Bay Grade 7 Math Course of Study FINAL
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TimestampDomainStrandsContent StatementLearning Target (I can statements) You can have multiple learning targets for one content statement. Put them all in the box. Use CTRL+ENTER to move to a second line within one box.Grading Period/ MonthConnected Math AlignmentSupplemental Resources/Lesson Ideas
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Assessment (formative and summative)Tier 3 Vocab (Content specific words)
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6/27/2012 10:01:52Ratios and Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.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 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.
I can find unit rates and use them to solve problems.
Q2Comparing & Scaling
Inv 2,3
Unit rates
Ratio
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6/27/2012 10:09:42Ratios and Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.2. 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 in 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.
I can recognize and represent proportional relationships between quantities.
I can decide whether two quantities are in a proportional relationship using a table or a graph.
I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions in proportional relationships.
I can represent proportional relationships using equations.
I can explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.
Q1,
Q2,
Q3,
Q4
Stretching & Shrinking
Inv 1,2,3,4
Comparing & Scaling
Inv 1,2,3
Moving Straight Ahead
Inv 1,2, 4
What Do You Expect
Inv 1,2,3,4,5
Filling & Wrapping
Inv 1
Samples & Pop
Inv 3
Proportional relationship
Equivalent ratios
Coordinate plane
Origin
Constant of proportionality
Table
Graph
Equations
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6/27/2012 10:11:57Ratios and Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.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.
I can set up and solve proportions.
I can use proportional relationships to solve multistep problems that involve ratios or percentages.
I can recognize proportional situations from a table, graph, or equation.  
Q1,
Q2,
Q3
Stretching & Shrinking
Inv 4
Comparing & Scaling
Inv 1,2,3
What Do You Expect?
Inv 1,2,3,4,5,
Interest
Tax
Mark up
Mark down
Gratuity
Commision
Fee
Percent error
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6/27/2012 10:41:01The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.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 lql 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). 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.
I can represent addition and subtraction on a horizontal or vertical line diagram.
I can describe situations in which opposite quantities combine to make 0.
I can Interpret sums of rational numbers by describing real-world contexts.
I can 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.
I can develop algorithms for adding, subtracting, multiplying, and dividing positive and negative numbers.
Q1,
Q4
Accentuate the Neg
Inv 1,2,4
Samples & Pop
Inv 1,3
Rational number
Opposites
Positive direction
Negative direction
Additive inverse
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6/27/2012 10:52:28The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.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 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 stratgies 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.
I can apply the distributive property to simplify expressions and solve problems.
I can understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.
I can apply properties of operations as stratgies to multiply and divide rational numbers.
I can convert a rational number to a decimal using long division.
Q1 Accentuate the Neg
Inv 3,4
Absolute value
Properties of operations
Distributive property
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6/27/2012 10:53:46The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.3. Solve real-world and mathematical problems involving the four operations with rational numbers.I can use models and rational numbers to represent and solve real world problems.Q1,
Q2,
Q3
Accentuate the Neg
Inv 1,2,3,4
Comparing & Scaling
Inv 3
Filling & Wrapping
Inv 2,3,4
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6/27/2012 11:00:28Expressions and EquationsUse properties of operations to generate equivalent expressions.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational conflicts.I can use parentheses and the order of operations in computations. Q2,
Q3
Moving Straight Ahead
Inv 3&4
Filling & Wrapping
Inv 1,3
Linear expressions
Factor linear exp
Expand linear exp
Rational conflicts
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6/27/2012 11:04:46Expressions and EquationsUse properties of operations to generate equivalent expressions.2. 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.
For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
I can use different forms of the same problem to understand the problem and how quantities expressed can be related.. Q1,
Q2,
Q3
Shapes and Designs
Inv 2
Moving Straight Ahead
Inv 3&4
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6/27/2012 11:11:42Expressions and EquationsSolve real-life and mathematical problems using numerical and algebraic expressions and equations.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 $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches 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.
I can use ratios, rates, proportions, and percents to solve multi-step real world and mathematical problems.
I can apply properties of operations to calculate with numbers in any form and convert between forms.
Q1,
Q2,
Q3
Accentuate the Neg
Inv 2,3,4
Comparing & Scaling
Inv 3
Moving Straight Ahead
Inv 1,2,3,4 
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6/27/2012 11:24:34Expressions and EquationsSolve real-life and mathematical problems using numerical and algebraic expressions and equations.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 greater than r or px + q less than 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.
I can solve real world and mathematical problems in which two or more variable have a linear relationship.  
I can solve problems and make decisions using information given in tables, graphs, and symbolic expressions.
I can solve problems and graph solutions of inequalities.
Q1,
Q2,
Q3
Shapes & Designs
Inv 2
Accentuate the Neg
Inv 1
Stretching & Shrinking
Inv 2,3,4
Comparing & Scaling
Inv 1,2,3
Moving Straight Ahead
Inv 1,2,3,4
Inequalities
px+q=r ; p(x+q)=r ; px+q>r ; p(x+q)<r ;
where p,q,r are specific rational #'s
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6/27/2012 11:27:36Geometry 6-8Draw, construct, and describe geometrical figures and describe the relationships between them.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.I can construct similar polygons. 
I can use scale factors and ratios to describe relationships among the side lengths of similar figures.
I can compute actual length and area from a scaled drawing.
I can reproduce a scaled drawing at a different scale.
Q1,
Q2,
Q3
Stretching & Shrinking
Inv 1,2,3,4
Filling & Wrapping
Inv 1
Scale
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6/27/2012 11:30:01Geometry 6-8Draw, construct, and describe geometrical figures and describe the relationships between them.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.I can find angle measures by estimation, by use of tools like protractors and angle rulers,a nd by reasoning with variables and equations.
I can, using appropriate tools, draw geometric shapes.
I can build a triangle when given measure of angles or of sides, and can deterimine when more than 1 triangle can be built or where measurements would not result in a triangle.
Q1,
Q3
Shapes & Designs
Inv 1,2,3
Stretching & Shrinking
Inv 1,3
Filling & Wrapping
Inv 2
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6/27/2012 11:32:45Geometry 6-8Draw, construct, and describe geometrical figures and describe the relationships between them.3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.I can describe the two-dimensional figures resulting from slicing three dimensional figures.Q3Filling & Wrapping
Inv 2
2-dim. figure
3-dim. figure
Plane
Right rect. prism
Right rect. pyramid
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6/27/2012 11:34:37Geometry 6-8Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.I can solve problems involving circumference and area of circles.
I can explain how circumference and area of a circle are related.
Q3Filling & Wrapping
Inv 3,4
Area of circle
Circumference
of circle
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6/27/2012 11:37:28Geometry 6-8Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.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 figureI can recognize and use the relationship of complementary and supplementary pairs of angles, such as those formed by interior and exterior angles of polygons.
I can use facts about supplementary, complementary, vertical and adjacent angles to write multi-step problems and solve a simple equation that will find an unknown angle in a give figure.
Q1Shapes & Designs
Inv 1,2,3
Supplementary < 's
Complementary <'s
Vertical <'s
adjacent <'s
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6/27/2012 11:39:38Geometry 6-8Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.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.I can recognize and solve real-world and mathematics problems involving volume and surface area of 2D and 3D triangles, quadrilaterals, polygons, cubes and right prisms. Q1,
Q3
Stretching & Shrinking
Inv 1,2,3,4
Filling & Wrapping
Inv 1,2,3,4
Area, Volume, Surface Area of:
Triangle,
Quadrilateral,
Polygon,
Cube,
Right prism
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6/27/2012 15:06:32Statistics and ProbabilityUse random sampling to draw inferences about a population.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.I can make valid generalizations about a population from a sample only if the sample is representative of that population.
I can explain that random sampling produces representative samples and supports valid inferences.
Q4Samples & Pop
Inv 2,3
Population
Random sampling
Representative sampling
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6/27/2012 15:10:03Statistics and ProbabilityUse random sampling to draw inferences about a population.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.
I can use data from a random sample to draw inferences about a population.
I can generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Q4Samples & Pop
Inv 2,3
Simulated samples
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6/27/2012 15:14:24Statistics and ProbabilityDraw informal comparative inferences about two populations.3. Formally 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 the 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.
I can assess the degree of visual overlap of two numerical data distributions with similar variabilities.
I can measure the difference between centers of distribution by expressing it as a multiple of a measure of variability.
I can use dot plots or other graphs to illustrate the overlap of two similar numerical data distributions.
Q4Samples & Pop
Inv 1,3
Visual overlap
Numerical data
Data distribution
Measure of variability
Distributions
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6/27/2012 15:17:41Statistics and ProbabilityDraw informal comparative inferences about two populations.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.
I can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Q4Samples & Pop
Inv 1,3
Meaure of center
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6/27/2012 15:21:37Statistics and ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.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.I can explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
I can understand the law of large numbers.
Q3,
Q4
What Do You Expect?
Inv 2,3,4,5
Samples & Pop
Inv 3
Probability
Expected Value
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6/27/2012 15:25:09Statistics and ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.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.
I can collect data on a chance event in order to predict the approximate relative frequency given the probability.
Q3What Do You Expect?
Inv 1,2,3,4

Frequency
Relative frequency
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6/27/2012 15:34:54Statistics and ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
For 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?
I can develop a probability model and use it to find probabilities of events and explain possible reasons for discrepancy.
I can develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
I can develop a probability model (which may not be uniform) by observing frequencies in data produced from a chance process.
Q3,
Q4
What Do You Expect?
Inv 1,2,3,4,5
Samples & Pop
Inv 2,3
Probability Model
-experimental
-theorhetical-equal prob
Chance process
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6/27/2012 15:43:20Statistics and ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.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 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?
I can find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
I can explain that the probabilty of a compound event is based on the fraction of outcomes in the sample space the event occurs in.
I can represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.
I can design and use a simulation to generate frequencies for compound events.
Q3What Do You Expect?
Inv 2,3,4,5
Organized lists
Tables
Tree diagrams
Simulation
Compound event
Sample space
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