Download Pacing Guide - 6th Grade Math 2nd 9 wks(in progress)

Ocean Springs School District 6th Grade – 2nd 9 Weeks Instructional Map
Common Core Standard
Topic
6
Standard
Expectations(s)
Students will be able
to
Clarity of the Standard
Vocabulary
Example:
Jason thinks that ¾ and .34 are equivalent. Is he correct? Explain why or why
not.
Proper fraction
Improper fraction
Mixed number
Termination decimal
Repeating decimal
Resources
Mathematical
Practices
Suggested
number of
days
Decimals,
Fractions, and
Mixed Numbers
6.NS.3
Fluently add, subtract,
multiply, and divide multi-digit
decimals using the standard
algorithm for each operation.
Additional
cluster
I Can:
6.NS.3 Fluently add
multi-digit decimal
numbers.
6.NS.3 Fluently
subtract multi-digit
decimal numbers.
6.NS.3 Fluently
multiply multi-digit
decimal numbers.
6.NS.3 Fluently
divide multi-digit
decimal numbers.
Example:
enVision
(TopicSection)
6-1
Circle all of the following that are equivalent to 37 divided by 5
A. 7.2
B. 7
2
5
C.
37
5
D. .01
6-2
E. 7.4
6-3
6-4
6.MP.2. Reason
abstractly and
quantitatively.
6.MP.7. Look for
and make use of
structure.
6.MP.8. Look for
and express
regularity in
repeated
reasoning.
Topic
6
7 days
6-5
Topic 7: Adding and
Subtracting Fractions and
Mixed Numbers
6.NS.4
Find the greatest common
factor of two whole numbers
less than or equal to 100 and
the least common multiple of
two whole numbers less than
I Can:
Example 1:
What is the least common multiple (LCM) of 18 and 24?
6.NS.4 Determine
the greatest common Example 2: Mr. Barrett’s class made a banner that is 6 ½ feet long and Ms.
factor (GCF) of two
Like Denominators
Common Multiples
Least Common
Multiple
Unlike Denominators
Least Common
Denominators
7-1
7-2
6.MP.1. Make
sense of
problems and
persevere in
solving them.
Topic
7
8 days
or equal to 12. Use the
distributive property to
express a sum of two whole
numbers 1–100 with a
common factor as a multiple
of a sum of two whole
numbers with no common
factor. For example, express
36 + 8 as 4 (9 + 2).
Additional
cluster
numbers less than or Alvarend’s class made a banner that is 7 1 feet long . How much longer is Ms.
5
equal to 100.
Alvarend’s banner?
6.NS.4 Justify the
LCM of two whole
numbers using math.
6.NS.4 Prove that
two whole numbers
have a common
factor based on the
distributive property.
7-3
7-4
7-5
7-6
6.MP.2. Reason
abstractly and
quantitatively
.
6.MP.3. Construct
viable arguments
and critique the
reasoning of
others.
6.MP.4. Model
with mathematics.
6.MP.6. Attend to
precision
6.RP.1
Understand the concept
of a
ratio and use ratio
language to describe
a ratio relationship
between two
quantities.
MAJOR
cluster
Example :
I Can:
6.RP.1 Write a ratio
to describe a
situation.
6.RP.1 Write a ratio
a
as a to b, , or
b
a:b. or describe it in
words.
A ratio is a comparison of two quantities which can be written as
a to b,
a
, or a:b.
b
A rate is a ratio where two measurements are related to each other. When
discussing measurement of different units, the word rate is used rather than
ratio. Understanding rate, however, is complicated and there is no universally
accepted definition. When using the term rate, contextual understanding is
critical. Students need many opportunities to use models to demonstrate the
relationships between quantities before they are expected to work with rates
numerically.
A comparison of 8 black circles to 4 white circles can be written as the ratio of
8:4 and can be regrouped into 4 black circles to 2 white circles (4:2) and 2 black
circles to 1 white circle (2:1).
7-7
6.MP.2. Reason
abstractly and
quantitatively
.
6.MP.6. Attend to
precision
Students should be able to identify all these ratios and describe them using “For
every…., there are …”
Topic 8: Multiplying
Fractions and Mixed
Numbers
This topic does not
have any 6th grade
CCSS as its focus.
It is taught as
preparation for
Topic 9 and reviews
multiplication of
fractions and
estimation.
I Can:
Fluently multiply
common fractions.
Fluently multiply
common fractions
with whole numbers.
8-1
Example 1: Eric says that if you multiply a whole number by a fraction, you get
something smaller than the whole number you started with.
a. Give an example that supports Eric’s statement.
b. Give an example that disproves Eric’s statement.
c. Explain what kind of fraction will always make his statement true.
8-2
8-3
8-4
Fluently change
mixed numbers into
improper fractions.
8-5
6.MP.2. Reason
abstractly and
quantitatively
.
6.MP.3. Construct
viable arguments
and critique the
reasoning of
others.
Topic
8
5 days
6.MP.7. Look for
and make use of
structure.
I can estimate
fractional products.
Topic 9: Dividing Fractions
and Mixed Numbers
6.NS.1
Apply the properties of
operations to generate
equivalent expressions. For
example, apply the
distributive property to the
expression 3 (2 + x) to
produce the equivalent
1
I Can:
6.EE.3 Apply the
properties of
operations to
generate equivalent
expressions.
1
Example 1 1 4 cups of nuts fill 2 of the container. How many cups fill it
entirely?
Common Misconception: Students may believe that dividing by ½ is the same
as dividing in half. Dividing by half means to find how many one-halves
there are in a quantity. Dividing in half means to take a quantity and split
it into two equal parts. Thus 7 divided by ½ = 14 and 7 divided in half
equals 3½.
Reciprocals
9-1
9-2
9-3
6.MP.2. Reason
abstractly and
quantitatively.
6.MP.3. Construct
viable arguments
and critique the
reasoning of
Topic
9
7 days
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.
MAJOR
cluster
6.EE.7
Solve real-world and
mathematical problems by
writing and solving equations
of the form x + p = q and px =
q for cases in which p, q and
x are all nonnegative rational
numbers.
MAJOR
cluster
6.NS.6
Identify when two
expressions are equivalent
(i.e., when the two
expressions name the same
others.
Students also write contextual problems for fraction division problems. For
2
1
example, the problem,
÷
can be illustrated with the following g word
3
6
problem:
2
1
Susan has of an hour left to make cards. It takes her about of an hour to
3
6
make each card. About how many can she make?
9-4
9-5
6.MP.4. Model
with mathematics.
6.MP.6. Attend to
precision.
6.MP.7. Look for
and make use of
structure.
I Can:
6.EE.7 Write an
equation from realworld situations and
then use inverse
operations to solve
the equation.
6.EE.7 Write and
solve equations of
the form x+p and
px=q (in which p,q,
and x are nonnegative rational
numbers)
I Can:
6.NS.2 Apply the
rules of division to
solve multi-digit
Students also write contextual problems for fraction division problems. For
2
1
example, the problem,
÷
can be illustrated with the following g word
3
6
problem:
2
1
Susan has of an hour left to make cards. It takes her about of an hour to
3
6
make each card. About how many can she make?
9-6
7
6.MP.1. Make
sense of
problems and
persevere in
solving them.
6.MP.2. Reason
abstractly and
quantitatively.
Solve for n: n = 42
6
6.MP.4. Model
with mathematics.
Find the pattern in this set of numbers and find the next number:
13, 11
2
3
1
, 10 , 9, ____
3
9-7
6.MP.3. Construct
viable arguments
and critique the
reasoning of
number regardless of which
value is substituted into
them). For example, the
expressions y + y + y and 3y
are equivalent because they
name the same number
regardless of which number y
stands for
problems.
others.
6.MP.7. Look for
and make use of
structure.
6.MP.8. Look for
and express
regularity in
repeated
reasoning.
MAJOR
cluster
Topic 10: Number and
Fraction Concepts
6.NS.5
.
Understand
that positive and
negative numbers are
used together to
describe quantities
having opposite
directions or values
6. NS. 6a
a. Recognize opposite
signs of numbers as
indicating locations on
opposite sides of 0 on
the number line;
recognize that the
opposite of the
opposite of a number is
the number itself,
I Can:
6.NS.5 Understand
that positives and
negatives represent
opposites.
6.NS.7c Define and
identify absolute
value.
6.NS.7c Use a
number line to find
the absolute value of
any number.
6.NS.7c Understand
absolute value as
the distance from
zero on the number
line
5. For example, 25 feet below sea level can be represented as -25; 25 feet above sea level
can be represented as + 25 and zero would be sea level
Example: Write a real-life example of each of the following numbers:
-13
+72
-26
6a. Students recognize that a number and its opposite are
equidistant from zero (reflections about the zero). The opposite sign (–) shifts the
number to the opposite side of 0.
Opposites
Integers
Absolute Value
10-1
6.MP.1. Make
sense of
problems and
persevere in
solving them.
6.MP.2. Reason
abstractly and
quantitatively.
6.MP.4. Model
with mathematics.
For example, – 4 could be read as “the opposite of 4” which
would be negative 4. In the example, – (–6.4) would be read as
Topic
10
10
days
e.g.,
– (–3) = 3, and that 0
is its own opposite
6.NS.7.c
Understand the absolute
value of a rational
number as its distance
from 0 on the number
line; interpret
absolute as magnitude
for a positive or
negative quantity in a
real-world situation.
6.NS.7c Apply
absolute value to
real world situations.
6.NS.7c Recognize
the symbol \\ as
representing
absolute value
Example: What is the opposite of 2 ½ ? Explain your answer.
Solution:- 2 ½ because it is the same distance from 0 on the
opposite side.
7c. For example, for an account balance of –30 dollars, write |–30| = 30
to describe the size of the debt in dollars.
Example 1:
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 line.
All
are
MAJOR
clusters
6. NS. 7
“the opposite of the opposite of 6.4” which would be 6.4. Zero
is its own opposite.
In real-world contexts, the absolute value can be used to
describe size or magnitude. For example, for an ocean depth of
900 feet, write | –900| = 900 to describe the distance below sea
level.
I Can:
6.NS.7 Students use inequalities to express the relationship
Understand ordering and 6.NS.7a. Compare
between two rational numbers, understanding that the value of
absolute value of
negative and positive numbers is smaller moving to the left on a number line. Common
rational numbers.
numbers
models to represent and compare integers include number line
a. Interpret statements 6.NS.7a Understand
models, temperature models and the profit-loss model. On a number
of inequality as
ordering or rational
line model, the number is represented by an arrow drawn from zero
statements about the
numbers
to the location of the number on the number line; the absolute
6.NS.7a Order
relative position of
value is the length of this arrow. The number line can also be
two numbers on a number rational numbers on
viewed as a thermometer where each point of on the number line is
a number line
line.
a specific temperature. In the profit-loss model, a positive
b. Write, interpret, and
number corresponds to profit and the negative number corresponds
10-2
6.MP.1. Make
sense of
problems and
persevere in
solving them.
6.MP.2. Reason
abstractly and
quantitatively.
6.MP.3. Construct
viable arguments
explain statements of
order for rational
numbers in real-world
contexts
MAJOR
clusters
6.NS.7b Write an
inequality to show
the relationship
between rational
numbers in real
world situations.
6.NS.7b Explain in
my own words how
to compare rational
numbers (written or
spoken)
to a loss. Each of these models is useful for examining values
but can also be used in later grades when students begin to
perform operations on integers.
and critique the
reasoning of
others.
a. Example :Write a statement to compare – 4 . and –2.
Explain your answer.
Solution: – 4 . < –2 because – 4
. is located to the left of –2 on the number line
Operations with integers are not the expectation at this level.
In working with number line models, students internalize the
order of the numbers; larger numbers on the right of the number
line and smaller numbers to the left. They use the order to
correctly locate integers and other rational numbers on the
number line. By placing two numbers on the same number line, they
are able to write inequalities and make statements about the
relationships between two numbers
6. MP.5 Use
appropriate tools
strategically.
b. 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
Example :The balance in Sue’s checkbook was –$12.55.
The balance in John’s checkbook was –$10.45. Write an inequality
to show the relationship between these amounts. Who owes more?
Example : 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°
6. NS.6c
Find and position
integers and other
rational numbers on a
horizontal line
Rational Number
I Can:
6.NS.6 Plot all
integers and other
6.NS.6 In elementary school, students worked with positive
fractions, decimals and whole numbers on the number line and in
quadrant 1 of the coordinate plane. In 6th grade, students extend
the number line to represent all rational numbers and recognize
10-3
6.MP.1. Make
sense of
problems and
persevere in
solving them.
diagram.
MAJOR
cluster
rational numbers on
number lines
6.NS.6 Order
rational numbers on
a number line
horizontally
6.MP.2. Reason
abstractly and
quantitatively.
that number lines may be either horizontal or vertical (which
facilitates the movement from number lines to coordinate grids.
Students recognize that a number and its opposite are
equidistant from zero (reflections about the zero). The opposite
sign (–) shifts the number to the opposite side of 0.
6.MP.3. Construct
viable arguments
and critique the
reasoning of
others.
6c. Students place the following numbers would be on a number
line:
3
11
–4.5, 2, 3.2, –35 , 0.2, –2, 2
6. MP.5 Use
appropriate tools
strategically.
8. Look for and
express regularity
in repeated
reasoning.
Sections 10-4, 10-5, 10-6, 10-7 WILL NOT be taught.
Please skip to Section 10-8
6.NS. 7d
Distinguish
comparisons of absolute
value from statements
about order.
I Can:
6.NS.7d
Distinguish
comparisons of
absolute value by
When working with positive numbers, 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.
10-8
6.MP.2. Reason
abstractly and
quantitatively.
6.MP.3. Construct
viable arguments
MAJOR
cluster
6. NS. 6b
6. NS.6c
b. Understand signs of
numbers in ordered
pairs as indicating
locations in quadrants
of the
coordinate plane;
recognize that when two
ordered pairs differ
only by signs, the
locations of the points
are related by
reflections
across one or both
axes.
c. Find and position
integers and other
rational numbers on a
horizontal or vertical
number line
statements of
order.
6.NS.7d
Understand that
absolute value
deals only with
distance from zero
(regular whole
numbers are their
true values)
I Can:
6.NS.6c Plot all
integers and other
rational numbers
on coordinate
planes
6.NS.6c Find the
position of integer
pairs and other
rational numbers
on a coordinate
plane.
6.NS.8 Graph
points in all four
quadrants of the
coordinate plane.
6.NS.8 Solve realworld problems by
and critique the
reasoning of
others.
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.
6. MP.5 Use
appropriate tools
strategically.
For example, recognize that an account balance less than –30 dollars
represents a debt greater than 30dollars.
6. MP.6 Attend to
precision.
Students worked with Quadrant I in elementary school. As the xaxis and y-axis are extending to include negatives, students
begin to with the Cartesian Coordinate system. Students recognize
the point where the x-axis and y-axis intersect as the origin.
Students identify the four quadrants and are able to identify the
quadrant for an ordered pair based on the signs of the
coordinates. For example, students recognize that in Quadrant II,
the signs of all ordered pairs would be (–, +).
Students understand the relationship between two ordered pairs
differing only by signs as reflections across one or both axes.
For example, in the ordered pairs (-2, 4) and (-2, -4), the ycoordinates differ only by signs, which represents a reflection
across the x-axis. A change is the x-coordinates from (-2, 4) to
(2, 4), represents a reflection across the y-axis. When the signs
of both coordinates change, [(2, -4) changes to (-2, 4)], the
ordered pair has been reflected across both axes.
Example1:
Graph the following points in the correct quadrant of the
coordinate plane.
( ½ , -3½ )
( - ½ , -3)
(0.25, 0.75)
Coordinate Plane
x-axis
y-axis
Quadrant
Ordered Pair
Origin
10-9
6.MP.1 Make
sense of
problems and
persevere in
solving them.
6.MP.2. Reason
abstractly and
quantitatively.
6. MP.6 Attend to
precision.
6.MP.7 Look for
and make use of
structure.
diagram; find and
position pairs of
integers and other
rational numbers on a
coordinate plane
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.
graphing points in
all four quadrants of
a plane(maps,
shapes, pictures)
6.NS.8 Solve
mathematical
problems by
graphing points in
all four quadrants of
a plane (maps,
shapes, pictures)
6.NS.8 Calculate
distances between
two points with the
same first or second
coordinates using
absolute values,
given only
coordinates.
If the points are reflected across the x-axis, what are the
coordinates of the reflected points? What similarities are
between coordinates of the original
point and the reflected point?
6. NS.8
Example 1:
What is the distance between (–5, 2) and (–9, 2)?
All
are
MAJOR
clusters
6. G.3
G.3 Draw polygons in
the coordinate plane
given coordinates for
the vertices; use
I Can:
6.G.3 Draw
polygons on a
coordinate plane
6.G.3 Students are given the coordinates of polygons to draw in
the coordinate plane. If both x-coordinates are the same (2, -1)
and (2, 4), then students recognize that a vertical line has been
created and the distance between these coordinates is the
distance between -1 and 4, or 5. If both the y-coordinates are
Perimeter
10-10
coordinates to find the
length of a side
joining points with the
same first coordinate
or the same second
coordinate. Apply these
techniques in the
context of solving
real-world and
mathematical problems.
ADDITIONAL cluster
given coordinates for
the vertices
6.G.3 Evaluate the
length of polygons
by using grid
models.
6.G.3 Determine the
length of the sides of
polygons in a
coordinate plane
given the same first
or second
coordinate.
6.G.3 Apply the
technique of using
coordinate planes
to find the length
of the side of
polygons in realworld situations.
the same (-5, 4) and (2, 4), then students recognize that a
horizontal line has been created and the distance between these
coordinates is the distance between -5 and 2, or 7. Using this
understanding, student solve real-world and mathematical
problems, including finding the area and perimeter of geometric
figures drawn on a coordinate plane.
Example 1:If the points on the coordinate plane below are the
three vertices of a rectangle, what are the coordinates of the
fourth vertex? How do you know? What are the length and width of
the rectangle? Find the perimeter of the rectangle.
Solution:
To determine the distance along the x-axis between the point (-4,
2) and (2, 2) a student must recognize that -4 is |-4| or 4 units
to the left of 0 and 2 is |2| or 2 units to the right of zero, so
the two points are total of 6 units apart
along the x-axis. Students should represent this on the
coordinate grid and numerically with an absolute value
expression, |-4| + |2| . The length is 6 and the width is 5.
The fourth vertex would be (2, -3).
The perimeter would be 5 + 5 + 6 + 6 or 22 units.