Q 3 = 9 3 Q 2 = 6 3 Q 1 = 3 3 Q 0 = 0 3 Q M1 = M3 3 Q M2 = M6 3 Q M3 = M Teacher Notes 2004 Texas Instruments Topics in Algebra 1

7 Common Student Errors (continued) Pattern Development for Multiplication and Division (continued) Investigation 2: What is the product of two negative numbers? Start with the last number sentence from Investigation 1 (3 M3 = M9). Keep decreasing the first term by 1 to create the sequence of multiplication values shown to the right. Notice that the values on the right side of the number sentences increase by 3. Observation: The product of two negative numbers is positive. Investigation 3: What are the division rules for multiplying signed numbers? Observation: Division rules are developed using multiplication as the inverse operation. The rules are similar. 3 M3 = M9 2 M3 = M6 1 M3 = M3 0 M3 = 0 M1 M3 = 3 M2 M3 = 6 M3 M3 = 9 M6 3 = M2 since 3 M2 = M6 M6 M2 = 3 since M2 3 = M6 Student Worksheet Notes with Answers Overview Tell students: 1. How to find the Overview, if necessary. 2. How to navigate the application, if necessary. 3. To scroll through the Overview on the graphing calculator. Point out new terms, definitions, and concepts, and tell students to look for them as they go through the Overview. Topics in Algebra Texas Instruments Teacher Notes 1-7

8 Observations The Observations help students understand operations with signed integers. If necessary, tell students how to find the Observations. Students see the answers on the following three screens. Observation 1 How far apart are the bird and the fish? Should the answer be positive or negative? Students write an explanation of their answers. The bird and the fish are +125 ft. apart. The distance is positive. (Students will see the answers on the next three screens. Signed numbers give a perspective as shown on the screens.) Explanations will vary. Students see grids explaining the rules. Observation 2 What is the sign of the answer to the problem M3 Q M11? The answer is positive. M3 Q M11 = 33. What are the rules for multiplying and dividing signed numbers? The product of a positive and negative number is negative. The product of two numbers with the same sign is positive. Rules for division are similar to the rules for multiplication. 1-8 Teacher Notes 2004 Texas Instruments Topics in Algebra 1

10 ³ Try-It!é on Your TI.83 Plus or TI.73 These keystroke exercises let students practice using the basic operation keys (\, T, M, F), the negation key (a), the parentheses keys (D E), and the absolute value function (1 NUM 1:abs( ). Tell students to follow the steps exactly on the graphing calculators. Example screens are displayed on the worksheets for students to compare with the graphing calculator screens. Additional problems These problems give students additional practice using the subtraction key (T), the negation key (a), and the absolute value function (1 NUM 1:abs( ). Remind them to follow the Order of Operations rules. Tell students to do the following calculations by hand, and then check the answers using the graphing calculator. 1. M4 + M12 Q M10 = Q M8 M10 Q 2 = M12 3. M30 M5 6 = 0 4. M12 +M28 = M4 Q M8 N M10 Q 2 = M M3 N 14 N M10 = M Teacher Notes 2004 Texas Instruments Topics in Algebra 1

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