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This Number Talk encourages students to think about multiples of 5, 6, and 12—numbers that students will see as denominators later in the lesson. It also prompts students to rely on doubling and on properties of operations to mentally solve multiplication problems. The reasoning elicited here will be helpful later in the lesson when students compare fractions by finding equivalent fractions with a common denominator.
To find products by doubling or by using properties of operations, students need to look for and make use of structure (MP7).
Find the value of each expression mentally.
Fraction Cards with Denominators 2, 3, 4, and 6
Fraction Cards with Denominators 5, 8, 10, 12, and 100
This activity allows students to practice comparing fractions and apply the comparison strategies they learned through a game. Students use fraction cards from an earlier lesson to play a game in groups of 2, 3, or 4. To win the game, a player must have the greater (or greatest) fraction of the cards played as many times as possible. This is Stage 6 of the Compare center.
Consider arranging students in groups of 2 for the first game or two (so that students would need to compare only 2 fractions at a time), and arranging groups of 3 or 4 for subsequent games. Before students begin playing, ask them to keep track of and record pairs of fractions that they find challenging to compare.
Play Compare Fractions with 2 players:
Play Compare Fractions with 3 or 4 players:
Record any sets of fractions that are challenging to compare here.
_________ and _________
_________ and _________
_________ and _________
_________ and _________
This activity prompts students to compare multiple fractions and put them in order by size. The work gives students opportunities to look for and make use of structure (MP7) in each set of fractions and make comparisons strategically. For instance, rather than comparing two fractions at a time and in the order they are listed, students could first classify the given fractions as greater or less than or 1, look for fractions with a common numerator or denominator, and so on.
If time is limited, consider asking students to choose two sets of fractions to compare and order.
Put each set of fractions in order, from least to greatest. Be prepared to explain your reasoning.
Invite students to share their strategies for comparing and ordering the fractions in the last activity. Record their responses.
Ask students to reflect on their understanding of fractions in this unit.
“What are some things about writing, representing, or comparing fractions that you didn’t know at the beginning of the unit but you know quite well now? Think of at least two specific things.”
We compared fractions using:
Example: To compare and , we can reason that:
We can also compare by writing equivalent fractions with the same denominator, or a common denominator. For example, to compare and , we can use 12 as the denominator:
Because is greater than , we know that is greater than .