Adding Fractions on Number Lines
Students will be able to add fractions with unlike denominators using a number line.
- Provide a scenario for the students that involves 4/5 + 1/5. For example, say, "There are two pies. Four-fifths of the pie left over is apple and one-fifth of the pie left over is pumpkin. 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, and have them show whatever drawings they created.
- Ask for a volunteer to come to the board and solve the problem using a number line.
- Tell students that today they'll build on their understanding of adding fractions with like denominators to add fractions with unlike denominators.
Explicit Instruction/Teacher modeling(10 minutes)
- Remind students that the denominator is the bottom number of a fraction and represents the total number of pieces of the whole, while the numerator is the top number and represents some of the parts of the whole (e.g., two-fifths represents 2 pieces of the total 5 pieces).
- Write 2/7 + 3/14 on the board. Say, "The students have collected 2/7 of the total amount of money they need to go to the field trip. An anonymous donor gives them 3/14 of the total they need. How much money do they have so far for their field trip?"
- Explain that the denominator is different so they cannot add the numerators 2 and 3 together. Tip: draw a number line of 2/7 and 3/14 to show that the total parts, or whole (i.e., denominator), is different. If they added 3/14 to 2/7 it would add too much.
- Think aloud finding multiples for the denominators 7 (e.g., 7, 14, 21, 28, etc.) and 14 (e.g., 14, 28, 42, 56, etc.) and write them on the board. Explain to students that a multiple is the result of multiplying a number by an integer (e.g., 4 x 4 = 12 where 12 is the multiple).
- Consider the list of multiples and then circle the least common multiple, or the smallest multiple they have in common (i.e., 14). Then, think aloud how to change the 7 in the denominator to 14 (i.e., multiplying 7 by 2) and multiply by the number 2 on the top and bottom so that you get a new expression of 4/14 + 3/14.
- Draw the addition problem on a number line and model how to add the fractions together. Always ask if the problem can be simplified. Compare the final answer to what the answer would have been if you added the fractions using unlike denominators.
Guided Practice(25 minutes)
- Ask students to turn and talk to their elbow partners about why it's important to change the denominators so that they are the same. Write some of their responses on the board.
- Provide a scenario for the students that involves 3/4 + 1/2. For example, say, "You are going to make a cupcake recipe and you want to know the total amount of dry ingredients that will be in the bowl. You have 1/2 cups of sugar and 3/4 cups of flour. How many cups of dry ingredients are in the bowl so far?"
- Ask students to work in partners to draw a visual to represent the equations on their whiteboards. Then, ask them to solve the problem using their whiteboards. Allow them to share their answers with new partners, and adjust their answers as necessary. Finally, choose volunteers to share their own answer with the class and explain their process.
- Have a volunteer explain how to add fractions when they have different denominators. They should understand the following steps:
- Check to make sure the denominator is the same.
- If the denominators are not the same, find the least common multiple for the denominators.
- Multiply the denominators and numerators by the same number that will make the denominator equal to the least common multiple.
- Add the fractions using a number line.
- Write the steps on the board for students to reference as they work with their partners to complete the Fraction Word Problems: Adding with Unlike Denominator worksheet. Distribute copy paper to show their work using a number line.
- Choose students to share their answers aloud.
Independent working time(13 minutes)
- Distribute the Fraction Action: Adding with Unlike Denominators worksheet and ask students to complete the problems on their own. Remind them to use the steps written on the board if they get stuck and do not know what to do next. Have them use their copy paper to draw their number lines.
- Allow one student to share a problem and ask the other students to critique the process the presenter used to add the problem. Review the rest of the answers with the class and offer corrections and support as necessary.
- Ask students to add fractions with like denominators before adding fractions with unlike denominators. Use the Add Fractions on a Number Line worksheet or the Adding Fractions with the Same Denominator exercise as support.
- Have students multiply the denominators by each other and then do the same to the numerators instead of finding the least common multiple. For example, with 2/3 + 1/4, you can multiply the numerator and denominator in two-thirds by the number 4 and multiply the numerator and denominator in one-fourth by the number 3 to get a new equation of 8/12 + 3/12.
- Allow them work in a small, teacher-led group with manipulatives as they create their common multiples and add the fractions. Have them use manipulatives to represent the fractions they're adding.
- Provide sentence frames and a key words list for the student explanations throughout the lesson.
- Pair students with struggling learners and ask them to explain their process to them.
- Have them create fraction word problems and switch with another student. Then, have them solve each other's word problems.
- Use the Adding Fractions with Unlike Denominators exercise for additional practice with adding fractions.
- Challenge students who are ready to work with mixed numbers to complete the worksheet Running with Word Problems: Practicing Adding Mixed Number Fractions instead of the worksheet Fraction Action: Adding with Unlike Denominators. Pair off students that completed the same activity. Allow students who worked with the mixed numbers to present one problem where they model how they added on the number line.
- Write the following word problem on the board and ask students to solve it on their copy paper: "Margot has 1/2 of her bookshelf empty. She wants to fill an additional 1/3 of the bookshelf. How much of the bookshelf is full?"
- Assess students on their ability to create fractions with the same denominator and then add the total. If students struggle to create an expression, create the expression for them after drawing a picture to represent the problem. Then, have them solve the equation using their number line to show their answer.
Review and closing(2 minutes)
- Ask students to explain why it's important to only add fractions that have the same denominators.
- Explain that understanding how to add simple fractions correctly will help them when they have to add mixed fractions.