6 th Grade Mathematics Quarter 2 Curriculum Map th Grade Math Quarter 2 1

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1 6 th Grade Quarter 2 Curriculum Map Unit 3: Integers and Rational Numbers 2 nd 9 Weeks Suggested Instructional Days: 38 Unit Summary (Learning Target/Goal): Apply and extend pervious understandings of numbers to the system of rational numbers. CCSS for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others. Unit Timeline Standards Learning Expectation & Vocabulary Resources Integers and Rational Numbers Apply and extend pervious understandings of numbers to the system of rational numbers. 3-4 days 6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. To understand absolute value/ordering- use inequalities to express the relationship between two rational numbers, understanding that the value of numbers is smaller moving to the left on a number line -7 < -5 As you move left of the number line, the numbers become smaller in value. As you move right of the number line, the numbers become greater in value. -7 is to the left of -5. This means that -7 < -5. Inequality Rational numbers Absolute value Integers Plot Opposites Negative Positive days 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. To interpret absolute value/ordering- write statements using < or > to compare rational number in context. Explanations should inequality rational numbers th Grade Math Quarter 2 1

2 6 th Grade Quarter 2 Curriculum Map reference the context rather than less than or greater than s A meteorologist recorded temperatures in four cities around the world. List these cities in order from coldest temperature to warmest temperature: Albany 5 Anchorage -6 Buffalo -7 Juneau -9 Reno 12 Solution: Juneau -9 Buffalo -7 Anchorage -6 Albany 5 Reno 12 absolute value integers plot opposites negative positive greater than less than equal to greater than or equal to less than or equal to days 6NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. Write 3 o C > 7 o C to express the fact that 3 o C is warmer than 7 o C. Understand absolute value as the distance from zero and recognize the symbols as representing absolute value For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. : Which numbers have an absolute value of 7 Solution: 7 and 7 since both numbers have a distance of 7 units from 0 on the number absolute value integers opposites negative/positive th Grade Math Quarter 2 2

3 6 th Grade Quarter 2 Curriculum Map days 6.NS.7d Distinguish comparisons of absolute value from statements about order. line. To compare absolute values the absolute value (distance from zero) of the number and the value of the number is the same; therefore, ordering is not problematic. However, negative numbers have a distinction that students need to understand. As the negative number increases (moves to the left on a number line), the value of the number decreases. For example, 24 is less than 14 because 24 is located to the left of 14 on the number line. However, absolute value is the distance from zero. In terms of absolute value (or distance) the absolute value of 24 is greater than the absolute value of 14. For negative numbers, as the absolute value increases, the value of the negative number decreases. absolute value compare greater than less than equal to 6-5 Begin by figuring out the value of x. x = -4 x is 4 away from 0. The absolute value of x is 4. Alternate Explanation: x = -4 Since -4 is negative, we know that x = -x. This means x = -4 = days 6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only To understand ordered pairs. Coordinate plane 4 quadrants Vertical Horizontal 7-2 Lab 7-2a 6 th Grade Math Quarter 2 3

4 6 th Grade Quarter 2 Curriculum Map by signs, the locations of the points are related by reflections across one or both axes. Enter the coordinates of each point as an ordered pair A: (4, -5) B: (1, -1) C: (5, 5) D: (5, -1) x-axis y-axis reflections ordered pair origin 3-4 days 6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 3-5 days 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. To position integers on a coordinate plane Integers Rational numbers 4 quadrants Vertical Horizontal x-axis y-axis Ordered pairs Origin Lab 7-1a To graph points in all quadrants 4 quadrants Plotting Ordered Pairs Coordinate Absolute Value th Grade Math Quarter 2 4

5 6 th Grade Quarter 2 Curriculum Map Find the length of the line segment. Length 4 units. Unit 4: Expressions & Equations 2nd 9 Weeks Suggested Instructional Days: 18 Unit Summary (Learning Target/Goal): Apply and extend previous understandings of arithmetic to algebraic expressions. Unit Timeline Standards Learning Expectation & Vocabulary Resources Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 2-3 days 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 3-5 days 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. Translate exponents into an equivalent multiplication sentence 3 2 is '3*3'. 19*19*19 is 6859 Write expressions with letters standing for numbers A number, x, decreased by the sum of 2x and 5 The product of twenty-seven and r is less Numerical expression Exponents Evaluate Represent Nth design/degree Variable Algebraic expression Value Math operations/functions variable numerical expression exponents evaluate represent nth design/degree Lab 2-2a 6 th Grade Math Quarter 2 5

6 6 th Grade Quarter 2 Curriculum Map days 6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. 5-7 days 6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations) than negative thirty-six times -47 = 27r < - 36(-47) Identify parts of an expression using mathematical terms Identify the underlined part. -9v + 34b + -96w + -4 = -285 Term 96b + 82s + -71f + 70f + 92 = equation Students evaluate algebraic expressions, using order of operations as needed. s Use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Evaluate the expression 3x + 2y when x is equal to 4 and y is equal to 2.4. Solution: The cost to rent a skating rink is $100 plus $5 per person. Write an expression variable algebraic expression value math operations/functions coefficient single entity term variable numerical expression exponents evaluate represent factor constant infinite numerical expression algebraic expression variable evaluate Lab 2-2a th Grade Math Quarter 2 6

7 6 th Grade Quarter 2 Curriculum Map days 6.EE.3: Apply the properties of operations to generate equivalent expressions. to find the cost for any number (n) of people. What is the cost for 25 people? Solution: The cost for any number (n) of people could be found by the expression, n. To find the cost of 25 people substitute 25 in for n and solve to get * 25 = 225. Understand the distributive property and use to write equivalent expressions. s Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 4(2a - 1) = Distribute 4 across 2a - 1 => 4(2a) = = 4 Formative Assessment Lesson: Laws of Arithmetic INTERIM ASSESSMENT 2: DECEMBER 9-13 REFLECTION/NOTES: distributive property properties of equality -addition -subtraction -multiplication -division equivalent expression distribute produce th Grade Math Quarter 2 7

8 6 th Grade Quarter 2 Curriculum Map LCPS 6 th Grade Math Unit Plan Quarter: 2 nd Suggested #of Days for Unit: 20 days Grade Level: 6th Domain Focus Area(s): Number Systems Essential Question and/or Learning Targets: Write, explain, and interpret statements involving rational numbers. Apply previous understandings of numbers to the system of rational numbers Assessment Strategies: (How will the students and I know when they are successful?) Pre-Assessment: Teacher created assessment Formative Assessment: CFA 2 nd quarter-test 1 Summative Assessment: Discovery interim assessment Learning Experiences: (What learning experiences will facilitate their success?) Activities/Lesson Depth of Knowledge Instructional Strategies Differentaited Instruction (Sped, CCSS Standards: (What should students know and be able to do?) 6.NS.6 thru 6.NS.8 Academic Vocabulary: Inequality Plotting Rational numbers Absolute value Integers Plot Negative Positive Opposites Greater than Less than Equal to Greater than or equal to Less than or equal to Coordinate plane Compare 4 quadrants Vertical Horizontal x-axis y-axis reflections ordered pair origin Mathematical Practices Addressed: X Make sense of problems and 6 th Grade Math Quarter 2 8

9 6 th Grade Quarter 2 Curriculum Map Math Snacks Video- DOK 1 Number Rights Math Snacks game-pearl DOK 3 diver Math Snacks-Gate DOK 3 Game Over Gopher-Math DOK 2 Snacks Lessons 6-1 thru 6-4 DOK 2 Teacher Notes: What was successful? What will you add/change/delete next time? Gifted, ELL) X Reason abstractly and Construct viable arguments/critique the reasoning of others X Model with mathematics X Use appropriate tools strategically X Attend to precision X Look for and make use of X Look for and express regularity in 6 th Grade Math Quarter 2 9

10 6 th Grade Quarter 2 Curriculum Map LCPS 6-12 Grade Math Unit Plan Quarter: 2 nd Suggested #of Days for Unit: 18 days Grade Level: 6th Domain Focus Area(s): Expressions and Equations Essential Question and/or Learning Targets: Write, identify, and evaluate expressions and equations and apply the properties of operations to generate equivalent expressions. Assessment Strategies: (How will the students and I know when they are successful?) Pre-Assessment: Teacher created assessment Formative Assessment: CFA 2 nd quarter-test 2 Summative Assessment: Discovery interim assessment CCSS Standards: (What should students know and be able to do?) 6.EE.1 thru 6.EE.3 Academic Vocabulary: Numerical expression Exponents Evaluate Represent Nth design/degree Variable Algebraic expression Value Math operations/functions Coefficient Single entity Term Factor Constant Infinite Propoerties of equality -addition -subtraction -multiplication -division 6 th Grade Math Quarter 2 10

11 6 th Grade Quarter 2 Curriculum Map Distribute Learning Experiences: (What learning experiences will facilitate their success?) Activities/Lesson Depth of Knowledge Lab 2-2a DOK 2-3 Lesson 2-2 DOK 2 Lesson 3-2 DOK 2 Lesson 3-7 DOK 2-3 Instructional Strategies Differentaited Instruction (Sped, Gifted, ELL) Mathematical Practices Addressed: X Make sense of problems and persevere in solving them X Reason abstractly and Construct viable arguments/critique the reasoning of others X Model with mathematics X Use appropriate tools strategically X Attend to precision X Look for and make use of X Look for and express regularity in repeated reasoning Teacher Notes: What was successful? What will you add/change/delete next time? 6 th Grade Math Quarter 2 11

12 6 th Grade Quarter 2 Curriculum Map th Grade Math Quarter 2 12