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3e37 : 1. Proportional reasoning involves comparisons and multiplicative relationships among ratiosa. Analyze proportional relationships and use them to solve real-world and mathematical problems. II will analyze proportional relationships .
I will use proportional relationships to solve real-world problems.
I will use proportional relationships to solve mathematical problems.
Analysis
Appl
Appl(CCSS: 7.RP)
Holt, Rinehart, and Winston
P. 343Proportional relationships1. Proportional reasoning involves comparisons and multiplicative relationships among ratiosb. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. MI will compute unit rates associated with ratios of fractions, including ratios of lengths.
I will compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quatities measured in different units.
Appl
Appl(CCSS: 7.RP.1)
Holt, Rinehart, and Winston
P. 346-347
Ratio
Unit Rate1. Proportional reasoning involves comparisons and multiplicative relationships among ratiosc. Identify and represent proportional relationships between quantities. I
i. Determine whether two quantities are in a proportional relationship. I
ii. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. C
iii. Represent proportional relationships by equations. C
iv. 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. II will identify proportional relationships between quantities.
I will represent proportional relationships between quantities.
I will make use of whether two quantities are in a proportional relationship.
I will identify the constant of proportionalty (unit rate) in tables of proportional relationships.
I will identify the constant of proportionalty (unit rate) in graphs of proportional relationships.
I will identify the constant of proportionalty (unit rate) in equations of proportional relationships.
I will identify the constant of proportionalty (unit rate) in diagrams of proportional relationships.
I will identify the constant of proportionalty (unit rate) in verbal descriptions of proportional relationships.
I will represent proportional relationships by equations.
I will interpret 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.
Know
Appl
Know
Comp
Comp(CCSS: 7.RP.2)
Holt, Rinehart, and Winston
P. 343
(CCSS: 7.RP.2a)
Holt, Rinehart, and Winston
(CCSS: 7.RP.2b)
Holt, Rinehart, and Winston
P. 565
(C Holt, Rinehart, and Winston CSS: 7RP.2c)
(CCSS: 7.RP.2d)
Holt, Rinehart, and Winston
Proportional
Equations1. Proportional reasoning involves comparisons and multiplicative relationships among ratiosd. Use proportional relationships to solve multistep ratio and percent problems. I
i. Estimate and compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL) I
ii. Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease (PFL) II will put to use proportional relationships to solve multistep ratio problems.
I will use proportional relationships to solve multistep percent problems.
I will estimate unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL).
I will compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL).
I will compute problems involving percent of a number.
I will compute problems involving discounts.
I will compute problems involving taxes.
I will compute problems involving simple interest.
I will compute problems involving percent increase.
I will compute problems involving percent decrease. (PFL)
Apply
Comp
Apply
Apply
Apply
Apply
Apply
Apply
Apply
Apply
(CCSS: 7.RP.3)
Holt, Rinehart, and Winston
P, 343
P. 347
P. 424, 425
Consumables
PFL
Percent
Increase
Discounts
Taxes
Simple Interest
Percentile
Percent Interest
Percent
Decrease2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently
a. Apply understandings of addition and subtraction to add and subtract rational numbers including integers. I
i. Represent addition and subtraction on a horizontal or vertical number line diagram. I
ii. Describe situations in which opposite quantities combine to make 0.5. I
iii. Demonstrate 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. I
iv. Show that a number and its opposite have a sum of 0 (are additive inverses). I
v. Interpret sums of rational numbers by describing real-world contexts. I
vi. Demonstrate subtraction of rational numbers as adding the additive inverse,
p q = p + (q). I
vii. 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
viii. Apply properties of operations as strategies to add and subtract rational numbers. I
I will apply understanding of addition to add numbers including integters.
I will apply understanding of subtraction to subtract numbers including integers.
I will determine addition on a horizontal or vertical number line diagram.
I will determine subtraction on a horizontal or vertical number line diagram.
I will defend situations in which opposite quantities combine to make 0.5.
I will produce
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.
I will explain that a number and its opposite have a sum of 0 (are additive inverses).
I will interpret sums of rational numbers by describing real-world contexts.
I will solve subtraction of rational numbers as adding the additive inverse, p=q = p + (-q).
I will show that the distance between two rational numbers on the number line is the absolute value of their difference.
I will apply this principle in real-world contexts.
I will model properties of operations as strategies to add rational numbers.
I will model properties of operations as strategies to subtract rational numbers.
Appl
Appl
Appl
Appl
Comp
Appl
Comp
Comp
Apply
Comp
Apply
Holt, Rinehart, and Winston
P. 112-114, 117-118
P. 117-118
Opposite
Quantities
Positive direction
Negative direction
Rational Numbers
Absolute Value
Poperties of Operation
Positive
Negative
Additive
Inverse2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently
b. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers including integers. I
i. Apply properties of operations to multiplication of rational numbers. I
ii. Interpret products of rational numbers by describing real-world contexts. I
iii. Apply properties of operations to divide integers. I
iv. Apply properties of operations as strategies to multiply and divide rational numbers. I
v. Convert a rational number to a decimal using long division. I
vi. Show that the decimal form of a rational number terminates in 0s or eventually repeats. I
I will apply previous understandings of multiplication and of fractions to multiply rational numbers including integers.
I will extend previous understandings of multiplication of fractions to multiply rational numbers including integers.
I will apply previous understandings of division of fractions to divide rational numbers including integers.
I will extend previous understandings of division of fractions to divide rational numbers including integers.
I will compute properties of operatons to multiplications of rational numbers.
I will show products of rational numbers by describing real-world contexts.
I will build properties of operations to divide integers.
I will apply properties of operations as strategies to multiply rational numbers.
I will apply properties of operations as strategies to divide rational numbers.
I will convert a rational number to a decimal using long division.
I will distinguish that the decimal form of a rational number terminates in 0s or eventually repeats.
Appl
Apply
Comp
Comp
Comp
Comp
CompHolt, Rinehart, and Winston
*mulitiplication - P. 121-123
*division P. 126-128
P. 121-123
P. 126-128
Integers
Properties of
Operation
-associative
-communicative
Decimal
Terminates2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently
c. Solve real-world and mathematical problems involving the four operations with rational numbers. I
I will utilitze real-world problems involving the four operations with rational numbers.
I will use mathematical problems involving the four operations with rational numbers.
ApplHolt, Rinehart, and Winston
P. 745, 7801. Properties of arithmetic can be used to generate equivalent expressionsa. Use properties of operations to generate equivalent expressions.
i. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. I
i. Demonstrate 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. I
Use ideas of fraction equivalence and ordering to: (CCSS:4.NF.1) S1B1
Explain equivalence of fractions using drawings and models. (CCSS: 4.NF.1)
Use the principle of fraction equivalence to recognize and generate equivalent fractions. (CCSS: 4.NF.1)
Use decimal notation for fractions with denominators 10 to 100. (CCSS: 4.NF.6) S1B1
Use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates. (CCSS: 6.NS.6) S1B1
Describe a rational number as appoint on the number line. (CCSS: 6.NS.6)
Use opposite signs of numbers to indicate locations on opposite sides of 0 on the number line. (CCSS: 6.NS.6a)
Identify that the opposite of the opposite of a number is the number itself. CCSS: 6.NS.6a)
Explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (CCSS: 6.NS.6b)
Find and position integers and other rational numbers on a horizontal or vertical number line diagram. (CCSS: 6.NS.6C)
Find and position pairs of integers and other rational numbers on a coordinate plane. (CCSS: 6.NS.6c)
Write and evaluate numerical expressions involving whole-number exponents. (CCSS: 6.EE.1) S1B1
_____________________________
Order and find absolute value of rational numbers. (CCSS: 6.NS.7) S1B2
Compare two fractions with different numerators and different denominators, 5 and justify the conclusions. (CCSS: 4.NF.2) S1B2
Use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates. (CCSS: 6.NS.6) S1B2
Describe a rational number as a point on the number line. (CCSS: 6.NS.6)
Use opposite signs of numbers to indicate locations on opposite sides of 0 on the number line. (CCSS: 6.NS.6a)
Identify that the opposite of the opposite of a number is the number itself. (CCSS: 6NS.6a)
Explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (CCSS: 6.NS.6b)
Find and position integers and other rational numbers on a horizontal or vertical number line diagram. (CCSS: 6.NS.6c)
Find and position pairs of integers and other rational numbers on a coordinate plane. (CCSS: 6.NS.6c)
_____________________________
Apply concepts of squares, primes, composites, factors, and multiples to solve problems. S1B3
Apply properties 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. (CCSS: 7.EE.3) S1B4
_____________________________
Analyze proportional relationships and use them to solve real-world and mathematical problems. (CCSS: 7.RP) S1B4
Use proportional relationships to solve multistep ratio and percent problems. (CCSS:7.RP.3) S1B1
_____________________________
Represent and analyze quantitative relationships between dependent and independent variables. (CCSS: 6.EE) S2B3
Use variables to represent two quantities in a real-world problem that change in relationship to one another. (CCSS:6.EE.9)
Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. (CCSS: 6.EE.9) S2B3
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (CCSS: 6.EE.9) S2B3
_____________________________
Classify and identify two-dimensional figures according to attributes of line relationships or angle size (CCSS:4.G.2) S4B2
_____________________________
Classify two-dimensional figures into categories based on their properties. (CCSS: 5.G) S4B2
Solve real-world and mathematical problems by graphing points in all four quadrants or the coordinate plane including the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. (CCSS:6.NS.8) S4B4
_____________________________
Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify are particular order. (Order of Operations). (CCSS:6.EE.2c)
_____________________________
Apply properties of operations to calculate with number in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (CCSS: 7.EE.3) S6B2
I will produce properties of operations to generate equivalent expressions.
I will apply properties of operations as strategies to add expressions with rational coefficients.
I will apply properties of operations as strategies to subtract linear expressions with rational coefficients.
I will apply properties of operations as strategies to factor linear expressions with rational coefficients.
I will apply properties of operations as strategies to expand linear expressions with rational coefficients.
I will determine that rewriting an expression in different forms in problem context can shed light on the problem.
I will determine that rewriting an expression in different forms in problem context can shed light on how the quantities in it are related.
I will use ideas of fraction equivalence to explain equivalence of fractions using drawings.
I will use ideas ordering explaining equivalence of fractions using models.
I will use ideas of fraction equivalence using the principle of fraction equivalence to recognize equivalent fractions.
I will use ideas of fraction equivalence using the principle of fraction equivalence to generate equivalent fractions.
I will use decimal notation
for fractions with denominators.
I will use number line diagrams to represent points on the line with negative number coordinates.
I will use number line coordinate axes to represent points in the plane with negative number coordinates.
I will use coordinate axis to represent points on the line with negative number coordinates.
I will use coordinate axes to represent points in the plane with negative number coordinates.
I will write numerical expressions involving whole-number exponents.
I will evaluate numerical expressions involving whole-number exponents.
_____________________
I will order absolute value of rational numbers.
I will find absolute value of rational numbers.
I will compare two fractions with different numerators and justify the conclusions.
I will compare two fractions with different denominators and justify the conclusions.
I will use number line diagrams to represent points on the line.
I will use coordinate axes to represent points on the
Line.
I will use number line diagrams to represent points in the plane with negative number coordinates.
I will use coordinate axes to represent to represent points in the plane with negative number coordinates.
I will describe a rational number as a point on the number line.
I will use opposite signs of numbers to indicate locations on opposite sides of 0 on the number.
I will identify that the opposite of a number is the number itself.
I will explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
I will find integers and other rational numbers on a horizontal number line diagram.
I will position integers and other rational numbers on a horizontal number line diagram.
I will find integers and other rational numbers on a vertical number line diagram.
I will position integers and other rational numbers on a vertical number line diagram.
I will find pairs of integers and other rational numbers on a coordinate plane.
I will position integers and other rational numbers on a coordinate plane.
I will find pairs of integers and other rational numbers on a coordinate plane.
I will position integers and other rational numbers on a coordinate plane.
I will apply concepts of squares to solve problems.
I will apply concepts of primes to solve problems.
I will apply concepts of composites to solve problems.
I will apply factors to solve problems.
I will apply multiples to solve problems.
I will apply properties operations to calculate with numbers in any form.
I will apply properties operations to convert between forms as appropriate.
I will assess the reasonableness of answers using mental computation.
I will assess the reasonableness of answers using estimation strategies.
____________________
I will analyze proportional relationships and use them to solve real-world problems.
I will analyze proportional relationships and use them to solve mathematical problems.
I will use proportional relationships to solve multistep ratio problems.
I will use proportional relationships to solve percent problems.
I will represent quantitative relationships between dependent variables.
I will analyze quantitative relationships between dependent variables.
I will represent quantitative relationships between independent variables.
I will analyze quantitative relationships between independent variables.
I will use variables to represent two quantities in a real-world problem that change in relationship to one another.
I will write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
I will classify two-dimensional figures according to attributes of line relationships or angle size.
I will identify two-dimensional figures according to attributes of line relationships or angle size.
____________________
I will classify two-dimensional figures into categories based on their properties.
I will solve real-world and mathematical problems by graphing points in all four quadrants or the coordinate plane including the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
_____________________
I will perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify are particular order.
I will apply properties of operations to calculate with number in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.Appl
Appl
Appl
Appl
Appl
Appl
Appl
Appl
Eval.
Appl
Appl
Appl
APPL
Appl
Appl
Anal
Appl
Anal
Anal
Comp
Comp
Appl
Appl
_______ApplHolt, Rinehart, and Winston
P. 28
P. 4.
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Equivalent
Expressions
Linear
Expressions
Rational
Coefficients
Fraction equivalence
Decimal Notation
Negative Number
Line diagrams
Rational Number
Coordinate axis
Numerical expressions
Absolute value
Numerator
Denominator
Negative number coordinates
Points
Positive Integers
Rational Numbers
Horizontal Number Line
Vertical Number Line
Integer
Squares
Primes
Composites
Factors
Multiples
Proportional relationships
Ratio
Dependent variables
Independent variables
Quantitative relationships
Line
Angle
Two-dimensional figure
Point
Quadrant
First Coordinate
Second Coordinate
Whole-number exponent
ROCKY FORD CURRICULUM GUIDE
SUBJECT: MATH GRADE: 7 TIMELINE: 1st Quarter
Grade Level ExpectationEvidence OutcomeStudent-Friendly
Learning ObjectiveLevel of
ThinkingResource Correlation
Academic Vocabulary
Learning Keys, 800.927.0478, HYPERLINK "http://www.learningkeys.org" www.learningkeys.org Page PAGE \* MERGEFORMAT 1
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