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i h Grade Math Curriculum Map
                                       7th    Grade Math Curriculum 


                                                                     Introduction
This document contains all mandated 2010 Arizona Mathematical Standards for ih                                     standards have been organized into
units and clusters. The units represent the major domain under which the identified                                    represents the collection of similar
concepts within the larger domain. Within these units and clusters the _6.+~~                                             to represent a logical progression
of the content knowledge. It is expected that all teachers follow the                                                        the following document.

                                                                   Organiza
Approximate Time
Approximate times are based on a 60-minute instructional session for grades 6-8.
                                                                  'Ii">.'.
                                                                                                         clusters must be taught prior to the 2013 AIMS
assessment.

Essential Questions
Essential Questions are to be posed to the students at the beginning                                             the cluster. They are designed to facilitate
conceptual development of the content and can be used as a tool for                                    order thinking and inquiry. The students should be
able to answer these on their own by the end of

Big Ideas
Big Ideas are the essential understandings                                              These are the enduring understandings we want students to carry
with them from grade level to grade level.                                              indicative of a student mastering the Big Idea, however they are not
always synonymous. Thus, in cases that the                                           does not include all components of the Big Idea, the Big Idea (tor
teacher use) has been provided in .


                                                                             process. Being aware of such misconceptions allows us to plan for them during



This document has been organized b                   ds and mathematical practices. The content standards are those that represent knowledge
specific to the mathematical standard (            ains). The mathematical practices describe varieties of expertise that mathematics educators at
all levels should seek to develop in their s    . These practices rest on important "processes and proficiencies" with longstanding importance in
mathematics education. The content standar and mathematical standards have been paired to represent possible combinations of content standards
with mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, the

8/1312012                                                                                                      Isaac Elementary School District
t h Grade Math Curriculum Map
pairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a deeper
level of understanding and/or should be connected to the other standards in the cluster.

Common Core/Cross Curricular
The standards in the Common Core/Cross Curricular column represent possible reading,                              language standards that can be reinforced
or taught through the mathematical content standards with which they are paired.

Priority
With input from grade level teachers, standards have been prioritized in two                                                  prioritized using a three-point
scale. Essential standards represent those that are heavily weighted on                                                       icable in multiple contexts.
Important standards are those that are applicable in many contexts and less                            state/national exaffls. Useful standards are those
with the least weight on state/national exams and are likely only useful in a SjJt::,;lU';             is denoted in the priority column with the codes E
(essential), I (important) and U (useful). This label applies to the content standar                The skill/process standards that are a priority for this
grade level are highlighted in blue and are expected to be maste~"at this grade level.

Key Vocabulary
The key vocabulary that should be taught for each ofthe                                                    vocabulary. These vocabulary words are coded
as tier one (1), tier two (2) or tier three (3). Tier one words are those                              should not be explicitly taught. Tier two words are
high utility words that can be used across content n~~n~ ~~ n~~b~+~                                     specific words.

Resources
The two types of resources listed are the W                                             Resources. All are suggestions that teachers may use to support
instruction. They are aligned to the standard                                           resources are useful Internet links that can be used for the teacher's
edification prior to instruction or as a tool during                                    are suggested pages from the adopted texts.

Unit/Cluster Project
The Unit/Cluster Projects                                                 to support students in making connections, critical thinking, higher order
thinking, and/or spiraling                                                  from all clusters within a unit while cluster project support the standards in a
particular cluster. While                                      do a project with every unit or cluster these resources will support project-based instruction
and practice should the tea.-w;;]

Assessment
The assessment section of the map                          for teachers to plan the dates that they will give a formative assessment for the cluster. It is
expected that each cluster be assessed                 eommon formative assessment.




8/1312012                                                                       2                               Isaac Elementary School District
t h Grade Math Curriculum Map
Other
Standards may appear more than once. Each time they should be taught within the context of                 andlor revisited to a deeper level of
knowledge. Underlined segments of a standard indicate an additional piece of the standard that             not covered in previous clusters.
[Bracketsl will occasionally appear though out the document and indicate clarification of the             Bracketed information is not a part of the
standard itself.

 Unit: Ratios of Proportional Relationships
 Cluster: Rate of Change

               Time: 3 weeks
                                Essential Questions

     •   Why is it important to know proportions?                                                dents will understand that proportional

                                                                                                           are used to solve real-world situation.




     •   How is rate of change and proportions                                         •   Students will understand that if two quantities are

                                                                                           proportional that one varies directly with another. As

                                                                                           the rate of one quantity changes, the other quantity

                                                                                           changes at on independent constant rate.


     •   What is a nronort
                                                                                       •   Students will understand proportional relationship can

                                                                                           be displayed in tables, graphs, and real-life

                                                                                           contextual situations




8/13/2012                                                               3                               Isaac Elementary School District
h
i     Grade Math Curriculum
    Priority I           Standard                                Mathematica I    Common                                           Resources
                                                                   Practices     Core/Cross                             Web Resources              Core
                                                                                 Curricular
            *S IC I P02. Find or use factors,                                                                                                  MC:4-1
            multiples, or prime factorization within a
            set of numbers.




            7.RP.1. Compute unit rates associated                7.MP.2.                                                                       MC: 6-1,6-2
            with ratios of fractions, including ratios of        7.MP.6.
            lengths, areas and other quantities                                                                        Ratio and Proportion
            measured in like or different units. For
            example, if a person walks !0 mile in each
            ~ hour, compute the unit rate as the
            complex fraction !0/~ miles per hour,
            t>rwi"nltmtlll 2 miles Der hour.
             7.RP.2. Recognize and represent                                                                           Proportions             MC: 6-3
            proportional relationships between                                                       inate pair        (Rectangle)
            quantities.                                                                       Coordinate plane
                                                                                              Equation                 Proportions (Cake)
            a. Decide whether two quantities are in a                                         Graph
            proportional relationship, e.g., by t~~inn ..:'''1                                Origin                   Proportions (What's
            for equivalent ratios in a table or
                                                                                              Proportions              your rate?)
            graphing on a coordinate plane and
                                                                                              Table
            observing whether the graph is a straight
                                                                                              Unit rate                Proportions (Walk the
            line through the origin.
                                                                                              Units                    plank)
            b. Identify the constant
            (unit rate) in tables,
            diagrams, and
            proportional

            c. Represent proportion'
            equations. For example,
            proportional to the number n
            purchased at a constant price p,
            relationship between the total cost
            number of items can be expressed as

            d. Explain what a point (x, y) on the graph
            of a proportional relaticlIls!Jipmellrls_in_--->

8/13/2012                                                                           4                             Isaac Elementary School District
t h Grade Math Curriculum
 Priority   I              Standard             Mathematical        Common                                         Resources
                                                  Practices        Core/Cross                           Web Resources            Core
                                                                   Curricular
                terms of the situation, with special
                attention to the points (0, 0) and (I, r)
                where r is the unit rate .
                                       .~~..~------~--~------------~~------------------~~~~--~~
                *S3C3P04. Translate hpl'llIP,>n                                                                              MC: 1-10,3-7
                and tables that represent a linear equation.


 Unit
 Project:

       sment:




8/13/2012                                                             5                           Isaac Elementary School District
7'h Grade Math Curriculum Map

 Unit: Ratios of Proportional Relationships
 Cluster: Ratio and Percent

 Approximate Time: 2 week

                                Essential Questions

     • 	 How is percent and proportions related?                                                    the relationship between




     • 	 What is the difference between percent change and net       :::~~~tuaems   will understand that percents are used to

                                                                         solve real-world problems that include: simple

                                                                         interest, tax, percent change, percent error, fees and

                                                                         commissions.



     • 	 Describe how                                                 • 	 Students will        proportions to scale real-world

         problems.                                                       figures. e.g. maps and building blueprints




8/1312012 	                                                      6                  Isaac Elementary School District
7thGrade Math Curriculum
  Priority I         Standard                         Mathematical         Common                                     Resources
                                                        Practices         Core/Cross                       Web Resources             Core
                                                                          Curricular
            *S I C3 P04. Estimate the measure                                                                                   MC: 6-4
            of an object in one system of units
            given the measure of that object in
            another system and the approximate
1------11
            conversion factor.
               ....
                n n n m _




            7.G.1. Solve problems involving          7.MP.l.         6-8.RST.7                                                  MC: 6-8
            scale drawings of geometric figures,     7.MP.2.         SC07-S I C2-04
            such as computing actual                 7.MP.3.         SS07 -S4C6-03
            and areas from a scale tiro>wino­        7.MP.4.         SS07 -S4C 1-0 I
            reproducing a scale                      7.MP.5.         SS07 -S4C 1-02
            different scale.                         7.MP.6.         ET07-SICI-OI
                                                     7.MP.7.
                                                     7.MP.8.
            7.RP.3. Use proportional                                                                                            MC: 6-9, 7-1, 7-2,
            relationships to solve multistep ratio                                                                              7-3, 7-4, 7-5, 7-6,
            and percent problems. Examples:                                                                                     7-7, 7-8, 7-9
            simple interest, tax, markups and
            markdowns, gratuities and
            commissions, fees, percent increase                                        Increase
            and decrease, percent error.                                               Markdowns markups
                                                                                       Percent
                                                                                       Ratio
                                                                                       Simple interest
                                                                                       Tax
 Unit
 Project:




8113/2012                                                                       7                     Isaac Elementary School District
7th   Grade Math Curriculum Map

 Unit: The Number System
 Cluster: The Number Line

                Time: 3 weeks




8113/2012                         8   Isaac Elementary School District
7th   Grade Math Curriculum
                                           Essential Questions                                         Big Ideas

        • 	 What is distance?                                                   •               will understand that absolute value is the



        • 	 What is a number?                                                                                       that all real numbers fit on

                                                                                                        t.."4RLlVllCU   and irrational

        • 	 How can the four arithematic operations can be representated on a

             line?                                                                  operations (addition, subtraction, multiplication,

                                                                                         division) can be representated on a number

        • 	 How is subtraction and the additive inverse related?

                                                                                • 	 Students will understand that subtracting a number

        • 	 How is division and the         multipli"(.ul~                         is the same as addings its additive inverse.

                                                                                • 	 Students will understant that dividing by a number

        •	   Whv Cl'In't von CllVHle hVA4:r~"3R:'~~:SS81>"""~,                    is the same as multiplying by its multiplicative

                                                                                    Inverse.

                                                                                • 	 Students        understand that you cannot divide by

                                                                                    o.




8113/2012 	                                                              9                     Isaac Elementary School District
7thGrade Math Curriculum
 Priority I           Standard                            Mathematical    Common                                       Resources
                                                            Practices    Core/Cross                         Web Resources                Core
                                                                         Curricular
            *SIC3POI. Estimate and apply
            benchmarks for rational numbers and
            common irrational numbers.




            *S IC3 P03. Estimate square roots of                                                                                 MC: 1-3, 12-1
            numbers less than 1000 by locating them
            between two consecutive whole numbers.

            7.NS.l. Apply and extend previous             7.MP.2.                                                                MC: 2-1, 2-2, 2-4,
            understandings of addition and subtraction    7.MPA.                                                                 2-5
            to add and subtract rational numbers;         7.MP.7.
            represent addition and subtraction on a
            horizontal or vertical number line diagram.

            a. Describe situations in which opposite
            quantities combine to make O. For example,
            a hydrogen afom has 0 charge because its
                                                                                      Inverse properties
            two consfifuenfs are oppositely charged.
                                                                                      Multiplicative
            b. Understand p + q as the number
                                                                                      inverse
            a distance I q I from p, in the positive or                               Minuend
            negative direction depending on whether q                                 Operations
            is positive or negative. Show that a number                               Opposite
            and its opposite have a sum                                               Subrahead
            additive inverses).                                                       Sum
            rational numbers b                                                        Variable
            contexts.                                                                 Vertical

            c. Understand
            numbers as adding
            - q    p + (-q). Show
            between two rational
            number line is the absolute
            difference, and apply this
            world contexts.

            d. Apply properties of operations as 

                      to add and subtract rational 


8/13/2012                                                                 10 
                        Isaac Elementary School District
t h Grade Math Curriculum
            numbers.

 Priority                   Standard                     Mathematical     Common                                       Resources 

                                                           Practices 
   Core/Cross                         Web Resources                Core
                                                                         Curricular
            *SIC I P03. Compare and order rational                                                                               MC: 4-9
            numbers using various models and
            representations.




            7.NS.2. Apply and extend previous            7.MP.2.                                                                 MC: 2-6,2-8
            understandings of multiplication and         7.MPA.
            division and of fractions to multiply and    7.MP.7.
            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
                                                                                      -Associative
            signed numbers. Interpret products of                                     -Identity
            rational numbers by describing rea                                        -Distributive
            contexts.                                                                 Quotient
                                                                                      Repatend
            b. Understand that integers can be                                        Terminates
            divided, provided that the
            zero, and every quotient
            non-zero divisor) is a
            and q are intege
            p/(-q). Interpret
            numbers by d

            c. Apply properties of 0
            strategies to multiply and
            numbers.

            d. Convert a rational number to a
            using long division; know that the
            form of a rational number terminates in Us
            or

8/13/2012                                                                 11                          Isaac Elementary School District
t h Grade Math Curriculum
 Unit
 Proiect:




 Unit: The Number System
 Cluster: Order of Operation

  ...........vjmate Time: 1 week




8/13/2012                          12   Isaac Elementary School District
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i       Grade Math Curriculum
                                    Essential Questions                                                     Big Ideas

          • 	 What are grouping symbols?                                             •	             symbols include: Parentheses, absolute

          • 	 A base raised to the 0 power is what value? Why?                                          and cube roots, brackets, and braces



          • 	 Do we apply the rules of multiplication before division whilst using                              ~lClllUll"   to evaluate expressions

             of operations to evaluate an expression?

          • 	 Do we apply the rules of addition before subtraction

             operations to evaluate an expression?




          • 	 When would we express a number in S~!~~~JDt!or                         • 	 Scientific notation is used to express very large

                                                                                          quantities and very small quantities.




                                                                                     • 	 Multiplying a number by an exponent with base 10

                                                                                          moves the decimal to the left or right.




8/1312012 	                                                                  13                     Isaac Elementary School District
t h Grade Math Curriculum
 Priority I               Standard                   Mathematical         Common                      Resources
                                                       Practices         Core/Cross        Web Resources            Core
                                                                         Curricular
              "'S IC2P04. Represent and interpret                                                               MC: 1-2, p. LA2
              numbers using scientific notation                                                                 LA5
              (positive exponents

              7.NS.3. Solve real-world and          7.MP.l.         6-8.RST.3                                   MC: 1-4
              mathematical problems                 7.MP.2.
              the four operations with rational     7.MP.5.
              numbers. (Computations with           7.MP.6.
              rational numbers extend the rules     7.MP.7.
              for manipulating fractions to         7.MP.8.
              ~~~~lov fractions.

 Unit
 Project:

 Assessment:




811312012                                                                       14    Isaac Elementary School District
i h Grade Math Curriculum Map
 Unit: Expressions and Equations 

 Cluster: Properties of Evaluating Expressions 


               Time: 1 week
                                  Essential Questions                                    Big Ideas

     • 	 What is a variable?                                                                     that a variable is    a




     • 	 What does it mean when one thing is equivalent to            *uu,",m"   will be able to use properties of operations

     • 	 What is a coefficient?                                            , subtract, factor, and expand expressions with




                                                                  • 	 Students will look at a given problem and be able to

                                                                     express it in a different context.




8/13/2012 	                                                  15                  Isaac Elementary School District
h
i     Grade Math Curriculum
     Priority I         Standard                       Mathematical         Common                      Resources
                                                         Practices         Core/Cross        Web Resources            Core
                                                                           Curricular
               7 .EE.1. Apply properties of           7.MP.2.         6-8.RST.5                                   MC: 1-8
               operations as strategies to            7.MP.6.
                                and expand linear     7.MP.7.
               expressions with rational
               coefficients.

               7.EE.2. Understand that rewriting an   7.MP.2.         6-8.WH5T.l b-c
               expression in different fonns in a     7.MP.6.         6-8.WH5T.2b-c
               problem context can shed light on      7.MP.7.         6-8.R5T.3
               the problem and how the quantities     7.MP.8.         6-8.R5T.7
               in it are related. For example, a +                    5507-55(2-09
               0.05a 1.05a means that "increase                       SC07-S2C2-03
                . 5%" is the same as
               1.05. "
    Unit
    Project:

    Assess




8/1312012                                                                         16    Isaac Elementary School District
i h Grade Math Curriculum Map

 Unit: Expressions and Equations
 Cluster: Solving Equations

            te Time: 2 weeks
                                  Essential Questions                                        Big Ideas

     •   How do we translate a written or verbal description                                     to create an equation or

         equation?                                                                                 text or real-world scenario.



     •   What is the difference between an expression and an                         will understand the difference between an

     •   What is an inequality?                                                        equation, and inequality.



                                                                      • 	 Students will be able to solve for a missing piece of

                                                                         information from a specific problem or text.



                                                                      • 	 Students       be able to check the reasonableness of

                                                                         an answer.




8/13/2012                                                      17 	                  Isaac Elementary School District
Grade Math Curriculum
 Priority I         Standard                        Mathematical         Common                                           Resources
                                                      Practices         Core/Cross                             Web Resources            Core
                                                                        Curricular
            *S3C3P02. Evaluate an expression                                                                                        MC: 1-6
            containing one or two variables by
            substituting numbers for the
            variables.
            7.EE.3. Solve multi-step real-life      7.MP.1.        6-8.WHST.l b-c                                                   MC: 1-7
            and mathematical problems posed         7.MP.2.        6-8.WHST2b
            with positive and negative rational     7.MP.3.        6-S.RST.7
            numbers in any form (whole              7.MP.4.        ET07-S6C2-03
            numbers, fractions, and decimals),      7.MP.5.
            using tools strategically. Apply        7.MP.6.
            properties of operations to calculate   7.MP.7.
            with numbers in any form; convert       7.MP.S.
            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 1110 ofher salary an
            hour, or $2.50, for a new salary of
            $27.50. Ifyou want to place a towel
            bar 9 314 inches long in the center
            ofa door that is 27 112 inches wide,
            you will need to place the bar about
            9 inches from each edge; this
            estimate can be used as a
            the exact compufntinJ
             7.EE.4. Use va

                                                                                     Inverse operations
            simple equations
            solve problems by
            the quantities.

            a. Solve word problems
            equations of the form px+q=r
            p(x+q)=r, where p, q, and rare
            specific rational numbers. Solve
            equations of these forms fluently.
            Compare an algebraic solution to an
            arithmetic solution. identifyina the
8/13/2012                                                                    18                           Isaac Elementary School District
t h Grade Math Curriculum
  Priority   I                Standard                    Mathematical    Common                                       Resources
                                                            Practices    Core/Cross                         Web Resources            Core
                                                                         Curricular
                 sequence of the operations used in
                 each approach. For example, fhe
                 perimefer of a recfang/e is 54 em. Ifs
                 lengfh is 6 em. Whaf is ifs widfh?

                 b. Solve word problems leading to
                 inequalities ofthe form px+ q>r or
                 px+q < r, where p, q, and rare
                 specific rational numbers. Graph the
                 solution set ofthe 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 ofsales you need to make,
                 and describe the solutions.
                 *SSC2P09. Solve logic problems
                 using mUltiple variables and                                         statement
                 multiple conditional statements                                      Logic
                        words. oictures. and charts.
                 *SSC2POlO. Demonstrate and                                           Deductive reasoning
                 explain that the process of solving
                       .     is a deductive
 Unit
 Project:




8/13/2012                                                                   19                         Isaac Elementary School District
h
t       Grade Math Curriculum Map

    Unit: Geometry
    Cluster: Angles

                    Time: 1 week
                                    Essential Questions                                    Big Ideas

          • 	 What is the difference between equal, approximate, and congruent?                     the difference between

                                                                                                   congruent.

          •   Which angle relationships are congruent? Which are not?

                                                                                   will utilize the properties of angles to solve

                                                                                  measure of an unknown angle.




8/13/2012 	                                                                20       Isaac Elementary School District
t h Grade Math Curriculum
 Priority   I               Standard                  Mathematical          Common                      Resources
                                                        Practices          Core/Cross        Web Resources            Core
                                                                           Curricular
                *S4CIP05. Identify corresponding
                parts of congruent figures.

                7.G.5. Use facts about               7.MP.3.         ET07-S I C4-0 I
                supplementary, complementary,        7.MP.4.
                vertical, and adjacent angles in a   7.MP.5.
                multi-step problem to write and      7.MP.6.
                solve simple equations for an        7.MP.7.
                unknown angle in a figure.




 Unit
 Project:




 Unit: Geometry
 Cluster: Geometric Properties




8/13/2012                                                                       21      Isaac Elementary School District
i h Grade Math Curriculum
                                Essential Questions                             Big Ideas

     •   What is a cross section?                          •            will be able to determine what type of 2-D

     •   What is a 3D shape?                                                    from a cross section of a 3-D figure.

     •   What is a 2D shape?

                                                                                        that the number of sides a

                                                                       directly translates to the sum of its interior




                                                                        will know what the parts of a triangle are

                                                               and how they are related to each other.




8113/2012                                             22                 Isaac Elementary School District
7thGrade Math Curriculum
  Priority I         Standard                          Mathematical         Common                                      Resources
                                                         Practices         Core/Cross                        Web Resources            Core
                                                                           Curricular
            *S4C I P04. Describe the
            relationship between the number of
            sides in a regular polygon and the
            sum of its interior angles.


            7.G.2. Draw (freehand, with ruler         7.MP.4.         6-8.R5T.4
            and protractor, and with technology)      7.MP.5.         6-8.R5T.7
            geometric shapes with given               7.MP.6.         6-8.WH5T.2b-2f
            conditions. Focus on constructing         7.MP.7.         51 C2-04
            triangles from three measures of          7.MP.8.         ET07-SIC2-01
            angles or sides, noticing when the                        ET07-S6C 1-03
            conditions detennine a unique
            triangle, more than one triangle, or
            no triangle.
            7.G.3. Describe the two-dimensional
            figures that result from slicing three­
            dimensional figures, as in plane
            sections of right rectangular prisms
            and right rectangular pyramids.
                                                                                        Cylinder
                                                                                        Face
                                                                                        Right prism
                                                                                        Right pyramid
                                                                                        Vertex
 Unit
 Proiect:




8/13/2012                                                                      23                       Isaac Elementary School District
7th Grade Math Curriculum Map

 U nit: Geometry
 Cluster: Circumference and Area

              te Time: 2 weeks
                                 Essential Questions                                                   Big Ideas


     • 	 What is the difference between perimeter, area, surface area and                                    determine the parts of a

                                                                                          . I.e. circumference, area, are, chord, diameter,

     • 	 Why is volume units cubed and surface area units

                                                                                                   understand that perimeter is the

                                                                                                   of length, having neither width nor



                                                                                 • 	 Students will understand that area is the

                                                                                    measurement of a surface space in a 2-D region, and

                                                                                    that the measuring tool used are squares that have a

                                                                                     length and width of one unit measure.

                                                                                 • 	 Students will understand that volume is the

                                                                                    measurement of space that a 3-D object can occupy,

                                                                                    and that the measuring tool used are cubes that have

                                                                                    a length, width, and height of one unit measure.


8/1312012 	                                                                 24                 Isaac Elementary School District
7th   Grade Math Curriculum Map

  Priority                Standard                    Mathematical         Common                                     Resources
                                                        Practices         Core/Cross                       Web Resources            Core
                                                                          Curricular
              7.GA. Know the fonnulas for the        7.MP.1.         6-S.WHST.ld 

              area and circumference of a circle     7.MP.2.         SC07-S2C2-03 

              and solve problems; give an            7.MP.3. 
       ET07-S6C2-03
              infonnal derivation of the             7.MP.4.         ET07-S I C4-0 I
              relationship between the               7.MP.5. 

              circumference and area of a circle.    7.MP.6. 

                                                       7.MP.7.
                                                     ,7.MP.S. _ _ _-I-_ _ _ _ _--'

              relationship between central angles
              and intercepted arcs; identify arcs
              and chords of a circle.
              *S4C4P02. Identify polygons
              having the same perimeter or area.

              *S5C I PO I. Create an algorithm to
              detennine the area of a given

              7.G.6. Solve real-world and                                              Faces
              mathematical problems involving                                          Net
              area, volume and surface area of                                         Surface area
              two- and three-dimensional objects                                       Volume
              composed of triangles,
              quadrilaterals, polygons, cubes, and
              right prisms.

 Unit
 Project:




8/1312012                                                                      25                     Isaac Elementary School District
i h Grade Math Curriculum Map

 Unit: Statistics and Probability
 Cluster: Stats and Data

                Time: 2 weeks
                                    Essential Questions                                           Big Ideas

     •   What is a random sample and why are they used to colelct data?                                       that a random sample is

                                                                                                U1.l~~ll,,;l;:>   and generalization about a

     •   How can we design a random sample from a population?                  population if there is an even representation.



                                                                                        will understand that there is a margin of

                                                                               error in making inferences with a random sample.




8113/2012                                                                 26             Isaac Elementary School District
h
i    Grade Math Curriculum
    Priority I         Standard                        Mathematica I         Common                                   Resources
                                                         Practices          Core/Cross                     Web Resources            Core
                                                                            Curricular
             7.SP.1. Understand that            17.MP.3.               5507-54(4-04
             statistics can be used to gain      7.MP.6.               5507-54(4-05
             information about a population                            5(07-53( 1-02
             by examining a sample of the                              5(07-54(3-04
             population; generalizations about                         ET07-54(2-01
             a population from a sample are                            ET07-54(2-02
             valid only if the sample is                               ET07 -S6C2-03
             representative of that population.
             Understand that random
             sampling tends to produce
             representative samples and
             sunnnrt v,;:alirl inf... r... n,......c
             "S2C1P01. Solve problems by
             selecting, constructing, and
             interpreting displays of data
             including mUlti-line graphs and

             *S2CIP02. Interpret trends in a
             data set, estimate values for
             missing data, and predict values                                            Prediction
             for points beyond the range of                                              Range
             the data set.                                                               Trends
             7.SP.2. Use data from a random                                              Simulated
             sample to draw inferences about
             a population with an unknown
             characteristic of i
             Generate multiple
             simulated
             size to gauge                                                   1(3-01
                                                                           -51 (3-02
             estimates or
                                                                       ET07-54C2-02
             example,
                                                                       ET07-56(2-03
             word length in
             randomly sampling
             the book; predict the
             school election based on
             randomly sampled survey
             Gauge how far off the estimate
             or Drediction miaht be.



8/13/2012                                                                       27                    Isaac Elementary School District
t h Grade Math Curriculum
  Priority   I       Standard   Mathematical    Common                      Resources
                                  Practices    Core/Cross        Web Resources            Core
                                               Curricular
 Unit
 Project:

 Assessment:




8113/2012                                         28        Isaac Elementary School District
Grade Math Curriculum Map

Unit: Statistics and Probability
Cluster: Data Graph and Analysis

     roximate Time: 2 weeks
                                Essential Questions                                                  Big Ideas

     •   Why is the average not a good measure of center to use when reporting                               that measures of center is a

         data?                                                                                              a set of data, except if there



     •   How do outliers affect a data set?

                                                                                           will use measure of center to express a set of

                                                                                      and correctly decide which measure of center

                                                                                 best fits a given set of data.




8/13/2012                                                              29                   Isaac Elementary School District
7thGrade Math Curriculum
  Priority I         Standard                    Mathematical         Common                                    Resources
                                                   Practices         Core/Cross                      Web Resources            Core
                                                                     Curricular
            7.SP.4. Use measures of center      7.MP.1.         6-8.WHST.l b
            and measures of variability for     7.MP.2.         ET07-S 1C3-01
            numerical data from random          7.MP.3.         ET07-S 1C3-02
            samples to draw informal            7.MP.4.         ET07-S4C2-0 1
            comparative inferences about        7.MP.S.         ET07-S4C2-02
            two populations. For example,       7.MP.6.         ET07-S6C2-03
            decide whether the words in a       7.MP.7.         SC07-S 1C3-0 1
            chapter of a seventh-grade                          SC07-S 1C3-0S
                                                                SC07-S 1C4-03
            science book are generally
                                                                SC07-S2C2-03
            longer than the words in a
                                                                SC07-S4C3-04
            chapter of a fourth-grade science                   SS07-S4C2-0 1
            book.

            *S2C1 P03. Identify outliers and
            determine their effect on mean,
            median, mode, and range.


            7.SP.3. Informally assess the
            degree of visual overlap of two                                       Measure of­
            numerical data distributions with                                     Variability
            similar variabilities, measuring
            the difference between the
            centers by expressing it as a
            multiple of a measure of
            variability. For
            mean height of
                                                                      1C3-01
            basketball
                                                                      1C3-02
            than the                                                -S4C2-01
            on the soccer                                       ET07-S4C2-02
            the variability                                     ET07-S6C2-03
            deviation) on
            dot plot, the
            the two distributions of
            noticeable.
 Unit
 Proiect:



8/1312012                                                                 30                    Isaac Elementary School District
t h Grade Math Curriculum Map




8/1312012                       31   Isaac Elementary School District
h
i       Grade Math Curriculum Map

    Unit: Statistics and Probability
    Cluster: Simple and Compound Events

                ate Time: 1 week
                                    Essential Questions                                                        Big Ideas

          • 	 How can probabilty be used to make informed predictions?                                                 that the probability of a

                                                                                                                           0, which is impossible to

          • 	 How does increasing the total number of possible outcomes affect the      happen, and 1, which is certain to happen.

             probability of a given situation?

                                                                                          Lqu;;lll~   will understand that the probability that an

                                                                                        even will occur is equal to the number of favorable

                                                                                        outcome divided by the total number of outcomes.



                                                                                     • 	 Students will understand that a sample space is a

                                                                                        diagram of all possible outcomes for a given

                                                                                        situation.




8/13/2012 	                                                                 32                         Isaac Elementary School District
t h Grade Math Curriculum
  Priority   I                  Standard                    Mathematical         Common                      Resources
                                                              Practices         Core/Cross        Web Resources             Core
                                                                                Curricular
                 7.5P.5. Understand that the probability    7.MP.4.        6-8.WH5T.1 b
                 of a chance event is a number between      7.MP.5.        5507-55C1-04
                 o and 1 that expresses the likelihood      7.MP.6.        ET07-51 C3-01
                 of the event occurring. Larger numbers     7.MP.7.        ET07-51 C3-02
                 indicate greater likelihood. A
                 probability near 0 indicates an unlikely
                 event, a probability around Y2
                 indicates an event that is neither
                 unlikely nor likely, and a probability
                 near 1 indicates a likely event.

                 7.5P.8. Find probabilities of compound     7.MP.1.
                 events using organized lists, tables,      7.MP.2.
                 tree diagrams, and simulation.             7.MP.4.
                                                            7.MP.5.
                 a. Understand that, just as with simple    7.MP.7.
                 events, the probability of a compound      7.MP.8.
                 event is the fraction of outcomes in the
                 sample space for which the compound
                 event occurs.

                 b. Represent sample spaces for
                 compound events using methods such
                 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 that
                 event.




                 answer to the question:
                 donors have type A
                 probability that it will take
                 donors to find one with
 Unit
 Project:



8113/2012                                                                           33       Isaac Elementary School District
h
i    Grade Math Curriculum
    Priority I          Standard                     Mathematical       Common                                       Resources
                                                       Practices       Core/Cross                         Web Resources              Core
                                                                       Curricular 	



    Unit: Statistics and Probability 

    Cluster: Theoretical and Experimental Probabilities 


                  Time: 2 weeks
                                       Essential Questions

        • 	 What are the similarities and differences between experimental and            Students will understand that probability is a theory

            theoritical probability?                                                          is the likelyhood that an event will happen, and




                                                                                      •   Students will understand that the more trials used in

                                                                                          an experimental probability, the closer the

                                                                                          probability of an event occuring gets closer to its

                                                                                          theoretical probability.




8113/2012 	                                                                34                       Isaac Elementary School District
7thGrade Math Curriculum
 Priority I           Standard                             Mathematical         Common                       Resources
                                                             Practices         Core/Cross         Web Resources                Core
                                                                               Curricular
            7.SP.6. Approximate the probability of a                      6-S.WHST.l a
            chance event by collecting data on the                        ET07-S1C2-01
            chance process that produces it and                           ET07-S 10-02
            observing its long-run relative
                                                                          ET07-S 1C2-03
            frequency, and predict the approximate
            relative frequency given the probability.                     ET07-S 1C3-0 1
            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.




            7.SP.7. 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
            discrepancy.

            a. Develop a uniform probability model by
            assigning equal probability to all outcomes,
            and use the model to dete
            probabilities of events.
            student is selected at
            find the probabilit
            and the probability

            b. Develop a
            may not be uniform)
            frequencies in data gen
            chance process. For
            approximate probability that a
            penny will land heads up or that
            tossed paper cup will land ODen-en
            down.


8113/2012                                                                        35         Isaac Elementary School District
7thGrade Math Curriculum
 Priority I           Standard                         Mathematical    Common                       Resources
                                                         Practices    Core/Cross         Web Resources                Core
                                                                      Curricular
            Do the outcomes for the spinning penny
            appear to be equally likely based on the
            observed freauencies?
 Unit
 Project:




8/1312012                                                              36          Isaac Elementary School District
7th   Grade Math Curriculum Map

 Unit: Displaying Data
 Cluster: Data displays

        roximate Time: 1 week
                                  Essential Questions                                                           Big Ideas

        • 	 What is a vertex-edge graph?                                                                            to read a vertex-edge diagram.

        • 	 How are vertex-edge graphs used in real life?

        • 	 What is the diflerence between a congurent transformation and a similar   Students will be able to use a Venn Diagram to

           transformation?                                                             J.Jl;;;:);;1U   algebraic problems.



                                                                                      Students will be able to translate, rotate, and reflect

                                                                                      geometric figures in a coordinate plane.




8/13/2012 	                                                                37                            Isaac Elementary School District
7thGrade Math Curriculum
  Priority I         Standard                    Mathematical 
    Common                      Resources
                                                   Practices 
    Core/Cross        Web Resources            Core
                                                                  Curricular
            *S2C3P02. Solve counting
            problems using Venn diagrams
            and represent the answer

            *S2C4P01. Use vertex-edge
            graphs and algorithmic thinking
            to represent and find solutions to
            practical problems related to
            Euler/Hamilton paths and
            circuits.
             *S4C2P01. Model the result of
            a double transformation
            (translations or reflections) of a
            2-dimensional figure on a
            coordinate plane using all four
            quadrants.


 Unit
 Project:




8/13/2012                                                            38        Isaac Elementary School District

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7th Grade Math Curriculum Map

  • 1. i h Grade Math Curriculum Map 7th Grade Math Curriculum Introduction This document contains all mandated 2010 Arizona Mathematical Standards for ih standards have been organized into units and clusters. The units represent the major domain under which the identified represents the collection of similar concepts within the larger domain. Within these units and clusters the _6.+~~ to represent a logical progression of the content knowledge. It is expected that all teachers follow the the following document. Organiza Approximate Time Approximate times are based on a 60-minute instructional session for grades 6-8. 'Ii">.'. clusters must be taught prior to the 2013 AIMS assessment. Essential Questions Essential Questions are to be posed to the students at the beginning the cluster. They are designed to facilitate conceptual development of the content and can be used as a tool for order thinking and inquiry. The students should be able to answer these on their own by the end of Big Ideas Big Ideas are the essential understandings These are the enduring understandings we want students to carry with them from grade level to grade level. indicative of a student mastering the Big Idea, however they are not always synonymous. Thus, in cases that the does not include all components of the Big Idea, the Big Idea (tor teacher use) has been provided in . process. Being aware of such misconceptions allows us to plan for them during This document has been organized b ds and mathematical practices. The content standards are those that represent knowledge specific to the mathematical standard ( ains). The mathematical practices describe varieties of expertise that mathematics educators at all levels should seek to develop in their s . These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The content standar and mathematical standards have been paired to represent possible combinations of content standards with mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, the 8/1312012 Isaac Elementary School District
  • 2. t h Grade Math Curriculum Map pairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a deeper level of understanding and/or should be connected to the other standards in the cluster. Common Core/Cross Curricular The standards in the Common Core/Cross Curricular column represent possible reading, language standards that can be reinforced or taught through the mathematical content standards with which they are paired. Priority With input from grade level teachers, standards have been prioritized in two prioritized using a three-point scale. Essential standards represent those that are heavily weighted on icable in multiple contexts. Important standards are those that are applicable in many contexts and less state/national exaffls. Useful standards are those with the least weight on state/national exams and are likely only useful in a SjJt::,;lU'; is denoted in the priority column with the codes E (essential), I (important) and U (useful). This label applies to the content standar The skill/process standards that are a priority for this grade level are highlighted in blue and are expected to be maste~"at this grade level. Key Vocabulary The key vocabulary that should be taught for each ofthe vocabulary. These vocabulary words are coded as tier one (1), tier two (2) or tier three (3). Tier one words are those should not be explicitly taught. Tier two words are high utility words that can be used across content n~~n~ ~~ n~~b~+~ specific words. Resources The two types of resources listed are the W Resources. All are suggestions that teachers may use to support instruction. They are aligned to the standard resources are useful Internet links that can be used for the teacher's edification prior to instruction or as a tool during are suggested pages from the adopted texts. Unit/Cluster Project The Unit/Cluster Projects to support students in making connections, critical thinking, higher order thinking, and/or spiraling from all clusters within a unit while cluster project support the standards in a particular cluster. While do a project with every unit or cluster these resources will support project-based instruction and practice should the tea.-w;;] Assessment The assessment section of the map for teachers to plan the dates that they will give a formative assessment for the cluster. It is expected that each cluster be assessed eommon formative assessment. 8/1312012 2 Isaac Elementary School District
  • 3. t h Grade Math Curriculum Map Other Standards may appear more than once. Each time they should be taught within the context of andlor revisited to a deeper level of knowledge. Underlined segments of a standard indicate an additional piece of the standard that not covered in previous clusters. [Bracketsl will occasionally appear though out the document and indicate clarification of the Bracketed information is not a part of the standard itself. Unit: Ratios of Proportional Relationships Cluster: Rate of Change Time: 3 weeks Essential Questions • Why is it important to know proportions? dents will understand that proportional are used to solve real-world situation. • How is rate of change and proportions • Students will understand that if two quantities are proportional that one varies directly with another. As the rate of one quantity changes, the other quantity changes at on independent constant rate. • What is a nronort • Students will understand proportional relationship can be displayed in tables, graphs, and real-life contextual situations 8/13/2012 3 Isaac Elementary School District
  • 4. h i Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular *S IC I P02. Find or use factors, MC:4-1 multiples, or prime factorization within a set of numbers. 7.RP.1. Compute unit rates associated 7.MP.2. MC: 6-1,6-2 with ratios of fractions, including ratios of 7.MP.6. lengths, areas and other quantities Ratio and Proportion measured in like or different units. For example, if a person walks !0 mile in each ~ hour, compute the unit rate as the complex fraction !0/~ miles per hour, t>rwi"nltmtlll 2 miles Der hour. 7.RP.2. Recognize and represent Proportions MC: 6-3 proportional relationships between inate pair (Rectangle) quantities. Coordinate plane Equation Proportions (Cake) a. Decide whether two quantities are in a Graph proportional relationship, e.g., by t~~inn ..:'''1 Origin Proportions (What's for equivalent ratios in a table or Proportions your rate?) graphing on a coordinate plane and Table observing whether the graph is a straight Unit rate Proportions (Walk the line through the origin. Units plank) b. Identify the constant (unit rate) in tables, diagrams, and proportional c. Represent proportion' equations. For example, proportional to the number n purchased at a constant price p, relationship between the total cost number of items can be expressed as d. Explain what a point (x, y) on the graph of a proportional relaticlIls!Jipmellrls_in_---> 8/13/2012 4 Isaac Elementary School District
  • 5. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular terms of the situation, with special attention to the points (0, 0) and (I, r) where r is the unit rate . .~~..~------~--~------------~~------------------~~~~--~~ *S3C3P04. Translate hpl'llIP,>n MC: 1-10,3-7 and tables that represent a linear equation. Unit Project: sment: 8/13/2012 5 Isaac Elementary School District
  • 6. 7'h Grade Math Curriculum Map Unit: Ratios of Proportional Relationships Cluster: Ratio and Percent Approximate Time: 2 week Essential Questions • How is percent and proportions related? the relationship between • What is the difference between percent change and net :::~~~tuaems will understand that percents are used to solve real-world problems that include: simple interest, tax, percent change, percent error, fees and commissions. • Describe how • Students will proportions to scale real-world problems. figures. e.g. maps and building blueprints 8/1312012 6 Isaac Elementary School District
  • 7. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S I C3 P04. Estimate the measure MC: 6-4 of an object in one system of units given the measure of that object in another system and the approximate 1------11 conversion factor. .... n n n m _ 7.G.1. Solve problems involving 7.MP.l. 6-8.RST.7 MC: 6-8 scale drawings of geometric figures, 7.MP.2. SC07-S I C2-04 such as computing actual 7.MP.3. SS07 -S4C6-03 and areas from a scale tiro>wino­ 7.MP.4. SS07 -S4C 1-0 I reproducing a scale 7.MP.5. SS07 -S4C 1-02 different scale. 7.MP.6. ET07-SICI-OI 7.MP.7. 7.MP.8. 7.RP.3. Use proportional MC: 6-9, 7-1, 7-2, relationships to solve multistep ratio 7-3, 7-4, 7-5, 7-6, and percent problems. Examples: 7-7, 7-8, 7-9 simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase Increase and decrease, percent error. Markdowns markups Percent Ratio Simple interest Tax Unit Project: 8113/2012 7 Isaac Elementary School District
  • 8. 7th Grade Math Curriculum Map Unit: The Number System Cluster: The Number Line Time: 3 weeks 8113/2012 8 Isaac Elementary School District
  • 9. 7th Grade Math Curriculum Essential Questions Big Ideas • What is distance? • will understand that absolute value is the • What is a number? that all real numbers fit on t.."4RLlVllCU and irrational • How can the four arithematic operations can be representated on a line? operations (addition, subtraction, multiplication, division) can be representated on a number • How is subtraction and the additive inverse related? • Students will understand that subtracting a number • How is division and the multipli"(.ul~ is the same as addings its additive inverse. • Students will understant that dividing by a number • Whv Cl'In't von CllVHle hVA4:r~"3R:'~~:SS81>"""~, is the same as multiplying by its multiplicative Inverse. • Students understand that you cannot divide by o. 8113/2012 9 Isaac Elementary School District
  • 10. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *SIC3POI. Estimate and apply benchmarks for rational numbers and common irrational numbers. *S IC3 P03. Estimate square roots of MC: 1-3, 12-1 numbers less than 1000 by locating them between two consecutive whole numbers. 7.NS.l. Apply and extend previous 7.MP.2. MC: 2-1, 2-2, 2-4, understandings of addition and subtraction 7.MPA. 2-5 to add and subtract rational numbers; 7.MP.7. represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make O. For example, a hydrogen afom has 0 charge because its Inverse properties two consfifuenfs are oppositely charged. Multiplicative b. Understand p + q as the number inverse a distance I q I from p, in the positive or Minuend negative direction depending on whether q Operations is positive or negative. Show that a number Opposite and its opposite have a sum Subrahead additive inverses). Sum rational numbers b Variable contexts. Vertical c. Understand numbers as adding - q p + (-q). Show between two rational number line is the absolute difference, and apply this world contexts. d. Apply properties of operations as to add and subtract rational 8/13/2012 10 Isaac Elementary School District
  • 11. t h Grade Math Curriculum numbers. Priority Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *SIC I P03. Compare and order rational MC: 4-9 numbers using various models and representations. 7.NS.2. Apply and extend previous 7.MP.2. MC: 2-6,2-8 understandings of multiplication and 7.MPA. division and of fractions to multiply and 7.MP.7. 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 -Associative signed numbers. Interpret products of -Identity rational numbers by describing rea -Distributive contexts. Quotient Repatend b. Understand that integers can be Terminates divided, provided that the zero, and every quotient non-zero divisor) is a and q are intege p/(-q). Interpret numbers by d c. Apply properties of 0 strategies to multiply and numbers. d. Convert a rational number to a using long division; know that the form of a rational number terminates in Us or 8/13/2012 11 Isaac Elementary School District
  • 12. t h Grade Math Curriculum Unit Proiect: Unit: The Number System Cluster: Order of Operation ...........vjmate Time: 1 week 8/13/2012 12 Isaac Elementary School District
  • 13. h i Grade Math Curriculum Essential Questions Big Ideas • What are grouping symbols? • symbols include: Parentheses, absolute • A base raised to the 0 power is what value? Why? and cube roots, brackets, and braces • Do we apply the rules of multiplication before division whilst using ~lClllUll" to evaluate expressions of operations to evaluate an expression? • Do we apply the rules of addition before subtraction operations to evaluate an expression? • When would we express a number in S~!~~~JDt!or • Scientific notation is used to express very large quantities and very small quantities. • Multiplying a number by an exponent with base 10 moves the decimal to the left or right. 8/1312012 13 Isaac Elementary School District
  • 14. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular "'S IC2P04. Represent and interpret MC: 1-2, p. LA2 numbers using scientific notation LA5 (positive exponents 7.NS.3. Solve real-world and 7.MP.l. 6-8.RST.3 MC: 1-4 mathematical problems 7.MP.2. the four operations with rational 7.MP.5. numbers. (Computations with 7.MP.6. rational numbers extend the rules 7.MP.7. for manipulating fractions to 7.MP.8. ~~~~lov fractions. Unit Project: Assessment: 811312012 14 Isaac Elementary School District
  • 15. i h Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Properties of Evaluating Expressions Time: 1 week Essential Questions Big Ideas • What is a variable? that a variable is a • What does it mean when one thing is equivalent to *uu,",m" will be able to use properties of operations • What is a coefficient? , subtract, factor, and expand expressions with • Students will look at a given problem and be able to express it in a different context. 8/13/2012 15 Isaac Elementary School District
  • 16. h i Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7 .EE.1. Apply properties of 7.MP.2. 6-8.RST.5 MC: 1-8 operations as strategies to 7.MP.6. and expand linear 7.MP.7. expressions with rational coefficients. 7.EE.2. Understand that rewriting an 7.MP.2. 6-8.WH5T.l b-c expression in different fonns in a 7.MP.6. 6-8.WH5T.2b-c problem context can shed light on 7.MP.7. 6-8.R5T.3 the problem and how the quantities 7.MP.8. 6-8.R5T.7 in it are related. For example, a + 5507-55(2-09 0.05a 1.05a means that "increase SC07-S2C2-03 . 5%" is the same as 1.05. " Unit Project: Assess 8/1312012 16 Isaac Elementary School District
  • 17. i h Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Solving Equations te Time: 2 weeks Essential Questions Big Ideas • How do we translate a written or verbal description to create an equation or equation? text or real-world scenario. • What is the difference between an expression and an will understand the difference between an • What is an inequality? equation, and inequality. • Students will be able to solve for a missing piece of information from a specific problem or text. • Students be able to check the reasonableness of an answer. 8/13/2012 17 Isaac Elementary School District
  • 18. Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S3C3P02. Evaluate an expression MC: 1-6 containing one or two variables by substituting numbers for the variables. 7.EE.3. Solve multi-step real-life 7.MP.1. 6-8.WHST.l b-c MC: 1-7 and mathematical problems posed 7.MP.2. 6-8.WHST2b with positive and negative rational 7.MP.3. 6-S.RST.7 numbers in any form (whole 7.MP.4. ET07-S6C2-03 numbers, fractions, and decimals), 7.MP.5. using tools strategically. Apply 7.MP.6. properties of operations to calculate 7.MP.7. with numbers in any form; convert 7.MP.S. 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 1110 ofher salary an hour, or $2.50, for a new salary of $27.50. Ifyou want to place a towel bar 9 314 inches long in the center ofa door that is 27 112 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a the exact compufntinJ 7.EE.4. Use va Inverse operations simple equations solve problems by the quantities. a. Solve word problems equations of the form px+q=r p(x+q)=r, where p, q, and rare specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution. identifyina the 8/13/2012 18 Isaac Elementary School District
  • 19. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular sequence of the operations used in each approach. For example, fhe perimefer of a recfang/e is 54 em. Ifs lengfh is 6 em. Whaf is ifs widfh? b. Solve word problems leading to inequalities ofthe form px+ q>r or px+q < r, where p, q, and rare specific rational numbers. Graph the solution set ofthe 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 ofsales you need to make, and describe the solutions. *SSC2P09. Solve logic problems using mUltiple variables and statement multiple conditional statements Logic words. oictures. and charts. *SSC2POlO. Demonstrate and Deductive reasoning explain that the process of solving . is a deductive Unit Project: 8/13/2012 19 Isaac Elementary School District
  • 20. h t Grade Math Curriculum Map Unit: Geometry Cluster: Angles Time: 1 week Essential Questions Big Ideas • What is the difference between equal, approximate, and congruent? the difference between congruent. • Which angle relationships are congruent? Which are not? will utilize the properties of angles to solve measure of an unknown angle. 8/13/2012 20 Isaac Elementary School District
  • 21. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4CIP05. Identify corresponding parts of congruent figures. 7.G.5. Use facts about 7.MP.3. ET07-S I C4-0 I supplementary, complementary, 7.MP.4. vertical, and adjacent angles in a 7.MP.5. multi-step problem to write and 7.MP.6. solve simple equations for an 7.MP.7. unknown angle in a figure. Unit Project: Unit: Geometry Cluster: Geometric Properties 8/13/2012 21 Isaac Elementary School District
  • 22. i h Grade Math Curriculum Essential Questions Big Ideas • What is a cross section? • will be able to determine what type of 2-D • What is a 3D shape? from a cross section of a 3-D figure. • What is a 2D shape? that the number of sides a directly translates to the sum of its interior will know what the parts of a triangle are and how they are related to each other. 8113/2012 22 Isaac Elementary School District
  • 23. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4C I P04. Describe the relationship between the number of sides in a regular polygon and the sum of its interior angles. 7.G.2. Draw (freehand, with ruler 7.MP.4. 6-8.R5T.4 and protractor, and with technology) 7.MP.5. 6-8.R5T.7 geometric shapes with given 7.MP.6. 6-8.WH5T.2b-2f conditions. Focus on constructing 7.MP.7. 51 C2-04 triangles from three measures of 7.MP.8. ET07-SIC2-01 angles or sides, noticing when the ET07-S6C 1-03 conditions detennine a unique triangle, more than one triangle, or no triangle. 7.G.3. Describe the two-dimensional figures that result from slicing three­ dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Cylinder Face Right prism Right pyramid Vertex Unit Proiect: 8/13/2012 23 Isaac Elementary School District
  • 24. 7th Grade Math Curriculum Map U nit: Geometry Cluster: Circumference and Area te Time: 2 weeks Essential Questions Big Ideas • What is the difference between perimeter, area, surface area and determine the parts of a . I.e. circumference, area, are, chord, diameter, • Why is volume units cubed and surface area units understand that perimeter is the of length, having neither width nor • Students will understand that area is the measurement of a surface space in a 2-D region, and that the measuring tool used are squares that have a length and width of one unit measure. • Students will understand that volume is the measurement of space that a 3-D object can occupy, and that the measuring tool used are cubes that have a length, width, and height of one unit measure. 8/1312012 24 Isaac Elementary School District
  • 25. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.GA. Know the fonnulas for the 7.MP.1. 6-S.WHST.ld area and circumference of a circle 7.MP.2. SC07-S2C2-03 and solve problems; give an 7.MP.3. ET07-S6C2-03 infonnal derivation of the 7.MP.4. ET07-S I C4-0 I relationship between the 7.MP.5. circumference and area of a circle. 7.MP.6. 7.MP.7. ,7.MP.S. _ _ _-I-_ _ _ _ _--' relationship between central angles and intercepted arcs; identify arcs and chords of a circle. *S4C4P02. Identify polygons having the same perimeter or area. *S5C I PO I. Create an algorithm to detennine the area of a given 7.G.6. Solve real-world and Faces mathematical problems involving Net area, volume and surface area of Surface area two- and three-dimensional objects Volume composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Unit Project: 8/1312012 25 Isaac Elementary School District
  • 26. i h Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Stats and Data Time: 2 weeks Essential Questions Big Ideas • What is a random sample and why are they used to colelct data? that a random sample is U1.l~~ll,,;l;:> and generalization about a • How can we design a random sample from a population? population if there is an even representation. will understand that there is a margin of error in making inferences with a random sample. 8113/2012 26 Isaac Elementary School District
  • 27. h i Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.1. Understand that 17.MP.3. 5507-54(4-04 statistics can be used to gain 7.MP.6. 5507-54(4-05 information about a population 5(07-53( 1-02 by examining a sample of the 5(07-54(3-04 population; generalizations about ET07-54(2-01 a population from a sample are ET07-54(2-02 valid only if the sample is ET07 -S6C2-03 representative of that population. Understand that random sampling tends to produce representative samples and sunnnrt v,;:alirl inf... r... n,......c "S2C1P01. Solve problems by selecting, constructing, and interpreting displays of data including mUlti-line graphs and *S2CIP02. Interpret trends in a data set, estimate values for missing data, and predict values Prediction for points beyond the range of Range the data set. Trends 7.SP.2. Use data from a random Simulated sample to draw inferences about a population with an unknown characteristic of i Generate multiple simulated size to gauge 1(3-01 -51 (3-02 estimates or ET07-54C2-02 example, ET07-56(2-03 word length in randomly sampling the book; predict the school election based on randomly sampled survey Gauge how far off the estimate or Drediction miaht be. 8/13/2012 27 Isaac Elementary School District
  • 28. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Unit Project: Assessment: 8113/2012 28 Isaac Elementary School District
  • 29. Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Data Graph and Analysis roximate Time: 2 weeks Essential Questions Big Ideas • Why is the average not a good measure of center to use when reporting that measures of center is a data? a set of data, except if there • How do outliers affect a data set? will use measure of center to express a set of and correctly decide which measure of center best fits a given set of data. 8/13/2012 29 Isaac Elementary School District
  • 30. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.4. Use measures of center 7.MP.1. 6-8.WHST.l b and measures of variability for 7.MP.2. ET07-S 1C3-01 numerical data from random 7.MP.3. ET07-S 1C3-02 samples to draw informal 7.MP.4. ET07-S4C2-0 1 comparative inferences about 7.MP.S. ET07-S4C2-02 two populations. For example, 7.MP.6. ET07-S6C2-03 decide whether the words in a 7.MP.7. SC07-S 1C3-0 1 chapter of a seventh-grade SC07-S 1C3-0S SC07-S 1C4-03 science book are generally SC07-S2C2-03 longer than the words in a SC07-S4C3-04 chapter of a fourth-grade science SS07-S4C2-0 1 book. *S2C1 P03. Identify outliers and determine their effect on mean, median, mode, and range. 7.SP.3. Informally assess the degree of visual overlap of two Measure of­ numerical data distributions with Variability similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For mean height of 1C3-01 basketball 1C3-02 than the -S4C2-01 on the soccer ET07-S4C2-02 the variability ET07-S6C2-03 deviation) on dot plot, the the two distributions of noticeable. Unit Proiect: 8/1312012 30 Isaac Elementary School District
  • 31. t h Grade Math Curriculum Map 8/1312012 31 Isaac Elementary School District
  • 32. h i Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Simple and Compound Events ate Time: 1 week Essential Questions Big Ideas • How can probabilty be used to make informed predictions? that the probability of a 0, which is impossible to • How does increasing the total number of possible outcomes affect the happen, and 1, which is certain to happen. probability of a given situation? Lqu;;lll~ will understand that the probability that an even will occur is equal to the number of favorable outcome divided by the total number of outcomes. • Students will understand that a sample space is a diagram of all possible outcomes for a given situation. 8/13/2012 32 Isaac Elementary School District
  • 33. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.5P.5. Understand that the probability 7.MP.4. 6-8.WH5T.1 b of a chance event is a number between 7.MP.5. 5507-55C1-04 o and 1 that expresses the likelihood 7.MP.6. ET07-51 C3-01 of the event occurring. Larger numbers 7.MP.7. ET07-51 C3-02 indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around Y2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.5P.8. Find probabilities of compound 7.MP.1. events using organized lists, tables, 7.MP.2. tree diagrams, and simulation. 7.MP.4. 7.MP.5. a. Understand that, just as with simple 7.MP.7. events, the probability of a compound 7.MP.8. event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such 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 that event. answer to the question: donors have type A probability that it will take donors to find one with Unit Project: 8113/2012 33 Isaac Elementary School District
  • 34. h i Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Unit: Statistics and Probability Cluster: Theoretical and Experimental Probabilities Time: 2 weeks Essential Questions • What are the similarities and differences between experimental and Students will understand that probability is a theory theoritical probability? is the likelyhood that an event will happen, and • Students will understand that the more trials used in an experimental probability, the closer the probability of an event occuring gets closer to its theoretical probability. 8113/2012 34 Isaac Elementary School District
  • 35. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.6. Approximate the probability of a 6-S.WHST.l a chance event by collecting data on the ET07-S1C2-01 chance process that produces it and ET07-S 10-02 observing its long-run relative ET07-S 1C2-03 frequency, and predict the approximate relative frequency given the probability. ET07-S 1C3-0 1 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. 7.SP.7. 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 discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to dete probabilities of events. student is selected at find the probabilit and the probability b. Develop a may not be uniform) frequencies in data gen chance process. For approximate probability that a penny will land heads up or that tossed paper cup will land ODen-en down. 8113/2012 35 Isaac Elementary School District
  • 36. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Do the outcomes for the spinning penny appear to be equally likely based on the observed freauencies? Unit Project: 8/1312012 36 Isaac Elementary School District
  • 37. 7th Grade Math Curriculum Map Unit: Displaying Data Cluster: Data displays roximate Time: 1 week Essential Questions Big Ideas • What is a vertex-edge graph? to read a vertex-edge diagram. • How are vertex-edge graphs used in real life? • What is the diflerence between a congurent transformation and a similar Students will be able to use a Venn Diagram to transformation? J.Jl;;;:);;1U algebraic problems. Students will be able to translate, rotate, and reflect geometric figures in a coordinate plane. 8/13/2012 37 Isaac Elementary School District
  • 38. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S2C3P02. Solve counting problems using Venn diagrams and represent the answer *S2C4P01. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems related to Euler/Hamilton paths and circuits. *S4C2P01. Model the result of a double transformation (translations or reflections) of a 2-dimensional figure on a coordinate plane using all four quadrants. Unit Project: 8/13/2012 38 Isaac Elementary School District