Monday-
Monday-Tuesday-Wednesday-Thursday-Friday-Pre-Planning: Unpacking the StandardsTEKS:
(R) - Readiness Standard
(S) -Supporting StandardThe student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
Ⓢ MATH.6.2B Identify a number, its opposite, and its absolute value.
Ⓢ MATH.6.2C Locate, compare, and order integers and rational numbers using a number line.
Ⓡ MATH.6.11A Locate points in all four quadrants using ordered pairs of rational numbers.Review/Quiz
The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
Ⓢ MATH.6.2B Identify a number, its opposite, and its absolute value.
Ⓢ MATH.6.2C Locate, compare, and order integers and rational numbers using a number line.
Ⓡ MATH.6.11A Graph points in all four quadrants using ordered pairs of rational numbers.Unit 5: Addition and Subtraction of Integers
The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
Ⓢ MATH.6.3C Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Ⓡ MATH.6.3D Add, subtract, multiply, and divide integers fluently.Unit 5: Addition and Subtraction of Integers
The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
Ⓢ MATH.6.3C Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Ⓡ MATH.6.3D Add, subtract, multiply, and divide integers fluently.Unit 5: Addition and Subtraction of Integers
The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
Ⓢ MATH.6.3C Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Ⓡ MATH.6.3D Add, subtract, multiply, and divide integers fluently.Verb(s)
- What verbs define the actions students will need to take when mastering this objective?locate,identfy,apply,order,compareapply, create, analyzeapply, create, analyzeapply, create, analyzeConcept
-What am I teaching?
-What do the students need to know?absolute value
comparison
coordinate plane
direction
integer
magnitude
operation
order
quadrantAddition and Subtraction of Integers – Students model and solve real-world problems involving addition and subtraction of integers.Addition and Subtraction of Integers – Students model and solve real-world problems involving addition and subtraction of integers.Addition and Subtraction of Integers – Students model and solve real-world problems involving addition and subtraction of integers.Context
Readiness:
Connections from previous grade level.
To what degree will this impact learning two years down the road?
Supporting:
What Readiness Standards or concepts from the Readiness Standards does it support?
How does it support the Readiness Standards?Prerequisites and/or Background Knowledge for Students
In Grade 5, students:
Described the key attributes of the coordinate plane including perpendicular number lines (axes), the origin, the
x-coordinate, and the y-coordinate;
Described the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane; and
Graphed in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table.
Background Knowledge for Teacher
Critical Content
Identify integers and absolute value;
Compare and order integers; and
Graph integers on a number line and in the coordinate plane.
Prerequisites and/or Background Knowledge for Students
In grade 5, students:
Multiplied with fluency a three-digit number by a two-digit number.
Solved for quotients of up to a four-digit dividend by a two-digit divisor.
Added and subtracted positive rational numbers fluently.
Background Knowledge for Teacher
Critical Content
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideas.
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideasPrerequisites and/or Background Knowledge for Students
In grade 5, students:
Multiplied with fluency a three-digit number by a two-digit number.
Solved for quotients of up to a four-digit dividend by a two-digit divisor.
Added and subtracted positive rational numbers fluently.
Background Knowledge for Teacher
Critical Content
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideas.
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideasPrerequisites and/or Background Knowledge for Students
In grade 5, students:
Multiplied with fluency a three-digit number by a two-digit number.
Solved for quotients of up to a four-digit dividend by a two-digit divisor.
Added and subtracted positive rational numbers fluently.
Background Knowledge for Teacher
Critical Content
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideas.
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
Add and subtract integers fluently; and
Analyze mathematical relationships to connect and communicate mathematical ideasI will know my students have mastered this standard when they can….CCRS 1.A1 Compare real numbers.
CCRS 1.B1 Perform computations with real and complex numbers
CCRS 1.C1 Use estimation to check for errors and reasonableness of solutions.
CCRS 3.A1 Identify and represent the features of plane and space figures.
CCRS 9.A1 Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
CCRS 9.A2 Use mathematical language to represent and communicate the mathematical concepts in a problem.
CCRS 9.C2 Create and use representations to organize, record, and communicate mathematical ideas.CCRS 1.B1 Perform computations with real (not complex) numbers.
CCRS 8.A1 Analyze given information.
CCRS 8.A3 Determine a solution.
CCRS 9.A3 Use mathematics as a language for reasoning, problem solving, making connections, and generalizingCCRS 1.B1 Perform computations with real (not complex) numbers.
CCRS 8.A1 Analyze given information.
CCRS 8.A3 Determine a solution.
CCRS 9.A3 Use mathematics as a language for reasoning, problem solving, making connections, and generalizingCCRS 1.B1 Perform computations with real (not complex) numbers.
CCRS 8.A1 Analyze given information.
CCRS 8.A3 Determine a solution.
CCRS 9.A3 Use mathematics as a language for reasoning, problem solving, making connections, and generalizingI will assess the standard by…..
Performance Expectation – By the end of this unit, students will identify a number, its opposite, and its absolute value. They will also locate, compare, and order integers and rational numbers using a number line, and graph points in all four quadrants using ordered pairs of rational numbers.
Performance Assessment – Pair students, and have them use playing cards to model addition of integers.
Let the red cards represent negative numbers and black cards represent positive numbers. Players divide the cards evenly between themselves. Players turn over two cards each and add them. See example below:
Player One: red 5 + red 2 = -7 Player Two: black 3 + red 4 = -1
The player with the greatest sum wins that round of cards. Play continues until one player has collected all of the cards. Students record their equations on paper and submit this as evidence of their learning. After playing the card game, have students write a personal reflection.
Performance Assessment – Pair students, and have them use playing cards to model addition of integers.
Let the red cards represent negative numbers and black cards represent positive numbers. Players divide the cards evenly between themselves. Players turn over two cards each and add them. See example below:
Player One: red 5 + red 2 = -7 Player Two: black 3 + red 4 = -1
The player with the greatest sum wins that round of cards. Play continues until one player has collected all of the cards. Students record their equations on paper and submit this as evidence of their learning. After playing the card game, have students write a personal reflection.
Performance Assessment – Pair students, and have them use playing cards to model addition of integers.
Let the red cards represent negative numbers and black cards represent positive numbers. Players divide the cards evenly between themselves. Players turn over two cards each and add them. See example below:
Player One: red 5 + red 2 = -7 Player Two: black 3 + red 4 = -1
The player with the greatest sum wins that round of cards. Play continues until one player has collected all of the cards. Students record their equations on paper and submit this as evidence of their learning. After playing the card game, have students write a personal reflection.
Vocabulary
(Academic and Content)absolute value
axes
cartesian plane
integer
opposite
quadrantadditive identity
additive inverse
commutative property
generalization
identity property
inverse operationadditive identity
additive inverse
commutative property
generalization
identity property
inverse operationadditive identity
additive inverse
commutative property
generalization
identity property
inverse operationLesson Topic (Content Objective)Students model and solve real-world problems involving operations on integers and develop an understanding of the algorithms involved.Students model addition of integers with manipulatives (such as two-color counters, pictorial models, or number lines). As students explore with manipulatives, they record their steps in a two-column format using pictures, numbers, and symbols in order to facilitate the transfer of their experiences from concrete models to pictorial representations finally to the abstract level. (See examples below.)
Help students make connections between previous knowledge and new learning experiences. Discuss the similarities and differences between operations on integers and operations on whole numbers. [MATH.6.1E, MATH.6.3C] [GQ #2, 3, 4]
Students model addition of integers with manipulatives (such as two-color counters, pictorial models, or number lines). As students explore with manipulatives, they record their steps in a two-column format using pictures, numbers, and symbols in order to facilitate the transfer of their experiences from concrete models to pictorial representations finally to the abstract level. (See examples below.)
Help students make connections between previous knowledge and new learning experiences. Discuss the similarities and differences between operations on integers and operations on whole numbers. [MATH.6.1E, MATH.6.3C] [GQ #2, 3, 4]
Students model addition of integers with manipulatives (such as two-color counters, pictorial models, or number lines). As students explore with manipulatives, they record their steps in a two-column format using pictures, numbers, and symbols in order to facilitate the transfer of their experiences from concrete models to pictorial representations finally to the abstract level. (See examples below.)
Help students make connections between previous knowledge and new learning experiences. Discuss the similarities and differences between operations on integers and operations on whole numbers. [MATH.6.1E, MATH.6.3C] [GQ #2, 3, 4]
ELPS (Language Objective)Provide English language learners sentence stems on index cards (e.g., The horizontal scale is called…, The vertical scale is called…, Absolute value represents …, etc.)ELPS C.4b Recognize directionality of English reading such as left to right and top to bottom.
ELPS C.4b Recognize directionality of English reading such as left to right and top to bottom.
ELPS C.4b Recognize directionality of English reading such as left to right and top to bottom.
Lesson CycleEngage:
Warm-Up/Opening (min)A mathematics game that reinforces students’ conceptual understanding of the coordinate plane
Hit the CoordinateA virtual manipulative that uses colored chips to demonstrate adding positive and
negative values
Color Chips - SubtractionA virtual manipulative that uses colored chips to demonstrate adding positive and
negative values
Color Chips - SubtractionA virtual manipulative that uses colored chips to demonstrate adding positive and
negative values
Color Chips - SubtractionExplore:
INM/Review (min):When students are comfortable graphing on a number line, move to graphing ordered pairs of the form (± x, ± y) in the coordinate system. They plot points in all four quadrants and associate the signs of the x- and y-coordinates of the ordered pairs with the quadrant numbers. Use a table such as the one below to record observations
Graphic OrganizersExplain:
Guided Practice (min):A review of the coordinate plane and its components
Coordinate Plane a BrainPop® video
Examination of the use of the zero pairs leads to a discussion of the fact that the final “operation” is really addition and the discovery of the “add the opposite” rule. Have students write narrative statements detailing the process. [MATH.6.3C]
The use of a vertical number line to demonstrate addition and subtraction of integers is illustrated in the activity, Integer Addition, and Subtraction – Hot Air Balloon.
Examination of the use of the zero pairs leads to a discussion of the fact that the final “operation” is really addition and the discovery of the “add the opposite” rule. Have students write narrative statements detailing the process. [MATH.6.3C]
The use of a vertical number line to demonstrate addition and subtraction of integers is illustrated in the activity, Integer Addition, and Subtraction – Hot Air Balloon.
Examination of the use of the zero pairs leads to a discussion of the fact that the final “operation” is really addition and the discovery of the “add the opposite” rule. Have students write narrative statements detailing the process. [MATH.6.3C]
The use of a vertical number line to demonstrate addition and subtraction of integers is illustrated in the activity, Integer Addition, and Subtraction – Hot Air Balloon.
Elaborate:
Independent Practice (min):HMH (2014), Texas Go Math!, Grade 6
Lesson 2.2 “Identifying Opposites and Absolute Value of Rational Numbers,” pp. 37 – 42HMH (2014), Texas Go Math!, Grade 6:
Lesson 5.1 “Adding Integers with the Same Sign,” pp. 117 – 122
HMH (2014), Texas Go Math!, Grade 6:
Lesson 5.1 “Adding Integers with the Same Sign,” pp. 117 – 122
HMH (2014), Texas Go Math!, Grade 6:
Lesson 5.1 “Adding Integers with the Same Sign,” pp. 117 – 122
Evaluate:
Closing ( min.):Formative Assessment – Give students a list of integers and have them explain, using complete sentences, how to order these integers from least to greatest (e.g., 6, -3, 4, -7, 1, -2; Solution: -7, -3, -2, 1, 4, 6) using a number line to graph each integer and compare the distance of each to the origin. [MATH.6.2B, MATH.6.2C]
Quiz³ Formative Assessment – Using the vocabulary terms, students write a narrative describing how to model addition and subtraction of integers. C.5b [MATH.6.3C] [GQ #2]
³ Formative Assessment – Using the vocabulary terms, students write a narrative describing how to model addition and subtraction of integers. C.5b [MATH.6.3C] [GQ #2]
³ Formative Assessment – Using the vocabulary terms, students write a narrative describing how to model addition and subtraction of integers. C.5b [MATH.6.3C] [GQ #2]
ReinforcementMaterials/ Resources:Texas Go Math!
pencils
manipulatives
note paper
journal
smartbroad
graphpaperTexas Go Math!
pencils
manipulatives
note paper
journal
smartbroad
graphpaperTexas Go Math!
pencils
manipulatives
note paper
journal
smartbroad
graphpaperTexas Go Math!
pencils
manipulatives
note paper
journal
smartbroad
graphpaperHomework5.1 AB worksheetMODIFICATIONS and/or ACCOMODATIONS:
-Gifted and Talented
-ELL/ ESL
-Special EducationInstructional Accommodations for Diverse Learners,Cues, Questions
Provide English language learners sentence stems on index cards (e.g., The horizontal scale is called…, The vertical scale is called…, Absolute value represents …, etc.). C. 2c, C.5d [MATH.6.1E,
Instructional Accommodations for Diverse Learners,Cues, Questions
ELPS C.3b Expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication.
Instructional Accommodations for Diverse Learners,Cues, Questions
ELPS C.3b Expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication.
Instructional Accommodations for Diverse Learners,Cues, Questions
ELPS C.3b Expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication.
*All lesson plans are subject to revisions and addendums by teacher.
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