After this lesson, students will be able to compare fractions with different numerators and denominators. Students will be able to record the results of fraction comparisons with symbols >, =, or <, and justify the conclusions.
Introduction (15 minutes)
- Call students together as a group and ask them if they have ever played the card game War before. For students who have never seen this game previously, quickly demonstrate the game by dividing a deck of cards in half between two students. Have the two students pull the top card off their half of the decks and declare the winner of the hand to be the student with the higher numbered card.
- Explain that today students are going to be playing this game with fractions. They will be playing Fraction Wars.
- In order to play this game, students will need to make fraction playing cards. Brainstorm as a group some fractions students might want to include in their decks. (Possibilities include: 1/2, 1/3, 1/4, 3/8, etc.) List some common fractions up on the board, such as 1/2, 1/3, 1/4, for students as they create their fraction cards.
- Pass out index cards or squares of scrap paper along with pens/pencils to students, so that they can make their cards.
Explicit Instruction/Teacher Modeling (20 minutes)
- After students have finished making their fraction cards, call them back together as a group.
- Remind students that when deciding the winner in a fraction war, they must know which fraction is larger. Ask students, “What are some different ways to determine which fraction is larger?”
- Once students have offered various suggestions, point out to students that drawing pictures can be a quick way to visually compare two fractions.
- Another way to quickly compare two fractions is to compare them to a benchmark fraction. For example, if students need to compare 1/4 and 5/8, they know that 1/4 is less than 1/2, and 5/8 is greater than 1/2. Thus, 5/8 must be larger.
- A third possibility might be to create the same denominator. For example, when comparing 1/2 and 3/8, students might realize that 1/2 is greater, because 1/2 is the same as 4/8, and 4/8 is more than 3/8. Encourage students to be creative and keep thinking of other ways to determine which fraction is larger.
- Remind students that a number can be greater than, less than, or equal to another number. The same is true with fractions. They should already very familiar with the equal sign (=), which is used to show two numbers are equal.
- Since students have probably had less exposure to the greater than (>) and less than (<) signs, remind them to think of the symbols as an alligator’s mouth. The mouth wants to eat the bigger number, so it always is open on the side of the bigger number.
- Tell students that they are ready to play the game. Explain to students that they will be recording their games.
- Pass out sheets of lined paper. Have students create 3 columns, and label the top of each: My Fraction, My Partner’s Fraction, and Justification.
Guided Practice/Interactive Modeling (10 minutes)
- Demonstrate a round of the game for students by having two students pull a card from the top of their fraction deck. Have the class record these fractions on the first line of their papers under the columns My Fraction and My Partner’s Fraction.
- As a class, determine which fraction is greater, or if the two are equal, and place the appropriate sign between the two columns. Together, in the Justification column, draw a picture of the two fractions or write a brief explanation proving why one fraction is greater than or equal to the other.
- Play another round of the game using the same process, but this time chose student volunteers to demonstrate how to fill in the chart. Have the volunteers determine which fraction is greater, and show sample justifications for their reasoning.
- If students feel comfortable with the game and how to record their work, students can move on to independent working time. Otherwise, continue playing a few more rounds of the game with student volunteers.
Independent Working Time (20 minutes)
- At this point, students should be broken-up into partners to play the game.
- Remind the class that they must record their fraction wars and justify how they knew a fraction was greater than, less than, or equal to another. They will be sharing this information with the class later
- Tell students that each pair of partners must agree on which fraction wins the fraction war.
- While students play, float around the classroom to check in with students individually and correct any misunderstandings.
- Enrichment: For students in need of a greater challenge, creating groups of three where three fractions instead of two are being compared can increase the difficulty. Students can also be required to justify their answers in more than one way (ex. through both a words and pictures).
- Support: For students who need a little extra help, being paired with a student who has a greater understanding of fractions can offer the opportunity for peer assistance/scaffolding. Having students draw a visual of the fractions on the back of their cards can help students to more quickly and easily visually compare the fractions, too. Limiting the activity to more common fractions is also an option.
Assessment (10 minutes)
- To assess student understanding during the course of the lesson, float around the room while students are playing the game with partners. This allows for brief check-in assessments with students to determine whether they are actually understanding the concepts.
- At the conclusion of the lesson, collect students’ written game records to determine if there are errors using symbols, or an inability to justify the comparisons. Looking over these sheets can provide insight into whether the class as a whole is struggling with understanding something, if individual students have some misconceptions that should be corrected, or if everyone is on the right path.
- Assign students to play 10-15 hands of Fraction Wars at home for homework, completing a written game record. This provides another opportunity to monitor individual student progress and understanding.
Review and Closing (15 minutes)
- Call students together as a group. Tell them that they are going to have the opportunity to share about their experiences playing Fraction Wars.
- Ask the group: Were there any fractions you had a hard time comparing? If so, how did you figure it out? What are some different ways you justified your answers? Did two partners ever disagree? If so, what methods did they use to come to an agreement?
- Before students are done, remind them that there are three different signs used to compare fractions: greater than (>), less than (<), and equal to (=). Remind them that they can keep these signs straight if they think about how the open side of the mouth always wants to eat the bigger number. Encourage students to use pictures and comparisons to benchmark fractions when comparing two fractions.