Math: Fraction Concepts and Fraction Addition and Subtraction

Represent Fractions (including Fractions Greater Than One and Mixed Numbers)

• 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; – S RC1
  • 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; – S RC1
• 4.3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. – S RC1 [include measuring lengths to the nearest half, fourth, eighth, and tenth of a unit, as appropriate]

Equivalent Fractions

• 4.3C determine if two given fractions are equivalent using a variety of methods; – S RC1

Compare Fractions with Like and Unlike Denominators

• 4.3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <; – R RC1

Add and Subtract Fractions with Like Denominators

• Computation
  • 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; – R RC2
    • 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; and – S RC2
• Problem Solving (These are some of the problem contexts students should encounter in this unit.)
  • 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. – R RC3 [word problems using measurement contexts, focus on fractions in this unit, addition and subtraction only in this unit]
  • 4.9B solve one- and two-step [addition and subtraction] problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. – S RC4

Building Fluency with Multiplication and Division (Suggested: 21 days)

• Estimation (Use to verify reasonableness of products and quotients)
  • 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; – S RC2
• Multiply Whole Numbers
  • 4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings; – S RC2
  • 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; – S RC2
• Divide Whole Numbers
  • 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor; – S RC2

Counting Patterns (Suggested: 3 days)

• RRISD 4.3 Skip count by rational numbers starting from 0 and other starting numbers and describe patterns observed while counting; [Skip count by thirds and sixths.]

Revisiting Whole Number Place Value (Suggested: 12 days)

• 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; – R RC1
  • 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; – S RC1
  • 4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =; – S RC1
  • 4.2D round whole numbers to a given place value through the hundred thousands place; – S RC1

Representing and Solving Story Problems (Suggested: 12 days)

• Computation and Problem Solving
  • 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; and – S RC2
  • 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm; – R RC2
  • 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; – S RC2
  • 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor; – S RC2
  • 4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. – R RC2
  • 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. – R RC3
  • 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. – S RC4
• Represent Problem Situations (Strip Diagrams and Equations)
  • 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; – R RC2

Telling Time (Ongoing)

• 2.9G read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.