1 Unit 1 Place Value Concepts Essential TEKS 4.2B: represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals Whole numbers Decimals 4.2B: represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals Whole numbers Decimals 4.2G: relate decimals to fractions that name tenths and hundredths 4.2G: relate decimals to fractions that name tenths and hundredths Complementary TEKS 4.2A: interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left 4.2A: interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left 4.2C: compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or = 4.2C: compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or = 4.2D: round whole numbers to a given place value through the hundred thousands place 4.2D: round whole numbers to a given place value through the hundred thousands place 4.2E: represent decimals, including tenths and hundredths, using concrete and visual models and money Read and write decimals Visual models Money 4.2E: represent decimals, including tenths and hundredths, using concrete and visual models and money Read and write decimals Visual models Money 4.2F: compare and order decimals using concrete and visual models to the hundredths Compare decimals Order decimals 4.2F: compare and order decimals using concrete and visual models to the hundredths Compare decimals Order decimals 4.3G: represent fractions and decimals to the tenths or hundredths as distances from zero on a number line 4.3G: represent fractions and decimals to the tenths or hundredths as distances from zero on a number line 4.2H: determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 4.2H: determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line
 2 Unit 2 Addition and Subtraction Essential TEKS 4.4A: add and subtract whole numbers and decimals to the hundredths place using the standard algorithm Add whole numbers Subtract whole numbers Add and subtract decimals 4.4A: add and subtract whole numbers and decimals to the hundredths place using the standard algorithm Add whole numbers Subtract whole numbers Add and subtract decimals Complementary TEKS 4.4G: round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Estimate sums Estimate differences 4.4G: round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Estimate sums Estimate differences 4.8C: solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate 4.8C: solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate
 3 Unit 3 Multiplication and Division Essential TEKS 4.4H: solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders Multiplication facts Multiplication word problems Division facts Division word problems Interpret remainders Multi-step problems 4.4H: solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders Multiplication facts Multiplication word problems Division facts Division word problems Interpret remainders Multi-step problems 4.4C: represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15 4.4C: represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15 Complementary TEKS 4.4B: determine products of a number and 10 or 100 using properties of operations and place value understandings 4.4B: determine products of a number and 10 or 100 using properties of operations and place value understandings 4.4D: use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties Multiplication facts Multiply 1-digit numbers using models Multiply 1-digit numbers Multiply 2-digit numbers using models Multiply 2-digit numbers Multiplication strategies 4.4D: use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties Multiplication facts Multiply 1-digit numbers using models Multiply 1-digit numbers Multiply 2-digit numbers using models Multiply 2-digit numbers Multiplication strategies 4.4E: represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations Divide 2-digit numbers Divide larger numbers 4.4E: represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations Divide 2-digit numbers Divide larger numbers 4.4F: use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor Divide 2-digit numbers Divide larger numbers Division strategies 4.4F: use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor Divide 2-digit numbers Divide larger numbers Division strategies 4.4G: round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Estimate products Estimate quotients Mixed operations 4.4G: round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Estimate products Estimate quotients Mixed operations
 4 Unit 4 Numerical Expressions, Equations and Patterns in Input-Output Tables Essential TEKS 4.5A: represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity Expressions and equations Strip diagrams 4.5A: represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity Expressions and equations Strip diagrams 4.5B: represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence 4.5B: represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence
 5 Unit 5 Fractions Representations, Relationships and Computations Essential TEKS 4.3D: compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < Use models Use benchmark fractions 4.3D: compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < Use models Use benchmark fractions 4.3E: represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations Addition Subtraction Mixed operations Real-world problems 4.3E: represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations Addition Subtraction Mixed operations Real-world problems Complementary TEKS 4.3A: represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b 4.3A: represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b 4.3B: decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations 4.3B: decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations 4.3C: determine if two given fractions are equivalent using a variety of methods Model equivalent fractions Equivalent fractions 4.3C: determine if two given fractions are equivalent using a variety of methods Model equivalent fractions Equivalent fractions 4.3F: evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole Compare sums and differences Determine reasonableness 4.3F: evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole Compare sums and differences Determine reasonableness 4.3G: represent fractions and decimals to the tenths or hundredths as distances from zero on a number line 4.3G: represent fractions and decimals to the tenths or hundredths as distances from zero on a number line
 6 Unit 6 Data Analysis Essential TEKS 4.9A: represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions Frequency tables Line plots Stem-and-leaf plots 4.9A: represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions Frequency tables Line plots Stem-and-leaf plots Complementary TEKS 4.9B: solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot Frequency tables Line plots Stem-and-leaf plots 4.9B: solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot Frequency tables Line plots Stem-and-leaf plots
 7 Unit 7 Geometry and Measurement Essential TEKS 4.5D: solve problems related to perimeter and area of rectangles where dimensions are whole numbers Perimeter Area Area and perimeter 4.5D: solve problems related to perimeter and area of rectangles where dimensions are whole numbers Perimeter Area Area and perimeter 4.6D: classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size Triangles Quadrilaterals 4.6D: classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size Triangles Quadrilaterals 4.7C: determine the approximate measures of angles in degrees to the nearest whole number using a protractor 4.7C: determine the approximate measures of angles in degrees to the nearest whole number using a protractor 4.8C: solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate Measurement Money Time 15. 4.8C: solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate Measurement Money Time 15. Complementary TEKS 4.5C: use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w) Perimeter Area Area and perimeter 4.5C: use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w) Perimeter Area Area and perimeter 4.6A: identify points, lines, line segments, rays, angles, and perpendicular and parallel lines Parallel, perpendicular, and intersecting lines Points, lines, and angles Angles 4.6A: identify points, lines, line segments, rays, angles, and perpendicular and parallel lines Parallel, perpendicular, and intersecting lines Points, lines, and angles Angles 4.6B: identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure 4.6B: identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure 4.6C: apply knowledge of right angles to identify acute, right, and obtuse triangles 4.6C: apply knowledge of right angles to identify acute, right, and obtuse triangles 4.7A: illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers 4.7A: illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers 4.7B: illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers 4.7B: illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers 4.7D: draw an angle with a given measure 4.7D: draw an angle with a given measure 4.7E: determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures 4.7E: determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures 4.8A: identify relative sizes of measurement units within the customary and metric systems Customary units Metric units 4.8A: identify relative sizes of measurement units within the customary and metric systems Customary units Metric units 4.8B: convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table Customary units Metric units 4.8B: convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table Customary units Metric units 4.10B: calculate profit in a given situation 4.10B: calculate profit in a given situation
 8 Unit 8 Personal Financial Literacy, STAAR Review, and STAAR Testing Complementary TEKS 4.10A: distinguish between fixed and variable expenses 4.10A: distinguish between fixed and variable expenses 4.10C: compare the advantages and disadvantages of various savings options 4.10C: compare the advantages and disadvantages of various savings options 4.10D: describe how to allocate a weekly allowance among spending; saving, including for college; and sharing 4.10D: describe how to allocate a weekly allowance among spending; saving, including for college; and sharing 4.10E: describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending 4.10E: describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending
 9 Unit 9 Representing and Solving Fraction Problems Essential TEKS 4.3D: compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < Compare fractions Order fractions 4.3D: compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < Compare fractions Order fractions 4.3E: represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations Addition Subtraction Mixed operations 4.3E: represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations Addition Subtraction Mixed operations Complementary TEKS 4.3C: determine if two given fractions are equivalent using a variety of methods 4.3C: determine if two given fractions are equivalent using a variety of methods