Mathematics Scope & Sequence Grade 4 Revised: May 24, 2016 First Nine Weeks (39 days) Whole Numbers Place Value 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 4.2A interpret the value of each placevalue 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 = 4.2D round whole numbers to a given place value through the hundred thousands place Interpret the value of each place-value position as 10 times the position to the right. (4.2A) Multiply or divide a given number by 10 and interpret value by looking at the placement of the decimal (4.2A) Discover the patterns within the place value chart such as: 10,000; 1,000; 100; 10; 1; 1/10; 1/100 (4.2A) Represent the value of the digit in whole numbers through 1,000,000,000 using expanded notation and numerals such as 285=(2 x 100) + ( 8 x 10) + (5 x 1). (4.2B) Compare whole numbers to 1,000,000,000 using the symbols <, >, or =. (4.2C) Order whole numbers to 1,000,000,000 using place value and number lines. (4.2C) Compare whole numbers using place value and number lines. (4.2C) Compare and order whole numbers using expanded notation. (4.2C) 7-8 Textbook Sections: 1.1, 1.2, 1.3, 1.4 Round whole numbers to a given place value through the hundred thousands place. (4.2D) 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 4.2G relate decimals to fractions that name tenths and hundredths. Represent the value of the digit in decimals to the hundredths using expanded notation and numerals. (4.2B) Relate decimals to fractions that name tenths and hundredths. (4.2G) Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line. (4.2H) Decimal Place Value 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 4.2E represent decimals, including tenths and hundredths, using concrete and visual models and money 4.2F compare and order decimals using concrete and visual models to the hundredths 4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 4.3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line Locate hundredths on a number line that is marked in tenth and locate tenths on a number line that is marked in hundredths. (4.2H) Represent decimals, including tenths and hundredths, using concrete models, visual models and money. (4.2E) Explain the connection between 0.1 and $0.10. (4.2E) Compare decimals to the hundredths using concrete and visual models to the hundredths, such as base ten blocks. (4.2F) Order decimals using concrete and visual models to the hundredths. (4.2F) Explain the connection between equivalent decimals such as 0.1 shown with one base ten long and 0.10 shown with 10 base ten units. (4.2F) Connect the value of a decimal number to the value of the equivalent fraction, such as 0.1 = 1/10. (4.2G) Represent decimals as distances from zero on a number line. (4.3G) 9-10 Represent a decimal on a number line that is marked in tenths; or a decimal in the tenths on a number line that is marked in hundredths. (4.3G) Textbook Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 First nine weeks curriculum continued on next page.
Add and Subtract Whole Numbers and Decimals 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm 4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition and subtraction, multiplication, or division as appropriate 4.2D round whole numbers to a given place value through the hundred thousands place Add whole numbers and decimals to the hundredths place using the standard algorithm. (4.4A) Subtract whole numbers and decimals to the hundredths place using the standard algorithm. (4.4A) Explain why decimal numbers should be lined up according to the decimal point. (4.4A) Connect addition of whole numbers to addition of decimals. (4.4A) Round whole numbers to a given place value through the hundred thousands place. (4.2D) Solve word problems using addition and subtraction, involving money. (4.8C) 5-6 Textbook Sections: 6.1, 6.2, 6.3, 6.4, 6.5, 16.3 Multiply by 1-Digit Numbers 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 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Determine products of a number and 10 or 100 using the commutative, associative, and distributive properties. (4.4B) Determine products of a number and 10 or 100 using place value understandings. (4.4B) Analyze results when multiplying by 10 or 100 to develop an understanding of the pattern of numbers. (4.4B) Round to the nearest 10, 100, or 1,000 to estimate solutions involving whole numbers.(4.4g) Estimate solutions involving whole numbers using compatible numbers. (4.4G) Explain the difference between rounding and estimating. (4.4G) Apply strategies and algorithms to multiply up to a four-digit number by a one-digit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) 11-12 Textbook Sections: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8
Second Nine Weeks (39 ) 4.4H solve with fluency one and two step problems involving multiplication and division, including interpreting remainders Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. (4.4C) Multiply 2- Digit Numbers 4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings 4.4C represent the product of 2 two digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15 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 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Compare the arrays of perfect squares (squares) to those that are not perfect squares (rectangles). (4.4C) Investigate the relationship of the dimensions (rows and columns) to the factors of a given number. (4.4C) Interpret multiplication as repeated addition or multiples. (4.4C) Apply strategies and algorithms to multiply up to a two-digit number by a two-digit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) Explain the significance of placing a zero place holder when multiplying by the tens digit. (4.4D) Round to the nearest 10, 100, or 1,000 to estimate solutions involving whole numbers.(4.4g) Estimate solutions involving whole numbers using compatible numbers. (4.4G) 9-10 Explain the difference between rounding and estimating. (4.4G) Textbook Sections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7 4.4H solve with fluency one and two step problems involving multiplication and division, including interpreting remainders 4.4E represent the quotient of up to a fourdigit whole number divided by a one digit whole number using arrays, area models, or equations Demonstrate that multiplication and division are inverse operations. (4.4E) 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 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Demonstrate understanding that division represents sharing equally or forming equal groups. (4.4E) Solve with fluency one-step problems involving multiplication and division, including interpreting remainders. (4.4H) Solve with fluency two-step problems involving division, including interpreting remainders. (4.4H) 7-8 Evaluate remainders in real life situations. Ex. Karen needs 30 cans of soda for a party. If soda is sold by the 122 pack, how many 12 packs should she buy? (4.4H) Round to the nearest 10, 100, or 1,000 to estimate solutions involving whole numbers.(4.4g) Estimate solutions involving whole numbers using compatible numbers. (4.4G) Textbook Sections: 9.1, 9.2, 9.3, 9.4, 9.5 Second nine weeks curriculum continued on next page. Justify the difference between rounding and estimating. (4.4G)
4.4H solve with fluency one and two step problems involving multiplication and division, including interpreting remainders Apply strategies to divide up to a four-digit dividend by a onedigit divisor such as patterns of tens, hundreds, and thousands and basic facts. (4.4F) Divide by 1-Digit Numbers 4.4E represent the quotient of up to a fourdigit whole number divided by a one digit whole number using arrays, area models, or equations 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four digit dividend by a one digit divisor 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers Apply algorithms to divide up to a four-digit dividend by a onedigit divisor (4.4F) Represent the quotient of up to a four-digit by a one-digit whole number using arrays, area models, or equations. (4.4E) Round to the nearest 10, 100, or 1,000 to estimate solutions involving whole numbers.(4.4g) 7-8 days Estimate solutions involving whole numbers using compatible numbers. (4.4G) Understand and demonstrate the difference between rounding and estimating. (4.4G) Algebra: Multi-Step Problems Textbook Sections: 10.1, 10.2, 10.3, 10.4, 10.5 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm 4.4H solve with fluency one and two step problems involving multiplication and division, including interpreting remainders 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 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 4.4D 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 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four digit dividend by a one digit divisor Textbook Sections: 11.1, 11.2, 11.3,11.4, 16.4 Represent multi-step problems involving the four operations with whole numbers using strip diagrams, representing an unknown quantity as a letter. (4.5A) Represent multi-step problems involving the four operations with whole numbers using equations, representing an unknown quantity as a letter. (4.5A) Solve with fluency one-step/two-step problems involving multiplication and division, including interpreting remainders. (4.4H) Use strategies and algorithms to multiply up to a four-digit number by a one-digit number. (4.4D) Use strategies and algorithms to multiply up to a two-digit number by a two-digit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) Explain the process of placing a zero place holder when multiplying by the tens digit. (4.4D) Use strategies to divide up to a four-digit dividend by a one-digit divisor (4.4F) Use algorithms to divide up to a four-digit dividend by a one-digit divisor (4.4F) Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. (4.4A) Add and subtract whole numbers and decimals using various strategies (4.4A) Solve word problems using all four operations. (4.8C) 5-6 days
Third Nine Weeks (47 ) Determine if fractions are equivalent by using a variety of methods including pictures and common denominators (4.3C) Draw pictorial models of fractions with an emphasis on the wholes being the same size. (4.3C) Fraction Concepts 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 Represent the decomposition of fractions as a sum of unit fractions, such as 3/4=1/4+1/4+1/4; Including improper fractions such as 6/5=1/5+1/5+1/5+1/5+1/5+1/5. (4.3A) Decompose a fraction in a variety of ways, such as 7/8 = 3/8+4/8 or 7/8 = 6/8 +1/8.(4.3B) Solve 7/8+6/8 by decomposing 6/8 into 5/8+1/8, then joining 7/8 and 1/8 to make a whole, resulting in a conceptual model of 1 5/8. (4.3B) Justify the decomposing of fractions using visual fraction models (4.3B) Represent the results of decomposing a fraction with symbolic representations (4.3B) 6-7 4.3C determine if two given fractions are equivalent using a variety of methods Textbook Sections: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, Comparing Fractions 4.3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < 4.3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line Compare two fractions with different numerators and denominators using concrete and pictorial models (4.3D) Analyze concrete objects and pictorial models to compare fractional parts using comparison terminology (less than one whole, equal to one whole, or greater than one whole). (4.3D) Compare fractions by using benchmark fractions, such as thinking about whether a fraction is more than one half or less than one half. (4.3D) Compare fractions by finding common denominators (4.3D) Represent the comparison of the two fractions with different numerators and denominators with symbols >,<, or = (4.3D) Represent fractions as distances from zero on a number line. (4.3G) 4-5 Represent a fraction on a number line that is marked in tenths; or a fraction in the tenths on a number line that is marked in hundredths. (4.3G) Textbook Sections: 4.1, 4.2, 4.3 Add and Subtract 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 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 Represent addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line. (4.3E) Solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build properties of operations. (4.3E) Evaluate the reasonableness of sums and differences of fractions using benchmark fractions that include ¼, ½, ¾, and 1, which refer to the same whole. (4.3F) 8-9 Textbook Sections: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7
Number Patterns, Perimeter, and Area 4.5B represent problems using an inputoutput 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 4.5D solve problems related to perimeter and area of rectangles where dimensions are whole numbers 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 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). Textbook Sections: 12.1, 12.2, 12.3, 12.4, 12.5 Represent problems using an input-output table to generate a number pattern that follows a given rule, represent relationships of values, and their position in the sequence. (4.5B) Represent problems using numerical expressions to generate a number pattern that follows a given rule, represent relationships of values, and their positions in the sequence. (4.5B) Describe the pattern What s the rule? using mathematical words, numbers, and symbols, including variables. (4.5B) Analyze models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l+2w), and the special form for perimeter of a square (4s). (4.5C) Analyze models to determine the area of a rectangle (l x w). (4.5C) Solve problems involving perimeter and area of rectangles where dimensions are whole numbers.(4.5d) Distinguish between situations that represent perimeter and situations that represent area. (4.5D) Apply strategies and algorithms to multiply up to a two-digit number by a two-digit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) 7-8 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 Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. (4.6A) Represent parallel and perpendicular lines, vertically, horizontally, diagonally and with even and uneven lengths. (4.6A) Geometry Concepts 4.6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines 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 Identify acute, right, and obtuse triangles using knowledge of right angles. (4.6C) Identify and describe right, acute, and obtuse angles using concrete objects such as straws, pattern blocks, corner of paper, etc. (4.6C) Classify two dimensional figures based on presence or absence of parallel or perpendicular lines (4.6D) Classify two dimensional figures based on presence or absence of angles of a specified size. (4.6D) 6-7 Identify and draw one or more lines of symmetry, if they exist for a two- dimensional figure. (4.6B) Distinguish between horizontal and vertical lines of symmetry as well as multiple lines of symmetry within a shape. (4.6B) Textbook Sections: 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 Third nine weeks curriculum continued on next page.
4.7C determine the approximate measures of angles in degrees to the nearest whole number using a protractor Illustrate (draw) the measure of an angle in whole numbers where the center of a circle is the vertex of the angle that is cut out by the rays of the angle (4.7A) Measure Angles 4.7A illustrate the measure of an angle as a 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 1 degree and an angle that cuts n/360 out of any circle whose center is at the angle vertex has a measure of n degrees; angle measures are limited to whole numbers. 4.7D draw an angle with a given measure Illustrate degrees as whole number 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. 45 is 45/360 (4.7B) Illustrate that straight angles measure 180 (4.7B) Orient angles in a variety of ways. (4.7B) Determine the approximate measures of angles in degrees to the nearest whole number using a protractor. (4.7C) Connect the sets of numbers on the protractor to the type of angle that is being measured as well as the image of an angle with zero degrees. For example, if an angle is acute, then the number must be less than 90. (4.7C) 5-6 4.7E determine the measure of an unknown angle formed by two non overlapping adjacent angles given one or both angle measures Draw an angle with a given measure. (4.7D) Identify the first ray drawn as the zero mark on the protractor. (4.7D) Determine the measure of an unknown angle formed by two non-overlapping adjacent angles if given one or both angles (4.7E) Textbook Sections: 14.1, 14.2, 14.3, 14.4, 14.5
Customary and Metric Measures Fourth Nine Weeks (52 days) 4.8C solve problems that deal with measurements of length, intervals of time, liquid volume, mass, and money using addition, subtraction, multiplication, or division as appropriate 4.8A identify relative sizes of measurement units within the customary and metric systems 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 Textbook Sections: 15.1, 15.2, 15.3, 15.4, 15.5, 15.6, 15.7 Identify relative sizes of measurement units including units of length, capacity, and weight in the customary and the metric systems. (4.8A) Convert measurements within the same system from a smaller unit to a larger unit when given other equivalent measures represented in a table. (4.8B) Convert measurements within the same system from a larger unit to a smaller unit when given other equivalent measures represented in a table. (4.8B) Connect conversions with paired data in a table. (4.8B) Solve word problems using the four operations involving length, liquid volumes, and mass. (4.8C) 7-8 7-8 Time 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 Solve word problems using intervals of time. (4.8C) 7-3 - 4 Represent and Interpret Data Textbook Sections: 16.1, 16.2 4.9A represent data on a frequency table, dot plot, or stem and leaf plot marked with whole numbers and fractions 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 Textbook Sections: 17.1, 17.2, 17.3, 17.4, 17.5, 17.6 Fourth nine weeks continued on next page. Represent data on different types of graphs including frequency tables, dot plots, stem-and leaf plot. (4.9A) Create frequency tables, dot plots/line graphs, and stem-andleaf plots marked with whole numbers and fractions. (4.9A) Select the appropriate type of graph for a given set of data. (4.9A) Solve one-step and two step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. (4.9B) 7-8
4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm Distinguish between fixed and variable expenses. (4.10A) Compare advantages and disadvantages of savings options. (4.10C) Describe how to allocate a weekly allowance among spending, saving, and sharing (4.10D) Financial Literacy 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 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four digit dividend by a one digit divisor 4.10A distinguish between fixed and variable expenses 4.10B calculate profit in given situations 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 4.10E describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending Describe how financial institutions keep money safe (4.10E) Describe how banks lend money (4.10E) Describe how banks charge interest on the money they lend (4.10E) Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. (4.4A) Add and subtract whole numbers and decimals using various strategies (4.4A) Explain why decimal numbers should be lined up according to the decimal point. (4.4A) Use strategies and algorithms to multiply up to a four-digit number by a one-digit number. (4.4D) Use strategies and algorithms to multiply up to a two-digit number by a two-digit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) Use strategies and algorithms to divide up to a four-digit dividend by a one-digit divisor (4.4F) 6-7 Textbook Sections: 18.1, 18.2, 18.3,18.4,18.5 Calculate profit by subtracting costs incurred by the money made. (4.10B) STAAR Review Math STAAR Monday, May 8, 2017 Fourth nine weeks curriculum continued on next page. 8
Continue to work on the TEKS below to achieve mastery: Mastery of addition and subtraction of whole numbers and decimals, as well as multiplication and division of whole numbers is the goal. 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm Represent multi-step problems involving the four operations with whole numbers using strip diagrams, representing an unknown quantity as a letter. (4.5A) Work for Mastery 4.4H solve with fluency one and two step problems involving multiplication and division, including interpreting remainders 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 Supporting Standard(s 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 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four digit dividend by a one digit divisor Represent multi-step problems involving the four operations with whole numbers using equations, representing an unknown quantity as a letter. (4.5A) Solve with fluency one-step/two-step problems involving multiplication and division, including interpreting remainders. (4.4H) Use strategies and algorithms to multiply up to a four-digit number by a onedigit number. (4.4D) Use strategies and algorithms to multiply up to a two-digit number by a twodigit number. (4.4D) Multiply numbers using strategies such as mental math, partial products, commutative property, the associative property, the distributive property, and base ten blocks. (4.4D) Explain the process of placing a zero place holder when multiplying by the tens digit. (4.4D) Use strategies to divide up to a four-digit dividend by a one-digit divisor (4.4F) Use algorithms to divide up to a four-digit dividend by a one-digit divisor (4.4F) Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. (4.4A) Add and subtract whole numbers and decimals using various strategies (4.4A) Solve word problems using all four operations. (4.8C)