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7th Grade Math Curriculum Guide 7-1-2014 Common Core Mathematical Practices “Describe varieties of expertise that math educators should seek to develop and engage in their students…. emphasize a combination of procedure and understanding. Developed from (a) NCTM Process Standards of problem solving, reasoning and proof, communication, representation, and connections- (b) National Research Council’s research on adaptive reasoning, strategic competence, and conceptual understanding, procedural fluency 1. Make sense of problems and persevere in solving them – Math proficient students should have the capacity to check their answers to problems using different methods and to ask, Does this make sense? ….Understand other approaches and to see correspondences between different approaches. 2. Reason abstractly and quantitatively – Emphasizes two complimentary abilities… the ability to decontextualize (move toward abstraction) and to contextualize (move toward symbolization) 3. Construct viable arguments and critique the reasoning of others – Listen and read the arguments of others, decide if they make sense and ask questions to clarify how they can improve an argument 4. Model with mathematics – Students can apply the mathematics that they know to solve problems in everyday life. 5. Use appropriate tools strategically –Use of tools such as pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, mathematical software packages 7th Grade Math Curriculum Guide 7-1-2014 6. Attend to precision – Demonstrate the ability to communicate precisely with each other 7. Look for and make use of structure – Students will be able to discern patterns or structure in mathematical situations 8. Look for and express regularly in repeated reasoning – Students will recognize mathematical repetition and for general methods and shortcuts in their problem solving methods 7th Grade Math Curriculum Guide 7-1-2014 Common Core K-12 Anchor Standards for Mathematics K 1 2 3 4 5 6 7 8 Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Ratios and Proportional Relationships Ratios and Proportional Relationships The Number System Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten The Number System The Number System Expressions and Equations Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Expressions and Equations Expressions and Equations Functions Numbers and Operations Fractions Numbers and Operations Fractions Numbers and Operations Fractions Statistics and Probability Statistics and Probability Statistics and Probability Geometry Geometry Geometry Geometry Geometry Geometry Counting and Cardinality Geometry Geometry Geometry High School High School High School High School High School Number and Quantity Overview Algebra Functions Geometry Statistics and Probability The Real Number System Seeing Structure in Expressions Interpreting Functions Congruence Interpreting Categorical and Quantitative Data Quantitities Arithmetic with Polynomials and Rational Functions Building Functions Similiarity, Right Triangles, and Trigonometry Making Inferences and Justifying Conclusions The Complex Number System Creating Equations Linear, Quadratic, and Exponential Models Circles Conditional Probability and the Rules of Probability Vector and Matrix Quantities Reasoning with Equations and Inequalities Trigonometric Functions Geometric Measurement and Dimension Using Probability to Make Decisions Modeling with Geometry 7th Grade Math Curriculum Guide 7-1-2014 Common Core Standards and Seventh Grade Mathematics – Mendota Elementary School District #289 Units of Study Correlated with CCSS P-Priority Standard S-Supporting Standard 1 Rational Numbers 2 Expresions and Equations 3 Ratios and Proportional Relationships 4 Percents and Proportional Relationships 5 Inferences 6 Probability 7 Geometry and Construction Essential Outcomes 8 Geometry: Area, Volume, Surface Area, Scale Ratio and Proportional Relationships (RP) Essential Outcome 1 Students will analyze proportional relationships and use them to solve real world and mathematical problems p p p p p p p p p p Target 7.RP 1.0 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas of other quantities measured in the like or different units. Target 7.RP 2.0 Recognize and represent proportional relationships between quantities a. Decide whether two quantities are in a proportional relationship. e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships c. Represent proportional relationships by equations d. Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate Target 7.RP 3.0 Use proportional relationships to solve multistep ratio and percent problems. The Number System (NS) Essential Outcome 2 Students will apply and extend previous 7th Grade Math Curriculum Guide 7-1-2014 understandings of operations with fractions to add, subtract, multiply, and divide rational numbers P P P P P P P P Target 7 NS 1.0 Apply and extend previous understandings of addition and subtraction to add and to subtract rational numbers: represent addition and subtraction on a horizontal or vertical number line diagram a. Describe situations in which opposite quantities combine to make 0 b. Understand p+q as the number located a distance {q} from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Intepret sums of rational numbers by describing real world contexts c. Understand subtraction of rational numbers as adding the additive inverse, p-q + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers Target 7 NS 2.0 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1) (-1) =1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real world contexts b. Understand that integer can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then – (p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real world contexts c. Apply properties of operations as strategies to multiply and divide rational numbers d. Convert a rational number to a decimal using long division: know that the decimal form of a 7th Grade Math Curriculum Guide 7-1-2014 rational number terminates in 0’s or eventually repeats. Target NS 3.0 Solve real world and mathematical problems involving the four operations with rational numbers P Expressions and Equations (EE) Essential Outcome 3 Students will use properties of operations to generate equivalent expressions Target 7.EE 1.0 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients Target 7.EE 2.0 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. P P Essential Outcome 4 Students will solve real life and mathematical problems using numerical an algebraic expressions and equations P p P P P Target 7 EE 3.0 Solve multi step real-life mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies Target 7 EE 4.0 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px+q =r and p(x+q) =r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach b. Solve word problems leading to inequalities of the form px +qr or px + q< r where p,q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Geometry (G) 7th Grade Math Curriculum Guide 7-1-2014 Essential Outcome 5 Students will draw, construct, and describe geometrical figures and describe the relationships between them p p p p p p Target 7 G.1.0 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale Target 7 G.2.0 Draw (freehand, with ruler and proptractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle Target 7 G 3.0 Describe the two-dimensional figures that result from slicing three dimensional figures as in plane sections of right rectangular prisms and right rectangular pyramids Essential Outcome 6 Students will solve real-life and mathematical problems involving angle measure area, surface area, and volume p p p p p p p p Target 7.G.4.0 Know the formulas for the area and circumference of a circle and use them to solve a problems” give informal derivation of the relationship between the circumference and the area of a circle Target 7 G 5.0 Use facts about supplementary, complementary, vertical, and adjacent angles in multi step problem to write and to solve simple equations for an unknown angle in a figure Target 7 G 6.0 Solve real world and mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms Statistics and Probability Essential Outcome 7 Students will use random sampling to draw inferences about a population p p Target 7.SP 1.0 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends 7th Grade Math Curriculum Guide 7-1-2014 p p to produce representative samples and support valid inferences Target 7.SP 2.0 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples of the same size to gauge the variation in estimates or predictions Essential Outcome 8 Students will draw informal comparative inferences about two populations p p Target 7 SP 3.0 Informally assess the degree of visual overlap of two numerical data distributions with similar variability’s, measuring the difference between the centers by expressing it as multiple of a measure of variability p p Target 7 SP 4.0 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations Essential Outcome 9 Students will investigate chance processes and develop, use, and evaluate probability models p p p p p p Target 7 SP 5.0 Understand that the probability of chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near ) indicates and unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event Target 7 SP 6.0 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing it long run relative frequency, and predict the approximate relative frequency given the probability Target 7 SP 7.0 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies: if the agreement is not good, explain possible sources of the discrepancy a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process Target 7 SP 8.0 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations 7th Grade Math Curriculum Guide 7-1-2014 p a. p b. p c. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language identify the outcomes in the sample space which compose the event Design and use a simulation to generate frequencies for compound events 7th Grade Math Curriculum Guide 7-1-2014 Operations with Rational Numbers Targets/Standards Expressions and Equations Targets/Standards Ratios and Proportional Relationships Targets/Standards Percents and Proportional Relationships Targets/Standards Inferences 7.NS.1a 7.NS.1b 7.NS.1c 7.NS.1d 7.NS.2a 7.NS.2c 7.NS.2d 7.NS.3 7.EE.1 7.EE.2 7.EE.3 7.EE.4a 7.EE.4b 7.EE.5 7.EE.6 7.RP.1 7.RP.2a 7.RP.2b 7.RP.2c 7.RP.2d 7.RP.3 7.G.1 7.RP.1 7.RP.2 7.RP.3 7.SP.1 7.SP.2 7.SP.3 7.SP.4 Pacing 4-5 Weeks Pacing 6-8 Weeks Pacing 2-3 Weeks Pacing 3-4 Weeks Pacing 2-3 weeks Probability Geometry: Classification and Construction Targets/Standards Geometry: Area, Volume, Surface Area, Scale Targets/Standards Unit Name/Topic Unit Name/Topic Targets/Standards Targets/Standards 7.G.1 7.G.2 7.G.3 7.G.4 7.G.5 7.G.6 7.G.1 7.G.2 7.G.3 7.G.4 7.G.5 7.G.6 7.EE.4 7.EE.5? 7.EE.6? Pacing 3-4 Weeks Pacing 3-4 Weeks Targets/Standards 7.SP.1 7.SP.2 7.SP.3 7.SP.4 7.SP.5 7.SP.6 7.SP.7.a 7.SP.7.b 7.SP.8 7.SP.8.a 7.SP.8.b 7.SP.8.c Targets/Standards 7th Grade Math Curriculum Guide Pacing 4-5 Weeks 7-1-2014 7th Grade Math Curriculum Guide Unit Names #1 Operations with Rational Numbers Chapters Pacing FourFive Weeks 7-1-2014 Assessment Targets Target 7 NS 1.0 Apply and extend previous understandings of addition and subtraction to add and to subtract rational numbers: represent addition and subtraction on a horizontal or vertical number line diagram 7.NS.1a Describe situations in which opposite quantities combine to make 0 7.NS.1b Understand p+q as the number located a distance {q} from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Intepret sums of rational numbers by describing real world contexts Target 7.NS 1c Understand subtraction of rational numbers as adding the additive inverse, p-q + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real world contexts. 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers Target 7 NS 2.0 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1) (-1) =1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real world contexts Target NS 2c Apply properties of operations as strategies to multiply and divide rational numbers Target NS.2dConvert a rational number to a decimal using long division: know that the decimal form of a rational number terminates in 0’s or eventually repeats. Target NS 3.0 Solve real world and mathematical problems involving the four operations with rational numbers #2 Expressions and Equations Six-Eight Weeks Target 7.EE 1.0 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients Target 7.EE 2.0 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Target 7 EE 3.0 Solve multi step real-life mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Essential Questions Big Ideas 7th Grade Math Curriculum Guide 7-1-2014 Target 7 EE 4.0 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Target 7.EE. 4a Solve word problems leading to equations of the form px+q =r and p(x+q) =r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach Target 7.EE 4b Solve word problems leading to inequalities of the form px +qr or px + q< r where p,q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Target 7 EE 5.0 Use facts about supplementary, complementary, vertical, and adjacent angles in multi step problem to write and to solve simple equations for an unknown angle in a figure Target 7 EE 6.0 Solve real world and mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms #3 Ratios and Proportional Relationships TwoThree Weeks Target 7.RP 1.0 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas of other quantities measured in the like or different units. Target 7.RP 2.0 Recognize and represent proportional relationships between quantities Target 7.RP.2a Decide whether two quantities are in a proportional relationship. e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin Target 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships Target 7.RP.2c Represent proportional relationships by equations Target 7.RP.2adExplain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate Target 7.RP 3.0 Use proportional relationships to solve multistep ratio and percent problems. Target 7 G.1.0 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale #4 Percents and Proportional Relationships ThreeFour Weeks Target 7.RP 1.0 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas of other quantities measured in the like or different units. Target 7.RP 2.0 Recognize and represent proportional relationships between quantities Target 7.RP 3.0 Use proportional relationships to solve multistep ratio and percent problems. 7th Grade Math Curriculum Guide #5 Inferences TwoThree Weeks 7-1-2014 Target 7.SP 1.0 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences Target 7.SP 2.0 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples of the same size to gauge the variation in estimates or predictions Target 7 SP 3.0 Informally assess the degree of visual overlap of two numerical data distributions with similar variability’s, measuring the difference between the centers by expressing it as multiple of a measure of variability Target 7 SP 4.0 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations #6 Probability FourFive Weeks Target 7.SP 1.0 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences Target 7.SP 2.0 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples of the same size to gauge the variation in estimates or predictions Target 7 SP 3.0 Informally assess the degree of visual overlap of two numerical data distributions with similar variability’s, measuring the difference between the centers by expressing it as multiple of a measure of variability Target 7 SP 4.0 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations Target 7 SP 5.0 Understand that the probability of chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near ) indicates and unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event Target 7 SP 6.0 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing it long run relative frequency, and predict the approximate relative frequency given the probability Target 7 SP 7.0 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies: if the agreement is not good, explain possible sources of the discrepancy Target 7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the 7th Grade Math Curriculum Guide 7-1-2014 model to determine probabilities of events Target 7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process Target 7 SP 8.0 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations Target 7.SP.8aUnderstand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs Target 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language identify the outcomes in the sample space which compose the event Target 7.SP.8c Design and use a simulation to generate frequencies for compound events. #7 Geometry: Classification and Construction ThreeFour Weeks Target 7 G.1.0 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale Target 7 G.2.0 Draw (freehand, with ruler and proptractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle Target 7 G 3.0 Describe the two-dimensional figures that result from slicing three dimensional figures as in plane sections of right rectangular prisms and right rectangular pyramids Target 7.G.4.0 Know the formulas for the area and circumference of a circle and use them to solve a problems” give informal derivation of the relationship between the circumference and the area of a circle Target 7 G 5.0 Use facts about supplementary, complementary, vertical, and adjacent angles in multi step problem to write and to solve simple equations for an unknown angle in a figure Target 7 G 6.0 Solve real world and mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms #8 Geometry: Area, Volume, Surface Area, Scale ThreeFour Weeks Target 7 G.1.0 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale Target 7 G.2.0 Draw (freehand, with ruler and proptractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle Target 7 G 3.0 Describe the two-dimensional figures that result from slicing three dimensional figures as in plane sections of right rectangular prisms and right rectangular pyramids 7th Grade Math Curriculum Guide 7-1-2014 Target 7.G.4.0 Know the formulas for the area and circumference of a circle and use them to solve a problems” give informal derivation of the relationship between the circumference and the area of a circle Target 7 G 5.0 Use facts about supplementary, complementary, vertical, and adjacent angles in multi step problem to write and to solve simple equations for an unknown angle in a figure Target 7 G 6.0 Solve real world and mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms Target 7 EE 4.0 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.5? 7.EE.6? Unit Operations with Rational Numbers Expressions and Equations Ratios and Proportional Relationships Percents and Proportional Relationships Operations with Rational Numbers Inferences Probability Geometry: Classification and Construction Geometry: Area, Volume, Surface Area, Scale Front Loaded Vocabulary 7th Grade Math Curriculum Guide 7-1-2014 Assessment Worksheet Assessment (Objective-Performance Task): Describe the objective or performance assessment as it will be presented to the students. If performance based, include the rubric with levels of performance for each of the targeted criteria and a description of what they will produce or perform. Include an engaging scenario (situation, challenge, role, audience, performance / product) that focuses the student attention on why they are completing the performance tasks. In addition, provide brief descriptions of four scaffolded common assessments that will be integrated into the lessons. Linking Performance Assessment Tasks and Unit Assessments: Pre-Test Task 1 Task 2 Task 3 Task 4 Post Test (Formative) Recognize Interpret Apply Evaluate (Summative) List Summarize Model Justify Describe Compare Analyze Create Progress Monitoring Target Checks Unit Number Assessment Type Pre-Assessment Description and Post Assessment Description “Describe the assessment(s) as it will be presented to the students. If a performance based assessment, include the Rubric with levels of performance for each of the criteria.” Formative Assessments Tasks (Target Checks) that will be used during instruction to check student learning– Task #1, Task #2, Task #3, Task #4 Selected Response Pre-Assessment – Students will complete a fifteen question selected response assessment based on the unit targets. Constructed Response Post Assessment – Students will complete an objective assessment that includes multiple choice, T/F, and short written responses. Task #1 – List the steps in the process Task #2-Compare the two processes Performance Assessment Task #3- Apply the process in a lab setting Task #4- Evaluate the data generated from the lab experience 7th Grade Math Curriculum Guide #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 7-1-2014