Math: Deepening Fraction Number Sense and Connecting Whole Number Addition and Subtraction Concepts to Fractions

Represent Fractions (including Improper Fractions 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]
  • 4.9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions; – R RC4

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

• 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 (Some of the types of problems students should be solving during 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

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

Operations & Algebraic Reasoning

• Computation (The types of computation students should be doing when solving word problems during spiral review.)
  • 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm; – R RC2
  • 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
  • 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
  • 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; and – S RC2
• Problem Solving (Some of the types of problems students should be solving during spiral review.)
  • 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 [word problems using measurement contexts, whole numbers, all four operations]
  • 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
• Representations (Pictorial and Symbolic)
  • 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