Download Mathematics - Grade 7 - Rahway Public Schools

CURRICULUM
FOR
MATHEMATICS
GRAD E 7
This curriculum is part of the Educational Program of Studies of the Rahway Public Schools.
ACKNOWLEDGMENTS
Dr. Kevin Robinson, Program Supervisor of STEM
The Board acknowledges the following who contributed to the preparation of this curriculum.
Leslie Breen
Dr. Roya Basu
Christine H. Salcito, Assistant Superintendent for Curriculum and Instruction
Subject/Course Title:
Date of Board Adoptions:
Mathematics
Grade 7
September 17, 2013
Revised August 26, 2014
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area: Mathematics
Unit Title: Ratios & Proportional Relationships
Target Course/Grade Level: Grade 7
Unit Summary: Students will analyze proportional relationships and use them to solve problems.
Approximate Length of Unit: Eight weeks integrated throughout the school year.
Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21 st Century Life & Career Skills, Science and
Technology
LEARNING TARGETS
Language Arts Literacy
RI.7.4
Determine the meaning of words and phrases as they are used in a text, including figurative, connotative and technical
meanings.
21st Century Standards
9.1.4.A.1
9.1.8.A.1
9.1.12.A.1
Recognize a problem and brainstorm ways to solve the problem individually or collaboratively.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving
skills.
Apply critical thinking and problem-solving strategies during structured learning experiences.
Domain:
7.RP Ratios & Proportional Relationships
Standards: 7.RP A 1-3 Ratios & Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
1.
2.
2a.
2b.
2c.
2d.
3.
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like
or different units.
Recognize and represent proportional relationships between quantities.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on
a coordinate plane and observing whether the graph is a straight line through the origin.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items
purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention
to the points (0, 0) and (1, r) where r is the unit rate.
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and
markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Unit Understandings
Students will understand that...
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
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

Complex fractions are units rates when division is applied.
Two quantities are in a proportional relationship if their graph is a line that passes through the origin.
Two quantities are in a proportional relationship if a constant of proportionality is calculated.
Proportional relationships are represented by equations.
Proportional relationships are used to solve multi-step ratio and percent problems.
Unit Essential Questions
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How can you compute ratios and unit rates?
How is it possible to determine if two quantities are in a proportional relationship?
How can you find the unit rate with complex fractions?
How can you represent a proportional relationship with an equation?
How can you use ratios to solve real world problems?
How is the unit rate shown on the graph of a proportional relationship?
What is a constant of proportionality?
How is a proportional relationship different from other relationships?
Knowledge and Skills
Students will know and be able to…
 Key vocabulary: Ratio, unit rate, proportional relationship, constant of proportionality, percent increase and decrease, percent
error, sales tax, commission, interest, interest rate, markup, and discount.
 Compute a unit rate from a complex fraction.
 Identify the constant of proportionality in tables, graphs, equations, diagrams and verbal descriptions.
 Represent proportional relationships with equations.
 Solve multi-step ratio and percent problems.
 Understand that in a proportional relationship, the value of y in the point (1,y) is the unit rate.
 Informally understand that the unit rate is the measure of a line’s slope.
 Explain what the point (x,y) means in a proportional relationship.
 Solve real world problems using ratios.
 Solve problems involving percent, percent increase/decrease, and percent error.
 Solve problems involving simple interest.
 Solve problems involving scale drawings.
 Identify similar and congruent figures.
 Find unknown side lengths of similar figures.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
 Formal and informal assessments
 Written, verbal and slate assessments
 Teachers observations of independent assignments
 Chapter quizzes and end of chapter tests
 Daily exit slips
 Observation of use of hands on materials (Manipulative)
 Evaluation of multiple choice questions, short constructed response and open ended questions
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
 Extra practice worksheet
 Re-teach Worksheet
 Enrichment Worksheet
 Use of online Multilingual Glossary (ESL)
 Hands on activities
RESOURCES
Teacher Resources:


Math in Focus textbook and eBook
Math in Focus Teaching Resources CD
Equipment Needed:
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Chart paper
Dry erase markers
Slate boards
Exit tickets
Index cards
Calculator
Multiplication table
Student reference book
Overhead projector
Manipulative
Textbooks
Notebooks
Worksheets
Pencils and erasers
Rulers
Compass
Protractor
Circle Cut-Outs
Scissors
Unit Cubes
Technology Resources for Students:
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Game - Find equal ratios
http://www.arcademicskillbuilders.com/games/ratio-blaster/ratio-blaster.html
Video- Compute unit rates associated with ratios of fractions
https://learnzillion.com/lessonsets/107-compute-unit-rates-associated-with-ratios-of-fractions
Video – Different screen sizes - Equal ratios by PBS Math Club
https://www.youtube.com/watch?v=VyhRv_MuxvA
Game - Write an equation for a proportional relationship.
http://www.ixl.com/math/grade-8/write-an-equation-for-a-proportional-relationship
Technology Resources for Teachers/Parents:
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
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
MIF – Math Background Video- Direct and Indirect Proportion
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volA/data/mifpdv/Chapter5.html
MIF – Podcast Video- Developing Critical Thinking with Singapore Math
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313
MIF Transition Resource Map
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313
Useful websites for teachers to explore:
1. https://my.hrw.com
2. http://illuminations.nctm.org
3. http://www.ixl.com (the activities on this website are broken down by specific CCSS standards under each and
every domain)
4. https://sites.google.com/site/emilou2010/
Digital Tools for Teachers/Students:





MIF – Algebra Tiles
http://my.hrw.com/math11/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html
MIF – Fraction/Decimal Grid
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.htmll
MIF – Integer Chips
http://my.hrw.com/math06_07/nsmedia/tools/Integer_Chips/Integer_Chips.html
MIF – Graphing Calculator
http://my.hrw.com/math11/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
MIF – Multilingual Glossary
http://my.hrw.com/math11/math06_07/nsmedia/tools/glossary/msm/glossary.html
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area: Mathematics
Unit Title: The Number System
Target Course/Grade Level: Grade 7
Unit Summary: Students will apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide
rational numbers.
Approximate Length of Unit: Eight weeks integrated throughout the school year.
Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21 st Century Life & Career Skills, Science and
Technology
LEARNING TARGETS
Language Arts Literacy:
RI.7.4
W.7.4
Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical
meanings; analyze the impact of a specific word choice on meaning and tone.
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and
audience.
21st Century Standard
9.1.4.C.1
9.1.8.C.1
9.1.8.D.1
Practice collaborative skills in groups, and explain how these skills assist in completing tasks in different settings (at home, in
school, and during play).
Determine an individual’s responsibility for personal actions and contributions to group activities.
Employ appropriate conflict resolution strategies.
Domain: 7.NS The Number System
Standards: 7.NS 1-3 The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
1.
1a.
1b.
1c.
1d.
2.
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.
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.
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.
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.
Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational
numbers
2a.
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.
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.
Apply properties of operations as strategies to multiply and divide rational numbers.
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.
Solve real-world and mathematical problems involving the four operations with rational numbers.
2b.
2c.
2d.
3.
Unit Understandings
Students will understand that…
 The properties of operations extend to all rational numbers.
 Negative numbers have real-world contexts.
 Addition and subtraction may be represented on a number line.
 Distance between two rational numbers on the number line is the absolute value of their difference.
 Every quotient of integers (with non-zero divisor) is a rational number.
 The decimal form a rational number either terminates or repeats.
 Additive inverses have a sum of 0.
 Subtracting rational numbers is equivalent to adding the additive inverse.
 Rational numbers satisfy the properties of operations .
Unit Essential Questions
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What is a rational number?
What is an additive inverse?
How do you add and subtract rational numbers?
How do you multiply and divide rational numbers?
How do you solve real-world problems involving the four operations with rational numbers?
Why is the distributive property important for the rules of multiplying signed numbers?
How is absolute value related to the difference of two rational numbers?
Knowledge and Skills
Students will know and be able to…
 Key Vocabulary: Number line, positive/negative number, absolute value, rational number, additive inverse and product/
quotient.
 Add and subtract rational numbers.
 Multiply and divide rational numbers.
 Understand that the distance between two rational numbers is the absolute value of their difference.
 Interpret sums, differences, products and quotients of rational numbers by describing real-world contexts.
 Solve real-world problems involving the four operations with rational numbers.
 Solve mathematical problems involving the four operations with rational numbers.
 Understand that the decimal form of a rational number terminates in 0’s or repeats.
 Additive inverses have a sum of 0.
 Apply properties of operations to add, subtract, multiply and divide rational numbers.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
 Formal and informal assessments
 Written, verbal and slate assessments
 Teachers observations of independent assignments
 Chapter quizzes and end of chapter tests



Daily exit slips
Observation of use of hands on materials (Manipulative)
Evaluation of multiple choice questions, short constructed response and extended constructed responses
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
 Extra practice worksheets
 Enrichment worksheets
 Cooperative learning activities
 Use of online Multilingual Glossary (ESL)
 Hands on activities
RESOURCES
Teacher Resources:


Math in Focus textbook and eBook
Math in Focus Teaching Resources CD
Equipment Needed:













Chart paper
Dry erase markers
Slate boards
Exit tickets
Index cards
Calculator
Overhead projector
Manipulative
Textbooks
Notebooks
Pencils and erasers
Rulers
Number lines
Technology Resources for Students:



Game - Integer addition and subtraction rules
http://www.ixl.com/math/grade-7/integer-addition-and-subtraction-rules
Video – Add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram
https://learnzillion.com/lessonsets/411-add-and-subtract-rational-numbers-represent-addition-and-subtraction-on-a-horizontal-orvertical- number-line-diagram
Game - Integer multiplication and division rules
http://www.ixl.com/math/grade-7/integer-multiplication-and-division-rules
Technology Resources for Teachers/Parents:
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
MIF – Math Background Video- The Real Number System
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volA/data/mifpdv/Chapter1.html
MIF – Math Background Video- Rational Number Operations
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volA/data/mifpdv/Chapter2.html
MIF – Podcast Video- Problem Solving in Mathematics
http://my.hrw.com/mif_6/mif_2012/student/grade7_volA/tabpages/mathtool/video.html?videoxml=ref:SM_006
MIF Transition Resource Map
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313 (Rational Number Operations)
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313
(The Real Number System)

Useful websites for teachers to explore:
1. https://my.hrw.com
2. http://illuminations.nctm.org
3. http://www.ixl.com (the activities on this website are broken down by specific CCSS standards under each and
every domain)
4. https://sites.google.com/site/emilou2010/
Digital Tools for Teachers/Students:





MIF – Algebra Tiles
http://my.hrw.com/math11/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html
MIF – Fraction/Decimal Grid
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.htmll
MIF – Integer Chips
http://my.hrw.com/math06_07/nsmedia/tools/Integer_Chips/Integer_Chips.html
MIF – Graphing Calculator
http://my.hrw.com/math11/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
MIF – Multilingual Glossary
http://my.hrw.com/math11/math06_07/nsmedia/tools/glossary/msm/glossary.html
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area: Mathematics
Unit Title: Expressions & Equations
Target Course/Grade Level: Grade 7
Unit Summary: Students will use properties of operations to generate equivalent expressions. Students will solve real-life and
mathematical problems using numerical and algebraic expressions and equations.
Approximate Length of Unit: Eight weeks integrated throughout the school year.
Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21st Century Life & Career Skills, Science and
Technology
LEARNING TARGETS
Language Arts Literacy
SL.7.1
SL.7.1a
SL.7.1b
SL.7.1c
Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on
grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by
referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as
needed.
Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas
that bring the discussion back on topic as needed.
21st Century Standards
9.1.4.B.1
9.1.8.B.1
9.1.8.B.2
Participate in brainstorming sessions to seek information, ideas, and strategies that foster creative thinking.
Use multiple points of view to create alternative solutions.
Assess data gathered to solve a problem for which there are varying perspectives (e.g., cross-cultural, gender-specific,
generational), and determine how the data can best be used to design multiple solutions.
Domain:
7. EE Expressions and Equations
Standards: 7. EE 1-4 Expressions and Equations
Use properties of operations to generate equivalent expressions.
1.
2.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the
quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
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.
4.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities
to solve problems by reasoning about the quantities.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational
numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the
sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm.
What is its width?
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational
numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a
salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an
inequality for the number of sales you need to make, and describe the solutions.
4a.
4b.
Unit Understandings
Students will understand that…
 The properties of operations are applied as strategies to add, subtract, factor and expand linear expressions with rational
coefficients.
 Algebraic expressions, equations and inequalities can represent real-world situations.
 Equivalent expressions can show how quantities are related.
 Algebraic solutions to linear equations follow a sequence of operations.
 The solution set of an inequality is shown graphically.
 Using the properties of operations, numbers have equivalent forms.
Unit Essential Questions
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What is the difference between an algebraic expression and a numerical expression?
What is an equation?
What is an inequality?
What is the difference between an algebraic expression and an equation?
How do you solve for a given variable in an equation of the forms px + q = r and p(x + q) =r?
How do you solve for a given variable in an inequality of the form px + q > r or px + q < r?
How do you display the solution set of an inequality graphically?
When is it necessary to use the distributive property?
How are algebraic and arithmetic solutions similar? How are they different?
How would you represent a real-world situation with an equation or an inequality?
How do you apply the properties of operations to calculate numbers in different forms?
How do equivalent expressions explain how the quantities in it are related?
Knowledge and Skills
Students will know and be able to…
 Key Vocabulary: Variable, algebraic expression, numerical expression, coefficient, equivalent expressions, equation, solution,
and inequality.
 Simplify algebraic expressions by combining like terms.
 Recognize that the expression obtained after simplifying is equivalent to the original expression.
 Solve real world problems using algebraic expressions.
 Solve equations and inequalities in one variable.
 Use a table or graph to represent a linear equation.
 Use substitution to determine whether a given number is a solution of an inequality.
 Represent the solutions of an inequality on a number line.
 Solve real world problems by writing equations and inequalities.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
 Formal and informal assessments
 Written, verbal and slate assessments





Teachers observations of independent assignments
Chapter quizzes and end of chapter tests
Daily exit slips
Observation of use of hands on materials (Manipulative)
Evaluation of multiple choice questions, short constructed response and extended constructed responses
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
 Extra practice worksheets
 Enrichment worksheets
 Cooperative learning activities
 Use of online Multilingual Glossary (ESL)
 Hands on activities
RESOURCES
Teacher Resources:


Math in Focus textbook and eBook
Math in Focus Teaching Resources CD
Equipment Needed:


















Chart paper
Dry erase markers
Slate boards
Exit tickets
Index cards
Calculator
Student reference book
Overhead projector
Manipulative
Textbooks
Notebooks
Pencils and erasers
Rulers
Number line
Scissors
Yard Stick
Algebra tiles
Balance scale
Technology Resources for Students:





Game - Simplify variable expressions using properties
http://www.ixl.com/math/grade-7/simplify-variable-expressions-using-properties
Video – Rewrite an expression to understand how the quantities are related.
https://learnzillion.com/lessonsets/204-rewrite-an-expression-to-understand-how-the-quantities-are-related
Game - Distributive property
http://www.ixl.com/math/grade-7/distributive-property
Game - Properties of addition and multiplication
http://www.ixl.com/math/grade-7/properties-of-addition-and-multiplication
Video – Linear equations
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/algebra--linearequations-2
Technology Resources for Teachers/Parents:





MIF – Math Background Video- Algebraic Expressions
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volA/data/mifpdv/Chapter3.html
MIF – Math Background Video- Algebraic Equations and Inequalities
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volA/data/mifpdv/Chapter4.html
MIF – Podcast Video- Problem Solving in Mathematics
http://my.hrw.com/mif_6/mif_2012/student/grade7_volA/tabpages/mathtool/video.html?videoxml=ref:SM_006
MIF Transition Resource Map
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313 (Algebraic Expressions)
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821313 (Algebraic Equations and Inequalities)
Useful websites for teachers to explore:
1. https://my.hrw.com
2. http://illuminations.nctm.org
3. http://www.ixl.com (the activities on this website are broken down by specific CCSS standards under each and
every domain)
4. https://sites.google.com/site/emilou2010/
Digital Tools for Teachers/Students:





MIF – Algebra Tiles
http://my.hrw.com/math11/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html
MIF – Fraction/Decimal Grid
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.htmll
MIF – Integer Chips
http://my.hrw.com/math06_07/nsmedia/tools/Integer_Chips/Integer_Chips.html
MIF – Graphing Calculator
http://my.hrw.com/math11/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
MIF – Multilingual Glossary
http://my.hrw.com/math11/math06_07/nsmedia/tools/glossary/msm/glossary.html
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area: Mathematics
Unit Title: Geometry
Target Course/Grade Level: Grade 7
Unit Summary: Students will draw, construct and describe geometrical figures and describe the relationships between them. Students will
solve real-life and mathematical problems involving angle measure, area, surface area and volume.
Approximate Length of Unit: Eight weeks integrated throughout the school year.
Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21st Century Life & Career Skills, Science and
Technology
LEARNING TARGETS
Language Arts Literacy
SL.7.4
SL.7.5
Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts,
details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation.
Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient
points.
21st Century Standards
9.1.4.B.1
9.1.8.B.1
9.1.12.B.1
Participate in brainstorming sessions to seek information, ideas, and strategies that foster creative thinking.
Use multiple points of view to create alternative solutions.
Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving
problems, using multiple perspectives.
Domain:
7.G Geometry
Standards: 7.GA 1 – 6 Geometry
Draw, construct and describe geometrical figures and describe the relationships between them
1.
2.
3.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale
drawing and reproducing a scale drawing at a different scale.
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on
constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle,
more than one triangle, or no triangle.
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids.
Solve real-life and mathematical problems involving angle measure, area, surface area and volume
4.
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of
the relationship between the circumference and area of a circle.
5.
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve
simple equations for an unknown angle in a figure.
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
6.
Unit Understandings
Students will understand that…
 The actual length and area may be computed from a scale drawing.
 Slicing a three-dimensional figure creates a specific two-dimensional figure.
 There is a relationship between a circle’s circumference and its area.
 Angle facts of polygons enable simple equations to be used to find an unknown angle.
 There is a classification system for polygons.
 There are real-world applications involving area, surface area and volume.
 Formulas are used to find the area and circumference of circles.
 When constructing a figure with given conditions a unique figure may or may not be constructed
 Triangles are classified by both their angle measures and their side lengths.
 The surface area of a prism or pyramid is the sum of the area of its faces.
 The volume formula for prisms is the product of the base area and its height.
 The volume formula for pyramids is one-third the product of the base area and its height.
Unit Essential Questions
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What is area and surface area?
How do you find the area and circumference of circles?
What is the relationship between the circumference and area of a circle?
What is volume?
What are the differences between area, surface area, and volume?
How is it possible to use area, surface area and volume to solve real world problems?
What is a net?
How can you use a net to find the area of a three-dimensional figure?
How do you compute actual lengths and areas from a scale drawing?
How are polygons classified?
How do you find an unknown angle measure in a polygon?
How can you construct a polygon with given conditions?
Is there a relationship between two and three-dimensional figures?
Knowledge and Skills
Students will know and be able to…
 Key vocabulary: formula, base, radius, diameter, circumference, pyramid, prism, surface area, volume, supplementary,
complementary, vertical, adjacent angles and scale drawing.
 Find the area of given polygons and circles.
 Find the volume of given prisms and pyramids.
 Find the surface area of given prisms and pyramids.
 Find an unknown angle measure of a given polygon.
 Recognize that constructing a triangle from given conditions may or may not result in a unique triangle.
 Construct a polygon from given conditions.
 Solve real-world problems involving area, surface area and volume.
 Scale drawings may be used to find actual lengths and areas.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
 Formal and informal assessments
 Written, verbal and slate assessments





Teachers observations of independent assignments
Chapter quizzes and end of chapter tests
Daily exit slips
Observation of use of hands on materials (Manipulative)
Evaluation of multiple choice questions, short constructed response and extended constructed responses
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
 Extra practice worksheets
 Enrichment worksheets
 Cooperative learning activities
 Use of online Multilingual Glossary (ESL)
 Hands on activities
RESOURCES
Teacher Resources:


Math in Focus textbook and eBook
Math in Focus Teaching Resources CD
Equipment Needed:

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














Chart paper
Dry erase markers
Slate boards
Exit tickets
Index cards
Calculator
Student reference book
Overhead projector
Manipulative
Textbooks
Notebooks
Worksheets
Pencils and erasers
Rulers
Compass
Protractor
Circle Cut-Outs
Scissors
Unit Cubes
Technology Resources for Students:




Game - scale drawings and scale factors
http://www.ixl.com/math/grade-7/scale-drawings-and-scale-factors
Video – Solve problems involving scale drawings of geometric figures.
https://learnzillion.com/lessonsets/199-solve-problems-involving-scale-drawings-of-geometric-figures
Game - perimeter, area and volume - changes in scale
http://www.ixl.com/math/grade-7/perimeter-area-and-volume-changes-in-scale
Practice lining up and reading a protractor while you measure a set of angles in a fun learning activity
http://www.mathplayground.com/measuringangles.html
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

Virtual protractor
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html
Video - Describe the two-dimensional figures that result from slicing three-dimensional figures
https://learnzillion.com/lessonsets/200-describe-the-twodimensional-figures-that-result-from-slicing-threedimensional-figures
Video – Draw geometric shapes given the length of sides
https://learnzillion.com/student/lessons/1069-draw-geometric-shapes-given-the-length-of-sides
Technology Resources for Teachers/Parents:

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
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
MIF – Math Background Video- Volume and Surface Area of Solids
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volB/data/mifpdv/Chapter8.html
MIF – Math Background Video- Geometric Construction
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volB/data/mifpdv/Chapter7.html
MIF – Math Background Video- Angle Properties and Straight Lines
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volB/data/mifpdv/Chapter6.html
MIF – Podcast Video- Problem Solving in Mathematics
http://my.hrw.com/mif_6/mif_2012/student/grade7_volA/tabpages/mathtool/video.html?videoxml=ref:SM_006
MIF Transition Resource Map
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821351 (Angle Properties and Straight Lines)
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821351 (Geometric Construction)
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821351 (Volume and Surface Area of Solids)
Useful websites for teachers to explore:
1. https://my.hrw.com
2. http://illuminations.nctm.org
3. http://www.ixl.com (the activities on this website are broken down by specific CCSS standards under each and
every domain)
4. https://sites.google.com/site/emilou2010/
Digital Tools for Teachers/Students:





MIF – Algebra Tiles
http://my.hrw.com/math11/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html
MIF – Fraction/Decimal Grid
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.htmll
MIF – Integer Chips
http://my.hrw.com/math06_07/nsmedia/tools/Integer_Chips/Integer_Chips.html
MIF – Graphing Calculator
http://my.hrw.com/math11/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
MIF – Multilingual Glossary
http://my.hrw.com/math11/math06_07/nsmedia/tools/glossary/msm/glossary.html
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area: Mathematics
Unit Title: Statistics & Probability
Target Course/Grade Level: Grade 7
Unit Summary: Students will use random sampling to draw inferences about a population. Students will draw informal comparative
inferences about two populations. Students will investigate chance processes and develop, use and evaluate probability models.
Approximate Length of Unit: Eight weeks integrated throughout the school year.
Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21st Century Life & Career Skills, Science and
Technology
LEARNING TARGETS
Language Arts Literacy
L.7.4a
Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the
meaning of a word or phrase.
L.7.4d
Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or
in a dictionary).
21st Century Standards
9.1.4.C.1
9.1.8.C.1
9.1.12.C.5
Domain:
Practice collaborative skills in groups, and explain how these skills assist in completing tasks in different settings (at home, in
school, and during play).
Determine an individual’s responsibility for personal actions and contributions to group activities.
Assume a leadership position by guiding the thinking of peers in a direction that leads to successful completion of a
challenging task or project.
7.SP Statistics & Probability
Standards: 7.SP.A 1 – 8 Statistics & Probability
Use random sampling to draw inferences about a population
1.
2.
Understand that statistics can be used to gain information about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if the sample is representative of that population. Understand
that random sampling tends to produce representative samples and support valid inferences.
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example,
estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election
based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Draw informal comparative inferences about two populations.
3.
4.
Informally assess the degree of visual overlap of two numerical data distributions with similar variability’s, measuring the
difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of
players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the
variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is
noticeable.
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative
inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are
generally longer than the words in a chapter of a fourth-grade science book.
Investigate chance processes and develop, use, and evaluate probability models.
5.
6.
7.
7a.
7b.
8.
8a.
8b.
8c.
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event
occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around
1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its
long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling
a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed
frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine
probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be
selected and the probability that a girl will be selected.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land
open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample
space for which the compound event occurs.
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event
described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the
event.
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation
tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at
least 4 donors to find one with type A blood?
Unit Understandings
Students will understand that…
 Statistics is used to gain information about a population.
 A method to collect data about a population is to conduct a survey.
 Samples must be representative of the population being sampled for generalizations to be valid.
 There are different sampling methods.
 A sample that is not representative is a biased sample.
 A random sample removes the potential for bias that other sampling methods have.
 Data from a random sample may be used to draw inferences about a population.
 Visuals, such as a dot plot, may be used to show differences between data distributions.
 Data from random samples are used to compare different populations.
 The possible results of an experiment are outcomes.
 An event is a collection of outcomes.
 Probability measures the likelihood that an event will occur.
 Probability is measured as a number between 0 and 1.
 An impossible event has a probability of 0.
 As the probability of an event gets closer to 1, the more likely that event will occur.
 Theoretical probability is based on knowing all of the equally likely outcomes.
 Experimental probability is based on repeated trials.
 Probability is used to make predictions.
 There are often discrepancies between probability models and observed frequencies.
 Organized lists, tables, tree diagrams and simulation are used to find probabilities of compound events.
 The probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
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To find the probability that event A or event B occurs you add the probabilities of the events and subtract the probabilities of both
events.
The sum of the probabilities of complementary events is always 1.
To find the probability that event A and event B occurs you multiply the probabilities of the events.
Organized lists, tables and tree diagrams may be used to represent sample spaces for compound events.
A simulation generates frequencies for compound events.
A simulation is used to make predictions.
Unit Essential Questions
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What is statistics used for?
What is a population?
What is a random sample?
When is a random sample valid?
What are numerical data distributions?
How can you use data from random samples to compare two populations?
What is probability?
What is the difference between theoretical and experimental probability?
How would you use probability to predict the likelihood of an event occurring?
How do you find probabilities of compound events?
What are sample spaces?
How could you represent sample spaces?
What is a simulation used for?
Knowledge and Skills
Students will know and be able to…
 Key vocabulary: statistics, population, data, random sample, probability, event, sample space, tree diagrams and simulation.
 Use a random sample to form generalizations about a population.
 Visually show numerical data distributions.
 Understand probability of an event (simple or compound).
 Understand that the probability of an event is a number between 0 and 1.
 Find the probability of a simple or compound event.
 Explain the difference between theoretical and experimental probability.
 Use probability to make a prediction.
 Use organized lists, tables, tree diagrams and simulation to find probabilities of compound events.
 Understand and represent sample spaces.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
 Formal and informal assessments
 Written, verbal and slate assessments
 Teachers observations of independent assignments
 Chapter quizzes and end of chapter tests
 Daily exit slips
 Observation of use of hands on materials (Manipulative)
 Evaluation of multiple choice questions, short constructed response and open ended questions
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
 Extra practice worksheets
 Enrichment worksheets
 Cooperative learning activities
 Use of online Multilingual Glossary (ESL)
 Hands on activities
RESOURCES
Teacher Resources:


Math in Focus textbook and eBook
Math in Focus Teaching Resources CD
Equipment Needed:

















Chart paper
Dry erase markers
Slate boards
Exit tickets
Index cards
Calculator
Multiplication table
Student reference book
Overhead projector
Manipulative
Textbooks
Notebooks
Worksheets
Pencils and erasers
Rulers
Number cubes
Scissors
Technology Resources for Students:





Game - Identify representative random and biased samples
http://www.ixl.com/math/grade-7/identify-representative-random-and-biased-samples
Estimate population size using proportions.
http://www.ixl.com/math/grade-7/estimate-population-size-using-proportions
Game - Changes in mean, median, mode and range
http://www.ixl.com/math/grade-7/changes-in-mean-median-mode-and-range
Game - Probability of opposite mutually exclusive and overlapping-events.
http://www.ixl.com/math/grade-7/probability-of-opposite-mutually-exclusive-and-overlapping-events
Video – Understanding the Probability of Chance Events
https://learnzillion.com/lessonsets/88-understand-the-probability-of-chance-events
Technology Resources for Teachers/Parents:





MIF – Math Background Video- Statistics
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volB/data/mifpdv/Chapter9.html
MIF – Math Background Video- Probability
http://my.hrw.com/mif_6/mif_2012/assets/grade7_volB/data/mifpdv/Chapter10.html
MIF – Podcast Video- Problem Solving in Mathematics
http://my.hrw.com/mif_6/mif_2012/student/grade7_volA/tabpages/mathtool/video.html?videoxml=ref:SM_006
MIF Transition Resource Map
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821351 (Statistics)
http://my.hrw.com/tabnav/controller.jsp?isbn=9780547821351 (Probability)
Useful websites for teachers to explore:
1. https://my.hrw.com
2. http://illuminations.nctm.org
3. http://www.ixl.com (the activities on this website are broken down by specific CCSS standards under each and
every domain)
4. https://sites.google.com/site/emilou2010/
Digital Tools for Teachers/Students:





MIF – Algebra Tiles
http://my.hrw.com/math11/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html
MIF – Fraction/Decimal Grid
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.htmll
MIF – Integer Chips
http://my.hrw.com/math06_07/nsmedia/tools/Integer_Chips/Integer_Chips.html
MIF – Graphing Calculator
http://my.hrw.com/math11/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
MIF – Multilingual Glossary
http://my.hrw.com/math11/math06_07/nsmedia/tools/glossary/msm/glossary.html