Subtracting Negative Integers


 Loren Henderson
 3 years ago
 Views:
Transcription
1 Subtracting Negative Integers Notes: Comparison of CST questions to the skill of subtracting negative integers. 5 th Grade/65 NS2.1 Add, subtract, multiply and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. 6 th Grade/65 NS2.3 Solve addition, subtraction, multiplication and division problems, including those that arise in concrete situations, that use positive and negative integers and combinations of these operations. 7 th Grade/65 Total # of Total # of Concept Questions Benchmark Questions 22 0 (1 Subtraction w/ answer) 17 0 (4 Adding / Integers) 14 0 (3 Absolute Value) NS1.2 Add, subtract, multiply and divide rational numbers (integers, fractions and terminating decimals) and take positive rational numbers to whole number powers. Although the skill itself is not emphasized in the test, experience tells us that students still struggle when working with the concept of negative and positive numbers and operations. This is the order in which to introduce integers: 1. Using a number line to add integers (developing the language used for working with integers) 2. Tile spacers (concrete) Page 1 of 26 10/17/10
2 3. Introduce the rules of adding integers (by now students have figured it out, anyway) 4. Introduce subtracting integers: number line, tile spacers, decomposing, rules Once students have developed the number sense necessary to succeed in adding and subtracting integers, they can transfer that skill into adding and subtracting positive and negative decimals and fractions and combining like terms. Regarding this lesson: This lesson assumes students have had little exposure to different strategies, and a general weakness in working with integers, so there is a lot of scaffolding embedded. Please be sure to begin the lesson where your students needs are. Page 2 of 26 10/17/10
3 Subtracting Negative Integers WarmUp Quadrant II: 3 rd Grade #46, NS2.8 Tony had $20. He paid $8 for a ticket to a baseball game. At the game, he bought a hotdog for $3. What amount of money did Tony have then? Quadrant I: 5 th Grade #47, AF1.2 If n = 31, what is the value of 6 n? Show two ways to solve. Quadrant III: 6 th Grade #27, NS2.3 Solve: One morning, the temperature was 5 below zero. By noon, the temperature rose 20 Fahrenheit (F) and then dropped 8 F by evening. What was the evening temperature? Show at least two ways to solve. Quadrant IV: 7 th Grade #59, AF4.1 Solve: What is the value of x if  3x 2 =  7? What are some errors students might make? What are some errors students might make? Today s Objective: Develop a variety of strategies to solve addition and subtraction problems, while providing opportunities to develop number sense regarding adding and subtracting integers. Page 3 of 26 10/17/10
4 Subtracting Negative Integers WarmUp Solutions Quadrant II: 3 rd Grade #46, NS2.8 Tony had $20. He paid $8 for a ticket to a baseball game. At the game, he bought a hotdog for $3. What amount of money did Tony have then? Quadrant I: 5 th Grade #47, AF1.2 If n = 31, what is the value of 6 n? = = 6 (31) = 0 25 ( 3) ( 8) = 25 = $ = $9 _ = 24 negatives = 24 Quadrant III: 6 th Grade #27, NS2.3 Solve: One morning, the temperature was 5 below zero. By noon, the temperature rose 20 Fahrenheit (F) and then dropped 8 F by evening. What was the evening temperature? ( 8) = 20 ( 5) ( 8) = 20 ( 13) = 7 13 ( 13) = 7 0 = 7 Possible errors: adding positive integers Quadrant IV: 7 th Grade #59, AF4.1 Solve: What is the value of x if  3x 2 =  7?  3x 2 =  73x 2 = x = x = x = x = 3 Possible errors: adding 2 to both sides, 7 2 Page 4 of 26 10/17/10
5 Standard: 7NS1.2: Add, subtract, multiply and divide rational numbers (integers, fractions and terminating decimals) and take positive rational numbers to whole number powers. Objective: Students will be able to add and subtract integers. Define Integers: Any member of the set I= So, integers are the positive and negative whole numbers, including zero. APK (Activate Prior Knowledge): Where do we see integers in the real world? See bullet note for possible student responses be sure to include ideas that students may have missed. [weight gain/loss, football yards gained/lost, stock market gains/losses, bank deposits and withdrawals, temperatures, elevation above and below sea level, elevators, escalators, parking garages ] Show a number line and ask: Where are the bigger numbers on the number line? [right, right of zero] The smaller numbers? [left, left of zero] Where are the positive numbers on the number line? [to the right of zero] The negative numbers? [to the left of zero] Do positive numbers have a greater value than negative numbers? [yes] How do you know? [they are to the right of negative numbers, any number to the right of another number is greater, when you move to the right on a number line the numbers increase in value] Page 5 of 26 10/17/10
6 Which number is greater: 3 or 2? [3] How do you know? [3 is to the right of 2] Which number is greater: 7 or 2? [2] How do you know? [2 is to the right of 7] Students should be able to articulate and justify their responses: [the number that is the furthest to the right on a number line has a greater value, if both numbers are negative, the number closest to zero has the greatest value] Check for Understanding: List several pairs of numbers and have students state either the bigger or the smaller of the two. List three numbers and have students order the numbers from greatest to least, least to greatest. Number Line Concept Development: If I were to add two integers, 3 and 5, using a number line, what would be a good strategy for me to do this? [start at 3 and move 5 to the right, end up at 8; 3 5 = 8] So, if I am adding positive integers, I move to the right. What if I am adding negative integers? Which direction would I move? [to the left] So, let s add a positive 3 with a negative 5: 3 (5). What number do I start with? [3] ( 5) What am I adding to that? [5] Is this a positive or negative? [negative] Page 6 of 26 10/17/10
7 If I were adding a positive 5, I would move to the right, but I am not. I m adding a negative 5; which direction do I move? [left] Where do I end up on the number line? [negative 2] Let s try again: 7 (3). Where do I start on the number line? [7] ( 3) What am I adding to that? [3] Is that a positive or negative? [negative] If I were adding a positive 3, I would move to the right, but I am not. I m adding a negative 3; which direction do I move on the number line? [left] Where do I end up on the number line? [4] So, 7 (3) = 4. Again: 4 (5). Where do I start on the number line? [4] ( 5) What am I adding to that? [5] Is that a positive or a negative? [negative] Page 7 of 26 10/17/10
8 If I were adding a positive 5, I would move to the right, but I am not. I am adding the opposite of 5, or a negative 5, so which direction do I move on the number line? [left] Where do I end up? [9] So, what is our equation? [4 (5) = 9] Let s try another: Where do I start on the number line? [6] 5 What am I adding to that? [5] Is that a positive or a negative number? [positive] Which direction do I move on the number line? [right] Where do I end up on the number line? [1] What is our equation? [6 5 = 1] Let s try a word problem together: One morning, the temperature was 5 below zero. By noon, the temperature rose 20 Fahrenheit (F) and then dropped 8 F by evening. What was the evening temperature? What integer represents five degrees below zero? [5] What does it mean when a temperature rose twenty degrees? What math operation would that be? [adding 20, positive 20] Page 8 of 26 10/17/10
9 Finally, what math operation represents dropping eight degrees? [negative 8, subtracting 8] So, what is the equation for this word problem? [5 20 (8) =] = ( 8) = Where do I start on the number line? [5] What are we adding to that? [20] Is that a positive or negative number? [positive] Since this number line is vertical, which direction do we move on it? [up] Where are we on the number line? [15] What are we adding to that? [8] Which direction do we move? [down] Where are we on the number line? [7] Page 9 of 26 10/17/10
10 What is our equation? [5 20 (8) = 7] You Tries: a) 7 (9) = 2 ( 9) b) = 37 (Holt 7, L 15) ( 22) *Note: At this point, some students may see that they will keep the sign of the number that has the greatest absolute value. Take a moment to frontload students with the concept of zero pairs. Zero Pair Concept Development: Imagine I am standing at zero on a number line. If I take one step to the right, where would I be on the number line? [positive 1] Now I will take one step to the left. Where am I on the number line? [zero] Now imagine you are on the ground floor in an elevator and you take it one floor up (1). You stay on the elevator and ride it one floor down (1). Where do you end up? [ground floor, back where you started, zero] Page 10 of 26 10/17/10
11 What if you are at the top of the staircase, and you take 7 steps down (7); you forgot something upstairs and took 7 steps up (7). Where did you end up? [back where you started, zero] These examples illustrate zero pairs. A working definition for the concept of zero pairs is: any number or variable and its opposite equals zero. The value of a Positive 1 and Negative 1 create a zero; therefore we have a zero pair. The value of a Positive 27 and Negative 27 create a zero; zero pair. The value of a Positive x and a Negative x create a zero: zero pair. Ask for students to give examples of zero pairs. Tile Spacers Concept Development: Let s work with integers in a different way. If I am adding 3 5, how many positives do I need to represent 3? [3] Draw three positives. How many positives do I need to represent 5? [5] Draw five positives next to the three positives. How many positives do I have altogether? [8] What is our equation? [3 5 = 8] Page 11 of 26 10/17/10
12 If I am adding 3 5, how many negatives do I need to represent 3? [3] Draw three negative symbols How many positives do I need to represent 5? [5] Draw five positive symbols next to the three negative symbols I now have 3 negatives and 5 positives. Remember our examples with going up one floor and then down one floor what number do we have when there is a number and its opposite, like a positive 7 and a negative 7? [zero] If I matched one negative with one positive, what concept would that represent? [zero, zero pair] How many zero pairs do we have? [3] Take them away. What is left? [2 positives] Page 12 of 26 10/17/10
13 We keep the sign of what we have the most of; since we have more positives than negatives, our answer is positive 2. What is our equation? [3 5 = 2] Let s try another: 3 (5). How many positives do I have? [3] Draw three positives. How many negatives? [5] Draw five negatives next to the three positives Are there any zero pairs? [3] Take them away. What is left? [2 negatives] Since we keep the sign of what we have the most of, what is our equation? [3 (5) = 2] Page 13 of 26 10/17/10
14 You Tries: a) 4 (3) (3) = 7 We ve added (combined) the numbers and kept the sign of what we have the most of.  b) 18 (7) (7) = 11 (Holt 7, L 14) We found zero pairs (combined the numbers) and kept the sign of what we have the most of Page 14 of 26 10/17/10
15 Concept Closure: Give students the following two stems and have them work with an elbow partner to see if they can articulate the rules for adding integers: If the signs are the same If the signs are different Give students time to process, and then debrief. Ask groups to share their ideas. [If the signs are the same, add the numbers and keep the sign. ] [If the signs are different, subtract the numbers and keep the sign of what you have the most of. ] Using this language is key. Subtracting Integers Have students compare the following two problems: 3 (5) and 3 5 Use the number line and tile spacers to model. Traditional: Signs are different; subtract and keep the sign of what you have the most of. 3 (5) = 2 ( 5) = 2 Page 15 of 26 10/17/10
16 3 5 = 2 ( 5) The rule for subtracting integers is to rewrite the subtraction problem into an addition problem, and then add the opposite of the integer. So, 3 5 becomes three plus the opposite of five: = 3 (5) which are the same two problems we ve compared. We will need to rewrite all of our subtraction problems so that they are addition ones. You Try Rewriting: What is the opposite of 8? [8] 5 (8) = 5 8 What is the opposite of 35? [35] = 32 (35) What is the opposite of 25? [25] 75 (25) = But, why is subtracting a negative the same as adding a positive? Check student responses. If I have gone into debt in my checking account because I am $25 overdrawn, do I have a positive balance or a negative balance? [negative, 25 dollars] Page 16 of 26 10/17/10
17 If someone was going to take my debt away as a gift to me, what would they have to do? [they would take away negative $25] What would the balance be in my account? [zero dollars] Even though I don t have any money, is that better than having $25 in my account? [yep!] What would that look like as a math problem? Write the following: 25 (25) = 0 If someone was willing to help me out like this, what would they have to do in order to bring my checking account balance to zero if I have  $25? They would have to give me $25! Positive 25. So, knowing the integer rule for subtraction is to rewrite a subtraction problem into an addition one and then adding the opposite integer, we would need to think about my banking situation like this : Write the following: 25 (25) = 025 (25) = 0 Does anyone see an example of a zero pair? [yes!] Where is it? [25 and 25, negative 25 and positive 25] If I were using a number line for this situation, Write the following: 25 (25) = 0 Page 17 of 26 10/17/10
18 Where would I start on the number line? [25] If I was going to add negative 25, which direction would I go? [left] But I m not, I m doing the opposite of adding negative 25, I m going to subtract negative 25, so which direction do I go? [right] Where do I end up on the number line? [0]  ( 25) When adding a negative number, move to the left. Since we are subtracting a negative number, we move to the right. Let s try one more guided practice, Write the following: 14 8 = We need to change our subtraction to addition and add the opposite integer. Write the following, and ask for students response on rewriting: 14 8 = 14 (8) [14 plus 8] Page 18 of 26 10/17/10
19 Now, where do we start on the number line? [14] We are adding the opposite of 8; is this a positive or negative 8? [negative] Which direction do we move on the number line? [left] Where do we end up? [6] ( 8) You Tries 17 (10) = = 7 Traditional: Signs are different; subtract and keep the sign of what you have the most of = 7 Page 19 of 26 10/17/10
20 You Tries (continued ) 14 (14) = ( 14) = 0 Traditional: Signs are different; subtract and keep the sign of what you have the most of = 0 Decomposing Concept Development: Let s try one more strategy with some problems we ve already worked through: decomposing. 3 5 = 3 (5) = 2 Traditional: Signs are different; subtract and keep the sign of what you have the most of. 3 5 = 3 (5) = 3 (3) (2) = 0 (2) = 2 Given Rewrite as addition problem Decompose 5 to create a zero pair Identity Property of Addition Answer *Note: The use of the third column frontloads students for success in geometry, where they will be required to justify their work with twocolumn proofs. In this context, having students write the justifications is an option, but explicit discussion of the math reasoning and properties is highly recommended. Page 20 of 26 10/17/10
21 17 (10) = = 7 Traditional: Signs are different; subtract and keep the sign of what you have the most of. 17 (10) = = 7 (10) 10 = 0 10 = 7 Given Rewrite as addition Decompose to create a zero pair Identity Property of Addition Answer 14 8 = 14 (8) = 6 Traditional: Signs are different; subtract and keep the sign of what you have the most of. Same problem 14 8 = 14 (8) = 6 Traditional: Signs are different; subtract and keep the sign of what you have the most of = 14 (8) = 6 8 (8) = 6 0 = = 14 (8) = 8 6 (8) = 6 8 (8) = 6 0 = 6 Given Rewrite as addition Decompose to create a zero pair Identity Property of Addition Answer Given Rewrite as addition Decompose to create a zero pair Commutative Property of Addition Identity Property of Addition Answer Page 21 of 26 10/17/10
22 You Tries (Holt 7, L 15) 18 (25) = = 7 Traditional: Signs are different; subtract and keep the sign of what you have the most of. 88 (10) = = 78 Traditional: Signs are different; subtract and keep the sign of what you have the most of. 15 x; x = (10) = = 5 Traditional: Signs are different; subtract and keep the sign of what you have the most of. 18 (25) = = = 0 7 = 788 (10) = = 78 (10) 10 = = (10) = = 5 (10) 10 = 5 0 = 5 Given Rewrite as addition Decompose to create a zero pair Identity Property of Addition Answer Given Rewrite as addition Decompose to create a zero pair Identity Property of Addition Answer Given Rewrite as addition Decompose to create a zero pair Identity Property of Addition Answer Page 22 of 26 10/17/10
23 Now let s practice it all! (Holt 7, L 15) Traditional Number Line Tile Spacers Decompose 15 (10) 15 (10) 15 (10) 15 (10) = = = = = = 5 (10) 10 Traditional: Signs are different; subtract and keep the sign of what you have the most of = 5 0 = 5 = 55 (15) 5 (15) 5 (15) 5 (15) = = = = = = Traditional: Signs are different; subtract and keep the sign of what you have the most of. = 0 10 = 10 = 10 Page 23 of 26 10/17/10
24 15 (12) 15 (12) 15 (12) 15 (12) = = = = = = 3 (12) 12 Traditional: Signs are different; subtract and keep the sign of what you have the most of = 3 0 = = 3 Page 24 of 26 10/17/10
25 18 (25) 18 (25) 18 (25) 18 (25) = = = = = 7 25 = Traditional: Signs are different; subtract and keep the sign of what you have the most of = 0 7 = = 7 Page 25 of 26 10/17/10
26 15 (20) 15 (20) 15 (20) 15 (20) = = = = = = Traditional: Signs are the same; add and keep the sign. 35 = = 30 5 = 35 = 35 Page 26 of 26 10/17/10
Unit 7 The Number System: Multiplying and Dividing Integers
Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will
More informationIntegers (pages 294 298)
A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write
More information25 Integers: Addition and Subtraction
25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers
More informationAccentuate the Negative: Homework Examples from ACE
Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 1215, 47, 4952 Investigation 2: Adding and Subtracting Rational Numbers, ACE 1822, 38(a),
More informationAdding and Subtracting Positive and Negative Numbers
Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number
More informationExponents. Exponents tell us how many times to multiply a base number by itself.
Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,
More informationMultiplying and Dividing Listen & Learn PRESENTED BY MATHMANIAC Mathematics, Grade 8
Number Sense and Numeration Integers Multiplying and Dividing PRESENTED BY MATHMANIAC Mathematics, Grade 8 Integers Multiplying and Dividing Introduction Welcome to today s topic Parts of Presentation,
More informationLesson Plan Warehouse Grade 7 Adding Integers
CCSSM: Grade 7 DOMAIN: The Number System Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard: 7.NS.1: Apply
More informationProperties of Real Numbers
16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should
More informationPreAlgebra Lecture 6
PreAlgebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationWarmUp. Today s Objective/Standards: Students will use the correct order of operations to evaluate algebraic expressions/ Gr. 6 AF 1.
WarmUp CST/CAHSEE: Gr. 6 AF 1.4 Simplify: 8 + 8 2 + 2 A) 4 B) 8 C) 10 D) 14 Review: Gr. 7 NS 1.2 Complete the statement using ,. Explain. 2 5 5 2 How did students get the other answers? Other: Gr.
More informationAdding and Subtracting Integers Unit. Grade 7 Math. 5 Days. Tools: Algebra Tiles. FourPan Algebra Balance. Playing Cards
Adding and Subtracting Integers Unit Grade 7 Math 5 Days Tools: Algebra Tiles FourPan Algebra Balance Playing Cards By Dawn Meginley 1 Objectives and Standards Objectives: Students will be able to add
More informationListen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7
Number Sense and Numeration Integers Adding and Subtracting Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A
More informationMathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L34) is a summary BLM for the material
More informationSolve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers
More informationIntegers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationLesson 2.2. 44 Lesson 2.2 ~ Adding Integers
Adding Integers Lesson 2.2 EXPLORE! integer Chips Integer chips are helpful for modeling integer operations. Each blue chip will represent the integer 1. Each red chip will represent the integer 1. When
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationPart 1 Expressions, Equations, and Inequalities: Simplifying and Solving
Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words
More informationUsing Proportions to Solve Percent Problems I
RP71 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More informationMULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.
1.4 Multiplication and (125) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with
More informationAdding & Subtracting Integers
WARDEN AVE P.S. Adding & Subtracting Integers Number Sense & Numeration Unit #1 Grade 7 Math 20142015 School Year This miniunit will run from September 1526 and must be handed in on Friday Sept. 26th
More informationSample Fraction Addition and Subtraction Concepts Activities 1 3
Sample Fraction Addition and Subtraction Concepts Activities 1 3 College and CareerReady Standard Addressed: Build fractions from unit fractions by applying and extending previous understandings of operations
More informationLesson Plan  Rational Number Operations
Lesson Plan  Rational Number Operations Chapter Resources  Lesson 312 Rational Number Operations  Lesson 312 Rational Number Operations Answers  Lesson 313 Take Rational Numbers to WholeNumber
More informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
More informationWarmUp ( 454 3) 2 ( 454 + 2) 3
WarmUp ) 27 4 ST/HSEE: 4 th Grade ST Review: 4 th Grade ST t school, there are 704 desks to place into classrooms. If the same number of desks is placed in each classroom, how many desks will be in each
More informationMANCHESTER COLLEGE Department of Education. Length: 25 minutes Grade Intended: PreAlgebra (7 th )
LESSON PLAN by: Kyler Kearby Lesson: Multiplying and dividing integers MANCHESTER COLLEGE Department of Education Length: 25 minutes Grade Intended: PreAlgebra (7 th ) Academic Standard: 7.2.1: Solve
More informationRational Number Project
Rational Number Project Fraction Operations and Initial Decimal Ideas Lesson : Overview Students estimate sums and differences using mental images of the 0 x 0 grid. Students develop strategies for adding
More informationGrade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours
Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade
More informationClifton High School Mathematics Summer Workbook Algebra 1
1 Clifton High School Mathematics Summer Workbook Algebra 1 Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:
More informationObjective. Materials. TI73 Calculator
0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI73 Calculator Integer Subtraction What s the Difference? Teacher
More informationMath and FUNDRAISING. Ex. 73, p. 111 1.3 0. 7
Standards Preparation Connect 2.7 KEY VOCABULARY leading digit compatible numbers For an interactive example of multiplying decimals go to classzone.com. Multiplying and Dividing Decimals Gr. 5 NS 2.1
More informationAlgebra 1. Practice Workbook with Examples. McDougal Littell. Concepts and Skills
McDougal Littell Algebra 1 Concepts and Skills Larson Boswell Kanold Stiff Practice Workbook with Examples The Practice Workbook provides additional practice with workedout examples for every lesson.
More informationGrade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills
Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate
More information6 Mathematics Curriculum
New York State Common Core 6 Mathematics Curriculum GRADE Table of Contents 1 Rational Numbers GRADE 6 MODULE 3 Module Overview... 3 Topic A: Understanding Positive and Negative Numbers on the Number Line
More informationGrade 6 Mathematics Performance Level Descriptors
Limited Grade 6 Mathematics Performance Level Descriptors A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 6 Mathematics. A student at this
More informationOA310 Patterns in Addition Tables
OA310 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20
More informationActivity 1: Using base ten blocks to model operations on decimals
Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division
More informationB I N G O INTEGER BINGO. On the next page are a series of Integers, Phrases and Operations. 1. Cut out each of the integers, phrases and operations;
Unit 4: Integers They are positive and negative WHOLE numbers The zero is neutral The sign tells the direction of the number: Positive means to the right of zero on a number line Negative means to the
More informationLesson Plan  Integers, Opposites, Absolute Value
Lesson Plan  Integers, Opposites, Absolute Value Chapter Resources  Lesson 31 Integers and the Number Line  Lesson 31 Integers and the Number Line Answers  Lesson 32 Opposites and Absolute Value
More informationChapter 8 Integers 8.1 Addition and Subtraction
Chapter 8 Integers 8.1 Addition and Subtraction Negative numbers Negative numbers are helpful in: Describing temperature below zero Elevation below sea level Losses in the stock market Overdrawn checking
More informationNF512 Flexibility with Equivalent Fractions and Pages 110 112
NF5 Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
More informationFractions as Numbers INTENSIVE INTERVENTION. National Center on. at American Institutes for Research
National Center on INTENSIVE INTERVENTION at American Institutes for Research Fractions as Numbers 000 Thomas Jefferson Street, NW Washington, DC 0007 Email: NCII@air.org While permission to reprint this
More informationOpposites are all around us. If you move forward two spaces in a board game
TwoColor Counters Adding Integers, Part II Learning Goals In this lesson, you will: Key Term additive inverses Model the addition of integers using twocolor counters. Develop a rule for adding integers.
More informationIntegers, I, is a set of numbers that include positive and negative numbers and zero.
Grade 9 Math Unit 3: Rational Numbers Section 3.1: What is a Rational Number? Integers, I, is a set of numbers that include positive and negative numbers and zero. Imagine a number line These numbers are
More informationPREPARATION FOR MATH TESTING at CityLab Academy
PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRETEST
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More informationStudent Outcomes. Lesson Notes. Classwork. Discussion (10 minutes)
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 8 Student Outcomes Students know the definition of a number raised to a negative exponent. Students simplify and write equivalent expressions that contain
More informationMeasurement with Ratios
Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve realworld and mathematical
More informationLesson 3: Using Inequalities to Problem Solve
Lesson 3: Using Inequalities to Problem Solve Selected Content Standards Benchmarks Addressed: N1M Demonstrating that a rational number can be expressed in many forms, and selecting an appropriate form
More informationSection 4.1 Rules of Exponents
Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells
More informationMathematics. Mathematical Practices
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with
More informationLesson 4: Efficiently Adding Integers and Other Rational Numbers
Classwork Example 1: Rule for Adding Integers with Same Signs a. Represent the sum of 3 + 5 using arrows on the number line. i. How long is the arrow that represents 3? ii. iii. How long is the arrow that
More informationExample 1: Bar Model Decompose Traditional. Solution Bar Model Decompose Traditional
Note taking guide: Solving equations with variables on both sides of the equal sign Example 1: #1 #2 You Try for Example 1: Solution Page 1 of 20 MDC@ACOE 10/26/10 Note taking guide: Solving equations
More informationParamedic Program PreAdmission Mathematics Test Study Guide
Paramedic Program PreAdmission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page
More informationLesson/Unit Plan Name: Patterns: Foundations of Functions
Grade Level/Course: 4 th and 5 th Lesson/Unit Plan Name: Patterns: Foundations of Functions Rationale/Lesson Abstract: In 4 th grade the students continue a sequence of numbers based on a rule such as
More informationThe Crescent Primary School Calculation Policy
The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationLesson 11: Volume with Fractional Edge Lengths and Unit Cubes
Lesson : Volume with Fractional Edge Lengths and Unit Cubes Student Outcomes Students extend their understanding of the volume of a right rectangular prism with integer side lengths to right rectangular
More informationWays We Use Integers. Negative Numbers in Bar Graphs
Ways We Use Integers Problem Solving: Negative Numbers in Bar Graphs Ways We Use Integers When do we use negative integers? We use negative integers in several different ways. Most of the time, they are
More informationFINAL SIOP LESSON PLAN. Preparation
Name: Stephanie Hart DOMINICAN UNIVERSITY OF CALIFORNIA FINAL SIOP LESSON PLAN Content Area: Mathematics, Solving Inequalities Grade Level: 8 English Learners: This is a sheltered class within a mainstream
More informationWelcome to Basic Math Skills!
Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots
More informationAddition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15
Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123
More informationMultiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20
SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed
More informationInteger Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.
More informationLesson 2. Operations with Integers. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 2 Operations with Integers Objectives Add and subtract integers Determine the absolute value of a number Solve word problems that involve adding
More informationAddition and Subtraction of Integers
Addition and Subtraction of Integers Integers are the negative numbers, zero, and positive numbers Addition of integers An integer can be represented or graphed on a number line by an arrow. An arrow pointing
More informationSIMPLIFYING ALGEBRAIC FRACTIONS
Tallahassee Community College 5 SIMPLIFYING ALGEBRAIC FRACTIONS In arithmetic, you learned that a fraction is in simplest form if the Greatest Common Factor (GCF) of the numerator and the denominator is
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More informationSuccessful completion of Math 7 or Algebra Readiness along with teacher recommendation.
MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL:... 811 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION
More information1.2 Linear Equations and Rational Equations
Linear Equations and Rational Equations Section Notes Page In this section, you will learn how to solve various linear and rational equations A linear equation will have an variable raised to a power of
More informationProgress Check 6. Objective To assess students progress on mathematical content through the end of Unit 6. Looking Back: Cumulative Assessment
Progress Check 6 Objective To assess students progress on mathematical content through the end of Unit 6. Looking Back: Cumulative Assessment The MidYear Assessment in the Assessment Handbook is a written
More informationUNIT 3 VOCABULARY: INTEGERS
1º ESO Bilingüe Page 1 UNIT 3 VOCABULARY: INTEGERS 3.1. Some uses of negative numbers There are many situations in which you need to use negative numbers. POSITIONS A submarine which is sailing 700 m below
More information2 Mathematics Curriculum
New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic C: Read and Write Three Digit Numbers Within 1000 in Unit, Numeral, Expanded, and Word Forms 2.NBT.3, 2.NBT.1 Focus Standard:
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationSession 7 Fractions and Decimals
Key Terms in This Session Session 7 Fractions and Decimals Previously Introduced prime number rational numbers New in This Session period repeating decimal terminating decimal Introduction In this session,
More informationSeriously Simple Sums! Vedic Maths Free Tutorial. Maths Tips and Tricks to Improve Your Math Abilities
Copyright Notice This ebook is free! Maths Tips and Tricks to Improve Your Math Abilities This publication is protected by international copyright laws. You have the author s permission to transmit this
More informationDay One: Least Common Multiple
Grade Level/Course: 5 th /6 th Grade Math Lesson/Unit Plan Name: Using Prime Factors to find LCM and GCF. Rationale/Lesson Abstract: The objective of this two part lesson is to give students a clear understanding
More informationMath Matters: Why Do I Need To Know This? 1 Probability and counting Lottery likelihoods
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Four 1 Probability and counting Lottery likelihoods Objective: To demonstrate the
More information3.2 Methods of Addition
.2 Methods of Addition Objectives Relate addition stories to number bonds. Write two addition facts for a given number bond. Solve picture problems using addition. Learn addition facts through, and the
More informationIntroduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman
Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children
More informationUsing Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera
Using Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera 1 Overall Unit Objective I am currently student teaching Seventh grade at Springville Griffith Middle
More informationGrade 6 Mathematics Common Core State Standards
Grade 6 Mathematics Common Core State Standards Standards for Mathematical Practice HOW make sense of problems, persevere in solving them, and check the reasonableness of answers. reason with and flexibly
More information1 LESSON 1.1. Adding and Subtracting Integers. Adding Integers with the Same Sign ESSENTIAL QUESTION
Adding and Subtracting Integers? MODULE 1 LESSON 1.1 ESSENTIAL QUESTION Adding Integers with the Same Sign How can you use addition and subtraction of integers to solve realworld problems? 7.NS.1, 7.NS.1b,
More informationSolution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together
Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a
More informationMultiplication. Year 1 multiply with concrete objects, arrays and pictorial representations
Year 1 multiply with concrete objects, arrays and pictorial representations Children will experience equal groups of objects and will count in 2s and 10s and begin to count in 5s. They will work on practical
More informationLESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:
LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals.
More informationPrentice Hall. California Edition of Algebra 1  Classics Edition (Smith/Charles) 2008. Grade 8
Prentice Hall Grade 8 California Edition of Algebra 1  Classics Edition (Smith/Charles) 2008 C O R R E L A T E D T O California s Map for a Basic Grade Level Program Grade 8 PROGRAM DESCRIPTION Prentice
More informationLESSON 5  DECIMALS INTRODUCTION
LESSON 5  DECIMALS INTRODUCTION Now that we know something about whole numbers and fractions, we will begin working with types of numbers that are extensions of whole numbers and related to fractions.
More information63 Solving Systems by Elimination
Warm Up Simplify each expression. 1. 2y 4x 2(4y 2x) 2. 5(x y) + 2x + 5y Write the least common multiple. 3. 3 and 6 4. 4 and 10 5. 6 and 8 Objectives Solve systems of linear equations in two variables
More information0.8 Rational Expressions and Equations
96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions  that is, algebraic fractions  and equations which contain them. The reader is encouraged to
More informationInteger Instruction That Works: Best Practices for Instruction of Integers for All Students Including LEP Learners Math, LEP Grades 58
Integer Instruction That Works: Best Practices for Instruction of Integers for All Students Including LEP Learners Math, LEP Grades 58 Frustrated by the fact that your students incorrectly apply the rule
More informationUnit 6 Number and Operations in Base Ten: Decimals
Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,
More informationAccuplacer Arithmetic Study Guide
Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how
More informationAlgebra Unit Plans. Grade 7. April 2012. Created By: Danielle Brown; Rosanna Gaudio; Lori Marano; Melissa Pino; Beth Orlando & Sherri Viotto
Algebra Unit Plans Grade 7 April 2012 Created By: Danielle Brown; Rosanna Gaudio; Lori Marano; Melissa Pino; Beth Orlando & Sherri Viotto Unit Planning Sheet for Algebra Big Ideas for Algebra (Dr. Small)
More informationEE65 Solving Equations with Balances Pages 77 78
EE65 Solving Equations with Balances Pages 77 78 STANDARDS 6.EE.B.5, 6.EE.B.6 Goals Students will use pictures to model and solve equations. Vocabulary balance equation expression sides (of an equation)
More informationMATH 90 CHAPTER 1 Name:.
MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 9 Order of Operations
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More information