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6 Grade math resource lesson plan April 28-2,2014 Standards 6th grade 6.ee.1 write and evaluate numerical expressions involving whole-number exponents. 6.ee.2A/b/c write, read, and evaluate expressions in which letters stand for numbers 6.ee.6 use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that variable can represent an unknown number, or, depending on the purpose at hand, any number ina specified set. FYI PASS Testing APRIL 6-9,2014 7 Grade math resource lesson plan April 28-2,2014 Standards 7th grade 6.ee.6 use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7.ns.3 solve real-world and mathematical problems involving the four operations with rational numbers. FYI PASS Testing APRIL 6-9,2014 A variety of methods will be used to accommodate the needs of individual learners such as: o IEP’s and 504 Plans are followed o hands-on activities o discussions through whole group and shoulder buddies o informational text strategies (steps to problem solving) o note taking • CFU throughout the lesson and in closure. I will be looking for at least 80% skill mastery daily. • Homework and classwork will be graded on the following scale: 100 -All Completed, 75- if 75% is completed, 60- if 60% is completed or less. “getting into shape classroom project” “getting into shape classroom project” Directions These pictures must be mounted on the paper provided in your packet, using glue sticks. Please trace or outline the shape within the picture with a black marker. You will also write the word and its’ definition on the page (Please Write NEAT). “getting into shape” Page Example Parallel Lines -lines that are in the same plane and never intersect. PASS Review Unit 1-Number and Operations Compare and order integers The Number Line Negative Numbers (-) Positive Numbers (+) (The line continues left and right forever.) Bell Work Monday, April 28,2014 On a map, 1 inch = 52 miles. If the distance between two cities measures 2 &1/2 inches. How many miles apart are they. Agenda • Bell Work • Review Instructions for “Getting into Shapes” Project • Review Essential Question • Relevance • Prior learning • Modeling (I Do) • Guided Practice (We Do) • Closure/CFU • Reflection • Independent Practice ( You Do)(CFU) • Early finishers- work on math project • HAVE A GREAT DAY! Essential Question How do I compare and order integers? Comparing and Ordering Integers Relevance Integers are whole numbers and their opposites (positive numbers, zero, and negative numbers). Negative numbers are numbers less than zero. The opposite of a number is the number that is the same distance form 0 on a number line, but on the opposite side of 0. For example, 4 and -4 are opposites. Comparing and Ordering Integers Real Life Application: Integers can be used in real-life situations. Some keywords that indicate positive integers are gained, increased, rose, above, more, and up. Some keywords that indicate negative integers are lost, decreased, dropped, below, less, and down. Comparing and Ordering Integers Integers are compared almost in the same way as whole numbers, but with addition of some rules. Steps for comparing integers: 1.If we compare numbers with different signs, then negative number is less than positive. 2.If numbers are both positive then this is the case when we compare whole numbers. 3.If numbers are both negative then we compare numbers without signs. The bigger positive number, the smaller negative. For example, if we compare -3 and -5, then we compare 3 and 5 (numbers without signs). Since 3<5 then −3>−5 . Comparing and Ordering Integers -- I Do Example 1. Compare 4567 and -12345. Numbers are with different signs. Negative number is always less than positive. Therefore, 4567>−12345 . Example 2. Compare -300 and 0. 0 is always bigger than any negative number, so −300<0 . Example 3. Compare -12 and -234. Compare numbers without signs: 12 and 234. Since 12<234 then −12>−234 . Comparing and Ordering Integers- We Do Example 4. Compare -234 and -123. Compare numbers without signs: 234 and 123. Since 234>123 then −234<−123 . Example 5. Compare -2345 and -2346. Compare numbers without signs: 2345 and 2346. Since 2345<2346 then −2345>−2346 . Example 6. Compare -456 and 12. Answer: −456<12 . Hint: numbers are with different signs. Comparing and Ordering Integers- Reflection Which did you move from to compare fractions on the number line? Left to Right What is the first step to ordering integers using a number line? Find the integers on a number line to see exactly where they are located. Comparing and Ordering Integers Independent Practice/ You Do Ordering Integers Skill Sheet *You may work with a partner to complete skill. Teacher will circulate classroom to provide extra assistance if needed.* Tuesday, April 29,2014 Bell work Lesson6: Expressions, equations, and inequalities How can the following expression be written using the distributive property? 8(5+12) Agenda Bell Work Review Instructions for “Getting into Shapes” Project Review Essential Question Relevance Prior learning Modeling (I Do) Guided Practice (We Do) Closure/CFU Reflection Independent Practice ( You Do)(CFU) Early finishers- work on math project HAVE A GREAT DAY! Essential Question How do I distinguish between the Number Properties: Associative, Commutative, and Distributive ? Relevance Why not learn about number properties? Because every math system you've ever worked with has obeyed these properties! You have never dealt with a system where a×b did not in fact equal b×a, for instance, or where (a×b)×c did not equal a×(b×c). Which is why the properties probably seem somewhat pointless to you. is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property. Why is the following true? 2(x + y) = 2x + 2y Since they distributed through the parentheses, this is true by the Distributive Property. Use the Distributive Property to rearrange: 4x – 8 The Distributive Property either takes something through a parentheses or else factors something out. Since there aren't any parentheses to go into, you must need to factor out of. Then the answer is "By the Distributive Property, 4x – 8 = 4(x – 2)" The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means 2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. Rearrange, using the Associative Property: 2(3x) They want you to regroup things, not simplify things. In other words, they do not want you to say "6x". They want to see the following regrouping: (2×3)x Simplify 2(3x), and justify your steps. In this case, they do want you to simplify, but you have to tell why it's okay to do... just exactly what you've always done. Here's how this works: 2(3x) original (given) statement (2×3)x by the Associative Property 6x simplification (2×3 = 6) Why is it true that 2(3x) = (2×3)x? Since all they did was regroup things, this is true by the Associative Property. The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property. Use the Commutative Property to restate "3×4×x" in at least two ways. They want you to move stuff around, not simplify. In other words, the answer is not "12x"; the answer is any two of the following: 4 × 3 × x, 4 × x × 3, 3 × x × 4, x × 3 × 4, and x × 4 × 3 Why is it true that 3(4x) = (4x)(3)? Since all they did was move stuff around (they didn't regroup), this is true by the Commutative Property. Number Properties: I Do Write the property that is represented by the given equation: 6 x 11=11 x 6 Commutative Property 2(x+3) – 2x+6 Associative Property (14 x 3) x 8= 14 x (3 x 8) Distributive Property Associative Property/Commutative Property/Distributive Property Number Properties: We Do 3a + 7a – 5b Commutative Property (3a + 7a) – 5b Associative Property a(3 + 7) – 5b Distributive Property Write the property that is represented by the given equation: Number Properties: Reflection Any time they refer to the Commutative Property what do they want you to do with the numbers? “Move them around” Any time they refer to the Associative Property, what od they want you to do with the numbers? They want you to regroup things Any time they refer in a problem to using the Distributive Property, what do they want you to do with the numbers? They want you to take something through the parentheses (or factor something out) Number Properties: Independent Practice BUCKLE DOWN PASS Skill Sheets Pages 60-63 *You may work with a partner to complete skill. Teacher will circulate classroom to provide extra assistance if needed.* Wednesday, April 30,2014 PASS Review Lesson6: writing Expressions What is the value of t in the equation below? 13t=143 Agenda • Bell Work • Review Instructions for “Getting into Shapes” Project • Review Essential Question • Relevance • Prior learning • Modeling (I Do) • Guided Practice (We Do) • Closure/CFU • Reflection • Independent Practice ( You Do)(CFU) • Early finishers- work on math project • HAVE A GREAT DAY! Essential Question How do I write an expression using variables, symbols, and/or numbers? Relevance Knowing how to evaluate algebraic expressions can help you determine the amount of your paycheck. A variable is a letter that represents an unknown number. Variables are used in expressions and equations. 2n + 4 C = 2F – 7 When you multiply a number by a variable, you do not need a multiplication sign between them. You can write the number directly in front of the variable. Above, 2n is the same as 2 x 4 An expression is a mathematical phrase made of variables, symbols, and/or numbers and operations. To translate a written phrase into an algebraic expression, you need to identify the operations. The operations link the individual terms; they are addition, subtraction, multiplication, and division. For Example Write and algebraic expression to represent “four plus three times a number.” Let n = the number. What is the main operation? The word plus indicates addition. What the terms to be added? 4 and 3n Four plus three times a number 4 + 3n The algebraic expression can be written as 4 + 3n or 3n + 4. When the main operation is subtraction or division, the order in which the terms are written does matter. Example Write an algebraic expression to represent “six less than twice a number.” Let z=the number. The phase less than indicates subtraction. The two terms in the expression are 6 and 2z. You may be asking yourself which of the following expressions is correct: 6-2z or 2z-6? The word than in less than indicates that you have to switch the order of the terms in the expression from how they appear in the description. The algebraic expression can be written as 2z-6. Writing Expressions: I Do Underline the part of the phrase that indicates the main operation, then write an expression. 1. Sixteen more than a number____________________ 2. The product of a number and eleven______________ 16 + n N x 11 Writing Expressions : We Do Nine increased by a number 9 + n Twenty –five decreased by a number 25 - n A number doubled by ten n(10) Writing Expressions: Reflection Tell in your own words, the difference between numbers and variables. Writing Expressions: Independent Practice Writing Expressions PASS Skill Sheet *You may work with a partner to complete skill. Teacher will circulate classroom to provide extra assistance if needed.* Pages 65-68 Thursday, may 1,2014 PASS Review Lesson 6: equations and inequalities Sara own 23 fewer CDs than Kathy. Kathy owns k CDs. Write an expression for the situation. Agenda • Bell Work • Review Instructions for “Getting into Shapes” Project • Review Essential Question • Relevance • Prior learning • Modeling (I Do) • Guided Practice (We Do) • Closure/CFU • Reflection • Independent Practice ( You Do)(CFU) • Early finishers- work on math project • HAVE A GREAT DAY! Essential Question How do I solve equations? Relevance Knowing how to solve equations mentally can help you solve problems in science. To solve an equation, you need to isolate the variable (get it alone on one side of the equation). Use inverse operations to find the value of the variable. Remember that addition and subtraction are inverse operations; one “undoes” the other. To undo addition, use subtraction. To undo subtraction, use addition. Example: Solve the following equation for x. 7+x=30 Use inverse operations to get the variable alone on one side of the equation. 7+ x=30 7+x-7=30-7 X=23 The solution to the equation is x=23. Solve the following equation for s. S – 9 = 18 Use inverse operations to get the variable alone on one side of the equation. S – 9 = 18 S – 9 + 9 = 18 + 9 S = 27 The solution to the equation is s= 27. Solve the following equation for y. 12 x y = 84 Use inverse operations to get the variable alone on one side of the equation. 12 x y =84 12 x y / 12= 84/12 Y= 7 The solution to the equation is y=7. Solve the following equation for n. N/8=6 Use inverse operations to get the variable alone on one side of the equation. n / 8 =6 n / 8 x 8= 6 x 8 n=48 The solution to the equation is n=48. When writing equation to represent and solve realworld problems, you do the following. 1. Find all the information you need to know. 2. Now you can write an equation. 3. There may be more than one way to write and equation to represent the situation. 4. Use inverse operations to get the variable alone on one side of the equation. 5. Solve the equation. Writing Equations: I Do Look at the example on page 72 and read along Check to see if I followed the correct steps 1. Underline my key information. 2. Write my equation. 3. Remember Mrs. Toomer, there may be more than one way to write and equation to represent the situation. 4. Did I Use inverse operations to get the variable alone on one side of the equation. 5. Did I solve the equation. Writing Equations : We Do A tour bus holds 84 passengers. Each seat holds 3 people. How many passenger seats are on the bus? (Let x = the number of passenger seats.) There are ___passenger seats on the bus. Writing Equations: Reflection Tell in your own words, the steps for solving equations. Writing Expressions: Independent Practice Writing Equations PASS Skill Sheet *You may work with a partner to complete skill. Teacher will circulate classroom to provide extra assistance if needed.* Pages 72=73 Friday, may 2,2014 Students will work on regular education assignments and tests that requires extra assistance If a student does not have any regular education assignments, they will work on their geometry projects for resource.