· Web viewShow that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Distance Addend Sum

School District: Mathematics 2012-2013 Grade: 7 Updated on: 9/12/2012

Unit 1: The Number System, Addition and Subtraction (Integers)(1 Week)

Spiral: Operations with fractions and decimals, one-step equations and inequalitiesConcepts Skills Common Core Standards Vocabulary

Integers (Additive Inverse)

(Major, 70%)

I can describe situations in which opposite quantities combine to make 0.

7.NS.1a. 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.

Additive inverseIntegers

Adding Signed Numbers

(Major, 70%)

I can add signed numbers using the number line.

I can define absolute value as a distance on the number line.

I can show that a number and its opposite have a sum of zero (additive inverse) using the number line.

I can solve real-world problems requiring addition of integers.

I can add signed numbers using a scientific calculator.

7.NS.1b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

DistanceAddendSumIntegers

Subtraction Of Integers

(Major, 70%)

I can subtract signed numbers using the number line.


I can show that subtraction is equivalent to adding the additive inverse.

I can solve real-world problems requiring

7.NS.1c. 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.

Additive inverseAbsolute valueDistance


subtraction of integers. I can calculate the distance

between two integers by finding the absolute value of their difference.

I can subtract signed numbers using a scientific calculator.

Integers And Properties Of Operations

(Major, 70%)

I can add and subtract integers using the properties of operations.

I can add and subtract integers using a scientific calculator.

7.NS.1d. Apply properties of operations as strategies to add and subtract rational numbers.

Commutative propertyAssociative propertyDistributive propertyAdditive inverse


Unit 2: The Number System, Addition and Subtraction (rational numbers)(1 Week)

Spiral: Operations with fractions and decimals, ratios and proportions

Concepts Skills Common Core Standards VocabularyRational Numbers (Additive

Inverse)

(Major, 70%)

I can describe situations in which opposite quantities combine to make 0.

7.NS.1a. 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.

Additive inverseRational numbers

Adding Signed Numbers

(Major, 70%)

I can add signed numbers using the number line.


I can show that a number and its opposite have a sum of zero (additive inverse) using the number line.

I can solve real-world problems requiring addition of rational numbers.

I can add signed numbers using a scientific calculator.

7.NS.1b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

DistanceAddendSumRational numbers


Subtraction Of Signed Numbers

(Major, 70%)

I can subtract signed numbers using the number line.


I can show that subtraction is equivalent to adding the additive inverse.

I can solve real-world problems requiring subtraction of rational numbers.

I can calculate the distance between two rational numbers by finding the absolute value of their difference.

I can subtract signed numbers using a scientific calculator.

7.NS.1c. 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.

Additive inverseAbsolute valueDistance

Rational Numbers And Properties Of Operations

(Major, 70%)

I can add and subtract rational numbers using the properties of operations.

I can add and subtract rational number using a scientific calculator.

7.NS.1d. Apply properties of operations as strategies to add and subtract rational numbers.

Commutative propertyAssociative propertyDistributive propertyAdditive inverse


Unit 3: The Number System, multiplication and division (integers)(1 Week)

Spiral: Operations with fractions (unlike denominators), properties of operations, plotting on the number line

Concepts Skills Common Core Standards VocabularyMultiplication Of Integers

(Major, 70%)

I can multiply positive and negative integers using properties of operations.

I can solve word problems involving multiplication of integers.

I can apply the distributive property to illustrate (-1) (-1) = 1 and other problems like this.

I can multiply positive and negative integers using a scientific calculator.

7.NS.2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Commutative propertyAssociative propertyDistributive propertyIntegersFractionsSigned numbers

Division Of Integers

(Major, 70%)

I can divide integers, provided the divisor is not zero.

I can define the quotients of integers as rational numbers.

I can rewrite a negative fraction in multiple forms –(2/3) = (-2/3) = (2/-3)

I can solve word problems involving division of integers.

7.NS.2b. 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.

DivisionRational numbersNegative symbolIntegerNumeratorDenominatorQuotientDivisor


I can interpret quotients of rational numbers in terms of a context (can’t have fractional people)

I can divide positive and negative integers using a scientific calculator.

Properties Of Operations With Multiplication And Division

(Major, 70%)

I can multiply integers using properties of operations.

I can divide integers using properties of operations.

I can multiply and divide integers using a scientific calculator.

7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.

Commutative propertyAssociative propertyDistributive propertyRational numbers


Unit 4: The Number System, multiplication and division (rational numbers)(1 Week)

Spiral: Operations with fractions and decimals, multiplication and division of integers, one-step equations and inequalities

Concepts Skills Common Core Standards VocabularyRational Number Conversions

(Major, 70%)

I can convert a fraction to a decimal using long division.

I can define a rational number as terminating in zeros or a repeating decimal.

I can convert a fraction to a decimal using a scientific calculator.

7.NS.2d. 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.

Long divisionRational numbersFractionsNumeratorDenominatorDivideTerminatesRepeats

Multiplication Of Signed Numbers

(Major, 70%)

I can multiply positive and negative rational numbers using properties of operations.

I can solve word problems involving multiplication of rational numbers.

I can apply the distributive property to illustrate (-1) (-1) = 1 and other problems like this.

I can multiply positive and negative rational numbers using a scientific calculator.

7.NS.2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Commutative propertyAssociative propertyDistributive propertyRational numbersFractionsSigned numbers


Division Of Rational Numbers

(Major, 70%)

I can divide rational numbers, provided the divisor is not zero.

I can define the quotients of integers as rational numbers.

I can rewrite a negative fraction in multiple forms –(2/3) = (-2/3) = (2/-3)

I can solve word problems involving division of integers.

I can interpret quotients of rational numbers in terms of a context (can’t have fractional people)

I can divide rational numbers using a scientific calculator.

7.NS.2b. 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.

DivisionRational numbersNegative symbolIntegerNumeratorDenominatorQuotientDivisor

Properties Of Operations With Multiplication And Division

(Major, 70%)

I can multiply rational numbers using properties of operations.

I can divide rational numbers using properties of operations.

I can multiply and divide rational numbers using a scientific calculator.

7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.

Commutative propertyAssociative propertyDistributive propertyRational numbers

Real World Problems With Integers

(Major, 70%)

I can identify the operation necessary to solve a word problem.

I can solve word problems using all 4 operations with rational numbers.

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.

AddSubtractMultiplyDivideRational numbersOrder of operations

Real World Problems With Rational Numbers

I can solve multi-step word problems with positive and negative rational numbers.

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

Rational numbersEstimationMental Computation


(Major, 70%) I can apply the properties of operations to solve real-world problems.

I can convert between different forms of rational numbers when solving word problems.

I can justify the reasonableness of my solution through mental computation and estimation.

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.

IntegersFractionsDecimalsEquivalent


Unit 5: Equations and Expressions(4 Weeks)

Spiral: Operations with fractions and decimals, one-step equations and inequalities, simplifying expressions

Concepts Skills Common Core Standards VocabularyTwo-Step Equations (Fluency

Requirement)

(Major, 70%)

I can solve one step equations with rational numbers.

I can solve two step linear equations. (combining like terms)

I can set up a two-step equation from a word problem.

I can solve a two-step equation created from a word problem.

I can solve a word problem using a sequence of operations (showing my work).

I can compare arithmetic solutions to algebraic solutions to the same word problem.

7.EE.4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Algebraic solutionArithmetic solutionTwo-step linear equationsProperty of EqualityInverse OperationsLinear equationsDistributive Property


Operations With Linear Expressions

(Major, 70%)

I can add linear expressions (combining like terms) with rational number coefficients.

I can subtract linear expressions (combining like terms) with rational number coefficients.

I can factor (gcf with numbers) linear expressions with rational number coefficients.

I can expand linear expressions (distributive property) with rational number coefficients.

I can apply properties of operations with the above skills.

7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

RationalCoefficientsAddSubtractFactorGCFProperties of operations expand (distribute) ConstantLike TermsMonomialBinomialVariable

Two-Step Inequality (Fluency Requirement)

(Major, 70%)

I can set up a two-step inequality from a word problem.

I can solve a two-step inequality created from a word problem.

I can graph the solution to a two-step inequality on a number line created from a word problem.

I can describe the solution to an inequality in the context of a word problem.

7.EE.4b. 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.

Two-step linear InequalitiesAt leastAt most≤, <,>,≥InequalitiesNumber lineClosed dot Open dotSolution setGraph the solution set


Unit 6: Ratios and Proportions(5 Weeks)

Spiral: Graphing in the coordinate plane, ratios and proportions, area formulas

Concepts Skills Common Core Standards VocabularyUnit Rates

(Major, 70%)

I can compute unit rates. I can simplify complex

fractions by division. I can convert quantities in

different units.

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 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.

RatioComplex fractionUnit rateRate ProportionEquivalent

Proportional Relationships

(Major, 70%)

I can write a proportional relationship.

I can calculate if a relationship is proportional by using cross products.

I can test for equivalent ratios in a table.

I can test for equivalent ratios by graphing in a coordinate plane.

I can define an equivalent ratio as a straight line through the origin.

7.RP.2a.Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Constant of proportionalityRate of changeSlopeCross productEquivalentOriginQuantities


Constant Of Proportionality

(Major, 70%)

I can calculate the constant of proportionality from a table.

I can calculate the constant of proportionality from a graph.

I can calculate the constant of proportionality from an equation.

I can calculate the constant of proportionality from a diagram.

I can calculate the constant of proportionality from a verbal description.

7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Constant of proportionalityUnit rateSlopeProportional relationshipRate of changeDirect proportional relationship

Proportional Relationships In Equations

(Major, 70%)

I can write an equation that represents a specific proportional relationship.

7.RP.2c. 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.

Proportional relationshipsEquationRateRatio

Scale Drawing

(Major, 70%)

I can set up a proportion using a scale drawing.

I can compute the actual length from a scale drawing.

I can calculate the actual area from a scale drawing.

I can apply a scale from one drawing to create a second scale for that drawing.

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.

Scale drawingAreaLengthsGeometric figures


Graphs Of Proportional Relationships

(Major, 70%)

I can explain what the x-coordinate means on a graph of a proportional relationship.

I can explain what the y-coordinate means on a graph of a proportional relationship.

I can describe the meaning of points on a graph of a proportional relationship.

I can explain that the y-coordinate divided by the x-coordinate for every point other than the origin equals the constant of proportionality.

7.RP.2d. 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.

Rate of proportionalityX-coordinateY-coordinateUnit rate


Unit 7: Percents(3 Weeks)

Spiral: two-step equations and inequalities (rational coefficients), ratios and proportions, box-and-whisker plots

Concepts Skills Common Core Standards VocabularyRatio And Percent Problems

(Major, 70%)

I can calculate percentages using proportions.

I can calculate original amount using proportional relationships.

I can calculate percent using proportional relationships.

I can calculate sales tax using proportional relationships.

I can calculate gratuities and commissions using proportional relationships.

I can calculate simple interest using proportional relationships and interest formula.

I can calculate markup and markdown using proportional relationships.

I can calculate percent increase/decrease using proportional relationships.

I can calculate percent error

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.

RatioProportionPercent


using proportional relationships.

I can calculate fees using proportional relationships.

I can identify and perform the operation necessary to answer the word problem.

Expressions In Different Forms

(Major, 70%)

I can rewrite an expression in different forms.

I can rewrite an expression to understand the context of a situation.

I can rewrite an expression to show how quantities in a relationship are related.

7.EE.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.”

Expressions


Unit 8: Statistics(4 Weeks)

Spiral: box-and-whisker plots, mean, median, mode, range, interquartile range, mean absolute deviation

Concepts Skills Common Core Standards VocabularySampling

(Supporting, 20%)

I can explain how statistics is used to gain information about a population.

I can evaluate the validity of a statistical sample from a population.

I can explain why random sampling produces a sample representative of a 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.

PopulationSampleRepresentative sampleBiased sampleRandom samplingInferencesValidity

Validity Of Samples

(Supporting, 20%)

I can draw inferences about a population with a certain characteristic from data gathered from a random sample.

I can generate multiple samples of the same size about a certain characteristic.

I can determine the validity of a sample based on how the data was gathered

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.

InferenceRandom samplingPopulationCharacteristic


Variability Of Data Distributions

(Additional, 10%)

I can describe the variability of two numerical data sets.

I can compute the mean absolute deviation

I can compute the range. I can compute the

interquartile range. I can describe how many

times larger/smaller the variability of one data set is to another.

I can read and interpret data from statistical representations (box-and-whisker plot, line/dot plot).

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.

Variability (how far away from the mean)Mean absolute deviationRangeOutlierInterquartile range

Measures Of Center And Variability

(Additional, 10%)

I can compare/contrast measures of center to draw conclusions about two random samples.

I can compare/contrast variability of two data sets to draw conclusions about two random samples.

I can read and interpret data from statistical representations (box-and-whisker plot, line/dot plot).

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.

Measures of central tendency (mean, median, mode)VariabilityRangeOutlierInterquartile range


Unit 9: Probability(4 Weeks)

Spiral: Equations and inequalities, operations with fractions, ratios and proportions

Concepts Skills Common Core Standards VocabularyProbability

(Supporting, 20%)

I can define the probability of an event as a number between 0 and 1.

I can define an unlikely event as having a probability near 0.

I can define a likely event as having a probability near 1.

I can define a probability near ½ as 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.

ProbabilityEventLikely eventUnlikely event

Probability Approximations

(Supporting, 20%)

I can collect data about an event.

I can calculate the experimental probability from data collected.

I can predict the relative frequency based on the experimental probability.

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.

ProbabilityEventOutcomesPossible outcomesFavorable outcomesTheoretical probabilityExperimental probabilityTrials


Theoretical Probability

(Supporting, 20%)

I can calculate simple probabilities of events.

I can determine the number of outcomes.

I can determine the number of desirable outcomes.

I can calculate the theoretical probability based on the number of desirable outcomes to the total number of outcomes.

I can compare/contrast uniform vs. non uniform probability models.

7.SP.7a. 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.7.SP.7b. 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?

OutcomesEventsSimple probabilityEqually likelyUniform probability modelProbability model (not uniform)Probability model (uniform)FrequenciesData

Compound Probability

(Supporting, 20%)

I can calculate the probability of a compound event as a fraction of outcomes in the sample space.

I can list the sample space of a compound event using lists, tables, or tree diagrams.

I can calculate the total number of outcomes using the Fundamental Counting Principle.

7.SP.8a. 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.7.SP.8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

ProbabilityTree diagramsSimulationSample spaceCompound eventsSimple eventsOutcomesFundamental Counting PrincipleListsTables

Simulation

(Supporting, 20%)

I can design a simulation to generate frequencies for compound events.

I can analyze results from a simulation.

7.SP.8c. 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?

SimulationCompound eventsData


Unit 10: Geometry with Circles and angles(3 Weeks)

Spiral: Review area and volume formulas, equations, graphing coordinatesConcepts Skills Common Core Standards Vocabulary

Area And Circumference

(Additional, 10%)

I can write the formula for the circumference of a circle.

I can write the formula for the area of a circle.

I can apply the formula for the circumference of a circle.

I can apply the formula for the area of a circle.

I can derive the relationship between the circumference and area of a circle.

7.G.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.

CircleCircumferenceAreaDiameterRadius

Angle Pair Relationships

(Additional, 10%)

I can define and identify supplementary angles.

I can define and identify complementary angles.

I can define and identify vertical angles.

I can define and identify adjacent angles.

I can solve multi-step word problems using facts about angle pairs.

I can write simple equations for an unknown angle in a figure.

I can solve simple equations

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.

Vertical anglesSupplementaryComplementaryAdjacent angles


for an unknown angle in a figure.

The following units are Post-Assessment StandardsUnit 11: Geometry (Two-Dimensional and Three-Dimensional Figures)

(8 Weeks)Spiral: Review area and volume formulas, equations, graphing coordinates

Concepts Skills Common Core Standards VocabularyTwo- And Three-Dimensional Figures (No Circles)

(Additional, 10%)

I can define area formulas of two-dimensional figures.

I can solve word problems involving area of two-dimensional figures.

I can define volume formulas of three-dimensional figures.

I can solve word problems involving volume of three-dimensional figures.

I can define surface area formulas of three-dimensional figures.

I can solve word problems involving surface area of three-dimensional figures.

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.

AreaVolumeSurface areaTwo- and three-dimensional figures

Slicing 3D Figures

(Additional, 10%)

I can describe the 2D figure that results from slicing a 3D right rectangular figures (prisms and pyramids).

7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular

SliceTwo-dimensional figuresPyramidRectangular prism


pyramids. CylinderTriangular pyramidCubeCone

Constructions

(Additional, 10%)

I can construct a triangle (freehand, with ruler and protractor, and technology) given three angle measures.

I can construct a triangle (with ruler and protractor and technology) given three side measures.

I can construct a geometric shape given side lengths /angle measures.

I can describe when angle measures determine more than one triangle (given angles equal 180°), or no triangle (given angles are greater or less than 180°)

I can describe when side measures determine a unique triangle (a+b>c) or no triangle (a+b ≤ c)

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.

Triangle inequality TheoremTriangle angle sum theoremGeometric figuresUniquely defined triangleAmbiguously defined triangleNonexistent triangle

Documents

· Web viewShow that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Distance Addend Sum