6th grade math quarter 2 curriculum...

6th Grade Mathematics Quarter 2 Curriculum Map 2013-2014

6th Grade Math Quarter 2

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Unit 3: Integers and Rational Numbers 2nd 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: 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 mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Unit Timeline Standards Learning Expectation & Example 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. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

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 Example -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

Prentice Hall Mathematics 6-2 6-4

3-5 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

Prentice Hall Mathematics 6-3



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Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

reference the context rather than “less than” or “greater than” Examples 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° Write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.

absolute value

integers

plot

opposites

negative

positive

greater than

less than

equal to

greater than or equal to less than or equal to

6-4

2-3 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. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure

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. Example: 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




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8. Look for and express regularity in repeated reasoning

line.

3-5 days 6.NS.7d Distinguish comparisons of absolute value from statements about order.

Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

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. Example

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 | = 4.

absolute value

compare

greater than

less than

equal to


3-5 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. Example

Coordinate plane 4 quadrants Vertical Horizontal

Prentice Hall Mathematics 7-2 Lab 7-2a



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by signs, the locations of the points are related by reflections across one or both axes. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

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. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

To position integers on a coordinate plane Example

Integers Rational numbers 4 quadrants Vertical Horizontal x-axis y-axis Ordered pairs Origin

Prentice Hall Mathematics 6-1 6-2 6-4 7-1 Lab 7-1a

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 graph points in all quadrants

4 quadrants Plotting Ordered Pairs Coordinate Absolute Value

Prentice Hall Mathematics 7-1 7-2



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Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

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 & Example 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. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Translate exponents into an equivalent multiplication sentence Example 32 is '3*3'. 19*19*19 is 6859

Numerical expression Exponents Evaluate Represent Nth design/degree Variable Algebraic expression Value Math operations/functions


3-5 days 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively

Write expressions with letters standing for numbers Example A number, x, decreased by the sum of 2x and 5 The product of twenty-seven and r is less

variable numerical expression exponents evaluate represent nth design/degree

Prentice Hall Mathematics 2-2 Lab 2-2a



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4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

than negative thirty-six times -47 = 27r < -36(-47)

variable algebraic expression value math operations/functions

5-7 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. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Identify parts of an expression using mathematical terms Example Identify the underlined part. -9v + 34b + -96w + -4 = -285 Term 96b + 82s + -71f + 70f + 92 = -250 equation

coefficient single entity term variable numerical expression exponents evaluate represent factor constant infinite

Prentice Hall Mathematics 1-1 1-2 1-5 1-6 2-2 3-6 3-7 Lab 2-2a

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) Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in

Students evaluate algebraic expressions, using order of operations as needed. Examples Use the formulas V = s3 and A = 6 s2 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: 3 • 4 + 2 • 2.4 12 + 4.8 16.8 The cost to rent a skating rink is $100 plus $5 per person. Write an expression

numerical expression algebraic expression variable evaluate

Prentice Hall Mathematics 1-2 2-1 3-2



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repeated reasoning 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, 100 + 5n. To find the cost of 25 people substitute 25 in for n and solve to get 100 + 5 * 25 = 225.

3-5 days 6.EE.3: Apply the properties of operations to generate equivalent expressions. Math practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Understand the distributive property and use to write equivalent expressions. Examples 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 × 1 4 × 2 = 8 4 × 1 = 4

distributive property properties of equality -addition -subtraction -multiplication -division equivalent expression distribute produce

Prentice Hall Mathematics 1-1 3-6 3-7

Formative Assessment Lesson: Laws of Arithmetic http://map.mathshell.org/materials/lessons.php?taskid=484&subpage=concept

INTERIM ASSESSMENT 2: DECEMBER 9-13 REFLECTION/NOTES:



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LCPS 6th Grade Math Unit Plan Quarter: 2nd

Suggested #of Days for Unit: 20 days Grade Level: 6th

Domain Focus Area(s): Number Systems CCSS Standards: (What should students know and be able to do?)

6.NS.6 thru 6.NS.8 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 2nd quarter-test 1

Summative Assessment: Discovery interim assessment

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

Learning Experiences: (What learning experiences will facilitate their success?) Mathematical Practices Addressed: X Make sense of problems and persevere in solving them Activities/Lesson Depth of

Knowledge Instructional Strategies

Differentaited Instruction (Sped,



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Gifted, ELL) X Reason abstractly and quantitatively

□ 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 structure

X Look for and express regularity in repeated reasoning

Math Snacks Video-Number Rights

DOK 1

Math Snacks game-pearl diver

DOK 3

Math Snacks-Gate DOK 3 Game Over Gopher-Math Snacks

DOK 2

Lessons 6-1 thru 6-4 DOK 2

Teacher Notes: What was successful? What will you add/change/delete next time?



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LCPS 6-12 Grade Math Unit Plan Quarter: 2nd

Suggested #of Days for Unit: 18 days Grade Level: 6th

Domain Focus Area(s): Expressions and Equations CCSS Standards: (What should students know and be able to do?) 6.EE.1 thru 6.EE.3

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 2nd quarter-test 2 Summative Assessment: Discovery interim assessment

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



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Distribute

Learning Experiences: (What learning experiences will facilitate their success?) Mathematical Practices Addressed: X Make sense of problems and persevere in solving them X Reason abstractly and quantitatively □ 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 structure X Look for and express regularity in repeated reasoning

Activities/Lesson Depth of Knowledge

Instructional Strategies

Differentaited Instruction (Sped, Gifted, ELL)

Lab 2-2a DOK 2-3 Lesson 2-2 DOK 2 Lesson 3-2 DOK 2 Lesson 3-7 DOK 2-3

Teacher Notes: What was successful? What will you add/change/delete next time?



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6th grade math quarter 2 curriculum...

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