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Transcript
Grade 6 Go Math! Quarterly Planner
12-13 Days
Chapter 1 Whole Numbers and Decimals
Big Idea: In 6th grade, students use basic facts and algorithms for operations with rational numbers and notions of equivalence to transform calculations into simpler ones. Fluency and accuracy with multidigit addition, subtraction, and division is the big idea along with a spotlight on greatest common factors and least common multiples. Students build on previous learning of the multiplicative structure as
well as prime and composite numbers.
Essential Question: How do you solve real-world problems involving whole numbers and decimals?
Standards: 6.NS 2, 6.NS 4, 6.NS 3
Emphasized Math Practice standard: MP 5 - Use appropriate tools strategically
ELD Standards:
ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations.
ELD.PI.6.9- Expressing information and ideas in oral presentations.
ELD.PI.6.3-Offering opinions and negotiating with/persuading others.
ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments.
ELD.P1.6.5-Listening actively and asking/answering questions about what was heard.
ELD.PI.6.12-Selecting and applying varied and precise vocabulary.
Lesson
Standards &
Math Practices
1.1
Divide MultiDigit Numbers
6.NS.2
MP.1, MP.2,
MP.3, MP.4
1.2
Prime
Factorization
6.NS.4
MP.1, MP.7,
MP.8
1.3
1.4
Least Common
Multiple
Greatest
Common Factor
6.NS.4
MP.4, MP.6
6.NS.4
MP.2, MP.4
Essential Question
Math Content/Strategies
Models/Tools
Go Math! Teacher
Resources G6
Connections
Vocabulary
How do you divide
multi-digit
numbers?
Apply estimation to long division to begin long
division algorithm, to determine numbers to use
after each regrouping and to check
reasonableness. Apply to 1-digit, 2-digit divisors
first.
Base-Ten Blocks
Base-Ten Grid Paper
Base Ten 15x20
Base Ten 50x70
Review division
(area models,
partial quotients)
estimation, long
division, compatible
numbers, remainder,
Review prime
factors/trees;
factor 40, 150
prime factorization,
prime factors, ladder
diagram
See Problem of the
Day 1.3 and
Vocabulary Builder
least common
multiple, prime
factorization
How do you write
the prime
factorization of a
number?
How can you find
the least common
multiple of two
whole
numbers?
How can you find
the greatest
common factor of
two whole
numbers?
Understand prime factorization as the breaking
apart of a number into all its prime factors
Find LCM by prime factorization or listing
multiples. Students will use LCM to find a least
common denominator and write equivalent
fractions.
Find GCF by prime factorization or listing factors.
Students will use GCF to simplify fractional
factors before multiplying, simplify fractional
products, and write equivalent algebraic
expressions
Factor Trees
Ladder Diagram
Prime Factorization
Listing Multiples
Academic Language
Support
ELD Standards
ELD Standards
ELA/ELD Framework
ELPD Framework
Access Strategies
Organizing Learning
for Student Access to
Challenging Content
Student Engagement
Strategies
Problem Solving Steps and
Approaches
Use a diagram to
show groups of
objects; Prime
Factorization,
Listing multiples;
Distributive
Property;
Estimation;
Multiplication
Strategies;
Base-Ten Blocks;
Long Division
Strategies;
Base Ten 15x20;
DRAFT
Journal
Find 56,794 ÷338. Write the
quotient twice, once with the
remainder as a fraction and
once with an r.
Describe 2 methods for
finding the prime
factorization of a number.
Explain when you would use
each method (finding
multiples or prime
factorization) for finding the
LCM and why.
Equitable Talk
Simplify fractions:
3/6, 72/100. Write
an equivalent
expression: 5n +
45
Greatest Common
Factor, prime
factorization, prime
factors, Distributive
Property, sum as a
product
Accountable Talk Simply
Stated
Equitable Talk
Conversation Prompts
Accountable Talk Posters
Five Talk Moves
Bookmark
Write a short paragraph to
explain how to use prime
factorization and the
Distributive Property to
express the sum of 2 whole
numbers as a product.
Base Ten 50x70;
Ladder Diagram
1.5
1.6
Problem
Solving: Apply
the Greatest
Common Factor
Add and
Subtract
Decimals
6.NS.4
MP.1, MP.4,
MP.5, MP.6
6.NS.3
MP.2, MP.6,
MP.7
Cooperative Learning Role
Cards
How can you use
the strategy draw
a diagram to help
you solve
problems involving
the CGF and the
Distributive
property?
Apply GCF and the Distributive Property to solve
problems.
How do you add
and subtract
multi-digit
decimals?
Review addition and subtraction of decimals (NBT
5.4). Use estimation and the inverse operation to
check reasonableness of answers.
6.NS.3
MP.1, MP.2,
MP.3, MP.6,
MP.7, MP.8
How do you
multiply multidigit decimals?
Extend understanding of multiplication of whole
numbers to decimals.
Model decimal division using base-ten blocks.
Extend understanding of division of whole
numbers to decimals.
1.7
Multiply
Decimals
1.8
Divide Decimals
by Whole
Numbers
6.NS.3
MP.1, MP.2,
MP.6
How do you divide
decimals by whole
numbers?
1.9
Divide with
Decimals
6.NS.3
MP.1, MP.2,
MP.8
How do you divide
whole numbers
and decimals by
decimals?
Cooperative
Learning
Extend the pattern of division by powers of ten.
Base Ten 15x20;
Base Ten 50x70;
Ladder Diagram
Decimal Models
Decimal Place Value
Chart
Digit Tiles
Base-Ten Blocks
Decimal Models
Decimal Place Value
Chart
Decimal Place Value
Chart
Base Ten 15x20;
Base Ten 50x70;
Decimal Place Value
Chart
Digit Tiles
DRAFT
Review the
Distributive
Property by
writing (4 x 5) + (4
x 7) = 4 (5 + ___)
Associative Property
of Addition, Greatest
Common Factor
Collaborative Learning
Table Mats
Seating Chart Suggestions
Vocabulary Strategy:
Have students work
in pairs to complete a
word map for key
terms.
Write a problem in which you
need to put as many of 2
different types of objects as
possible into equal groups.
Then use the GCF, Distributive
property, and a diagram to
solve your problem.
Project a menu
and have students
buy 2-3 side dishes
with $20.
tenths, hundredths,
thousandths,
difference, sum,
order of operations
Write a word problem that
involves adding or subtracting
decimals. Include the
solution.
6 x 5, 6 x 0.5, 0.6 x
5, .06 x 5, 0.6 x 0.5
tenths, hundredths,
thousandths
regroup, ones, tens,
hundreds, product,
order of operations
54 ÷ 6, 5.4 ÷ 6,
0.54 ÷ 6
tenths, hundredths,
thousandths
difference, subtract,
quotient, average
Have students work
in pairs. One student
holds up a
vocabulary card; the
other draws or writes
an example for that
term.
Explain the importance of
correctly placing the decimal
point in the quotient of a
division problem.
Present problem
on bottom left pg.
39A
compatible numbers,
divisor, quotient,
order of operations
Model:
Have students model
decimals using
decimal place value
mats, base ten blocks
and/or decimal
models.
Explain how dividing by a
decimal is different from
dividing by a whole number
and how it is similar.
Explain how to mentally
multiply a decimal number by
100.
Literacy Connection:
Have students create
real world problems
for which you could
use compatible
numbers to estimate
23,881 ÷ 54.
Literature
Connection Grab &
Go: A Drive Through
History
Read about how the
Alvarez family uses
multiplication and
division to plan their
vacation.
Have students color
code parts of a
division problem
(quotient, remainder,
dividend, and
divisor). Give it a
context and have
students discuss
what each part
means in context.
DRAFT
Literature Grab & Go:
Fabulous Fibonacci
Numbers; Halfpipe
Have students read
about adding and
subtracting decimals
to rank
snowboarders in a
competition.
Modeling: Use a
decimal place value
chart and/or base ten
blocks to add and
subtract decimals.
Modeling: Use Base
Ten Blocks to model
Decimal Division.
Literature
Connection Grab &
Go: A Peek into a
Tiny World
Students using a
stage micrometer to
make measurements
of tiny creatures.
DRAFT
Math Talk Frames:
Restate/Repeat
• I just heard you say
_________.
• Did you mean
__________?
• Let me see if I heard you
correctly, you said
_______.
• If I understand you
correctly, you
believe ______.
• It sounds like you think
that____.
Agree/Disagree
• I agree with (name),
when he/she said that
______.
• I agree with (name), and
the
reason is because ____.
• If ____, then ____ must
also be true.
• I disagree with (name)
because
_______.
Elaboration
• Since ______
then_____.
• An example might be
_________.
• I previously learned
______, and it
supports _________.
• If _____, then_____.
• Another example of this
is ______.
Add-on
• In addition to what has
been stated,
I think ________.
DRAFT
• I would add that
________ based
On _____ (evidence).
• What I just heard makes
me think
of __________.
• Building on what I
heard, I think
_____.
Connections
• Similarly to ______, I
think ____.
• Both examples
show_____.
• This is similar to ______.
• The first example shows
____, this is different than
_____.
• In the same way,
__________.
• ______ is like
_________.
• I think that _____ is like
______.
Call to Action
• Based on what we just
learned, I
think we should
_________.
• What can we do about
_______?
• I believe it is important
for us to
_______.
• Considering the
evidence, we should
______.
Assessments: Go Math Prerequisite Skills Inventory
Go Math Chapter 1 Test
Go Math Chapter 1 Performance Task: Orchestra Outing
Portfolio Assessment
DRAFT
Grade 6 Go Math! Quarterly Planner
15 Days
Chapter 2 Fractions
Big idea: Students use visual fraction models and equations to divide whole umber by fractions and fractions by fractions. 6th graders interpret the meaning of fractions, the meanings of multiplication and
division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense.
Essential Question: How can you use the relationship between multiplication and division to divide fractions?
Standards: 6.NS.6c, 6.NS.4, 6.NS.1
Math Practice Standards Emphasized: MP 7 - Look for and make use of structure
ELD Standards:
ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations.
ELD.PI.6.9- Expressing information and ideas in oral presentations.
ELD.PI.6.3-Offering opinions and negotiating with/persuading others.
ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments.
ELD.P1.6.5-Listening actively and asking/answering questions about what was heard.
ELD.PI.6.12-Selecting and applying varied and precise vocabulary.
Lesson
Standards &
Math Practices
Essential Question
Math Content/Strategies
Models/Tools
Go Math! Teacher
Resources G6
Connections
Vocabulary
Academic Language
Support
Cognates:
6.NS.6c
MP.2, MP.4
How can you
convert between
fractions and
decimals?
Convert fractions to decimals using long
division.
Decimal Models
Relating Fractions
Create list of words
that describe 0.5,
0.75. 0.43, 1.60
terminating,
repeating
decimals,
simplest form
2.2
Compare and
Order Fractions
and
Decimals
6.NS.6c
MP.4, MP.5
How can you
compare and order
fractions and
decimals?
Use number lines to understand benchmark
fractions, convert fractions to decimals to
compare on a decimal number line.
Decimal Models
Fraction Tiles
Fraction Number
Lines
Fraction # Line
Templates
See pg. 55A, Using a
Number Line to
Compare
numerator,
denominator,
equivalent
fractions
2.3
Multiply
Fractions
6.NS.4
MP.2, MP.6
How do you
multiply fractions?
Review multiplication of fractions (NBT 5.45.6). Use GCF to simplify.
Fraction Area
Squares
2.4
Simplify Factors
6.NS.4
MP.3, MP.6
How do you
simplify fractions
by using the GCF?
Extend understanding of simplifying fractions
to simplify prior to multiplication.
6.NS.1
MP.1, MP.4, MP.5
How can you use a
model to show
division of
fractions?
Use fraction strips to represent 1 whole, as
well as, the divisor and the quotient
6.NS.1
MP.1
How can you use
compatible
numbers to
estimate quotients
of fractions and
mixed numbers?
2.1
Fractions and
Decimals
2.5
2.6
Investigate Model Fraction
Division
Estimate
Quotients
Understand using compatible numbers as a
strategy to check the reasonableness of
answers when dividing fractions.
Fraction Tiles Color
Multiplication Table
Ladder Diagram
Fraction Strips,
Legos,
Fraction Tiles Color,
Fractions Seeing
Division Fraction #
Line Templates
Fraction Strips,
Legos, Pattern
Blocks,
Number Lines,
Fraction Tiles Color
DRAFT
See POD 2.3, pg.
59B and Fluency
Builder
See pg. 63A,
Teaching for Depth
Use fraction strips
or pattern blocks to
show 2÷1/3,
5/6÷1/6, 2/3÷1/6
See pg. 73A,
Teaching for Depth,
estimating using
benchmarks and
the number line.
simplest form,
order of
operations,
simplify, product,
GCF, numerators,
factors
fraction models
compatible
numbers,
quotient,
possible
estimates
Modeling: Have student
use fraction strips or
pattern blacks to model
operations with fractions.
Language Objective: Have
students write a note to
an absent classmate to
answer the essential
question.
Literacy Connection: Have
students write a story in
which the main character
needs to plant trees by
order of height.
Modeling: Use number
lines to order and
compare fractions and
decimals.
EL Strategy: Have
students write 20
Journal
Write an example of a fraction that
is a terminating decimal and a
fraction that is a repeating decimal.
Explain how you know your
examples are terminating or
repeating.
Explain how you would compare
the numbers 0.4 and 3/8.
Write and solve a word problem
that involves multiplying by a
fraction.
Show 2 ways to multiply 2/15 x
3/20. Then tell which way is easier
and justify your choice.
Explain how to use a model to show
2/6 ÷ 1/12 and 2/6 ÷ 4.
How is estimating quotients
different from estimating products?
2.7
Divide Fractions
2.8
Investigate Model Mixed
Number
Division
2.9
Divide Mixed
Numbers
2.10
Problem Solving
- Fraction
Operations
Extend strategies for dividing fractions to
include using a number line or reciprocals and
inverse operations.
6.NS.1
MP.1, MP.7, MP.8
How do you divide
fractions?
6.NS.1
MP.2, MP.4, MP.5
How can you use a
model to show
division of mixed
numbers?
Use pattern blocks and bar models/tape
diagrams to model division of mixed numbers.
6.NS.1
MP.1, MP.6
How do you divide
mixed numbers?
Review strategies of converting mixed
numbers and division of fractions to extend to
division of mixed numbers.
6.NS.1
MP.1, MP.2
How can you use
the strategy use a
model to help you
solve a division
problem?
Use a model (bar model/tape diagram) to
divide fractions to solve a problem.
Fraction Strips,
Legos, Pattern
Blocks,
Number Lines,
Fraction Tiles Color
Pattern Blocks, Bar
Models/Tape
Diagrams, Number
Lines,
Fraction Tiles Color
Fraction Strips,
Pattern Blocks,
Number Lines,
Fraction Tiles Color
Bar Models/Tape
Diagrams
Use pattern blocks
or Legos to solve
1÷6, 1/2÷6,1/3÷6
reciprocal,
multiplicative
inverse
Use patterns blocks
to model
2 1/2÷1/6. Then do
it with a number
line, bar model
Mixed number,
quotient, whole
numbers
Use fraction strips
to show 3 1/4÷1/2
Mixed numbers,
quotient,
simplest form
See About the
Math, pg. 89A and
POD 2.10, p. 89B
model,
equivalent
different fractions on
index cards and the
symbols < and >. Have
students create
inequalities using the
cards in pairs and read
them to each other.
Modeling: Use fraction
strips or pattern blocks to
model division of
fractions.
Write a word problem that involves
dividing a mixed number by a whole
number. Solve the problem and
describe how you found the
answer.
Explain how you would find how
many 1 ½ cup servings there are in
a pot that contains 22 ½ cups of
soup.
Vocabulary Builder:
Graphic Organizer
Literature Connection
Grab & Go:
Fair Share
DRAFT
Write a word problem that involves
2 fractions. Include the solution.
Explain how to draw a model that
represents (1 ¼ - ½)÷1/8
Modeling: Use number
lines to model division of
fractions.
2/5 ÷ 4 =
Vocabulary Builder: Word
Definition Map
Assessments: Go Math Chapter 2
Go Math Chapter 2 Performance Task: Clock Fractions
DRAFT
Grade 6 Go Math! Quarterly Planner
13-14 Days
Chapter 3 Rational Numbers
Big idea: At this level, students use fractions, decimals, and integers to represent real-world situations. They extend the number line to represent all rational numbers and recognize that number lines may be
either horizontal or vertical which helps 6th graders move from number lines to coordinate grids. The focus is to learn about negative numbers, their relationship to positive numbers, and the meaning and uses of
absolute value. This is the foundation for working with rational numbers, algebraic expressions and equations, functions, and the coordinate plane in 7th and 8th grades.
Essential Question: How do you write, interpret, and use rational numbers?
Standards: 6.NS.5, 6.NS.7a, 6.NS.6a, 6.NS.7a, 6.NS.7c, 6.NS.7d, 6.NS.6c, 6.NS.6b
Emphasized Math Practice Standard: MP 5 - Use appropriate tools strategically
ELD Standards:
ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations.
ELD.PI.6.9- Expressing information and ideas in oral presentations.
ELD.PI.6.3-Offering opinions and negotiating with/persuading others.
ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments.
ELD.P1.6.5-Listening actively and asking/answering questions about what was heard.
ELD.PI.6.12-Selecting and applying varied and precise vocabulary.
Lesson
How can you
use positive
and negative
numbers to
represent real
world
quantities?
How can you
compare and
order integers?
Understand the meaning of 0 in real world
situations. Understand positive and negative
numbers as quantities from 0..
Models/Tools
Go Math!
Teacher
Resources G6
Integer # Line
Integer # Line 2
Integer Mat
Compare and order fractions by using their
relative position on a number line.
Understand that numbers become greater as
you move right on a horizontal number
line or up on a vertical number line.
How can you
plot rational
numbers on a
number line?
Understand a rational number as a point on a
number line. Recognize that numbers with
opposite signs have locations on opposite
sides of 0.
6.NS.7a, 6.NS.7b
MP1, MP.5
How can you
compare and
order rational
numbers?
Understand how to change fractions and
decimals to the same form and plot on a
number line to use to order from least to
greatest.
Number Line
Present stats from
football game…yards
lost, gained, or $$
debit/credit
6.NS.7c
MP.2, MP.3, MP.4,
MP.8
How can you
find and
interpret the
absolute value
Understand absolute value as the distance
from 0.
Number Line
Present real-world
scenarios: Cecily has -30
dollars in her account.
Explain what that means.
Standards &
Math Practices
3.1
Understand
Positive and
Negative
Numbers
6.NS.5, 6.NS.6a
MP.5, MP.6, MP.7
3.2
How can you
compare and
order
integers?
6.NS.7a, 6.NS.7b
MP.5, MP.8
3.3
Rational
Numbers and
the Number
Line
6.NS.6a, 6.NS.6c
MP.2, MP.4, MP.7
3.4
Compare and
Order
Rational
Numbers
3.5
Absolute
Value
Essential
Question
Math Content/Strategies
Connections
Vocabulary
Explore real-world
situations: bank
accounts, temperature,
sea level, football
yardage
integers, opposites,
situation, number
line, distance
Integer # Line
Integer # Line 2
Thermometer,
checkbooks,
sports page
Use number lines,
thermometers, and
checkbooks to focus on
ordering and
inequalities.
absolute value,
temperatures, from
least to greatest,
vertical number line,
integers
Integer # Line
Integer # Line 2
Thermometer
Locate integers on
horizontal and vertical
number lines depending
on context
rational number,
absolute value,
temperatures, from
least to greatest,
vertical number line,
integers, magnitude
Common
denominators,
elevations, absolute
value, vertical
number line, integers
magnitude, absolute
value, number line
DRAFT
Academic Language
Support
Math Talk: Generate examples
of positive and negative
numbers as a class and record
them on a two column sheet.
Examples: a loss of 3 yards,
climbing 5 feet, taking three
steps back, receiving 4 dollars.
Have students take turns
generating a real world context
where the partner identifies the
integer being referenced.
Journal
Give 3 examples of when negative
numbers are used in daily life.
Explain how to use a number line
to compare 2 negative integers.
Give an example.
Modeling: Use a number line to
discuss negative and positive
numbers as opposites.
Describe how to plot -3 ¾ on a
number line.
Math Talk: Have each student 4
cards and have them write a
positive integer on one card
with a matching situation and a
negative integer on the third
card with a matching situation.
Have students take turns
flipping the cards to match the
integers with the situations.
Describe 2 situations in which it
would be helpful to compare or
order positive and negative
rational numbers.
Write 2 different real-world
examples. One should involve the
absolute value of a positive
number, and the other should
3.6
3.7
Compare
Absolute
Value
6.NS.7d
MP.1, MP.2
Rational
Numbers and
the
Coordinate
Plane
6.NS.6c
MP.6, MP.8
3.8
Ordered Pair
Relationships
6.NS.6b
MP.4, MP.7
3.9
Distance on
the
Coordinate
Plane
6.NS.8
MP.1, MP.5, MP.8
3.10
Problem
Solving • The
Coordinate
Plane
6.NS.8
MP.1, MP.5, MP.6
of rational
numbers?
How can you
interpret
comparisons
involving
absolute
value?
How do you
plot ordered
pairs of rational
numbers on a
coordinate
plane?
How can you
identify the
relationship
between points
on a coordinate
plane?
How can you
find the
distance
between two
points that lie
on a horizontal
or vertical line
on a coordinate
plane?
How can you
use the strategy
draw a diagram
to help you
solve a problem
on a coordinate
plane?
Understand absolute value as the distance
from 0. Determine absolute values in real
life situations and use absolute values to
compare which is greater.
Understand the order of (x, y) coordinates in
an ordered pair. Use the ordered pair to
move the given distance and plot on a
coordinate plane.
Coordinate Plane
Coordinate Plane
See About the Math, pg.
123A
quadrants, line
symmetry, line of
symmetry
See if students can
explain the difference
between the locations of
(3,2), and (2,3);
(-3,2) and (-2,3).
coordinate plane, xaxis, y-axis, origin,
ordered pair, xcoordinate, ycoordinate
Recognize the quadrants of a coordinate
plane and identify if values will have + or signs in each quadrant. Understand how
reflections across and axis affect the signs of
the coordinates.
Coordinate Plane,
Desmos,
Graphing
Website
Plot (3,1), (-3,1), (-3,-1),
(3,-1) and discuss how
the coordinates change.
reflection, quadrants,
line symmetry, line of
symmetry
reflection
Use the absolute value to find the distance
between two points on a coordinate plane.
Use graphing to help understand the position
of points in the four quadrants.
Coordinate Plane,
Desmos Graphing
Website
See About the Math, p.
135A
distance, coordinate
plane, coordinates,
vertical line, y-axis
EL Strategy: Have students draw
number lines to illustrate the
following: positive, negative,
zero, less than <, and greater
than >.
Modeling: Use number lines to
model positive and negative
numbers and compare integers.
involve the absolute value of a
negative number.
Give 2 numbers that fit this
description: a number is less than
another number but has a greater
absolute value. Describe how you
determined the numbers.
Describe how to graph the ordered
pair (-1, 4.5).
Literature Connection Grab &
Go: How much should it Cost?
Students read the book and
learn about negative integers as
Rosa repays a loan from her
father.
Explain to a new student how a
reflection across the y-axis
changes the coordinates of the
original point.
Literature Connection Grab &
Go: Searching for a Shipwreck
Students read the book and
learn how integers can describe
the sinking of the Titanic and
the discovery of its ruins.
Graph the points (-3,3), (-3,7), and
(4,3) on a coordinate plane.
Explain how to find their distance
from (-3,3) to (-3,7) and from (-3,3)
and (4,3).
Vocabulary Builder: Semantic
Mapping
Understand a word problem may have
multiple pieces of information, including
starting point, movements and distances. Use
information in the problem to graph
positions on a coordinate plane and find the
solution to the problem.
Maps, Coordinate
Plane
Assessments: Go Math Chapter 3 Test
Go Math Chapter 3 Performance Task: Negative Numbers Through History
**Common Assignment Critical Area 1 Performance Assessment The Number System: Math Carnival
Critical Area Project 1 The Number System: Sweet Success (See Chapter 1 TE)
DRAFT
Use a map and create a
problem which students
can solve.
coordinate plane,
graph the location,
located at
Write a problem that can be
solved by drawing a diagram on a
coordinate plane.