Download 6th-Grade-Math

6th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
2nd 9 Weeks
Unit 3: Integers and Rational Numbers
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
3-4 days
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
Integers and Rational
Numbers
Apply and extend
pervious understandings
of numbers to the system
of rational numbers.
3-5 days
Standards
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.
6.NS.7b Write, interpret, and
explain statements of order for
rational numbers in real-world
contexts.
Learning Expectation & Example
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
Vocabulary
Inequality
Rational numbers
Absolute value
Integers
Plot
Opposites
Negative
Positive
Resources
Prentice Hall
Mathematics
6-2
6-4
inequality
Prentice Hall
Mathematics
6-3
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.
To interpret absolute value/ordering- write
statements using < or > to compare rational
number in context. Explanations should
rational numbers
6th Grade Math Quarter 2
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2013-2014
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”
absolute value
Examples
plot
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°
6-4
integers
opposites
negative
positive
greater than
less than
equal to
greater than or equal
to
less than or equal to
Write –3 oC > –7 oC to express the fact that
–3 oC is warmer than –7 oC.
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.
Understand absolute value as the
distance from zero and recognize the
symbols | | as representing absolute
value
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
For example, for an account balance of –30
dollars, write |–30| = 30 to describe the size
of the debt in dollars.
absolute value
integers
Prentice Hall
Mathematics
6-1
opposites
negative/positive
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
6th Grade Math Quarter 2
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2013-2014
3-5 days
8. Look for and express regularity in
repeated reasoning
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
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
Prentice Hall
Mathematics
6-5
greater than
less than
equal to
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.
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
Coordinate plane
4 quadrants
Vertical
Horizontal
To understand ordered pairs.
Example
Prentice Hall
Mathematics
7-2
Lab 7-2a
6th Grade Math Quarter 2
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2013-2014
x-axis
y-axis
reflections
ordered pair
origin
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
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.
Enter the coordinates of each point as an ordered
pair A: (4, -5) B: (1, -1) C: (5, 5) D: (5, -1)
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
To graph points in all quadrants
4 quadrants
Plotting
Ordered Pairs
Coordinate
Absolute Value
Prentice Hall
Mathematics
7-1
7-2
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
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.
6th Grade Math Quarter 2
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2013-2014
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.
Suggested Instructional Days: 18 2nd 9 Weeks
Unit Summary (Learning Target/Goal): Apply and extend previous understandings of arithmetic to algebraic expressions.
Unit
Timeline
Standards
Learning Expectation & Example
Vocabulary
Resources
6.EE.1 Write and evaluate numerical Translate exponents into an equivalent
2-3 days
Numerical expression Prentice Hall
expressions involving whole-number
multiplication sentence
Exponents
Mathematics
exponents.
Example
Evaluate
3-2
Math practices:
Represent
1. Make sense of problems and
32 is '3*3'.
persevere in solving them
Nth design/degree
19*19*19 is 6859
2. Reason abstractly and
Variable
quantitatively
Expressions &
Algebraic expression
4. Model with mathematics
Equations
Value
5. Use appropriate tools strategically
6. Attend to precision
Math
Apply and extend
7. Look for and make use of
operations/functions
structure
previous understandings
8. Look for and express regularity in
of arithmetic to algebraic
repeated reasoning
expressions.
6.EE.2a Write expressions that
3-5 days
Write expressions with letters standing for
Prentice Hall
variable
record operations with numbers and
numbers
Mathematics
numerical
expression
with letters standing for numbers.
2-2
exponents
Example
Lab 2-2a
Math practices:
evaluate
1. Make sense of problems and
A number, x, decreased by the sum of 2x
represent
persevere in solving them
and 5
2. Reason abstractly and
nth design/degree
The product of twenty-seven and r is less
Unit 4: Expressions & Equations
quantitatively
6th Grade Math Quarter 2
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2013-2014
5-7 days
5-7 days
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
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.
than negative thirty-six times -47 = 27r < 36(-47)
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
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)
-9v + 34b + -96w + -4 = -285 Term
96b + 82s + -71f + 70f + 92 = 250 equation
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
Identify parts of an expression using
mathematical terms
Example
Identify the underlined part.
Students evaluate algebraic expressions,
using order of operations as needed.
Examples
variable
algebraic expression
value
math
operations/functions
coefficient
single entity
term
variable
numerical expression
exponents
evaluate
represent
factor
constant
infinite
numerical expression
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
algebraic expression
variable
Prentice Hall
Mathematics
1-1
1-2
1-5
1-6
2-2
3-6
3-7
Lab 2-2a
Prentice Hall
Mathematics
1-2
2-1
3-2
evaluate
The cost to rent a skating rink is $100
plus $5 per person. Write an expression
6th Grade Math Quarter 2
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2013-2014
repeated reasoning
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
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.
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.
distributive property
properties of equality
-addition
-subtraction
-multiplication
-division
equivalent expression
distribute
produce
Prentice Hall
Mathematics
1-1
3-6
3-7
4(2a - 1) =
Distribute 4 across 2a - 1 => 4(2a) - 4 × 1
4×2=8
4×1=4
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:
6th Grade Math Quarter 2
7 6th Grade Mathematics Quarter 2 Curriculum Map
LCPS 6th Grade Math Unit Plan
Suggested #of Days for Unit: 20 days
nd
Quarter: 2
Domain Focus Area(s):
2013-2014
CCSS Standards: (What should students know and be
Number Systems
able to do?)
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:
Grade Level: 6th
Teacher created assessment
Formative Assessment:
CFA 2nd quarter-test 1
Summative Assessment:
Discovery interim assessment
6.NS.6 thru 6.NS.8
Academic Vocabulary:
Inequality
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
Plotting
Learning Experiences: (What learning experiences will facilitate their success?)
Mathematical Practices Addressed:
Activities/Lesson
X Make sense of problems and persevere in solving them
Depth of
Knowledge
Instructional
Strategies
Differentaited
Instruction (Sped,
6th Grade Math Quarter 2
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2013-2014
Gifted, ELL)
Math Snacks VideoNumber Rights
Math Snacks game-pearl
diver
Math Snacks-Gate
Game Over Gopher-Math
Snacks
Lessons 6-1 thru 6-4
X Reason abstractly and quantitatively
□ Construct viable arguments/critique the reasoning of others
DOK 1
X Model with mathematics
DOK 3
X Use appropriate tools strategically
DOK 3
DOK 2
X Attend to precision
DOK 2
X Look for and express regularity in repeated reasoning
X Look for and make use of structure
Teacher Notes:
What was successful? What will you add/change/delete next time?
6th Grade Math Quarter 2
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2013-2014
LCPS 6-12 Grade Math Unit Plan
Suggested #of Days for Unit: 18 days
Quarter: 2nd
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 2nd quarter-test 2
Summative Assessment:
Discovery interim assessment
Grade Level: 6th
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
6th Grade Math Quarter 2
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2013-2014
Distribute
Learning Experiences: (What learning experiences will facilitate their success?)
Activities/Lesson
Depth of
Instructional
Differentaited
Knowledge
Strategies
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
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
Teacher Notes:
What was successful? What will you add/change/delete next time?
6th Grade Math Quarter 2
11 6th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
6th Grade Math Quarter 2
12