Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR. Updated: Thursday, December 02, 2010

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1 Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR 1

2 MATHEMATICS SCOPE & SEQUENCE Unit Title Dates Page 1. Rational Numbers... 9/2 10/29/ Proportion and Similarity... 11/1 12/17/ Algebraic Sense... 1/04 2/28/ Surface Area and Volume... 3/01 3/31/ Probability... 4/01 4/30/ Data... 5/ PE 7.5.B

3 Unit Name: Rational Numbers (33days) September 2, 2010 October 29, A Mentally add, subtract, multiply, and divide simple fractions, decimals, and percents. 7.1.A - Compare and order rational numbers using the number line, lists, and the symbols <, >, or = 7.1.A - Compare and order rational numbers using the number line, lists, and the symbols <, >, or = 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions 7.1.B - Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions 7.1.B - Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. Regular number talks throughout the year ATN: Problem 1.2 pg 8, 1.2 FU, ACE 9-14 Order rational numbers using a list and compare rational numbers using a the symbols < or > ATN: Problem 1.3A, 1.3 FU 3-8, ACE 8 & Compare rational numbers using a list and a number line ATN: Investigation 1 ACE #22, 23, 28, 29 ATN: Problem 2.1 pg 20, ACE 1-7 pg26 ATN: Problem 2.2 pg 22, ACE 8 & pg 27 Represent addition of positive and negative integers visually using chip boards. ATN: Investigation 2 Reflection and ACE #29-30 Solve single- and multistep word problems. ATN: Problem 3.1 pg 37 Represent subtraction of positive and negative 2 ATN does not teach rational number, only integers 2 Formative: Mathematical Reflection #1 and/or #2, pg 17 ATN does not teach rational number, only integers 2 ATN does not teach rational number, only integers 5 Formative: ACE pg 28 1 ATN does not teach rational number, only integers 1 *Make sure to see ATN: Problem 3.1 FU for PE 7.1.D on absolute value 3

4 integers visually using a chip board. 7.1.D - Define and determine the absolute value ATN: Problem 3.1 FU Pg 2 Formative: Mathematical of a number. 39; 3.2 FU pg 42; ACE #33 Reflection #5, pg 52 pg B - Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically.?? CMP2 ATN: Problem 2.2 ATN: Problem 3.2 pg 42, 3.2 FU ATN 3.3 ATN: Problem 3.4 pg 44 ACE #2-10, pg 47 6 Formative: ACE #11,12,15,16 pg 47 Summative? Students are not asked to specifically to define the abs. value of a number, but students are asked to name all integers that are 12 units from 0 *Recommend Cornell Notes 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions 7.1.B - Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. 7.1.B - Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. Represent subtraction of positive and negative integers visually and numerically. ATN: Investigation 3 ACE #1, 34 ATN: Problem 4.1 pg 54 ATN: Problem 4.2 pg 56 ATN: Problem 4.3 pg 57 Represent multiplication of positive and negative integers visually using patterns ATN: Problem 4.4 pg 59 Represent division of positive and negative 1 ATN does not teach rational number, only integers 5 1 4

5 integers visually and numerically. ATN: Investigation 4 1 ATN does not teach rational ACE #21, 28, number, only integers 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions 7.1.C - Fluently and accurately add, subtract, multiply, and divide rational numbers. 7.5.A Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. ATN: ACE #9-16, 22-25, pg61 ATN 5.1 and 5.2 ACE #6 pg 79 1 Skills are assessed in unit test for Accentuate the Negative but lessons do not specifically teach operations of rational numbers. 3 D-TAILS (Data, Title, Axes, Intervals, Scale). *Students may need supplemental practice Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. Assessment: (type) Common Assessment 1 day 5

6 Unit Name: Proportion and Similarity (22) November 1, 2010 December 17, D - Make scale drawings and solve problems related to scale. 7.5.A - Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. 7.2.C - Describe proportional relationships in similar figures and solve problems involving similar figures. 7.3.C Describe the effect that a change in scale factor on one attribute of a two- or three-dimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure. S&S: Problem 2.1 pg 16 Make scale drawings and solve problems related to scale. S&S: Problem 2.2 pg 19, 2.2 FU S&S: Problem 2.3 pg 21, 2.3 FU Add a column to the nose chart to capture area change. ACE 1-5,9,10 S&S Inv D - Make scale drawings and solve S&S Inv 4 4 problems related to scale. 7.2.B Solve single- and multi-step problems S&S Inv 5 3 Formative Assessments/ 2 Recommend use of CMP2 especially for Inv 2 and 4. Inv 2 has more accessible Wumps that focus on concept not point plotting. Inv 4 has a tie in for ratios and scale factor. And leads into Comparing and scaling with the interior ratios of figures. ACE for INV 2: 5-11 Inv 3: 2-4, Inv 4 : Formative: (After 2.2 FU) Check up pg 90 Formative: Mathematical Reflection #1-3 pg 27 Inv , 26, 36 Make sure students understand the attributes needed for objects to be similar Two figures are mathematically similar if and only if the ratios of all the pairs of corresponding sides are equal. *Recommend Cornell Notes on Scale factor & Similarity 6

7 involving proportional relationships and verify the solutions. ACE3-5, 7, 9, 14, B Solve single- and multi-step problems involving proportional relationships and verify the solutions. C&S Investigation 3 and ACE #1,2, 6, 9-18 C&S Inv 4 and ACE #1,8, Formative Assessments/ 7.2.G Determine the unit rate in a proportional relationship Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. Assessment: (type) Common Assessment 1 day 9 7

8 Unit Name: Algebraic Sense (31) January 4 Feb E - Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. 7.5.A Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. 7.2.H - Determine whether or not a relationship is proportional and explain your reasoning. 7.2.F - Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles. MSA 2.1, 2.2, 2.3, 2.4, 2.5 Ace 1,2,3,4,5,6,10,11,14,21 Represent linear relationships using graphs, tables, and equations, and make connections among the representations. Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. (CMP1) MEC Menu items Cowpen, Bullpens, Flowerbeds, Increasing Patterns 7.1.E Solve two step linear equations MSA Investigation 4 4.1, 4.2 and ACE #2-6,8, (CMP1) Formative Assessments/ 8 Formative: Mathematical Reflection #1&2 Not explicitly addressed. Linear relationships are addressed. No proportion. *Recommend Cornell Notes to introduce linear relationships and how they relate to proportions; Objectives hit linear not proportional D-TAILS (Data, Title, Axes, Intervals, Scale). *Students will need supplemental practice 8 The MEC items are better to use for the linear relationship and the interrelationship of tables, graph and equations F Write and equation that corresponds to a given problem and write a problem that corresponds to a given equation. MSA 4ACE 10, 13, 16, 17 (CMP1) E - Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. 4 Formative: Mathematical Similarity not explicitly addressed. Slope is addressed in MSA Inv. 5 and 8

9 7.2.F - Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles. 7.2.G - Determine the unit rate in a proportional relationship and relate it to the slope of the associated line. MSA Investigation 5.1, ACE Determine the slope of a line using graphs, tables and equations. Supplemental Materials: OSPI Modules 7.2.H - Determine whether or not a relationship is proportional and explain your reasoning. 7.2.E - Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. 7.2.I - Solve single- and multi-step problems involving conversions within or between measurement systems and verify the solutions. Partially Addressed in 7.2.E MSA Investigation Supplemental Materials: OSPI Modules Reflections #1&2, pg 70 Formative Assessments/ 3 Not Aligned 6, and relationships are made with triangles in SAS, but the connection is never made. *Recommend Cornell Notes on Slope MSA contains linear relationship, CAS Inv. 6 has Proportion in bold, no 7 th grade CMP text contain proportions. Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. 9

10 Unit Name: Surface Area and Volume (19) March 1 March E Determine the surface area and volume of rectangular prisms using the appropriate formulas and explain why the formulas work. F&W 2.1 with different number of blocks if desired ACE INV and Intentional review of 2 D shapes 7.3.D Solve single- and multi-step word problems involving surface area or volume and verify the solutions. F&W Inv. 2 and 3, Inv. 2 ACE, Inv. 3 ACE 5 MEC Menu items 7.3.B Determine the volume of pyramids and cones using formulas. 7.3.A Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work. F&W 4.1 pg 38, ACE 1ab,2ab,5,10,11 1 Need materials specific to volume of pyramids using formulas 2 Exit slip: ACE #6, pg43 Students may need review from Inv 1-3 or Cornell Notes as review 7.3.B Determine the volume of pyramids and cones using formulas. F&W 5 pg A Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work. F&W 4.2 pg 39, ACE 1c, 2c, 4 3 Exit slip: Follow up 4.2 #1 7.3.C Describe the effect that a change in scale factor on one attribute of a two- or threedimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure. 7.3.C Describe the effect that a change in scale factor on one attribute of a two- or threedimensional figure has on other attributes of the F&W: Problem 6.2 pg 59 Reinforce with entry tasks F&W Inv 6 ACE 6, pg 62 2 Formative: Mathematical Reflection #4,pg 40 2 Formative: Mathematical Reflection, pg 67 #1 & 2. Not directly addressed. (Also can be reviewed S&S Inv 3.1, 3.2, page 28 ACE 11-14, pg 36) Not completely addressed. 10

11 figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure. Reinforce with entry tasks 7.2.I - Solve single- and multi-step problems involving conversions within or between measurement systems and verify the solutions. Be specific to change one attribute from inches to Feet or CM to Meters within the problems. Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. Assessment: (type) Common Assessment 1 11

12 Unit Name: Probability April 1 April B Determine the theoretical probability of a particular event and use theoretical probability to predict experimental outcomes. 7.4.A Represent the sample space of probability experiments in multiple ways, including tree diagrams and organized lists. 7.4.A Represent the sample space of probability experiments in multiple ways, including tree WDYE Inv. 1.1,1. 2, ACE 7, 10 Inv 2.1,2.2 ACE 1-5 WDYE Inv 1.4 Inv 1 ACE 9 Inv 2 ACE 16 WDYE Inv 2.1 INV 1 ACE 20, Inv 2 ACE diagrams and organized lists. Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. Assessment: (type) 2 12

13 Unit Name: Data (9) May 1 [Ending Date] 7.4.C Describe a data set using measures of center (median, mean, and mode) and variability (maximum, minimum, and range) and evaluate the suitability and limitations of using each measure for different situations. Use test scores for all Measures of center and graphing. Print scores of all students without names D Construct and interpret histograms, stem-and-leaf plots, and circle graphs. 7.4.E Evaluate different displays of the same data for effectiveness and bias, and explain reasoning. Use test scores for all Measures of center and graphing. Print scores of all students without names. 6 Need to Specifically create histogram and stem and leaf and circle. Process Standards Addressed: 7.6.A Analyze a problem situation to determine the questions(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. Assessment: (type) 13

14 Unit Name: [Starting Date] [Ending Date] 7.5.B Write the prime factorization of whole numbers greater than 1, using exponents when appropriate. Process Standards Addressed: Assessment: (type) 14