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Kindergarten Math TEKS Tree Read Write Represent Whole numbers Use Comparative language Describe Two numbers (0 to 20) With objects/pictures Without objects/pictures K.2H • Written numerals K.7B • Compare Two objects Common attributes See Which object More of attribute Less of attribute Describe Difference Use Data Create Graphs Real-object Picture Draw Conclusions Real-object graphs Picture graphs (up to 20) K.2I • Compose Decompose With objects Numbers (up to 10) With pictures K.8B • K.3B • K.6E • Solve Word problems Use Objects Drawings Find Sums Differences Classify Sort 2-dimensional figures K.8C • Up to 10 Within 10 Regular Irregular 3-dimensional figures *NOTE: The classification of Kindergarten “readiness” standards on this document represents the reviewed and synthesized input from a sample of Texas mathematics teachers. This DOES NOT represent an endorsement of the Texas Education Agency. TEKS Student Expectations for implementation beginning 2015-2016. *Readiness Readiness Standards Standards K.2B • 1st Grade Math TEKS Tree Use 1.2C • 1.6A • Represent Numbers Up to 120 Represent Comparison Two numbers Use > (Greater than) < (Less than) = (Equal to) (up to 100) 1.2G • 1.3F • Generate Solve (given) Relationships Count By twos By fives By tens 1.4C • Value Pennies Nickels Dimes Addition Represent Word problems Subtraction 1.5D • 1.5G • Informal geometric language Identify 2-dimensional shapes Describe Attributes Use Formal geometric language Use Concrete models Pictorial models Number sentences Apply Properties of operations Add Subtract Two numbers Three numbers Spheres Cones Cylinders Rectangular prisms Cubes Triangular prisms 3-dimensional solids Describe Attributes Use Formal geometric language Describe Length Use Number Unit Tell Time Hour Half-hour Use Clocks Analog Digital Draw Conclusions Generate Answer Questions Use Information 1.7D • • Whole #’s • Up to 20 Whole unit 1.7E • 1.8C • *NOTE: The classification of first grade “readiness” standards on this document represents the reviewed and synthesized input from a sample of Texas mathematics teachers. This DOES NOT represent an endorsement of the Texas Education Agency. TEKS Student Expectations for implementation beginning 2014-2015. Circles Triangles Rectangles Squares Rhombuses Hexagons Identify 1.6E • Collection of: Determine Use Addition (within 20) Subtraction (within 20) Number sentence Use Shapes 1.6D • Problem situations Regular Irregular 2-dimensional Classify Sort Picture graphs Bar-type graphs *Readiness Readiness Standards Standards Objects Pictures Expanded form Standard form 2nd Grade Math TEKS Tree Forms Standard Word Expanded Represent Numbers Up to 1,200 Use Place value Compare Order Numbers Use Language Numbers Symbols 2.2B • 2.8B • Whole Up to 1,200 2.2D • 2.3B • Explain > (Greater than) < (Less than) = (Equal to) Spheres Cones Cylinders Rectangular prisms Cubes Triangular prisms Classify Sort 3-dimensional solids Use Formal geometric language Classify Sort Polygons Up to 12 sides Identify Number Sides Vertices Determine Solution Length Estimate Lengths Read Write Time Nearest minute Use Clocks Analog Digital Distinguish a.m. p.m. Write Solve Word problems One-step Addition or subtraction Use Data Pictographs Bar graphs 2.8C • More fractional parts → Smaller parts Fewer fractional parts → Larger parts 2.9E • Solve Word problems One-step & multi-step Addition & subtraction 2.4C • 2.4D • within 1,000 Use Strategies Generate Solve Problem situations (given) 2.5A • Determine Place value Algorithms 2.9G • Number sentence Addition Subtraction within 1,000 Value Coins Collection Up to $1 2.10C • *NOTE: The classification of second grade “readiness” standards on this document represents the reviewed and synthesized input from a sample of Texas mathematics teachers. This DOES NOT represent an endorsement of the Texas Education Agency. TEKS Student Expectations for implementation beginning 2014-2015. *Readiness Readiness Standards Standards Use 3rd Grade Math TEKS Tree As sums of: Numbers 3.2A • Use Compare Order Objects Pictorial models Numbers Expanded notation Whole numbers Up to 100,000 Comparisons < (less than) > (greater than) = (equal to) 3.2D • Represent 1-step problems Multiplication Division 2-step problems Multiplication Division Solve 3.4K • Objects Pictorial models Use Strategies • Equal groups • Arrays • Area models Operation properties Recall of facts 1-step problems Addition Subtraction 2-step problems Addition Subtraction Represent Represent Equivalent fractions Use Objects Pictorial models Compare Two fractions Reason About sizes 3.3F • 3.3H • Justify Use 3.4A • Conclusion Denominators: 2, 3, 4, 6, 8 Use Number lines Same numerator OR Same denominator Pictorial models Number lines Equations 1-step problems Multiplication Division 2-step problems Multiplication Division Represent Solve Symbols Words Objects Pictorial models Strategies Operation properties Relationship b/w + and − 1-step problems Addition Subtraction Solve 2-step problems 3.5A • Addition Subtraction TEKS Student Expectations for implementation beginning 2014-2015. 3.5B • Use Arrays Strip diagrams Equations Represent Relationships Real-world Number pairs (in table) 3.5E • Use Verbal descriptions Continued → Readiness Standards Compose Decompose Ten-thousands Thousands Hundreds Tens Ones 3rd Grade Math TEKS Tree 2-dimensional figures Classify Sort Readiness Standards 3.6A • 3-dimensional figures Use Attributes Formal geometric language Determine Area Use 3.8A • Rectangles • whole number side lengths 3.6C • 3.7B • Cones Cylinders Spheres Triangular prisms Rectangular prisms Cubes Multiplication Number of rows Number of squares in each row Perimeter Polygon Missing length Perimeter Other side lengths Data Frequency table Dot plot Pictograph Bar graph Given: Determine Summarize (multiple categories) • scaled intervals TEKS Student Expectations for implementation beginning 2014-2015. 4th Grade Math TEKS Tree Digit’s value Use Expanded notation Numerals Whole #’s to 1 billion Decimals to hundredths 4.2B • Decimals 4.2G • Relate to Tenths Hundredths Tenths Hundredths Two fractions Different numerators Different denominators Represent Comparison < (less than) = (equal to) > (greater than) Represent Solve Fraction addition Fraction subtraction Equal denominators Equal denominators Objects Building to number line Properties of operations 4.3D • 4.3E • Use Pictorial models 4.4A • Multi-step problems Use Strip diagrams Equations Represent Problems Use Input-output tables Numerical expressions Generate Rule 4.5B • Perimeter problems 4.5D • Solve Area problems Whole numbers Decimals To hundredths Subtract Whole numbers Decimals To hundredths Use Standard algorithm One-step problems Multiplication Division Two-step problems Multiplication Division Remainders TEKS Student Expectations for implementation beginning 2014-2015. Position in the sequence Value in the sequence Rectangles • Whole number side lengths Rectangles Classify 2-dimensional figures Parallel lines Perpendicular lines Size of angles 4.7C • Determine Angle measures Degrees Whole numbers Protractor Solve Problems Length Time Liquid volume Mass Money Use Addition Subtraction Multiplication Division Represent Data 4.8C • Solve Interpret Letter for unknown 4.6D • Building to number line Properties of operations Add 4.4H • Four operations Whole numbers 4.5A • Fractions Compare Represent 4.9A • • Whole numbers • Fractions Frequency table Dot plot Stem-and-leaf plot Readiness Standards Represent 5th Grade Math TEKS Tree Two decimals Thousandths Represent Comparison > (greater than) < (less than) = (equal to) Numerical expressions No exponents Grouping (up to 2 levels) 5.2B • 5.4F • Simplify Solve Decimal products Hundredths Situations Money Strategies Place value Properties of operations Relationship to whole number multiplication 5.3E • Use Solve Quotients of decimals 5.3G • To hundredths Up to 4-digit dividends Up to 2-digit divisors Rule 5.4C • Generate Pattern Graph 5.4H • Represent Solve Problems Perimeter Area Perimeter and area Volume Classify 2-dimensional figures Attributes Properties Use Graphic organizer Sets Subsets Graph Ordered pairs First quadrant Number patterns Input-output table Solve One-step problems Two-step problems 5.5A • 5.8C • • Whole numbers Use Add Strategies Algorithms Numbers Standard Positive Rational 5.3K • Subtract Numbers Positive Rational 5.3L • Divide Whole numbers Unit fractions By unit fractions By whole numbers Multi-step problems 5.4B • Represent Solve The four operations Whole numbers Use Equations Letter for unknown TEKS Student Expectations for implementation beginning 2014-2015. • y = ax •y=x+a 5.9C • Use Data Frequency table Dot plot Bar graph Stem-and-leaf plot Scatterplot Readiness Standards Compare Order 6th Grade Math TEKS Tree Order Rational numbers 6.3D • Add Subtract Multiply Divide Integers Integers Integers Integers Multiply Numbers Positive Rational Numbers Positive Rational Equivalent forms Fractions Decimals Percents Generate 6.4G • Problems Real-world Money Convert Units (same measurement system) Use Proportions Unit rates Use 6.5B • 6.6C • 6.11A • 6.12C • Solve Real-world problems Find Whole Part Percent From part and percent From whole and percent From part and whole Situations Verbal descriptions Tables Graphs Equations Represent 6.8D • Concrete Pictorial Models • y = kx •y=x+a Generate Expressions Use Order of operations Prime factorization Properties Inverse Identity Commutative Associative Distributive Area problems Rectangles Parallelograms Trapezoids Triangles Volume problems Rectangular prisms Points All four quadrants Ordered pairs: rational numbers Summarize Data Mean (Center) Median Range (Spread) Inner-quartile range Use Summaries Describe Center Shape Spread Summarize Categorical data Mode Frequency table Percent bar graph Use Summaries Numerical Graphical Describe Distribution Use Use 6.4H • Equivalent expressions 6.7D • 6.3E • Divide Generate Equivalent Numerical 6.7A • Whole number exponents TEKS Student Expectations for implementation beginning 2014-2015. Solve Graph 6.12D • 6.13A • Interpret Numeric data Dot plots Stem-and-leaf plots Histograms Box plots Readiness Standards Mathematical problems Real-world problems 6.2D • 7th Grade Math TEKS Tree Use 7.3B • Solve Addition Subtraction Multiplication Division Use Data Sample spaces Determine Probabilities 7.6I • Theoretical • simple/compound events Experimental Problems Apply Extend 7.4A• 7.4D • 7.5C • Represent Solve Operations Operations Rates of change Problems Use 7.7A • Pictorial Tabular Verbal Numeric Graphical Algebraic (like d=rt) Rates Ratios Percents Percent increase Percent decrease Financial literacy Mathematical problems Similar shapes Scale drawings Real-world problems Similar shapes Scale drawings Data Bar graphs Dot plots Circle graphs Solve Problems Part-to-whole Part-to-part Solve Problems From experiments Predictions Qualitative Quantitative Comparisons Qualitative Quantitative Represent Form: y = mx + b Relationships Linear Rectangular prisms Triangular prisms Rectangular pyramids Triangular pyramids 7.9A • Solve Volume problems 7.9B • Determine Circumference Area 7.9C • Determine Composite area Rectangles Squares Parallelograms Trapezoids Triangles Semi-circles Quarter circles Model Equations Inequalities 1 variable, 2-step 1 variable, 2-step Solve Equations Inequalities 1 variable, 2-step 1 variable, 2-step Compare Data Dot plots Box plots Compare Data Center Shape Spread Solve Use 7.6G • 7.6H • Use TEKS Student Expectations for implementation beginning 2014-2015. Circles 7.11A • 7.12A • Readiness Standards • simple/compound events Verbal descriptions Tables Graphs Equations 8th Grade Math TEKS Tree Order Set of rational numbers Mathematical probs. Real-world situations Representations Algebraic Figures 2-dimensional Coordinate plane Use 8.3C • Explain Effect Scale factor • Positive, rational • Center: origin Graph Relationships Proportional Interpret Unit rate Slope 8.7A • Solve Volume problems Use Knowledge of surface area Formulas for: Make Connections Lateral surface area Total surface area Determine Solutions Rectangular prisms Triangular prisms Cylinders 8.7B • (to L.A./S.A. problems) 8.4B• Use Data Rate of change (slope) 8.4C • Table Graph Mathematical probs. Real-world situations Use Trend line Make Predictions Mathematical probs. Real-world situations Use Pythagorean Theorem Converse Solve Problems Model Equations 1-variable Variable on both sides Rational coefficients Solve Equations 1-variable Variable on both sides Rational coefficients Use Representations Algebraic 8.7C • Determine y-intercept 8.8C • Linear relationships 8.5D • 8.5G • Identify Use Functions Representations 8.5I • Write Equations Model Linear relationships Ordered pairs Table Mapping Graph Verbal Numerical Tabular Graphical Form: y = mx+ b TEKS Student Expectations for implementation beginning 2014-2015. Cylinders Cones Spheres 8.10C • Explain Effect Translations Reflections Rotations • Over x-axis • Over y-axis • 90° • 180° Calculate Interest Simple Compound Compare Earnings Simple interest Compound interest 8.12D • • 270° • 360° Readiness Standards 8.2D • Algebra I TEKS Tree Determine Domain Range Linear/Mathematical Linear/Mathematical Determine Domain Range Quadratic functions Represent Domain Range With inequalities With inequalities Graph Quadratic functions Coordinate plane Key attributes x-intercept y-intercept Zeros Maximum/minimum value Vertex Axis of symmetry Reasonable Domains A.2A • Determine (real-world) Reasonable Ranges (real-world) Represent A.2C • Write Domain Range Using inequalities Using inequalities Linear equations Table Graph Verbal Description (in two variables) A.2I • Write Systems (2 linear equations) A.3B • Table Graph Verbal Description Calculate Rate of change Tabularly Graphically Algebraically Graph Linear functions Coordinate plane Key features x-intercept y-intercept Zeros Slope A.3C • Identify A.3D • Graph Linear inequalities 2-variable Coordinate plane A.5A • Solve Equations Distributive property Variables on both sides (linear, 1-variable) A.5C • Solve Systems (2 linear equations) Mathematical Real-world TEKS Student Expectations for implementation beginning 2015-2016. A.7A • Identify A.7C • A.8A • Determine Effects on f(x) = x2 af(x) f(bx) f(x – c) f(x) + d Solve Quadratic equations Factoring Taking square roots Completing the square Quadratic formula Write Exponential functions f(x) = abx Describe Mathematical probs. Real-world problems Growth Decay Graph Exponential functions Growth Decay Identify Key features y-intercept Asymptotes Factor Trinomials ax2 + bx + c Perfect square trinomials Simplify Expressions Algebraic Numeric Use Laws of exponents Integer exponents Rational exponents A.9C • A.9D • A.10E • A.11B • Readiness Standards A.6A • Continuous Discrete Continuous Discrete Graph 2A.2A • Analyze Describe Analyze 2A.2C • f(x) = x f(x) = 1/x f(x) = x3 f(x) = 3 x f(x) = bx f(x) = |x| f(x) = logb x Key features Relationship Determine Effects on f(x) = x 2A.4F • Solve Equations Quadratic Square root 2A.5A • Determine Effects on f(x) = bx and f(x) = logb x af(x) f(x) + d f(bx) f(x – c) 2A.5D • Solve Equations b is 2, 10, or e Domain Range Intercepts Symmetries Asymptotic behavior Maximum Minimum Function Inverse Exponential (y = abx) • a ≠ 0, b > 1 Logarithmic Include Quadratic/Square root Logarithmic/Exponential Domain and range restrictions 2A.6E • Solve Equations Absolute value Formulate Systems of equations 2A.6I • Solve Equations Rational 2A.6L • Formulate Solve 3 linear equations 2-variables 1 linear equation 1 quadratic equation Solve 3-variable systems Gaussian elimination Technology (matrices) Substitution Write Equation Parabola Attributes Vertex Focus Directrix Axis of symmetry Direction (opening) Include 2A.4B • Use • real solutions • linear • real solutions 3-variables 2A.3A • 2A.3B • 2A.4C • af(x) f(x) + d f(bx) f(x – c) b is 2, 10, or e TEKS Student Expectations for implementation beginning 2015-2016. Equations Inverse variation Linear factors Polynomials (degree 3) Polynomials (degree 4) Quadratic factors Polynomials (degree 3) Polynomials (degree 4) Factoring Sum of cubes Difference of cubes Grouping Determine 2A.7E • Include Continued → Readiness Standards Algebra II TEKS Tree Readiness Standards Algebra II TEKS Tree 2A.7F • Determine Sum Difference Product Quotient 2A.7H • Solve Equations Predict Make Decisions Use Data Rational expressions Rational expressions Rational expressions Rational expressions Rational exponents degree one and degree two Critical judgments 2A.8C • Linear Quadratic Exponential TEKS Student Expectations for implementation beginning 2015-2016. Geometry TEKS Tree G.2B • G.2C • Derive Use Formulas Verify Relationships Include Segment congruence Parallel lines Perpendicular Determine Equation (line) Distance Slope Midpoint Prove Congruence Apply Side-Angle-Side Angle-Side-Angle Side-Side-Side Angle-Angle-Side Hypotenuse-Leg Apply Angle-Angle criterion Verify Similar triangles Apply Proportionality Solve Problems Determine Side lengths Angle measures Right triangles Right triangles Apply Trigonometric ratios Sine Cosine Tangent Solve Problems G.6B • Parallel Perpendicular Through a given point Two triangles Image Transformations Determine • rigid • non-rigid • both Corresponding sides Composition of G.3B • Pre-image Transformations Include Dilations Center: any point Verify Conjecture False • rigid • non-rigid • both G.4C • Use Counterexample Investigate Patterns G.5A • Make G.6A • G.7B • Conjectures G.9A • Angles Parallel lines Triangle congruence Special segments Diagonals Interior/Exterior angles Verify Theorems Include Vertical angles Angles formed by a transversal Prove Equidistance Apply Relationships Special Right Triangles G.9B • Solve Problems TEKS Student Expectations for implementation beginning 2015-2016. • 30°-60°-90° • 45°-45°-90° Relationships Pythagorean Theorem Triangles Endpoints Points on perp. bisector Apply Determine Describe Dimensional changes Perimeter Area Surface area Volume Include Changes Proportional Non-proportional (effects of) G.10B • Continued → *Readiness Readiness Standards Standards Composition of Geometry TEKS Tree Determine Composite area Solve Problems Use Appropriate units Apply Formulas Include Prisms Pyramids Cones Cylinders Spheres Composite figures *Readiness Standards G.11B • G.11C • Solve Problems Use Appropriate units Apply Formulas Include Prisms Pyramids Cones Cylinders Spheres Composite figures Solve Problems Use Appropriate units G.11D • Triangles Parallelograms Trapezoids Kites Regular polygons Sectors Total surface area Lateral surface area Identify Events Independent (Dependent) Compute Probabilities With replacement Without replacement G.13C • Volume *NOTE: The classification of Geometry “readiness” standards on this document represents the reviewed and synthesized input of a sample Texas high school mathematics teachers. This DOES NOT represent an endorsement of the Texas Education Agency. TEKS Student Expectations for implementation beginning 2015-2016.
