Download Unit 1 Operations with Rational Numbers Math 7

Unit 1 Operations with Rational Numbers
Math 7
Unit Goals – Stage 1
Number of Days: 34 days
9/6/16 – 10/21/16
Unit Description: Students continue to build an understanding of the number line from their work in 6th grade. Students convert between the fraction
form to decimal form of a rational number using long division. They learn to add, subtract, multiply, and divide integers, while maintaining the properties of
operations and the relationships between addition and subtraction, and multiplication and division. Students will then apply their understanding to perform
the four operations on positive and negative rational numbers in the context of real-world situations.
Materials: number lines*, two-color counters*
(* Paper tool available at LBUSD Curriculum Intranet  Instructional Tools  Middle School  Mathematical Tools)
Standards for Mathematical Practice
Transfer Goals
SMP 1
Make sense of problems and
Students will be able to independently use their learning to…
persevere in solving them.
• Make sense of never-before-seen problems and persevere in solving them.
SMP 2
Reason abstractly and
• Construct viable arguments and critique the reasoning of others.
quantitatively.
Making Meaning
SMP 3
Construct viable arguments and UNDERSTANDINGS
ESSENTIAL
critique the reasoning of others. Students will understand that…
QUESTIONS
SMP 4
Model with mathematics.
Students will keep
• Integer operations can be represented in multiple ways using manipulatives,
SMP 5
Use appropriate tools
considering…
number lines, and real-world situations.
strategically.
• How are adding and
• Adding any two rational numbers, p + q, can be represented as the number
SMP 6
Attend to precision.
subtracting integers
located a distance |q| from p, in the positive or negative direction depending
SMP 7
Look for and make use of
related?
on whether q is positive or negative.
structure.
• How are multiplying
• The distance between two rational numbers on a number line is the absolute
SMP 8
Look for and express regularity
and dividing integers
value of their difference.
in repeated reasoning.
related?
• Rational numbers can be divided as long as the divisor is not zero; every
• When in the real-world
quotient of rational numbers is a rational number.
Standards for Mathematical Content
would you add,
• Applying previous understandings of properties of operations as strategies to
Clusters Addressed
subtract, multiply, or
add, subtract, multiply, and divide positive and negative rational numbers will
[m] 7.NS.A Apply and extend previous
divide rational
help solve real-world and mathematical problems.
understandings of
numbers?
operations with fractions to
Acquisition
add, subtract, multiply, and
KNOWLEDGE
SKILLS
divide rational numbers.
Students will know…
Students will be skilled at and/or be able to…
•
The
definition
of
academic
vocabulary
words,
• Add, subtract, multiply, and divide positive and
[m] 7.EE.B Solve real-life and
such as additive inverse, integers, opposites,
negative rational numbers to solve real-world and
mathematical problems
and rational number.
mathematical problems.
using numerical and
•
The
sum
of
opposite
numbers
is
zero.
•
Interpret rational numbers on a number line, including
algebraic expressions and
representing addition and subtraction expressions.
•
Any
subtraction
problem
can
be
written
as
an
equations.
equivalent addition problem.
• Apply properties of operations as strategies to add,
subtract, multiply, and divide rational numbers.
• The decimal form of a rational number
terminates in 0s or eventually repeats.
• Convert a fraction to a decimal using long division.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
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Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Assessed Grade Level Standards
Standards for Mathematical Practice
SMP 1
Make sense of problems and persevere in solving them.
SMP 2
Reason abstractly and quantitatively.
SMP 3
Construct viable arguments and critique the reasoning of others.
SMP 4
Model with mathematics.
SMP 5
Use appropriate tools strategically.
SMP 6
Attend to precision.
SMP 7
Look for and make use of structure.
SMP 8
Look for and express regularity in repeated reasoning.
Standards for Mathematical Content
[m] 7.NS.A
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and
subtraction on a horizontal or vertical number line diagram.
a.
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two
constituents are oppositely charged.
b.
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is
positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational
numbers by describing real‐world contexts.
c.
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two
rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.
d.
Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a.
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the
properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
b.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor)
is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing
real-world contexts.
c.
Apply properties of operations as strategies to multiply and divide rational numbers.
d.
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or
eventually repeats.
7.NS.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
[m] 7.EE.B
Solve real‐life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.3
Solve multi‐step real‐life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between
forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a
woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of
$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar
about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
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Posted 6/9/16
2016-2017
Unit 1 Operations with Rational Numbers
Math 7
Evidence of Learning – Stage 2
Assessment Evidence
Unit Assessment
Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in
this guide.
[m] 7.NS.A
• The student interprets rational number values on a number line, including representations of addition and subtraction expressions.
• The student applies properties of operations as strategies to add and subtract rational numbers.
• The student applies properties of operations as strategies to multiply and divide rational numbers.
• The student converts from a fractional form of rational numbers to a decimal form of rational numbers.
• The student solve real-world and mathematical problems involving the four operations with rational numbers.
[m] 7.EE.B
• The student applies properties of operations to evaluate numeric expressions, including converting between different forms of numbers.
For selected content, students will need to…
• Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
• Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
Other Evidence
Formative Assessment Opportunities
• Opening Tasks
• Informal teacher observations
• Checking for understanding using active participation strategies
• Exit slips/summaries
• Modeling Lessons (SMP 4)
•
•
•
•
•
Tasks
Formative Assessment Lessons (FAL)
Quizzes / Chapter Tests
Big Ideas Math Performance Tasks
SBAC Interim Assessment Blocks
Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
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Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will explore
operations with
rational numbers by
participating in the
Opening Task.
1 day
I will add integers
by…
4-5
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
OPENING TASK—Number Line Reasoning
This Opening Task is a Solo-Team-Teach activity.
Pass out the activity, Number Line Reasoning, and
have students work independently. If students are
struggling, you may play the interactive video “The
Number Line.” Next, have students work as a group to
come to a consensus and then have a class discussion
about students’ solutions utilizing Talk Moves to share
the different methods used. This task is a gateway into
the entire unit.
• Using manipulatives to create conjectures about the
rules for adding integers. (SMP 5, 7, 8)
• Using a horizontal and vertical number line diagram.
• Showing that a number and its opposite have a sum
of zero (called additive inverses).
• Explaining p + q as the number located a distance
|q| from p, in the positive or negative direction
depending on whether q is positive or negative.
(SMP 3)
• Interpreting sums of integers by describing realworld contexts. (SMP 2)
• Answering questions such as…
o Why do additive inverses have a sum of zero?
o How can you add integers using multiple
methods?
o How is adding integers similar to adding whole
numbers? How is it different?
•
•
•
Section 1.1
(Activities 2 and 3;
Examples 1, 2, 3, and 4)
Section 1.2
(Activities 1, 2, 3, and 4;
Examples 1, 2, and 3)
STEM Video: Freezing
Solid
Curriculum Intranet
Conceptual Understanding:
• Number Line Reasoning
• The Number Line
Interactive Video
Conceptual Understanding:
• Adding Integers with
Number Lines
• Adding Two-Digit Numbers
Task
• Additive Inverse Video
• myPD Course #2572:
Adding Integers With Two
Color Counters
Procedural Skills and
Fluency:
• Beat the Computer: Integer
Addition
• Tic-Tac-Toe: Adding
Integers
Application:
• NBC Learn Video –
Science of Golf: Math of
Golf Scoring
• STEM Video Performance
Task: Melting Matters
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
4
Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will subtract
integers by…
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
• Using manipulatives to create conjectures about the
• Section 1.3
rules for subtracting integers. (SMP 5, 7, 8)
(Activities 1, 2, 3, and 4;
Examples 1, 2, and 3)
• Showing that the distance between two integers on
a number line is the absolute value of their
difference.
• Explaining subtraction of integers as adding the
additive inverse, p − q = p + ( − q ) . (SMP 3)
• Interpreting differences of integers by describing
real-world contexts. (SMP 2)
• Answering questions such as…
o Why do you add the inverse when subtracting?
o How can you subtract integers using multiple
methods?
o How is subtracting integers similar to subtracting
whole numbers? How is it different?
4-5
days
Curriculum Intranet
Conceptual Understanding:
• Subtracting Integers Using
Two-Color Counters
PowerPoint
• Subtracting Two-Digit
Numbers Task
• Which One Doesn’t
Belong? Integer
Operations on the Number
Line
Procedural Skills and
Fluency:
• Comic Strip Activity:
Adding and Subtracting
Integers
• Game Closet: Top This
• Math-O: Adding and
Subtracting Integers
• Tic-Tac-Toe: Adding and
Subtracting Integers
Application:
• Cliff Diving Task
• Differences of Integers
Task
• Modeling: How Much Did
the Temperature Drop?
(SMP 4)
2-3
days
I will check my
understanding of
operations with
rational numbers by
participating in the
FAL.
FORMATIVE ASSESSMENT LESSON
(choose one)
• Adding and Subtracting Directed Numbers
(SMP 1, 2, 3, 5, 6, 7, 8)
• Using Positive and Negative Numbers in Context
(SMP 1, 2, 3, 4, 6, 7, 8)
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
5
Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will multiply
integers by…
•
•
•
•
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Using manipulatives to create conjectures about the
• Section 1.4
rules for multiplying integers. (SMP 5, 7, 8)
(Activities 1, 2, 3, and 4;
Examples 1, 2, 3, and 4)
Explaining why the product of two negative numbers
• Section 2.4
must be positive using properties, i.e. (–1)(–1) = 1.
(Only Activity 1)
(SMP 3)
Interpreting products of integers in real-world
contexts. (SMP 2)
Answering questions such as…
o How can you multiply integers using multiple
methods?
o How is multiplying integers similar to multiplying
whole numbers? How is it different?
4-5
days
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
Curriculum Intranet
Conceptual Understanding:
• Multiplying Two-Digit
Numbers Task
• myPD Course #2574:
Multiplying Integers with
Two Color Counters
Procedural Skills and
Fluency:
• Beat the Computer: Integer
Multiplication
• Game Closet: Right on
Target
• How Do They Fit?: Add,
Subtract, Multiply Integer
Operations
• Product Game: Integers
Application:
• Multiply to Make −64 Task
• The Running Videos Task
6
Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will divide integers
by…
•
•
•
•
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Using manipulatives to create conjectures about the
• Section 1.5
rules for dividing integers. (SMP 5, 7, 8)
(Activities 1, 2, 3, and 4;
Examples 1, 2, 3, and 4)
Explaining that integers can be divided as long as
the divisor is not zero and know that every quotient
of integers is a rational number. (SMP 3)
Interpreting quotients of integers in real-world
contexts. (SMP 2)
Answering questions such as…
o Compare and contrast multiplying and dividing
integers.
o How can you divide integers using multiple
methods?
o How is dividing integers similar to dividing whole
numbers? How is it different?
4-5
days
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
7
Curriculum Intranet
Conceptual Understanding:
• Dividing Positive and
Negative Numbers Video
• Dividing Two-Digit
Numbers Task
• Missing Factor Model for
Dividing Integers
• myPD Course #2467:
Dividing Integers with Two
Color Counters
Procedural Skills and
Fluency:
• Beat the Computer: Integer
Division
• Connect 4: Multiplying and
Dividing Integers
• Math-O: Mixed Operations
with Integers
• Substituting Negative
Values into Algebraic
Expressions
Posted 6/9/16
Unit 1 Operations with Rational Numbers
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will apply
operations of
rational numbers
by…
•
•
•
•
•
9-10
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Converting a fraction into a decimal using long
• Section 2.1
division.
(Examples 1 and 2)
Adding, subtracting, multiplying, and dividing
• Section 2.2
positive and negative decimals, fractions, and mixed
(Activities 1, 2, and 3;
numbers.
Examples 1, 2, 3, and 4)
Solving real-world and mathematical problems
• Section 2.3
involving the four operations with positive and
(Activities 1 and 2;
negative rational numbers.
Examples 1, 2, 3, and 4)
Applying properties and order of operations as
• Section 2.4
strategies to add, subtract, multiply, and divide
(Activities 2, 3, and 4;
positive and negative rational numbers.
Examples 1, 2, 3, and 4)
Answering questions such as…
• STEM Video: Carpenter or
o When would you need to add, subtract, multiply,
Joiner
or divide rational numbers in a real-world
context?
o How is adding rational numbers similar to adding
integers? How is it different?
Curriculum Intranet
Conceptual Understanding:
• Converting Rational
Numbers Video
• Decimal Expansions of
Fractions Task
• Operations on the Number
Line Task
• Which One Doesn’t
Belong? Rational Numbers
Procedural Skills and
Fluency:
• Converting Between
Fractions and Decimals
Task
• Decimal Maze
• Product Game: Multiplying
Rational Numbers
Application:
• Differences and Distances
Task
• Who is the Better Batter?
Task
• STEM Video Performance
Task: Precisely Perfect
1-2
days
I will prepare for the
unit assessment on
operations with
rational numbers
by…
• Incorporating the Standards for Mathematical
Practice (SMPs) along with the content standards to
review the unit.
•
•
•
•
Ch. 1 Study Help (p. 20)
Ch. 1 Review (p. 35 – 37)
Ch. 2 Study Help (p. 56)
Ch. 2 Review (p. 71 – 73)
Application:
• Bottling Performance Task
• Downloads Performance
Task
• Elevator Task
Unit Assessment
1 day
At this point, all standards addressed in the Math 7 SBAC Interim Assessment Block – Number System have been covered.
This block may now be administered.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
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Posted 6/9/16