In third grade, students began to recognize that there were fractions that were located on the same place on a number line but had different names like 1/2, 2/4, and 3/6. In fourth grade, students extend their understanding of equivalent fractions.
The key ideas focused on (Standards 4.NF.1 & 4.NF.2) in this unit include:
- Finding equivalent fractions for a given fractions
- Proving two fractions are equivalent using models, reasoning, or computations
- Comparing and ordering fractions
Fourth grade students develop a deeper understanding of the meaning of equivalence. A fraction can be represented in multiple ways, and equivalent fractions name the same number. Students will visualize this concept using area models and number lines.
Fourth grade students also learn to generate equivalent fractions. Through explorations that begin with creating models to show equivalent fractions, listing and observing them, and looking for patterns, they discover connections between the numerators and denominators. Once they understand the meaning of an equivalent fraction and they can be generated by multiplying the fraction by any representation of 1 (e.g., 5/5, 10/10, 100/100), students are able to generate their own equivalent fractions, providing them with the foundation they will need to add and subtract fractions with unlike denominators in grade 5.
In third grade students compared fractions with like numerators and denominators and became aware of the idea that the size of the whole matters when comparing fractions. Fourth grade students compare and order fractions, even if both the numerator and denominator are different and will explore different strategies for doing so. Students will use their understanding of equivalent fractions to compare and order fractions from least to greatest or greatest to least. They will do so by reasoning about the fractions by using benchmarks, or by comparing the denominators of fractions with the same numerator, or comparing numerators of fractions with the same denominator.
At the end of Unit 3, students should be able to:
- Explain why fractions are equivalent
- Find equivalent fractions for a given fraction
- Compare and order fractions
4.1 Standards for Unit 2:
4.NF.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.
4.NF.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.
4.MD.2 - Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
*4.MD.2 is a standard that will appear in every unit in 4th grade and will be covered more thoroughly in Unit 7