3 5-11) 3: & 1 #1 7.RP.1 1/2 1/4 1/2/1/4 2 3 #2 #3 #4 6 2 ½ 2 #5 (0, 0) (1, 4 #6 7.RP.3 7.G.1 #7 7.G.2 4: & 6 #1 7.RP.3 #2 7.RP.3, 7.SP.SP.1, 7.SP.

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1 7 th Grade Math Quarter 3 (Jan 5- March 11) Unit 3: Ratios & Proportions Week 1 #1 7.RP.1 Calculate and interpret unit rates of various quantities involving ratios of fractions that contain like and different units using real world examples such as speed and unit price. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Week2/Week 3 #2 7.RP.2a Determine if a proportional relationship exists between two quantities e.g. by testing for equivalent ratios in a table or graph on the coordinate plane and observing whether the graph is a straight line through the origin. #3 7.RP.2b Identify the constant of proportionality (unit rate) from tables, graphs, equations, diagrams, and verbal descriptions. #4 7.RP.2c Write equations to model proportional relationships in real world problems. For example, if a recipe that serves 6 people calls for 2 ½ cups of sugar. How much sugar is needed if you are serving only 2 people? #5 7.RP.2d Represent real world problems with proportions on a graph and describe how the graph can be used to explain the values of any point (x, y) on the graph including the points (0, 0) and (1, r), recognizing that r is the unit rate. Week 4 #6 7.RP.3 7.G.1 Solve multi-step ratio and percent problems using proportional relationships, including scale drawings of geometric figures, simple interest, tax, markups and markdowns, gratuities and commissions, and fees. #7 7.G.2 Use freehand, mechanical (i.e. ruler, protractor) and technological tools to draw geometric shapes with given conditions (e.g. scale factor), focusing on constructing triangles. Unit 4: Statistics & Probability Week 5/Week 6 #1 7.RP.3 Solve multi-step ratio and percent problems using proportional relationships (simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error). #2 7.RP.3, 7.SP.1 Distinguish between valid and invalid samples from a population by determining if the sample is representative of the subgroups within the population (e.g. if the class had 50% girls and the sample had 25% girls, then the number of girls was not representative of the whole population). #3 7.SP.1, 7.SP.2 Use random sampling to produce a representative sample, develop valid inferences about a population with an unknown characteristic of interest, and compare the variation in estimates using multiple samples of the same and different size. Week7/Week 8 #4 7.SP.3, 7.SP.4 Visually and numerically compare the means and variations of two distinct populations (such as the mean height of different sports teams) to draw informal comparative inferences about measures of center and variability using graphical representations and statistical calculations. #5 7.SP.5 Interpret and express the likelihood of a chance event as a number between 0 and 1, relating that the probability of an unlikely event happening is near 0, a likely event is near 1, and 1/2 is neither likely nor unlikely. #6 7.RP.3 7.SP.6 Conduct experimental probability events that are both uniform (rolling a number cube multiple times) and non-uniform (tossing a paper cup to see if it lands up or down) to collect and analyze data to make predictions for the approximate relative frequency of chance events.

2 Week 9 #7 7.SP.7 Develop uniform and non-uniform theoretical probability models by listing the probabilities of all possible outcomes in an event, for instance, the probability of the number cube landing on each number being 1/6. Then, conduct an experiment of the event using frequencies to determine the probabilities of each outcome and use the results to explain possible sources of discrepancies in theoretical and experimental probabilities. #8 7.SP.8 Design a simulation of a compound probability event and determine the sample space using organized lists, tables, and tree diagrams, calculate the fractional probabilities for each outcome in the sample space, and conduct the simulation using the data collected to determine the frequencies of the outcomes in the sample space. Week 10: Review/District Assessment-Quarter 3 7 th Grade Math Quarter 3 ( ) Central Consolidated School District Major supporting additional Objective/CCSS Skills, Strategies, Concepts, and Questions Task Evidence/Activities/Math Practices/Calculator Unit 3: Ratios & Proportions Students continue to work with unit rates from 6th MP2. Reason abstractly and quantitatively. grade; however, the comparison now includes fractions MP6. Attend to precision. compared to fractions. The comparison can be with like MP4. Model with mathematics. or different units. Fractions may be proper or improper Week 1 #1 I can calculate and interpret unit rates of various quantities involving ratios of fractions that contain like and different units using real world examples such as speed and unit price. 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. How are unit rates represented? How does a unit rate represent a real-world situation? How do I interpret a unit rate (using words and mathematically)? When the ratio of a to b is scaled up or down to the ratio a/b to 1, a/b to 1 is referred to as a unit ratio or rate. YES Calculator Tasks have a real-world context. ii) Tasks do not assess unit conversions. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Week2/Week 3 #2 I can determine if a proportional relationship exists between two quantities e.g. by testing for equivalent ratios in a table or graph on the coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing Students understanding of the multiplicative reasoning used with proportions continues from 6th grade. Students determine if two quantities are in a proportional relationship from a table. Fractions and decimals could be used with this standard. 7.RP.2- Testing for proportionality involves determining if one quantity is a constant multiple of the other. When the values that describe the relationship appear in a table or as discrete points on a graph, all such values must be tested. Proportionality tests include: - testing to see if the ratio ofy to x (or x to y) simplifies to a constant value; MP2. Reason abstractly and quantitatively. MP5. Use appropriate tools strategically Yes Calculator i) Tasks have thin context 2 or no context. ii) Tasks are not limited to ratios of whole numbers. iii) Tasks use only coordinates in Quadrant 1 and use only a positive constant of proportionality.

3 for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. - testing to see if the ratio of y to x (or x to y) for each (x, y) pair produces equivalent ratios; - determining if y = kx is a true statement for all quantities of x and y in the relationship; and - graphing, and determining that the graph of the quantities forms a straight line and passes through (0, 0), since (0, 0) makes the equation y = kx a true statement. 7.RP.2a- #3 I can identify the constant of proportionality (unit rate) from tables, graphs, equations, diagrams, and verbal descriptions. 7.RP.2b Recognize and represent proportional relationships between quantities b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Example: The graph below represents the price of the bananas at one store. What is the constant of proportionality? Solution: From the graph, it can be determined that 4 pounds of bananas is $1.00; therefore, 1 pound of bananas is $0.25, which is the constant of proportionality for the graph. Note: Any point on the line will yield this constant of proportionality. Students write equations from context and identify the coefficient as the unit rate which is also the constant of proportionality MP2. Reason abstractly and quantitatively. MP8. Look for and express regularity in repeated reasoning. MP5. Use appropriate tools strategically NO Calculator i) Tasks may or may not have a context. ii) Tasks sample equally across the listed representations (graphs, equations, diagrams, and verbal descriptions). iii) Tasks use only coordinates in Quadrant 1 and use only a positive constant of proportionality.

4 #4 I can write equations to model proportional relationships in real world problems. For example, if a recipe that serves 6 people calls for 2 ½ cups of sugar. How much sugar is needed if you are serving only 2 people? 7.RP.2c Recognize and represent proportional relationships between quantities 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. #5 I can represent real world problems with proportions on a graph and describe how the graph can be used to explain the values of any point (x, y) on the graph including the points (0, 0) and (1, r), recognizing that r is the unit rate. 7.RP.2d Recognize and represent proportional relationships between quantities 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. Constructing verbal models can also be helpful. A student might describe the situation as the number of packs of gum times the cost for each pack is the total cost in dollars. They can use this verbal model to construct the equation. Students can check their equation by substituting values and comparing their results to the table. The checking process helps student revise and recheck their model as necessary. The number of packs of gum times the cost for each pack is the total cost. (g x 2 = d) How do I interpret a distance time graph and determine a point of intersection? Example: The graph below represents the cost of gum packs as a unit rate of $2 dollars for every pack of gum. The unit rate is represented as $2/pack. Represent the relationship using a table and an equation. Solution: Table: Equation: d = 2g, where d is the cost in dollars and g is the packs of gum A common error is to reverse the position of the variables when writing equations. Students may find it useful to use variables specifically related to the quantities rather than using x and y. MP2. Reason abstractly and quantitatively. MP8. Look for and express regularity in repeated reasoning NO Calculator Tasks have a context. ii) Tasks use only coordinates in Quadrant 1 and use only a positive constant of proportionality. MP2. Reason abstractly and quantitatively MP4. Model with mathematics No Calculator Tasks use only coordinates in Quadrant 1 and use only a positive constant of proportionality

5 Week 4 #6 I can solve multi-step ratio and percent problems using proportional relationships, including scale drawings of geometric figures, simple interest, tax, markups and markdowns, gratuities and commissions, and fees. 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. 7.G.1 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 #7 I can use freehand, mechanical (i.e. ruler, protractor) and technological tools to draw geometric shapes with given conditions (e.g. scale factor), focusing on constructing triangles. 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 7.RP.3 In 6th grade, students used ratio tables and unit rates to solve problems. Students expand their understanding of proportional reasoning to solve problems that are easier to solve with cross-multiplication. Students understand the mathematical foundation for cross-multiplication. 7.G.1 Students determine the dimensions of figures when given a scale and identify the impact of a scale on actual length (one-dimension) and area (two-dimensions). Students identify the scale factor given two figures. Using a given scale drawing, students reproduce the drawing at a different scale. Students understand that the lengths will change by a factor equal to the product of the magnitude of the two size transformations. What are the steps for solving problems involving scale drawings of geometric figures? What are the steps for computing actual lengths and areas from a scale drawing? How does one reproduce a scale drawing at a different scale? Students draw geometric shapes with given parameters. Parameters could include parallel lines, angles, perpendicular lines, line segments, etc. What are the characteristics of angles and sides that will create geometric shapes, especially triangles? 7RP3 MP1. Make sense of problems and persevere in solving them. #6 Use proportional relationships in real world context. MP4. Model with mathematics. #6 Represent proportional relationships symbolically. MP2. Reason abstractly and quantitatively. MP6. Attend to precision Yes Calculator Tasks will include proportional relationships that only involve positive numbers. 7G1 MP2. Reason abstractly and quantitatively. MP5. Use appropriate tools strategically MP4. Model with mathematics. #6 Represent proportional relationships symbolically. YES Calculator i). Tasks may or may not have context. MP2. Reason abstractly and quantitatively. #7 Notice geometric conditions that determine a unique triangle MP3. Construct viable arguments and critique the reasoning of others. MP5. Use appropriate tools strategically. #7 Use technology when available. MP6. Attend to precision i) Tasks do not have a context. ii) Most of tasks should focus on the drawing component of this evidence statement.

6 Week 5/Week 6 Unit 4: Probability and Statistics #1 In 6th grade, students used ratio tables and unit rates to I can solve multi-step ratio and percent problems using proportional relationships (simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, solve problems. Students expand their understanding of proportional reasoning to solve problems that are easier to solve with cross-multiplication. Students understand the mathematical foundation for cross-multiplication. percent error. How are ratios and their relationships used to solve real world problems? 7.RP.3 What conditions help to recognize and represent Use proportional relationships to solve proportional relationships between quantities? multistep ratio and percent problems. How are proportional relationships used to solve Examples: simple interest, tax, markups multistep ratio and percent problems? and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error #2 I can distinguish between valid and invalid samples from a population by determining if the sample is representative of the subgroups within the population (e.g. if the class had 50% girls and the sample had 25% girls, then the number of girls was not representative of the whole population). 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. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and 7.SP.1 Students recognize that it is difficult to gather statistics on an entire population. Instead a random sample can be representative of the total population and will generate valid predictions. Students use this information to draw inferences from data. A random sample must be used in conjunction with the population to get accuracy. For example, a random sample of elementary students cannot be used to give a survey about the prom. Example 1: The school food service wants to increase the number of students who eat hot lunch in the cafeteria. The student council has been asked to conduct a survey of the student body to determine the students preferences for hot lunch. They have determined two ways to do the survey. The two methods are listed below. Determine if each survey option would produce a random sample. Which survey option should the student council use and why? 1. Write all of the students names on cards and pull them out in a draw to determine who will complete the survey. 2. Survey the first 20 students that enter the lunchroom. 3. Survey every 3rd student who gets off a bus Understand that statistics can be used to gain information about a population by examining a sample MP1. Make sense of problems and persevere in solving them. #1 Use problems that have several givens or must be decomposed before solving. MP2. Reason abstractly and quantitatively. MP5. Use appropriate tools strategically. MP6. Attend to precision YES calculator Tasks will include proportional relationships that only involve positive numbers. 7SP1 MP 4. Model with mathematics. MP2. Reason abstractly and quantitatively. #2 Present an argument and provide supporting justification YES Calculator 7RP3 MP1. Make sense of problems and persevere in solving them. MP2. Reason abstractly and quantitatively. MP5. Use appropriate tools strategically. MP6. Attend to precision YES calculator Tasks will include proportional relationships that only involve positive numbers.

7 commissions, fees, percent increase and decrease, percent error #3 I can use random sampling to produce a representative sample, develop valid inferences about a population with an unknown characteristic of interest, and compare the variation in estimates using multiple samples of the same and difference size. 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. 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 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. What factors affect the outcomes of a survey or study? What is sampling? How do you select a valid sample to survey or study? What are the criteria for determining if a survey is biased? Students collect and use multiple samples of data to make generalizations about a population. Issues of variation in the samples should be addressed. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. What is a random sample? How can random samples be used to make predictions about populations? Does a sample have to be random to make accurate predictions about populations? How are proportions used to estimate information about populations? 7SP1 MP 4. Model with mathematics. MP2. Reason abstractly and quantitatively. YES Calculator 7SP2 MP4. Model with mathematics YES Calculator

8 sampled survey data. Gauge how far off the estimate or prediction might be. Week 7/Week 8 #4 I can visually and numerically compare the means and variations of two distinct populations (such as the mean height of the different sports teams) to draw informal comparative inferences about measures of center and variability using graphical representations and statistical calculations. 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. 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. #5 I can interpret and express the likelihood of a chance event as a number between 0 and 1, relating that the probability of an This is the students first experience with comparing two data sets. Students build on their understanding of graphs, mean, median, Mean Absolute Deviation (MAD) and interquartile range from 6th grade. Students understand that: 1. A full understanding of the data requires consideration of the measures of variability as well as mean or median. 2. Variability is responsible for the overlap of two data sets and that an increase in variability can increase the overlap. 3. Median is paired with the interquartile range and mean is paired with the mean absolute deviation. Students compare two sets of data using measures of center (mean and median) and variability (MAD and IQR).Students identify the scale factor given two figures. How do scientists make estimations about a population size using a representative sample? How are the measures of variability used to analyze and compare data? How can variability affect the overlap of two data sets? How do I use the measures of center to compare two sets of data? How do I use the measures of variability to compare two sets of data? Which measure, center or variability, is the best comparison to use? This is the students first formal introduction to probability. Students recognize that the probability of any single event can be can be expressed in terms such as 7.SP.3 MP 4. Model with mathematics. Yes Calculator i) Tasks may use mean absolute deviation, range, or interquartile range as a measure of variability 7.SP.4 MP 4. Model with mathematics. Yes Calculator MP 4. Model with mathematics. #5 Determine probability experimentally YES Calculator

9 unlikely even happening is near 0, a likely event is near 1, and ½ is neither likely nor unlikely. 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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. #6 I can conduct experimental probability events that are both uniform (rolling a number cube multiple times) and nonuniform (tossing a paper cup to see if it lands up or down) to collect and analyze data to make predictions for the approximate relative frequency of chance events. 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. 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. impossible, unlikely, likely, or certain or as a number between 0 and 1. What is the likeliness of an event occurring based on the probability near 0, ½, or 1? How can events be described using probability? Students collect data from a probability experiment, recognizing that as the number of trials increase, the experimental probability approaches the theoretical probability. The focus of this standard is relative frequency -- The relative frequency is the observed number of successful events for a finite sample of trials. Relative frequency is the observed proportion of successful event, expressed as the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. Example: Each group receives a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles. Each group performs 50 pulls, recording the color of marble drawn and replacing the marble into the bag before the next draw. Students compile their data as a group and then as a class. They summarize their data as experimental probabilities and make conjectures about theoretical probabilities (How many green draws would are expected if 1000 pulls are conducted? 10,000 pulls?). Students create another scenario with a different ratio of marbles in the bag and make a conjecture about the outcome of 50 marble pulls with replacement. (An example would be 3 green marbles, 6 blue marbles, and 3 blue marbles.) Students try the experiment and compare their predictions to the experimental outcomes to continue to 7SP.6 MP 4. Model with mathematics. YES Calculator Tasks require the student to make a prediction based on long-run relative frequency in data from a chance process. 7RP3 MP1. Make sense of problems and persevere in solving them. MP2. Reason abstractly and quantitatively. MP5. Use appropriate tools strategically. MP6. Attend to precision YES calculator Tasks will include proportional relationships that only involve positive numbers.

10 Week 9 #7 I can develop uniform and non-uniform theoretical probability models by listing the probabilities of all possible outcomes in an event, for instance, the probability of the number cube landing on each number being 1/6. Then, conduct an experiment of the event using frequencies to determine the probabilities of each outcome and use the results to explain possible sources of discrepancies in theoretical and experimental probabilities. 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 example, if a student is selected at random explore and refine conjectures about theoretical probability. Example: A bag contains 100 marbles, some red and some purple. Suppose a student, without looking, chooses a marble out of the bag, records the color, and then places that marble back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these results, predict the number of red marbles in the bag. How can you represent the likelihood of an event occurring? How can data be used to make predictions? The experimental probability or relative frequency of outcomes of an event can be used to estimate the exact probability of an event. Experimental probability approaches theoretical probability when the number of trials is large. Probabilities are useful for predicting what will happen over the long run. Using theoretical probability, students predict frequencies of outcomes. Students recognize an appropriate design to conduct an experiment with simple probability events, understanding that the experimental data give realistic estimates of the probability of an event but are affected by sample size. Students need multiple opportunities to perform probability experiments and compare these results to theoretical probabilities. Critical components of the experiment process are making predictions about the outcomes by applying the principles of theoretical probability, comparing the predictions to the outcomes of the experiments, and replicating the experiment to compare results. Experiments can be replicated by the same group or by compiling class data. Experiments can be conducted using various random generation devices including, but not limited to, bag pulls, spinners, number cubes, coin toss, and colored chips. Students can collect data using physical objects or graphing calculator or web-based simulations. Students can also develop models for geometric probability (i.e. a target). How are the outcomes of given events distinguished as possible? MP 4. Model with mathematics. YES Calculator Simple events only

11 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 #8 I can design a simulation of a compound probability event and determine the sample space using organized list, tables, and tree diagrams, calculate the fractional probabilities for each outcome in the sample space, and conduct the simulation using the data collected to determine the frequencies of the outcomes in the sample space 7.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 How can you determine the likelihood that an event will occur? How are theoretical probabilities used to make predictions or decisions? What is the difference between theoretical and experimental probability? Students use tree diagrams, frequency tables, and organized lists, and simulations to determine the probability of compound events. Example 1: How many ways could the 3 students, Amy, Brenda, and Carla, come in 1st, 2nd and 3rd place? Solution: Making an organized list will identify that there are 6 ways for the students to win a race A, B, C A, C, B B, C, A B, A, C C, A, B C, B, A Example 2: Students conduct a bag pull experiment. A bag contains 5 marbles. There is one red marble, two blue marbles and two purple marbles. Students will draw one marble without replacement and then draw another. What is the sample space for this situation? Explain how the sample space was determined and how it is used to find the probability of drawing one blue marble followed by another blue marble. Example 3: A fair coin will be tossed three times. What is the probability that two heads and one tail in any order will results? Solution: MP 4. Model with mathematics MP 5. Use appropriate tools strategically. YES Calculator

12 events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? HHT, HTH and THH so the probability would be 3/8. How can you represent the probability of compound events by constructing models? What is the process to design and use a simulation to generate frequencies for compound events? Sometimes the outcome of one event does not affect the outcome of another event. (This is when the outcomes are called independent.) Tree diagrams and arrays are useful for describing relatively small sample spaces and computing probabilities, as well as for visualizing why the number of outcomes can be extremely large. Simulations can be used to collect data and estimate probabilities for real situations that are sufficiently complex that the theoretical probabilities are not obvious. Week 10: Review/District Assessment- Quarter 3 (Below) Math Practices Performance Level Descriptors (PLD) 7th grade PARCC Reference Sheet WIDA th grade Math CCSS Vocabulary *****Math Website Resources (lesson plans, worksheets, videos, notes) on website page K-12 Mathematical Practices MP.1: Make sense of problems and persevere in solving them. (problem solving) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Analyzes information given Looks for different ways to solve the problem (i.e. situation vs. solution) Knows and uses different representations (i.e. equation vs. table or graph) and/or manipulative Evaluates progress and changes plan if needed Explains using both pictures and words Makes connection to the way they solved the problem and how others solved the problem Uses basic fact fluency or fact strategies Promotes visible thinking using pictures and equations Gives time for students to discuss with others or class Encourages students to keep trying and builds supportive math community Uses explicit and precise language when using representations and definitions and expects students to do the same in their discussions Helps students make connections between representations, equations, and student thinking Engages students in metacognition Models problem situation, not problem solution.

13 MP.2: Reason abstractly and quantitatively. (number sense) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Task explicitly asks for justification or explanation Makes sense of quantities and their relationship in problem situations Recognizes that quantities can be represented in different ways Uses numbers and words to make sense of a problem Gives attention to the meaning of the numbers and knows which operation to choose Performs operations flexibly, accurately, and efficiently Uses multiple representations Connects numbers, symbols or units to quantities Justifies solutions Makes connections to how they solved a problem and how others solved the problem Reasons with attributes of geometric figures Promotes visible thinking using pictures and equations Uses physical representations (manipulatives, drawings) to model what happens to a variable when it changes and how that effects the other variable Gives time for students to discuss with others or class Encourages students to keep trying Uses explicit and precise language when using representations and definitions and expects students to be the same in their discussion Builds a supportive math community Helps make connections between representations, equations, student thinking, and content standard MP.3: Construct viable arguments and critique the reasoning of others. (math talk) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Communicates by using mathematical reasoning with objects, drawings, diagrams, equations Justifies solutions Makes connections between their own thinking and that of others Demonstrates actively listening by asking questions of others Makes statements to prove or disprove concepts or presented ideas Students understand different forms of reasoning (ie. deductive reasoning) and when to apply them Uses accurate vocabulary Promotes math talk and the critiquing of presented solutions Asks higher-order questions to facilitate discussion and presses for justification Gives time for students to construct their own ideas before small or large group discussions Expects students to be explicit and precise when using representations, definitions, and symbols Builds a supportive math community Helps make connections between the reasoning of students and content standard

14 MP.4: Model with mathematics. (representations and graphs) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Identifies important elements and quantities needed for a model Describes relationships of models and equation Chooses a representation Applies formulas/equations Uses models to draw conclusion Explains why it is a good model for the problem Recognizes and uses parts of a graph (i.e. title, labels, symbols, key) Expects students to justify their choice in models Gives students opportunity to evaluate the appropriateness of their model and that of others Helps make connections with the relationships between representation, equation, answer, student thinking, and content standard MP.5: Use appropriate tools strategically. (calculators, rulers, manipulative) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Uses mental computations fluently Knows which tools are appropriate for the task Knows when to use a tool Understands and uses properties of operations Uses estimation to find errors and check answer for reasonableness Justifies tool selection Allows students to choose appropriate learning tools Uses appropriate tools to represent, explore and deepen student understanding Models how different representations are tools Uses technology tools to deepen students understanding of a concept Helps make connections between tool, equation, student thinking, and content standard

15 MP.6: Attend to precision. (vocabulary, labeling, answers) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Uses appropriate math vocabulary Uses clear definitions in discussion Calculates accurately and efficiently Explains their reasoning with accurate mathematical language Uses proper unit labels with measuring Uses appropriate labels when graphing and solving story problems Determines when different levels of precision are needed and how precision affects results Communicates precisely using clear definitions Emphasizes the importance of precise communication Emphasizes the importance of precision of measurement Helps make connections between vocabulary, student thinking, unit labels, calculations, and content standard MP.7: Look for and make use of structure. (how numbers and shapes are organized) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Recognizes that quantities can be represented in different ways Uses properties of operations to make sense of problems Recognizes how numbers and shapes are organized Looks for patterns and structures in the number system Justify strategy for basic facts Uses models to prove equations Recognize how symbols help represent relationships and can be applied to new situations Gives students time to discuss connections Brings students back to the rule or properties being used Helps students look for patterns and structures in the number system Helps make connections between the structure used, equation, student thinking, and content standard Helps make connections to real world

16 MP.8: Look for and express regularity in repeated reasoning. (number pattern) The Math Task: The Student: The Teacher: Is an interesting problem Has more than one solution path which may be unpredictable Creates discussion Requires cognitive effort Connects to real world Relates to grade level CCSS Builds student understanding of grade level standard Leads students to look back and reflect on answer Explicitly asks for justification or explanation Notices number patterns Notices if calculations are repeated Applies more efficient computation strategies using number patterns Looks both for general methods and for shortcuts Encourages students to connect task to prior concepts taught Helps make connections between pattern, equation, student thinking, and content standard Performance Level Descriptors Grade 7 Mathematics Proportional Relationships 7.RP.1 7.RP.2a 7.RP.2b 7.RP.2c 7.RP.2d 7.RP RP.3-2 Sub-Claim A The student solves problems involving the Major Content for grade/course with connections to the Standards for Mathematical Practice. Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Analyzes and uses proportional relationships to solve real-world and mathematical problems, including multi-step ratio/percent problems. Computes unit rates of quantities associated with ratios of fractions. Analyzes and uses proportional relationships to solve real-world and mathematical problems, including multistep ratio/percent problems. Computes unit rates of quantities associated with ratios of fractions. Analyzes and uses proportional relationships to solve real-world and mathematical problems, including simple ratio/percent problems. Computes unit rates of quantities associated with ratios of fractions. Uses proportional relationships to solve real-world and mathematical problems, including simple ratio/percent problems. Computes unit rates of quantities associated with ratios of fractions. Decides whether two quantities are in a proportional relationship and identifies the constant of proportionality (unit rate) in tables, equations, diagrams, verbal descriptions and graphs. Interprets a point (x, y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Decides whether two quantities are in a proportional relationship and identifies the constant of proportionality (unit rate) in tables, equations, diagrams, verbal descriptions and graphs. Interprets a point (x, y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Decides whether two quantities are in a proportional relationship and identifies the constant of proportionality (unit rate) in tables, equations, diagrams, verbal descriptions and graphs. Interprets a point (x, y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Decides whether two quantities are in a proportional relationship and identifies the constant of proportionality (unit rate) in tables, equations, diagrams, verbal descriptions and graphs. Uses equations representing a proportional relationship to solve simple mathematical and real-world problems, including simple ratio and percent problems.

17 Sub-Claim A The student solves problems involving the Major Content for grade/course with connections to the Standards for Mathematical Practice. Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Represents proportional Represents proportional Represents proportional relationships by equations and uses them to solve mathematical and real-world problems, including multi-step ratio and percent problems. relationships by equations and uses them to solve mathematical and real-world problems, including multi-step ratio and percent problems relationships by equations and uses them to solve mathematical and real-world problems, including simpl ratio and percent problems. Compares proportional relationships given in different forms (tables, equations, diagrams, verbal, graphs). Determines when it is appropriate to use unit rate and understands when it has its limitations. Operations with Fractions 7.NS.1 7.NS.2 7.NS.3 7.EE.3 Expressions, Equations and Inequalities 7.EE.1 7.EE.2 7.EE.4 Performs operations on positive and negative rational numbers in mathematical and real-world problems. Represents addition and subtraction on a horizontal or vertical number line and recognizes situations in which opposite quantities combine to make zero. Determines reasonableness of a solution and interprets solutions in real-world contexts. Using the properties of operations, justifies the steps taken to solve multi-step mathematical and realworld problems involving rational numbers. Applies properties of operations as strategies to add, subtract, factor and expand linear expressions. Fluently solves multi-step linear equations with rational coefficients. Performs operations on positive and negative rational numbers in multistep mathematical and real-world problems. Represents addition and subtraction on a horizontal or vertical number line and recognizes situations in which opposite quantities combine to make zero. Determines reasonableness of a solution and interprets solutions in real-world contexts. Applies properties of operations as strategies to add, subtract, factor and expand linear expressions. Fluently solves multi-step linear equations with rational coefficients. Performs operations on positive and negative rational numbers in multistep mathematical and real-world problems. Represents addition and subtraction on a horizontal or vertical number line and recognizes situations in which opposite quantities combine to make zero. Determines reasonableness of a solution. Applies properties of operations as strategies to add, subtract, factor and expand linear expressions. Solves two-step linear equations with rational coefficients. Performs operations on positive and negative rational numbers in simple mathematical and real-world problems. Represents addition and subtraction on a horizontal or vertical number line and recognizes situations in which opposite quantities combine to make zero. Applies properties of operations as strategies to add, subtract and expand linear expressions. Solves two-step linear equations with rational coefficients. In mathematical or real-world contexts, uses variables to represent quantities, construct and In mathematical or real-world contexts, uses variables to represent quantities, construct and In a mathematical or real-world context, uses variables to represent quantities, construct and solve In a mathematical context, uses variables to represent quantities, construct and solve simple

18 solve simple equations and inequalities, and graph and interpret solution sets. solve simple equations and inequalities, and graph and interpret solution sets. simple equations and inequalities, and graph solution sets. equations and inequalities, and graph solution sets. Sub-Claim B Representing Geometric Figures 7.G.2 7.G.3 Describes the relationship between equivalent quantities that are expressed algebraically in different forms in a problem context and explains their equivalence in light of the context of the problem. Rewrites an expression in different forms. Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the Standards for Mathematical Practice Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Draws, with precision, geometric figures freehand, with a ruler and protractor or with technology and describes their attributes. Constructs triangles with given angle and side conditions and notices when those conditions determine a unique triangle, more than one triangle or no triangle. Describes two-dimensional figures that result from slicing threedimensional figures by a plane which may or may not be parallel or perpendicular to a base or face Draws geometric figures freehand, with a ruler and protractor or with technology and describes their attributes. Constructs triangles with given angle and side conditions and notices when those conditions determine a unique triangle, more than one triangle or no triangle. Describes two-dimensional figures that result from slicing threedimensional figures by a plane which may or may not be parallel or perpendicular to a base or face. Draws geometric figures freehand, with a ruler and protractor or with technology and describes their attributes. Constructs triangles with given angle and side conditions. Describes the two-dimensional figures that result from slicing three-dimensional figures by a plane parallel or perpendicular to a base or face. Draws geometric figures freehand, with a ruler and protractor, or with technology and describe some of their attributes. Constructs triangles with given angle and side conditions.