# 1.4 - Fractions

The student will

a)  represent and solve practical problems involving equal sharing with two or four sharers; and

b)  represent and name fractions for halves and fourths, using models.

### BIG IDEAS

• So that I can understand equal sharing with two or four friends
• So that I can name halves and fourths when I am sharing food, toys, or grouping friends in our classroom

### UNDERSTANDING THE STANDARD

 Practical situations with fractions should involve real-life problems in which students themselves determine how to subdivide a whole into equal parts, test those parts to be sure they are equal, and use those parts to re-create the whole.When working with fractions, the whole must be defined.Fractions can have different meanings: part-whole, division, measurement, ratio, and operator.  The focus of this grade level is to develop the idea of equal sharing (division) and part-whole relationships.  Fraction notation will be introduced in grade two.An equal sharing problem is an idea that young children understand intuitively because of their experiences sharing objects with siblings, friends, etc.  Consider the following examples:Two children sharing six sandwichesTwo children sharing one sandwichFour children sharing one piece of paperFour children sharing two browniesFraction models that can be continuously divided should be used at this grade (e.g., cookies, brownies).  It is important to use models that can be continuously divided when there are remainders so those remainders can be cut into as many equal parts as needed.Students should be encouraged to observe and state what happens as you add more sharers, noticing that when more sharers are added, the smaller the share will be for each person.Equal parts may be different shapes but maintain the same value (e.g., a sandwich could be cut in two equal pieces vertically, horizontally, or diagonally to represent halves).The words denominator and numerator are not required at this grade, but the concepts of part and whole are required for understanding of a fraction.Students should use the vocabulary for halves and fourths, but should not be expected to use fraction notation at this level. Informal, integrated experiences with fractions at this level will help students develop a foundation for deeper learning at later grades. Understanding the language of fractions furthers this development.Students should have opportunities to make connections and comparisons among fraction representations by connecting concrete or pictorial representations with spoken representations (e.g., “one-half,” “one out of two equal parts, ”or “one-half is more than one-fourth of the same whole”).

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Share a whole equally with two or four sharers, when given a practical situation. (a)
• Represent fair shares pictorially, when given a practical situation. (a)
• Describe shares as equal pieces or parts of the whole (e.g., halves, fourths), when given a practical situation. (a)
• Represent halves and fourths of a whole, using a region/area model (e.g., pie pieces, pattern blocks, paper folding, and drawings). (b)
• Name fractions represented by drawings or concrete materials for halves and fourths. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018