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Fractions and Word Problems
Students will be able to solve fraction word problems with tape diagrams.
- Provide a scenario for the students that involves 3 − 1 5/8. For example, say, "There were three pies. The students ate 1 5/8 of the pies. How much pie is left over?" Ask students to solve for the problem on their whiteboards using whatever method they choose.
- Have students share their answers with their elbow partner. Gather their background knowledge by asking them questions about the numerator, denominator, and how they got their answer. Then have them show whatever drawings they created.
- Ask for a volunteer to come to the board and solve the problem using a tape diagram. Remind students that a tape diagram, or bar model, is a visual model that use rectangles to represent the parts of a whole.
- Tell students that today they'll show their understanding of fractions by solving word problems that involve fractions.
Explicit Instruction/Teacher modeling(8 minutes)
- Explain to students they'll focus on reading the problem, drawing a tape diagram to show their understanding of the problem, and writing about their answer. Display the Selling Fractions worksheet and think aloud your observations about the worksheet.
- Fold a sheet of copy paper so that it has six boxes total with three boxes in each row when you hold it horizontally. Students can do each of the steps (i.e., draw, write an equation, write a sentence) in its own box. (Note: these will be multi-step word problems so they will need one row of boxes for the first equation and another row for the second equation.)
- Model reading the problem more than once and circling key information within the problem (e.g., "whole lemon meringue," "3/4 apple," "1/4 apple price," "1/8 apple price"). Then, draw a tape diagram in the first box of the copy paper that represents the information given in the problem (e.g., two tape diagrams that represent the two different pies divided into fractions according to the amount bought).
- Write an expression or equation about the given information. (For example, if 1/2 + 1/8 + 1/8 = 3/4 of an apple pie, then $6 + $1 + $1 = $8 total cost for the apple pie; the second equation would be $12 lemon meringue + $8 apple = $20 total amount spent.)
- Solve the problem in the drawing and equation boxes, and then for the last box write a sentence about the answers.
Guided Practice(15 minutes)
- Ask a student to recap the process you used to solve the first problem. Then, have students talk you through step-by-step how to solve the next problem about how much money Brett spent on his pieces of pie. Then, discuss how you can get two different prices (i.e., based on the menu prices, if you add up 1/8 five times you will pay $5 for 5/8 of the pie, but if you add the price for 1/2 of a pie and then add an additional 1/8 piece of pie price, you will pay $7). Emphasize that in these cases the work they show is crucial to prove their answer and explain their processes.
- Have them turn and talk to their elbow partner about the steps they need to follow to solve the problems on their own. Ask for a volunteer to discuss the steps needed to solve the problems (i.e., read, draw, write an expression/equation, write a sentence). Write the steps on the board for them to follow as they work on their problems in pairs.
- Have students work together with the problems involving Brett, Lulu, and Timothy in the Selling Fractions worksheet. Monitor their progress and make sure they are following the reading, drawing, and writing steps you've laid out for them.
Independent working time(15 minutes)
- Ask students to complete the rest of the Selling Fractions worksheet on their own. Have them follow the three steps (i.e., read, draw, and write about the problem) to show their understanding and thought process.
- Allow students to share their answers with their partners once they've completed the problems. Make sure they can explain how they've solved the problems. Choose one to three students to share their answers, drawings, and explanations.
- Allow students to use manipulatives and any method they choose to solve their word problems (e.g., tape diagrams, number lines, bar models, etc.).
- Review equivalent fractions and how to solve them by finding the least common multiple or multiplying the denominators by each other.
- Provide sentence frames and a keywords list for the student explanations throughout the lesson.
- Provide word problems that are relatable to them and that they can visualize or draw easily.
- Read the word problems for the students a few times and then allow them to work on solving the problems on their own.
- Pair them with struggling learners and ask them to explain their process to the students.
- Allow them to work on the Strawberry Fractions worksheet for their formative assessment.
- Have them create their own fraction word problems and switch with another student. Then, have them solve each other's word problems. Make sure they include mixed numbers and three or more fractions in their word problems.
- Distribute the Multi-Step Fraction Word Problems worksheet and ask students to complete the problems on their own. Have them use their copy paper and number their problems so they can easily identify their work.
- Have them read the problem, draw a picture to show their understanding of the information, write an equation/expression, solve the problem, and then write a sentence about the solution.
Review and closing(5 minutes)
- Review some of the questions from the assessment based on students' responses. Ask for volunteers to share their processes.
- Ask students to share with their partners the benefits or drawbacks for drawing and writing about their answers. Have a few students share their ideas.
- Explain that sometimes drawing and writing about an answer can challenge them to fully understand their answer, and may even encourage them to change their answer so that it makes more sense.