Primary Standards:
MAFS.4.NF.1.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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.
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 ½. 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.
Content Knowledge:
In 3rd grade, students began to recognize that there were fractions that were located on the same place on a number line, (or using the same whole partitioned in different ways) but had different names like ,
,
. In this Unit, students extend their understanding of equivalent fractions and use that understanding to compare two fractions.
4th 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 can visualize these using number lines and area models (rectangles, squares, & circles). Students will also generate equivalent fractions through explorations that begin with creating models, listing and observing them, and looking for patterns. As students attempt to understand and explain this, they may enVision they are multiplying the fraction by 1 (,
,
…) resulting in a new name for the same fractional value. In this Unit, students will also compare two fractions with unlike numerators and denominators using various strategies of their choosing. Students should be tasked with developing their own strategies, which may include reasoning using benchmark fractions, comparing denominators, finding equivalent fractions, or renaming fractions to have the same denominator. It is not the goal of the standards that students be taught to use particular strategies, it is more important that students reason and justify about their thinking process in comparing two fractions.
GCG 1: Learning Goal: As a mathematician, I can Use models to determine if two fractions are equivalent and generate equivalent fractions
- Step 1: Use area models to determine if two fractions are equivalent
- Step 2: Use number lines to determine if two fractions are equivalent
- Step 3: Generate equivalent fractions using models
GCG 2: Learning Goal: As a mathematician, I can Connect multiplication generalizations to create equivalent fractions
- Step 1: Look for multiplication patterns when generating equivalent fractions with models
- Step 2: Develop and use multiplication (by a fraction equal to 1) as a strategy when generating equivalent fractions
GCG 3: Learning Goal: As a mathematician, I can Use models and symbols to compare fractions