Current Standard - Fraction Equivalence and Comparison

  • In this unit, students will be exploring fractions.  In the third grade, students were introduced to equivalent fractions using visual representations.  In the fourth grade, students will continue exploring equivalent fractions with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. They will also be introduced to formal rules and algorithms for creating equivalent fractions and comparing fractions with different numerators and different denominators.

      

    equivalent fractions                        greater than one  

    finding

     

    decomposing       decompose greater

     Critical Vocabulary:

     benchmark fractions
     equivalent fraction
     numerator  denominator
     models
     hundredth
     common denominator
     common numerator
     mixed number
     tenth
     unit fraction

     

    Standards:

     

    MAFS.4.NF.1.1- Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (DOK 3)

     

    MAFS.4.NF.1.2- Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (DOK 2)

Past Standard - Multiplication and Division of Whole Numbers

  • We are currently finishing up our unit on multiplication and division of whole numbers.  Students have learned a variety of methods to solve these types of problems.  For example, multiplication problems can be solved using area models and partial products.  Division problems can be solved using repeated subtraction or partial quotients.

      

    Area Models Partial Products
     area model  partial products
    Partial Quotients or Repeated Subtraction  
    partial quotients  

     

    Critical Vocabulary

     Equations

     Rectangular arrays

     Area models

     Product/Partial Products

     Factors

     Symbol

     Quotient  

     Dividend

     Divisor

     Remainder

     Estimation

     Variable/unknown number

     

     Standards:

    MAFS.4.NBT.2.5 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (DOK 2)

    MAFS.4.NBT.2.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (DOK 2)

    MAFS.4.OA.1.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (DOK 2)

    MAFS.4.OA.1.3 – Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (DOK 2)