EL Support Lesson
Visually Multiplying Fractions
Students will be able to multiply fractions using an area model.
Students will be able to review their thinking as they multiply fractions using color-coding and area models.
- Tell students you went to a party and you have ⅔ of your cake left. Ask them to draw a tape diagram on a piece of scrap paper that represents how much cake you have left over.
- Observe student work to gather information about their ability to represent fractions pictorially and whether they can solve the problem. Have students share their pictures with their partners.
- Tell them that you brought the remaining cake to the teacher's lounge and ½ of it fell down on your way there.
- Give them a minute to think about how to figure out how to find out the remaining amount of cake using their tape diagrams. Have them write notes on the Review Your Thinking! worksheet. (Note: they're not expected to know the answer yet, but this is a good way to gather background information on how familiar they are with fractions and representing them in pictorial models.)
- Explain that during the lesson they'll learn how to make fractional parts of fractions to figure out what is remaining using area models. In this case, they'll find out what fraction of your birthday cake is left over.
Explicit Instruction/Teacher modeling(6 minutes)
- Model how to solve the multiplication problem (i.e., ½ × ⅓) using an area model and note the similarities and differences between an area model and tape diagram (e.g., tape diagrams show one fraction, while area models show two, etc.).
- Explain that the length of the rectangle should represent ⅔ of the cake left over and should have the rectangle split vertically into thirds, with two of the three pieces shaded in. Then the width should represent ½ of the cake that fell. The rectangle should be divided horizontally in half with one half shaded. The shaded pieces that overlap represent the numerator and the total pieces in the whole rectangle represent the denominator (i.e., 2/6, or ⅓ when simplified).
- Distribute and read the vocabulary card for area model and have students read the definition and copy your teacher markings from the board onto the back of their vocabulary card for the term "area model." Also, create a multiplication equation for the visual on the front of the area model vocabulary card (i.e., ½ × ⅓ = ⅙) and label the sides of the area model with the correct fraction.
- Explain that the visual of the area model represents the multiplication of fractions. The word problem asked students to determine a fractional piece of another piece. The keyword that showed multiplication in this case was "of." Tell them that the word "of" tells us we need to multiply because it is showing there is a fractional part of a different fractional part.
- Ask a student to paraphrase the process you used for solving the cake problem aloud to the class. Allow other students to add to the explanation as necessary.
Guided Practice(7 minutes)
- Display the A Fraction of a Wall worksheet and ask students to think about how they would solve problem #1. Then, ask them to think about what operation they will use and why.
- Have them write their thoughts on the first cell of the Review Your Thinking! worksheet and then turn and talk to their partners about their strategy. Before they separate into partners, model answers using the following sentence frames:
- "I hadn't considered that ____."
- "This makes me realize that ____."
- Have volunteers share their ideas on how to solve the problem. Allow other students to correct misconceptions. Make sure everyone has an idea on how to solve the problem before allowing them to break off into groups to solve it.
- Ask volunteers to share their area models.
Group work time(12 minutes)
- Tell students to recount how they solved the problem about the fallen cake and the A Fraction of a Wall problem. Now, have them talk in partners and reassess their understanding from the beginning of the lesson on the Review Your Thinking! worksheet. Allow them to discuss their new ideas about solving area models for fraction multiplication and write them down in the middle cell.
- Assign them Problem #2 from the A Fraction of a Wall worksheet and read the problem aloud. Then, give the students one minute to think about how they will solve the problem. Allow volunteers to share their ideas aloud and then have them solve the problem on their own.
- Choose volunteers to share their work with the class and solve the problem for the class. Correct any misconceptions and model using the sentence frames written on the board to model reviewing your thinking about area model multiplication with fractions and its applicability to real-world situations. For example, "I didn't realize that all rectangles in the real world could be area models too," or "I hadn't considered that I would have to solve a subtraction problem to find the wall space left to paint before I solved the multiplication problem."
Additional EL adaptations
- Allow students to use their home language (L1) or their new language (L2) in all discussions.
- Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
- Provide reference materials in their L1 to assist in their vocabulary word acquisition.
- Allow them to color-code the area model and use folded paper to further emphasize the overlap with the fractional pieces. Cut out the pieces too if necessary.
- Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
- Ask them to consider what happens to the denominator as they multiply the fractions and have them make suggestions as to why the denominator gets bigger.
- Challenge them to create their own real-world problem involving multiplication that does not immediately suggest students should multiply the given fractions.
- Refer to the last cell of the Review Your Thinking! worksheet and ask students to write down one thing they learned from the lesson and something they still wonder about the topic. Provide the following sentence frames:
- "I learned ____."
- "Before I thought ____, now I think ____."
- "I wonder ____."
Review and closing(5 minutes)
- Allow one student to share their assessment information and allow the other students to answer the presenter's question.
- Ask students to consider if area models can help them solve larger fractions, for instance 14/27 × 4/19. Have them consider the challenges and benefits involved.
- Explain that area models are great when you have to multiply smaller fractional units, but they can get more difficult as the denominator gets larger because the amount of pieces of the whole increase. Tell students that area models can help them visually understand the math behind multiplying fractions, but they'll soon learn a faster way to solve the problems.