Math Grade Seven Unit 1- The Number System (NS)

Transcription

1 Math Grade Seven Unit 1- The Number System (NS) Time Frame: 7 weeks Description: - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Enduring Understandings: *Relationships among numbers and number systems form the foundations of number sense and mathematical communication. *There are many ways to represent a quantity. *Strategies can be used to build fluency and extend knowledge of the number system. Vocabulary: Rational numbers, integers, additive inverse Essential Questions: *What makes an answer exact? *What makes an estimate reasonable? *What makes a strategy for computing effective and efficient? **Unless otherwise noted all resources are taken from Pre-Algebra Prentice Hall Mathematics. Copyright 2007** Standards Topics Activities Resources Assessments 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 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 - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - Compare and order rational numbers both positive and negative - Add integers using a number line - Add integers using a model - Teacher Modeling. - Number Lines Students model addition and subtraction of rational numbers on number lines. - Think-Pair-Share Students work in pairs to apply properties of operations as strategies to add and subtract rational numbers. - Justification Students use justification to prove answers. - Exit Ticket/Admit Ticket Addition and subtraction of rational numbers. Connected Math a) Accentuate the Negative Inv. 2: Adding and Subtracting Integers b) Accentuate the Negative: Inv. 1: Extending the Number System Inv. 2: Adding and Subtracting Integers c) Accentuate the Negative: Inv. 2: Adding and Subtracting Integers d) Accentuate the Negative: Inv. 2: Adding and Subtracting Integers Q:\MathCurricCommit teematerials\model Unit 1 Q:\MathCurricCommit teematerials\model Unit 1

2 have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers. - Subtract integers using a number line - Subtract integers using a model Absolute Value Inv. 4: Properties of Operations Prerequisites: 5.1, 5.3 Standard Resources: 1.4, 1.5, 1.6, 4.6 b) Standard Solutions Lesson Plan CCS: Adding and Subtracting Integers c) Standard Solutions Lesson Plan CCS: Using Distance to Discover Absolute Value 7.NS.2. 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 integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - Multiply integers - Divide integers - Teacher Modeling. - Number Lines Students model multiplication and division of rational numbers on number lines. - Think-Pair-Share Students work in pairs to apply properties of operations as strategies to multiply and divide rational numbers. - Justification Students use justification to prove answers. - Exit Ticket/Admit Ticket Addition and subtraction of rational numbers. Connected Math a) Accentuate the Negative: Inv. 3: Multiplying and Dividing Integers Inv. 4: Properties of Operations Prerequisites: 4.1, 4.2, 4.3, 4.4, 5.2, 5.4 Standard Resources: a-c) 1.9 d) 6.5 a) Standard Solutions Lesson Plan CCS: Multiplying Integers b) Standard Solutions Lesson Plan CCS: Q:\MathCurricCom mitteematerials\mod el Unit 1 Q:\MathCurricCom mitteematerials\mod el Unit 1

3 Interpret quotients of rational numbers by describing realworld 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 rational number terminates in 0s or eventually repeats. Rational Quotients of Integers c) Standard Solutions Lesson Plan CCS: Applying Properties of Operations d) Standard Solutions Lesson Plan CCS: Converting Fractions to Decimals 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) - Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - Adding, subtracting, multiplying, and dividing rational numbers using real world word problems. - Problem Solving Instruction. - Model steps. - Create a Problem Students create a real-world and mathematical problem involving any of the four operations and rational numbers. - Exit Ticket/Admit Ticket Solve a real-world problem involving one or more of the four operations and rational numbers. Throughout Connected Math Accentuate the Negative Inv. 2: Adding and Subtracting Integers Inv. 3: Multiplying and Dividing Integers Inv. 4: Properties of Operations Standard Solutions Lesson Plan CCS: Rational Number Problems Q:\MathCurricCom mitteematerials\mod el Unit 1 Q:\MathCurricCom mitteematerials\mod el Unit 1

4 Math Grade Seven Unit 2- Expressions and Equations Time Frame: 7 weeks Description: - Use properties of operations to generate equivalent expressions. - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. Enduring Understandings: *The relationships among quantities can often be expressed symbolically and represented in more than one way. *Patterns, relations, and functions can be recognized and understood mathematically. *Algebraic representations are used to communicate and generalize patterns in mathematics. Vocabulary: Coefficients, like terms, distributive property, factor, numeric expressions, algebraic expressions, maximum, minimum Essential Questions: *How can multiple representations be used to express relationships? *How can expressions and equations be used to represent practical problems symbolically? *How can change be described mathematically? **Unless otherwise noted all resources are taken from Pre-Algebra Prentice Hall Mathematics. Copyright 2007** Standards Topics Activities Resources Assessments 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - Use properties of operations to generate equivalent expressions. - Evaluate a numerical expression, with parentheses and exponents, using order of operations. - Teacher Modeling - Student Discovery - Think-Pair-Share Students solve problems such as: Joseph thinks the two expressions 2(3a-2) + 4a and 10a 2 are equivalent. Is he correct? Why or why not? Connected Math Moving Straight Ahead: Inv. 3: Solving Equations Inv. 4: Exploring Slope 1.2, 2.1, 2.2 Model Unit 2 Model Unit 2 7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the - Use properties of operations to generate equivalent expressions. - Exit Ticket/Admit Ticket Linear expressions with rational coefficients. - Problem Solving Instruction - Model steps. 1.1, 1.3, 2.3, 2.4 Model Unit 2

5 problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Writing Equations - Think, pair, share - Student Discovery - Students may create several different expressions depending upon how they group the quantities in the problem. Solve problems and discuss strategies. Students may match problems with equivalent representations as modeled in the standards. Model Unit 2 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. - Multi-step problem solving using real world scenarios. - Ex.) Whole number, fractions, and decimals - Exit Ticket/Admit Ticket Write three expressions to represent a problem. Choose the expression that is most useful. - Problem Solving Instruction - Model steps. - Think, pair, share - Exit Ticket/Admit Ticket Multi-step real-life mathematical problem with positive and negative rational numbers. Connected Math Variables and Patterns Inv. 2: Analyzing Graphs and Inv. 3: Rules and Equations Inv. 4: Calculator and Graphs Accentuate the Negative Inv. 1: Extending the Number System Inv. 2: Adding and Subtracting Integers Inv. 3: Multiplying and Dividing Integers Inv. 4: Properties of Operations Moving Straight Ahead Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Model Unit 2 Model Unit 2

6 Inv. 3: Solving Equations Inv. 4: Exploring Slope 2.5, 2.6 Standard Solutions Lesson Plan CCS: Multi-Step Real-Life and Mathematical Problems 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. - Use the distributive property to simplify an algebraic expression. - Solve a 2-step linear inequality in one variable. - Determine the graph of the solutions to a 2- step linear inequality in one variable. - Problem Solving Instruction - Model steps. - Exit Ticket/Admit Ticket Equations and real-world problems. - Think, pair, share Such as: Jessica had $38 dollars to spend on school supplies. After buying 10 pens, she had $16.20 left. How much did each pen cost? : The sum of three consecutive even numbers is 36. What is the smallest of these numbers? Connected Math Variables and Patterns: Inv. 1: Variables,, and Coordinate Graphs Inv. 2: Analyzing Graphs and Inv. 3: Rules and Equations Moving Straight Ahead Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope Moving Straight Ahead: Inv. 2: ACE 44 a b Model Unit 2 Model Unit 2

7 Math Grade Seven Unit 3 Ratio and Proportion Time Frame: 7 weeks Description: - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Draw, construct, and describe geometrical figures and describe the relationships between them. Enduring Understandings: *Attributes of objects can be measured using processes and quantified units, and using appropriate techniques, tools, and formulas. *All constructions are based on the properties of geometric figures. *Proportional relationships express how quantities change in relationship to each other. Vocabulary: Unit rates, ratio, proportional relationships, proportions, constant of proportionality, complex fractions, percent, simple interest, rate, principal, tax, discount, markup, markdown gratuity, commissions, fee, percent of error, scale drawing, dimensions, scale factor, plane sections, right rectangular prism, right rectangular pyramids, parallel, perpendicular. Essential Questions: *How can multiple representations be used to express relationships? *How can similar objects be compared? **Unless otherwise noted all resources are taken from Pre-Algebra Prentice Hall Mathematics. Copyright 2007** Standards Topics Activities Resources Assessments 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. 7.RP.2. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Determine a unit rate. - Use a unit rate to solve a problem. - Solve using like and different unit rates. - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Teacher Modeling - Exit Ticket/Admit Ticket Unit rates and ratios. - Teacher Modeling. Students may work 6.1 Standard Solutions Lesson Plan CCS: The Complex Race: Computing Unit Rates as Complex Fractions Connected Math: Comparing and Scaling a)inv. 4: Making Sense of Proportions Q:\MathCurricComm itteematerials\model Unit 3 Q:\MathCurricComm itteematerials\model Unit 3 Q:\MathCurricComm itteematerials\model

8 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. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 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. - Solve a proportion using tables, graphs, and equations. - Writing proportional relationships and equations. - Determine a graph that can represent a situation involving a varying rate of change. together to analyze proportionate relationships by using tables and/or coordinate graphs. - Exit Ticket/Admit Ticket Proportional relationships. b) Comparing and Scaling Inv. 3: Comparing and Scaling Rates Inv. 4: Making Sense of Proportions Moving Straight Ahead: Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope c)variables and Patterns: Inv. 1: Variables,, and Coordinate Graphs Inv. 2: Analyzing Graphs and Inv. 3: Rules and Equations Inv. 4: ACE 13 And Comparing and Scaling: Inv. 4: Making Sense of Proportions Unit 3 Q:\MathCurricComm itteematerials\model Unit 3 Stretching and Shrinking: Inv. 4: Similarity and Ratios Inv. 5: Using Similar Triangles and Rectangles and Moving Straight Ahead: Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope

9 d) Variables and Patterns: Inv. 2: Analyzing Graphs and And Comparing and Scaling: Inv. 3: ACE 9, 10 And Moving Straight Ahead: Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope a) 6.2, 6.10 c. 6.6, 6.7 c ) Standard Solutions Lesson Plan CCS: Equation Matchup: An Introduction to Linear Equations d. Standard Solutions Lesson Plan CCS: Graphing Proportional Relationships

10 7.RP.3. Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Solving proportional problems with real world financial problems. - Teacher Modeling Students may use proportional relationships to solve problems involving simple interest, tax, gratuities and commissions. - Create a Problem Students create and solve a real-life word problem to exchange with a partner to solve. Connected Math: Variables and Pattern: Inv. 4: ACE 12 Comparing and Scaling: Inv. 1: Making Comparisons Inv. 2: Comparing Ratios, Percents, and Fractions Inv. 3: Comparing and Scaling Rates Inv. 4: Making Sense of Proportions Stretching and Shrinking: Inv. 4: Similarity and Ratios Inv. 5: Using Similar Triangles and Rectangles Q:\MathCurricComm itteematerials\model Unit 3 Q:\MathCurricComm itteematerials\model Unit 3 6.8, 6.9, 7.8 Standard Solutions Lesson Plan CCSS: An Introduction to Simple Interest Standard Solutions Lesson Plan CCS: Discovering Percent: Increase and Decrease Standard Solutions Lesson Plan CCSS: Gratuities and Commissions

11 7.G.1. Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. - Draw, construct, and describe geometrical figures and describe the relationships between them. - Teacher Modeling Students may analyze scale drawings to determine actual lengths. - Create a Problem Students create a scale drawing of a room in their home. - Exit Ticket/Admit Ticket Scale Drawing Connected Math: Stretching and Shrinking: Inv. 1: Enlarging and Reducing Shapes Inv. 2: Similar Figures Inv. 3: Similar Polygons Inv. 4: Similarity and Ratios Inv. 5: Using Similar Triangles and Rectangles Comparing and Scaling Inv. 4: Making Sense of Proportions Q:\MathCurricComm itteematerials\model Unit 3 Q:\MathCurricComm itteematerials\model Unit 3 6.3, 9.5, 9.7, Activity on Dilations pg506 7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. - Draw, construct, and describe geometrical figures and describe the relationships between them. - Teacher Modeling Students may draw geometric shapes with given conditions. Conditions may involve points, line segments, angles, parallelism, congruence, angles, and perpendicularity. Connected Math: Filling and Wrapping Inv. 1: Building Boxes Inv. 2: Designing Rectangular Boxes Inv. 3: Prisms and Cylinders Inv. 4: Cones, 9.3 Extension, 9.4 Q:\MathCurricComm itteematerials\model Unit 3 Q:\MathCurricComm itteematerials\model Unit 3 - Exit Ticket/Admit Ticket Draw a geometric shape with given conditions. Prerequisite Skill: Standard Solutions Lesson Plan CCS: Name That Quadrilateral

12 Math Grade Seven Unit 4 Statistics and Probability Time Frame: 7 weeks Description: - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Use random sampling to draw inferences about a population. - Draw informal comparative inferences about two populations. - Investigate chance processes and develop, use, and evaluate probability models. Enduring Understandings: *Change, in various contexts, both quantitative and qualitative, can be identified and analyzed. *Patterns provide insights into potential relationships. *The probability of an event s occurrence can be predicted with varying degrees of confidence. Vocabulary: random sampling, population, representative sample, inferences, variation/variability, distribution, measures of center, measures of variability, sample spaces Essential Questions: *How do I describe a pattern? *How can the relationship between quantities be represented? *How can change be expressed quantitatively? **Unless otherwise noted all resources are taken from Pre-Algebra Prentice Hall Mathematics. Copyright 2007** Standards Topics Activities Resources Assessments 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. - Analyze proportional relationships and use them to solve real- world and mathematical problems. - Teacher Modeling Students may use proportional relationships to solve problems involving simple interest, tax, gratuities and commissions. Connected Math: Variables and Pattern: Inv. 4: ACE 12 Comparing and Scaling: Inv. 1: Making Comparisons Inv. 2: Comparing Ratios, Percents, and Fractions Unit 4 Unit 4 - Create a Problem Students create and solve a real-life word problem to Inv. 3: Comparing and Scaling Rates

13 exchange with a partner to solve. Inv. 4: Making Sense of Proportions Stretching and Shrinking: Inv. 4: Similarity and Ratios Inv. 5: Using Similar Triangles and Rectangles 6.8, 6.9, 7.8 (See above sections as a reference) *Need more resources for analyzing and practice* 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. - Use random sampling to draw inferences about a population. - Create a Survey/Graph Students analyze graphs and create questions. - Justification Students justify the best survey option to use when gathering data. 3.3 Unit 4 Unit 4 7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. - Use random sampling to draw inferences about a population. - Estimate and predict based on random samples for a population. - Teacher Modeling - Exit Ticket/Admit Ticket Making inferences. Students collect data and draw inferences based on the results. - Create a Problem 12.8, 12.9 Unit 4 Unit 4

14 7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. - Draw informal comparative inferences about two populations. - Teacher Modeling - Dot plots Mean height and mean absolute deviation. - Think Pair-Share Students analyze a two dot plots to determine the difference between the centers. - Student Discovery - Students can readily find data as described in the example on sports team or college websites. Other sources for data include American Fact Finder (Census Bureau), Fed Stats, Ecology Explorers, USGS, or CIA World Fact book. Researching data sets provides opportunities to connect mathematics to their interests and other academic subjects. Connected Math: Data Distributions: Inv. 2: Making Sense of Measures of Center 12.1, 12.2, 12.3 *Need resources for higher level thinking* Unit 4 Unit 4

15 7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. - Draw informal comparative inferences about two populations. - Use measures of center to draw informal inferences about two populations - Teacher Modeling Measures of center and measures of variability. Students work in pairs to draw informal comparative inferences about two populations. They use measures of center and measures of variability. (Measures of center include mean, median, and mode. The measures of variability include range, mean absolute deviation, and interquartile range.) Connected Math: Data Distributions: Inv. 3: Comparing Distributions: Equal Numbers of Data Values Inv. 4: Comparing Distributions: Unequal Numbers of Data Values *Need Resources* Unit 4 Unit 4 - Justification 7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. - Investigate chance processes and develop, use, and evaluate probability models. - Understanding chance events between Teacher Modeling Probability of a chance event. Students review situations or chance events to decide the probability of unlikely, likely, or neither likely or unlikely. They understand that an unlikely event is closer to 0 and a likely event is closer to 1. ½ indicates an even with a chance. Connected Math: What Do You Expect? Inv. 1: ACE Standard Solutions Lesson Plan CCS: Likely or Unlikely *Need resources* Unit 4 Unit 4 - Think-Pair-Share - Exit Ticket/Admit Ticket Determine the probability of an event likely, unlikely, equally

16 likely. Students collect data and draw inferences based on the results. - Create a Problem Students create an example of each outcome likely, unlikely or equally likely. 7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. - Investigate chance processes and develop, use, and evaluate probability models. - Evaluate chance events to predict outcomes. - Teacher Modeling - Number Cubes (dice) Students work in pairs to approximate the probability of a chance event by collecting data number cubes, coins, marbles in a jar, etc. Students answer questions base on their observations. - Exit Ticket/Admit Ticket Connected Math: What Do You Expect? Inv. 1: Evaluating Games of Chance Inv. 2: Analyzing Situations Using an Area Model Inv. 3: Expected Value Inv. 4: Binomial Outcomes 12.7 Standard Solutions Lesson Plan CCS: Test the Theory Unit 4 Unit 4 - Probability *Need more practice and activities for high level thinking* 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 the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For - Investigate chance processes and develop, use, and evaluate probability models. - Develop a probability model from experimental and theoretical probability - Teacher Modeling. Students work in pairs to develop probability models to find probabilities of events. Students need multiple opportunities to perform probability experiments and compare these results Connected Math: What Do You Expect? a/b) Inv. 1: Evaluating Games of Chance Inv. 2: Analyzing Situations Using an Area Model Inv. 3: Expected Value Inv. 4: Binomial Outcomes Unit 4 Unit 4

17 example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? to theoretical probabilities. This can be accomplished using bag pulls, spinners, number cubes, coin toss, and colored chips, as well as other items. - Exit Ticket/Admit Ticket Probability - Think-Pair-Share a) 12.4 b) SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. 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. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. For - Investigate chance processes and develop, use, and evaluate probability models. - Evaluate compound events using organized lists, tables, tree diagrams, and experiments. - Calculate probability of independent events or dependent events. - Use permutations and combinations. - Teacher Modeling ganized lists, tables and tree diagrams Students work in pairs to find probabilities of compound events using organized lists, tables and tree diagrams. Student explain strategies used to determine outcome. - Create a Problem Students create a problem involving the probability of a compound event. - Exit Ticket/Admit Ticket Probability of a compound event. Connected Math: What Do You Expect? Inv. 1: Evaluating Games of Chance Inv. 2: Analyzing Situations Using an Area Model Inv. 3: Expected Value Inv. 4: Binomial Outcomes 12.5, 12.6 b) Standard Solutions: Admit Ticket *Need Resources- Practice for C* Unit 4 Unit 4

18 example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

19 Math Grade Seven Unit 5 - Geometry Time Frame: 7 weeks Description: - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. - Draw, construct, and describe geometrical figures and describe the relationships between them. - Solve real- life and mathematical problems involving angle measure, area, surface area, and volume. Enduring Understandings: *Geometry and spatial sense offer ways to interpret and reflect on our physical environment. *Measurement describes the attributes of objects and events. *Real world situations can be represented symbolically and graphically. *Vocabulary: Scale drawing, dimensions, scale factor, plane sections, right rectangular prism, right rectangular pyramids, parallel, perpendicular Vocabulary: scale drawing, dimensions, scale factor, plane sections, right rectangular prism, right rectangular pyramids, parallel, perpendicular, inscribed, circumference, radius, diameter, pi, supplementary, vertical, adjacent, complementary, pyramids, face, base Essential Questions: *How can multiple representations be used to express relationships? *What can we learn from studying patterns? *How does what we measure affect how we measure? **Unless otherwise noted all resources are taken from Pre-Algebra Prentice Hall Mathematics. Copyright 2007** Standards Topics Activities Resources Assessments 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. - Multi-step problem solving using real world scenarios. Ex.) Whole number, fractions, and decimals - Instruction -Model steps. - Think, pair, share - Exit Ticket/Admit Ticket Multi-step reallife mathematical problem with positive and negative rational numbers. Connected Math Variables and Patterns Inv. 2: Analyzing Graphs and Inv. 3: Rules and Equations Inv. 4: Calculator and Graphs Accentuate the Negative Inv. 1: Extending the Number System Inv. 2: Adding and Subtracting Integers Inv. 3: Multiplying and Dividing ri Unit 5 ri Unit 5

20 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Integers Inv. 4: Properties of Operations Moving Straight Ahead Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope 7.7 Standard Solutions Lesson Plan CCS: Multi-Step Real-Life and Mathematical Problems *Need Higher Level Practice with Real World Examples*

21 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. - Solve real- life and mathematical problems using numerical and algebraic expressions and equations. - Use the distributive property to simplify an algebraic expression. - Solve a 2-step linear inequality in one variable. - Determine the graph of the solutions to a 2-step linear inequality in one variable. - Problem Solving Instruction - Model steps. - Exit Ticket/Admit Ticket Equations and real-world problems. - Think, pair, share Such as: Jessica had $38 dollars to spend on school supplies. After buying 10 pens, she had $16.20 left. How much did each pen cost? : The sum of three consecutive even numbers is 36. What is the smallest of these numbers? Connected Math Variables and Patterns: Inv. 1: Variables,, and Coordinate Graphs Inv. 2: Analyzing Graphs and Inv. 3: Rules and Equations Moving Straight Ahead Inv. 1: Walking Rates Inv. 2: Exploring Linear Functions With Graphs and Inv. 3: Solving Equations Inv. 4: Exploring Slope Moving Straight Ahead: Inv. 2: ACE 44 a) , 7.7 b) *Need Higher Level Practice with Real World Examples* ri Unit 5 ri Unit 5

22 7.G.3. Describe the twodimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. - Draw, construct, and describe geometrical figures and describe the relationships between them. - Describe 2D shapes when sliced from 3D shapes. - Teacher Modeling - Student Discovery 9.3 *Need Resources ri Unit 5 ri Unit 5 - Comparing prisms and pyramids. 7.G.4. Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. - Solve real- life and mathematical problems involving angle measure, area, surface area, and volume. - Problems for circumference and area of circles. - Teacher Modeling Area and circumference. - Student Discovery - Students measure the circumference and diameter of several circular objects in the room (clock, trash can, door knob, wheel, etc.). Students organize their information and discover the relationship between circumference and diameter by noticing the pattern in the ratio of the measures. 9.6, 10.3 Standard Solutions Lesson Plan CCS: Discovering Pi Standard Solutions Lesson Plan CCS: Circular Thinking: Discovering the Area Formula for Circles ri Unit 5 ri Unit 5 - Think-Pair-Share

23 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - Draw, construct, and describe geometrical figures and describe the relationships between them. - Analyze angle relationships to write and use equations to solve for missing information. - Teacher Modeling Students analyze a drawing to find examples of supplementary, complementary, vertical and adjacent angles. - Exit Ticket/Admit Ticket Naming pairs of complementary and supplementary angles in a drawing. Connected Math: Stretching and Shrinking Inv. 3: ACE , 9.2 Standard Solutions Triangle Puzzle ri Unit 5 ri Unit 5 7.G.6. 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. - Solve real- life and mathematical problems involving angle measure, area, surface area, and volume. - Solve for area, volume, and surface area of the following shapes; triangles, quadrilaterals, polygons, cubes, and right prisms. - Teacher Modeling. - Create a Problem Students create and solve a problem involving area, volume or surface area. Students exchange problem with a partner to solve. - Exit Ticket/Admit Ticket Area, volume or surface area. Connected Math: Stretching and Shrinking Inv. 2: Similar Figures Inv. 3: Similar Polygons Filling and Wrapping Inv. 1: Building Boxes Inv. 2: Designing Rectangular Boxes Inv. 3: Prisms and Cylinders Inv. 4: Cones, Spheres, and Pyramids Inv. 5: Scaling Boxes 10.1, 10.2, 10.4, 10.5, 10.6, 10.7, 10.9 ri Unit 5 ri Unit 5