The purpose of this activity is for students to compare two fractions and identify which is greater in ways that make sense to them. Previously, students classified fractions based on their relationship to and 1 (whether they are less than or greater than these benchmarks). Students used these classifications to compare fractions. In this activity, students are presented with fractions that are in the same group (for example, both less than , or both greater than but less than 1), so students need to reason in other ways to make comparisons.

Monitor for and select students with the following approaches to compare fractions in Group 2 to share in the Activity Synthesis:

• Draw number lines or tape diagrams and reason informally about equivalent fractions.
• Use the distance of each fraction from 0, , or 1 to reason about the relative size.
• Reason about equivalent fractions numerically by writing out the multiplication.

The approaches are sequenced from more concrete to more abstract to support students as they compare fractions. Although students may compare in a number of ways, focus the discussion on the ways students relied on the idea of equivalence. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently. For an example for each approach, see Student Responses.

Representation: Internalize Comprehension. Activate background knowledge. Invite students to review the strategies they know for comparing fractions (reasoning about denominators or numerators, comparing to a benchmark, and writing equivalent fractions). Record students’ strategies on a visible display, including details (words or pictures) that will help them remember how to use the strategy.
Supports accessibility for: Conceptual Processing, Memory, Attention

• Invite previously selected students to share their reasoning about fractions in Group 2 in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “How are the ways of comparing the fractions the same?” (We had to find a way to deal with the different denominators.)
  • “How are they different?” (Some ways involved thinking about how close or how far away from 1 each fraction is. Other ways involved reasoning with equivalent fractions, and some showed the multiplication to write equivalent fractions.)
  Connect students’ approaches to the learning goal by asking:
  • “How does understanding equivalent fractions help you compare fractions that don’t have the same denominator?” (We could change one fraction so it had the same denominator as the other fraction. Then it was easier to compare them.)

The purpose of this activity is for students to compare pairs of fractions by writing one or more equivalent fractions. In all pairs of fractions given here, one denominator is a factor or a multiple of the other, which encourages students to convert one into an equivalent fraction with the same denominator as the other fraction. On repeated reasoning, students see that writing an equivalent fraction can facilitate the comparison (though in some cases, students may still find it efficient to reason in other ways).

This is the first time in IM Grade 4 that students use the symbols and to express comparisons, so some supports for reading aloud inequality statements are suggested in the Launch.

• Select students to share their responses and how they reasoned about the comparisons.