UK MATH GRADE 10 – EDmama UK

A. Numbers and Counting

A.01. Classify numbers as integers, rational, irrational, or real
A.02. Identify prime and composite numbers
A.03. Determine the prime factorization of a number
A.04. Find the highest common factor (HCF) of two or more numbers
A.05. Find the lowest common multiple (LCM) of two or more numbers
A.06. Convert between decimals, fractions, and percentages efficiently
A.07. Locate and compare rational numbers on a number line
A.08. Estimate the values of square roots and cube roots
A.09. Solve word problems involving HCF and LCM
A.10. Express recurring decimals as fractions
A.11. Explore the historical development and cultural significance of different number systems

B. Operations with Integers and Rational Numbers

B.01. Add, subtract, multiply, and divide integers with accuracy
B.02. Add and subtract rational numbers, expressing answers in simplest form
B.03. Multiply and divide rational numbers, applying rules for signs correctly
B.04. Evaluate numerical expressions involving integers using the order of operations
B.05. Evaluate numerical expressions involving rational numbers, including fractions and decimals
B.06. Evaluate algebraic expressions involving integer variables
B.07. Evaluate algebraic expressions involving rational variables
B.08. Apply the concepts of operations with integers and rational numbers to solve real-world problems

C. Ratios, Proportions, and Rates

C.01. Write ratios to represent relationships between quantities
C.02. Identify equivalent ratios and simplify ratios to their lowest terms
C.03. Calculate unit rates from given data
C.04. Determine unit rates involving fractions and mixed numbers
C.05. Compare unit prices to find the best value
C.06. Solve proportions using cross-multiplication
C.07. Apply proportions to solve word problems involving scaling and similarity
C.08. Estimate population sizes using proportional reasoning
C.09. Solve scale drawing problems involving maps and models
C.10. Connect proportional reasoning to real-world applications like currency conversion and mixture problems

D. Percentages and Their Applications

D.01. Convert fluently between percentages, fractions, and decimals
D.02. Solve basic percentage equations to find the part, whole, or percent
D.03. Solve word problems involving percentages in various contexts
D.04. Calculate percent of change (increase or decrease)
D.05. Solve word problems involving percent of change, such as growth or depreciation
D.06. Calculate the percentage of a number, including VAT, discount, and mark-up
D.07. Find the original price given the sale price and discount percentage
D.08. Solve multi-step problems involving successive percentages, like discounts and taxes
D.09. Apply percentages in financial literacy scenarios, such as calculating simple and compound interest

E. Expressions and Properties of Operations

E.01. Write variable expressions to represent mathematical relationships and real-world scenarios
E.02. Identify and apply the properties of addition and multiplication (commutative, associative, distributive, identity, inverse)
E.03. Apply the distributive property to expand and factor algebraic expressions
E.04. Simplify variable expressions using properties of operations and combining like terms
E.05. Write equivalent expressions using the properties of addition, subtraction, multiplication, and division
E.06. Simplify variable expressions involving like terms and the distributive property with multiple variables
E.07. Identify equivalent linear expressions using algebraic manipulation
E.08. Demonstrate how the properties of operations are fundamental to algebraic manipulation and problem-solving

F. Solving Linear Equations

F.01. Identify expressions and equations, distinguishing between the two
F.02. Write variable equations to represent real-world scenarios and mathematical relationships
F.03. Identify equivalent equations by applying properties of equality
F.04. Determine if a given value satisfies an equation by substitution
F.05. Apply properties of equality (addition, subtraction, multiplication, division) to solve equations
F.06. Solve one-step linear equations using inverse operations
F.07. Solve two-step linear equations using inverse operations
F.08. Solve advanced linear equations involving multiple steps and simplification
F.09. Solve equations with variables on both sides of the equation
F.10. Determine the number of solutions (none, one, or infinite) for a given linear equation
F.11. Create equations with no solutions or infinitely many solutions
F.12. Solve linear equations presented in word problems, translating words into algebraic expressions
F.13. Rearrange multi-variable equations to solve for a specific variable
F.14. Model and solve equations using algebra tiles
F.15. Solve equations using order of operations
F.16. Write and solve equations that represent diagrams
F.17. Solve equations: complete the solution
F.18. Solve linear equations: mixed review
F.19. Illustrate the use of linear equations in practical situations, such as calculating distances, costs, and quantities

H. Single-Variable Linear Inequalities

H.01. Identify solutions to inequalities by testing values
H.02. Write inequalities from graphs, representing solution sets on a number line
H.03. Graph inequalities on a number line, using appropriate notation for open and closed intervals
H.04. Solve one-step linear inequalities using addition and subtraction properties
H.05. Solve one-step linear inequalities using multiplication and division properties, paying attention to sign changes
H.06. Solve one-step linear inequalities
H.07. Solve two-step linear inequalities
H.08. Solve advanced linear inequalities involving multiple steps and simplification
H.09. Graph solutions to two-step linear inequalities on a number line
H.10. Graph solutions to advanced linear inequalities on a number line
H.11. Solve compound inequalities involving “and” and “or”
H.12. Write compound inequalities from graphs, representing the solution sets
H.13. Graph solutions to compound inequalities on a number line
H.14. Demonstrate the relationship between linear inequalities and real-world constraints, such as budgets and limitations
H.15. Solve advanced linear inequalities
H.16. Graph solutions to advanced linear inequalities

I. Relations and Functions

I.01. Identify the domain and range of relations from various representations (tables, graphs, mappings, lists of points)
I.02. Represent relations in different formats: tables, graphs, mappings, and lists of points
I.03. Identify independent and dependent variables in a relationship
I.04. Determine if a relation is a function using the definition of a function
I.05. Apply the vertical line test to identify functions from their graphs
I.06. Identify types of functions from graphs (linear, quadratic, exponential, etc.)
I.07. Evaluate a function for a given input value, f(x)
I.08. Evaluate a function by plugging in an expression
I.09. Complete a function table from a graph or equation
I.10. Find values using function graphs
I.11. Find solutions using a table
I.12. Approximate solutions using a table
I.13. Interpret functions using everyday language
I.14. Explore the concept of function composition and its applications
I.15. Connect the idea of functions to real-world phenomena, such as modeling population growth and physical processes

J. Direct and Inverse Variation

J.01. Identify proportional relationships from tables, graphs, and equations
J.02. Find the constant of variation in a direct or inverse variation relationship
J.03. Graph a proportional relationship on the coordinate plane
J.04. Write direct variation equations to model proportional relationships
J.05. Write and solve direct variation equations in various contexts
J.06. Identify direct variation and inverse variation from given information
J.07. Write inverse variation equations to model inversely proportional relationships
J.08. Write and solve inverse variation equations to solve problems
J.09. Model real-world scenarios using direct and inverse variation, such as the relationship between speed and travel time

K. Linear Functions

K.24. Write an equation for a line parallel to a given line, passing through a given point
K.25. Perform transformations on linear functions, including translations, reflections, and dilations
K.26. Explore real-world applications of linear functions, such as modeling distance, cost, and time
K.01. Identify linear functions from equations, graphs, and tables
K.02. Interpret points on the graph of a linear function in the context of the problem
K.03. Determine the gradient (slope) of a line from its graph
K.04. Calculate the gradient of a line from two given points
K.05. Find a missing coordinate using the gradient and another point on the line
K.06. Find the gradient and y-intercept of a linear equation in slope-intercept form (y = mx + c)
K.07. Graph a linear equation in slope-intercept form (y = mx + c)
K.08. Write an equation in slope-intercept form (y = mx + c) from a graph
K.09. Write an equation in slope-intercept form (y = mx + c) given the gradient and y-intercept
K.10. Write an equation in slope-intercept form (y = mx + c) from a table of values
K.11. Write an equation in slope-intercept form (y = mx + c) from a word problem
K.12. Rewrite linear equations to solve for y, expressing them in slope-intercept form
K.13. Write linear functions to solve word problems involving rates of change
K.14. Complete a table of values and graph a linear function from its equation
K.15. Compare linear functions presented as graphs, tables, and equations
K.16. Find x- and y-intercepts for equations in standard form (ax + by = c)
K.17. Graph a linear equation in standard form (ax + by = c)
K.18. Write the equations of horizontal and vertical lines
K.19. Graph horizontal and vertical lines
K.20. Graph a line using point-gradient form (y – y1 = m(x – x1))
K.21. Write an equation of a line in point-gradient form given a point and the gradient
K.22. Write an equation of a line in point-gradient form from its graph
K.23. Identify gradients of parallel lines and perpendicular lines

L. Simultaneous Equations

L.01. Determine if an ordered pair (x, y) is a solution to a system of simultaneous equations
L.02. Solve systems of simultaneous equations by graphing
L.03. Solve simultaneous equations by graphing: word problems
L.04. Find the number of solutions (none, one, or infinite) to a system of simultaneous equations by graphing
L.05. Determine the number of solutions to a system of simultaneous equations without graphing
L.06. Solve systems of simultaneous equations using the substitution method
L.07. Solve systems of simultaneous equations using substitution: word problems
L.08. Solve systems of simultaneous equations using the elimination method with matching coefficients
L.09. Solve systems of simultaneous equations using the elimination method
L.10. Solve systems of simultaneous equations using elimination: word problems
L.11. Solve systems of simultaneous equations using any appropriate method
L.12. Solve systems of simultaneous equations using any method: word problems
L.13. Model real-world scenarios using systems of equations, such as mixture problems and break-even analysis

M. Linear Inequalities in Two Variables

N. Exponential Notation and Indices

N.01. Evaluate indices with integer bases and positive exponents
N.02. Evaluate indices with decimal and fractional bases and positive exponents
N.03. Apply the product of powers rule with positive indices
N.04. Apply the power of a power rule with positive indices
N.05. Apply the quotient of powers rule with positive indices
N.06. Evaluate expressions using properties of indices: positive indices
N.07. Understand and apply the definition of negative indices
N.08. Apply the product of powers rule with integer indices
N.09. Apply the quotient of powers rule with integer indices
N.10. Apply the power of a power rule with integer indices
N.11. Evaluate expressions using properties of indices: integer indices
N.12. Identify equivalent expressions involving integer indices
N.13. Evaluate integers raised to positive unit fractions (roots)
N.14. Apply the product rule with positive unit fraction indices
N.15. Explore the connection between exponential notation and scientific notation

O. Number Sequences and Patterns

O.01. Identify arithmetic and geometric sequences
O.02. Find the common difference in an arithmetic sequence
O.03. Find the common ratio in a geometric sequence
O.04. Determine a specific term in an arithmetic sequence
O.05. Determine a specific term in a geometric sequence
O.06. Evaluate variable expressions for number sequences
O.07. Write variable expressions for arithmetic sequences using the general term formula
O.08. Write variable expressions for geometric sequences using the general term formula
O.09. Recognize sequences of square and cube numbers
O.10. Recognize and extend Fibonacci-type sequences
O.11. Number sequences: mixed review
O.12. Apply recursive formulas to generate terms in a sequence
O.13. Investigate the applications of sequences in financial mathematics, such as compound interest and annuities

P. Standard Form (Scientific Notation)

Q. Exponential Functions

Q.01. Evaluate an exponential function for a given input value
Q.02. Write exponential functions to model real-world phenomena, such as growth and decay
Q.03. Match exponential functions to their corresponding graphs
Q.04. Determine the domain and range of exponential functions
Q.05. Solve word problems involving exponential growth and decay
Q.06. Apply exponential functions to calculate compound interest
Q.07. Match exponential functions and graphs II
Q.08. Analyze the impact of different parameters on the shape of exponential functions
Q.09. Explore the applications of exponential functions in fields like biology, physics, and economics

R. Monomials

S. Polynomials

S.01. Understand and use polynomial vocabulary (degree, leading coefficient, constant term, etc.)
S.02. Model polynomials with algebra tiles, representing terms visually
S.03. Add and subtract polynomials using algebra tiles and combining like terms
S.04. Add and subtract polynomials algebraically, simplifying the resulting expression
S.05. Add polynomials to find the perimeter of geometric figures
S.06. Multiply a polynomial by a monomial using the distributive property
S.07. Multiply two polynomials using algebra tiles, visualizing the process
S.08. Multiply two binomials using the distributive property (FOIL method)
S.09. Multiply two binomials: special cases (difference of squares, square of a binomial)
S.10. Multiply polynomials of various degrees, expanding and simplifying the result
S.11. Connect polynomial operations to real-world applications, such as modeling area and volume

T. Factorising Polynomials

U. Quadratic Equations

U.01. Identify the key characteristics of quadratic functions from their graphs (vertex, axis of symmetry, intercepts)
U.02. Identify the key characteristics of quadratic functions from their equations
U.03. Complete a function table for a quadratic function
U.04. Match quadratic functions to their corresponding graphs
U.05. Graph a quadratic function by plotting points or using transformations
U.06. Solve a quadratic equation using square roots, isolating the variable term
U.07. Solve a quadratic equation using the zero product property, after factoring
U.08. Solve a quadratic equation with a leading coefficient of 1 by factorising
U.09. Solve a quadratic equation with other leading coefficients by factorising
U.10. Complete the square for a quadratic expression
U.11. Solve a quadratic equation by completing the square
U.12. Solve a quadratic equation using the quadratic formula
U.13. Apply the discriminant to determine the number of real solutions to a quadratic equation
U.14. Relate quadratic equations to real-world applications, such as projectile motion and optimization problems

V. Rational Functions and Expressions

V.01. Determine the asymptotes and excluded values of a rational function
V.02. Simplify complex fractions by multiplying by a common denominator
V.03. Simplify rational expressions by factoring and cancelling common factors
V.04. Multiply and divide rational expressions, simplifying the result
V.05. Divide polynomials using long division or synthetic division
V.06. Add and subtract rational expressions, finding a common denominator
V.07. Solve rational equations, checking for extraneous solutions
V.08. Apply rational functions to model real-world phenomena, such as average cost and inverse relationships

W. Coordinate Plane

X. Transformations of Geometric Shapes

X.01. Identify reflections, rotations, and translations of geometric figures
X.02. Graph the image of a figure after a translation, given the translation vector
X.03. Find the coordinates of the image of a point after a translation
X.04. Write the rule for a translation, given the original and image points
X.05. Graph the image of a figure after a reflection over a line
X.06. Find the coordinates of the image of a point after a reflection
X.07. Rotate polygons about a point by a given angle
X.08. Graph the image of a figure after a rotation
X.09. Find the coordinates of the image of a point after a rotation
X.10. Write the rule for a reflection or rotation, given the original and image points
X.11. Graph the image of a figure after a combination of reflections, rotations, and translations
X.12. Find the coordinates of the image of a point after a combination of transformations
X.13. Graph the image of a figure after a dilation
X.14. Find the coordinates of the image of a point after a dilation
X.15. Determine the scale factor of a dilation, given the original and image figures
X.16. Explore the concept of symmetry and its relationship to geometric transformations
X.17. Apply transformations to create patterns and tessellations

Y. Logic and Reasoning

Z. Congruence of Geometric Figures

Z.01. Identify congruent figures by visually comparing their shapes and sizes
Z.02. Write congruence statements, matching corresponding parts of congruent figures
Z.03. Determine side lengths and angle measures of congruent figures
Z.04. Apply the Side-Side-Side (SSS) Congruence Theorem to prove triangle congruence
Z.05. Apply the Side-Angle-Side (SAS) Congruence Theorem to prove triangle congruence
Z.06. Apply the Angle-Side-Angle (ASA) Congruence Theorem to prove triangle congruence
Z.07. Apply the Angle-Angle-Side (AAS) Congruence Theorem to prove triangle congruence
Z.08. Apply the Hypotenuse-Leg (HL) Congruence Theorem to prove right triangle congruence
Z.09. Demonstrate the importance of congruence in construction, engineering, and design

AA. Similarity of Geometric Figures

BB. Triangles and Trigonometry

BB.01. Apply Pythagoras’ theorem to find the missing side length in a right triangle
BB.02. Solve word problems involving Pythagoras’ theorem
BB.03. Apply the converse of Pythagoras’ theorem to determine if a triangle is a right triangle
BB.04. Define the trigonometric ratios (sine, cosine, tangent) for acute angles in a right triangle
BB.05. Define the reciprocal trigonometric ratios (cosecant, secant, cotangent)
BB.06. Find trigonometric function values of special angles (30°, 45°, 60°) without a calculator (sin, cos, tan)
BB.07. Find trigonometric function values of special angles (30°, 45°, 60°) without a calculator (csc, sec, cot)
BB.08. Find trigonometric function values using a calculator for any angle
BB.09. Use inverses of trigonometric functions to find angle measures
BB.10. Apply trigonometric ratios to find a missing side length in a right triangle
BB.11. Apply trigonometric ratios to find a missing angle measure in a right triangle
BB.12. Solve a right triangle, finding all side lengths and angle measures
BB.13. Apply trigonometry to solve real-world problems involving angles of elevation and depression
BB.14. Explore the applications of trigonometry in navigation, surveying, and engineering

CC. Perimeter, Area, and Composite Figures

CC.01. Calculate the perimeter of polygons
CC.02. Calculate the circumference of circles
CC.03. Calculate the perimeter of semicircles and quarter circles
CC.04. Calculate the area of triangles and quadrilaterals (squares, rectangles, parallelograms, trapezoids)
CC.05. Calculate the area of circles
CC.06. Calculate the area of semicircles and quarter circles
CC.07. Calculate the area of compound figures with triangles, semicircles, and quarter circles
CC.08. Calculate the area between two shapes
CC.09. Determine the relationship between area and perimeter of similar figures
CC.10. Apply concepts of perimeter and area to solve real-world problems involving fencing, flooring, and landscaping

DD. Three-Dimensional Figures

EE. Surface Area and Volume

EE.01. Calculate the surface area and volume of cuboids
EE.02. Calculate the surface area of prisms and cylinders
EE.03. Calculate the surface area of pyramids and cones
EE.04. Calculate the surface area of spheres
EE.05. Surface area: mixed review
EE.06. Calculate the volume of prisms and cylinders
EE.07. Calculate the volume of pyramids and cones
EE.08. Calculate the volume of spheres
EE.09. Calculate the volume of compound figures
EE.10. Volume: mixed review
EE.11. Understand the properties of similar solids and their corresponding dimensions
EE.12. Determine the relationship between the volume and surface area of similar solids
EE.13. Analyse the effects of changes in scale on perimeter, area, and volume
EE.14. Apply surface area and volume formulas to solve real-world problems involving packaging, construction, and design

FF. Circles: Arcs, Sectors, and Tangents

FF.01. Identify the parts of a circle (centre, radius, diameter, chord, arc, sector)
FF.02. Define and measure central angles in a circle
FF.03. Understand the concepts of arc length and sector area of a circle
FF.04. Calculate arc measure and arc length using proportions
FF.05. Calculate the area of sectors using proportions
FF.06. Circle measurements: mixed review
FF.07. Apply theorems related to arcs and chords in a circle
FF.08. Apply theorems related to tangent lines to a circle
FF.09. Determine the measures of angles formed by chords, secants, and tangents
FF.10. Determine the lengths of segments formed by chords, secants, and tangents
FF.11. Apply geometric properties of circles to solve practical problems involving circular objects and designs

GG. Geometric Constructions

HH. Vectors

II. Measurement and Units

II.06. Convert square units of length (e.g., cm² to m²)
II.07. Convert between cubic metres and litres
II.08. Convert cubic units of length (e.g., cm³ to m³)
II.09. Convert between metric and imperial units
II.10. Understand the concept of precision in measurement
II.11. Calculate the greatest possible error in a measurement
II.12. Determine the minimum and maximum possible area and volume based on given measurements
II.13. Calculate the percent error in a measurement
II.14. Calculate the percent error in area and volume calculations
II.15. Calculate density, mass, and volume using the density formula
II.16. Discuss the importance of accurate measurements and unit conversions in various scientific and engineering fields
II.01. Convert rates and measurements within the metric system
II.02. Work with metric mixed units, converting between different units
II.03. Convert rates and measurements within the imperial system
II.04. Work with imperial mixed units, converting between different units
II.05. Convert between square metres and hectares

JJ. Data Representation and Interpretation

JJ.01. Interpret data presented in tables, extracting relevant information
JJ.02. Interpret line graphs, identifying trends and relationships
JJ.03. Create line graphs from given data sets
JJ.04. Interpret bar graphs for categorical data
JJ.05. Create bar graphs for categorical data
JJ.06. Interpret bar graphs for grouped data
JJ.07. Create bar graphs for grouped data
JJ.08. Interpret line plots, analysing the distribution of data
JJ.09. Create line plots from given data sets
JJ.10. Interpret pie charts, understanding proportions and percentages
JJ.11. Interpret stem-and-leaf plots, extracting statistical information
JJ.12. Interpret box plots, identifying quartiles, median, and outliers
JJ.13. Choose the appropriate type of graph to represent different types of data

KK. Descriptive Statistics

KK.01. Calculate the mean, median, mode, and range of a data set
KK.02. Interpret charts and graphs to find the mean, median, mode, and range
KK.03. Solve problems where the mean, median, mode, or range is given, and a missing number needs to be found
KK.04. Calculate quartiles and interquartile range (IQR) for a data set
KK.05. Identify outliers in a data set using the IQR rule
KK.06. Identify an outlier and describe the effect of removing it on measures of central tendency
KK.07. Describe distributions in line plots (symmetric, skewed)
KK.08. Understand the difference between populations and samples
KK.09. Identify biased samples in data collection
KK.10. Create scatter plots from bivariate data
KK.11. Identify trends (positive, negative, no correlation) in scatter plots
KK.12. Make predictions using scatter plots and lines of best fit
KK.13. Identify outliers in scatter plots and their potential impact on the data
KK.14. Write an equation for a line of best fit on a scatter plot
KK.15. Distinguish between correlation and causation
KK.16. Apply statistical measures and visualizations to analyze data sets and draw meaningful conclusions

LL. Probability and Compound Events

LL.01. Calculate the probability of simple events
LL.02. Calculate the probability of simple events and their opposite events
LL.03. Calculate the probability of mutually exclusive events and overlapping events
LL.04. Determine experimental probability from observed data
LL.05. Make predictions using experimental probability
LL.06. Make predictions using theoretical probability
LL.07. Calculate the number of possible outcomes for compound events
LL.08. Calculate the probability of compound events
LL.09. Solve word problems involving the calculation of outcomes and probabilities
LL.10. Find probabilities using two-way frequency tables
LL.11. Identify independent and dependent events
LL.12. Calculate the probability of independent and dependent events
LL.13. Find conditional probabilities using two-way frequency tables
LL.14. Apply probability concepts to analyze risk and make informed decisions

Course Content

A. Numbers and Counting

A.01. Classify numbers as integers, rational, irrational, or real

A.02. Identify prime and composite numbers

A.03. Determine the prime factorization of a number

A.04. Find the highest common factor (HCF) of two or more numbers

A.05. Find the lowest common multiple (LCM) of two or more numbers

A.06. Convert between decimals, fractions, and percentages efficiently

A.07. Locate and compare rational numbers on a number line

A.08. Estimate the values of square roots and cube roots

A.09. Solve word problems involving HCF and LCM

A.10. Express recurring decimals as fractions

A.11. Explore the historical development and cultural significance of different number systems

B. Operations with Integers and Rational Numbers

B.01. Add, subtract, multiply, and divide integers with accuracy

B.02. Add and subtract rational numbers, expressing answers in simplest form

B.03. Multiply and divide rational numbers, applying rules for signs correctly

B.04. Evaluate numerical expressions involving integers using the order of operations

B.05. Evaluate numerical expressions involving rational numbers, including fractions and decimals

B.06. Evaluate algebraic expressions involving integer variables

B.07. Evaluate algebraic expressions involving rational variables

B.08. Apply the concepts of operations with integers and rational numbers to solve real-world problems

C. Ratios, Proportions, and Rates

C.01. Write ratios to represent relationships between quantities

C.02. Identify equivalent ratios and simplify ratios to their lowest terms

C.03. Calculate unit rates from given data

C.04. Determine unit rates involving fractions and mixed numbers

C.05. Compare unit prices to find the best value

C.06. Solve proportions using cross-multiplication

C.07. Apply proportions to solve word problems involving scaling and similarity

C.08. Estimate population sizes using proportional reasoning

C.09. Solve scale drawing problems involving maps and models

C.10. Connect proportional reasoning to real-world applications like currency conversion and mixture problems

D. Percentages and Their Applications

D.01. Convert fluently between percentages, fractions, and decimals

D.02. Solve basic percentage equations to find the part, whole, or percent

D.03. Solve word problems involving percentages in various contexts

D.04. Calculate percent of change (increase or decrease)

D.05. Solve word problems involving percent of change, such as growth or depreciation

D.06. Calculate the percentage of a number, including VAT, discount, and mark-up

D.07. Find the original price given the sale price and discount percentage

D.08. Solve multi-step problems involving successive percentages, like discounts and taxes

D.09. Apply percentages in financial literacy scenarios, such as calculating simple and compound interest

E. Expressions and Properties of Operations

E.01. Write variable expressions to represent mathematical relationships and real-world scenarios

E.02. Identify and apply the properties of addition and multiplication (commutative, associative, distributive, identity, inverse)

E.03. Apply the distributive property to expand and factor algebraic expressions

E.04. Simplify variable expressions using properties of operations and combining like terms

E.05. Write equivalent expressions using the properties of addition, subtraction, multiplication, and division

E.06. Simplify variable expressions involving like terms and the distributive property with multiple variables

E.07. Identify equivalent linear expressions using algebraic manipulation

E.08. Demonstrate how the properties of operations are fundamental to algebraic manipulation and problem-solving

F. Solving Linear Equations

F.01. Identify expressions and equations, distinguishing between the two

F.02. Write variable equations to represent real-world scenarios and mathematical relationships

F.03. Identify equivalent equations by applying properties of equality

F.04. Determine if a given value satisfies an equation by substitution

F.05. Apply properties of equality (addition, subtraction, multiplication, division) to solve equations

F.06. Solve one-step linear equations using inverse operations

F.07. Solve two-step linear equations using inverse operations

F.08. Solve advanced linear equations involving multiple steps and simplification

F.09. Solve equations with variables on both sides of the equation

F.10. Determine the number of solutions (none, one, or infinite) for a given linear equation

F.11. Create equations with no solutions or infinitely many solutions

F.12. Solve linear equations presented in word problems, translating words into algebraic expressions

F.13. Rearrange multi-variable equations to solve for a specific variable

F.14. Model and solve equations using algebra tiles

F.15. Solve equations using order of operations

F.16. Write and solve equations that represent diagrams

F.17. Solve equations: complete the solution

F.18. Solve linear equations: mixed review

F.19. Illustrate the use of linear equations in practical situations, such as calculating distances, costs, and quantities

H. Single-Variable Linear Inequalities

H.01. Identify solutions to inequalities by testing values

H.02. Write inequalities from graphs, representing solution sets on a number line

H.03. Graph inequalities on a number line, using appropriate notation for open and closed intervals

H.04. Solve one-step linear inequalities using addition and subtraction properties

H.05. Solve one-step linear inequalities using multiplication and division properties, paying attention to sign changes

H.06. Solve one-step linear inequalities

H.07. Solve two-step linear inequalities