standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
This optional activity allows students to practice adding tenths and hundredths (and to reinforce their ability to compare fractions) through a game. Students use fraction cards to play a game in groups of 2, 3, or 4. To win the game is to draw pairs of cards with the greater (or greatest) sum, as many times as possible.
Consider arranging students in groups of 2 for the first game or two (so that students would need to compare only 2 sums 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 add.
Required Materials
Materials to Copy
Fraction Action: Tenths, Hundredths
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2 for the first game or two, then groups of 3–4 for subsequent games, if time permits
Give each group one set of fraction cards from the blackline master.
Tell students that they will play one or more games of Fraction Action.
Demonstrate how to play the game. Invite a student to be your opponent in the demonstration game.
Read the rules as a class and clarify any questions students might have.
Activity
“Play one game with your partner.”
“As you play, you may come across one or more pairs of fractions whose sums are hard to find. Record those fractions. Be prepared to explain how you eventually figured out which sum is greater.”
“If you finish before time is up, play another game with the same partner, or play a game with the players from another group.”
15 minutes: group play time
Student Facing
Play Fraction Action with 2 players:
Shuffle the cards from your teacher. Place the cards in a stack, face down.
Each player turns 2 cards over and adds the fractions on the cards.
Compare the sums. The player with the greater sum wins that round and keeps all four cards.
If the sums are equivalent, each player turns one more card over and adds the value to their sum. The player with the greater new sum keeps all cards.
The player with the most cards wins the game.
Play Fraction Action with 3 or 4 players:
The player with the greatest sum of fractions wins the round.
If 2 or more players have the greatest sum, those players turn two more cards over and find their sum. The player with the greatest sum keeps all the cards.
Record any pair of fractions whose sum is challenging to find here.
________ and ________
________ and ________
________ and ________
________ and ________
Student Response
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Activity Synthesis
Invite groups to share some of the challenging expressions they recorded and how they eventually determined the sums.
As one group shares, ask others if they have other ideas about how the fractions could be added.


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