Unit Fraction Division

Transcription

1 Unit Fraction Division Student Probe What is 5? 3 Answer: 5 A common misconception would be that the students over-generalize their understanding of multiplication and their solution would be 5 3. Lesson Description This lesson is intended to help students develop an understanding of division of whole number and fractions. The lesson will focus on using the number line as a tool for students to develop the conceptual foundation to help them connect the computation to division of whole numbers. Rationale Students are most proficient at applying computational procedures when they understand why those procedures make sense. Although conceptual understanding is foundational for the correct use of procedures, students often are taught computational procedures with fractions without an adequate explanation of how or why the procedures work. (IES, 00) Preparation Prepare copies of Fraction Number Line and provide blue and red markers for each student. At a Glance What: Division of whole number by unit fraction. Division of unit fraction by a whole number Common Core State Standard: CC.5.NF.7a. & CC.5.NF.7b. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (a) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. (b) Interpret division of a whole number by a unit fraction, and compute such quotients. Mathematical Practices: Model with mathematics. Attend to precision. Look for and make use of structure. Who: Students who have difficulty with division of fractions Grade Level: 5 Prerequisite Vocabulary: quotient, expression, equation, divisor, dividend, value Prerequisite Skills: multiplication and division of whole numbers Delivery Format: Individual, small group Lesson Length: 5 to 0 minutes Materials, Resources, Technology: Visual display, two- color counters, Fraction Number Line Student Worksheets: Fraction Number Line

2 Lesson The teacher says or does. Jack hiked 8 miles with his friends. They stopped to rest every miles. How many rest stops did they have?. What kind of operation did you use to get to the solution? 3. Can anybody model this process using the number line?. So 8 =. (Note: Write this equation on the board.) We are looking for how many s we can measure in 8. Sometimes we say this as how many times goes into If Jack and his friends rested every half mile, how many times did they rest? (Encourage the students to use the number line initially to visualize the process.) Write on the board: 8 6 (Help the students to connect the equation to the visual representation.) 6. If Jack and his friends rested every quarter mile, how many times did they rest? (Students may require more practice to reinforce this part of the lesson before proceeding.) rest stops. Division Model measuring by s on the number line times. Refer to Multiplying and Dividing Whole Numbers. Model If students are unable to see the - s or groups of, use the diagram in Teacher Notes, or cut out a inch strip and iterate across the number line. 6 Use a half inch strip or a color marker and count the number of times you are able to iterate the half inch unit across 8. You may want to share that there are 6 groups of units each. This will connect to their understanding of the relationship of multiplication and division. 3 Be prepared to have quarter inch strips and assist students to iterate the strips to show the number of groups.

3 The teacher says or does The next part of the lesson uses partitive division. Students will be asked to find the size of each group, rather than the number of groups. Encourage students to use the number line to help in working out the given situations. 7. Jack and his friends travelled 8 miles and they stopped times, including their final stop for the day. How far did they travel before their first rest stop? (Assume they travelled the same distance between stops.) Write on the board: 8 miles Cut out a strip, folding it into fourths, to show equal lengths. (Help the students to connect the equation to the visual representation.) 8. Jack and his friends had to travel mile. They stopped and rested times, including their final destination. How far did they travel before their first rest stop? (Assume they travelled the same distance between stops.) (Use the number line with If students continue to have difficulty, proceed to Step 9. If not, skip Step 9 and proceed to Step 0. quarters to show cut into equal groups.)

4 The teacher says or does 9. We want to divide. (Cut a strip from a sheet of paper and fold it in half (hamburger fold). Place a large X on one of the sides. Show students the of the paper with the X on it.) What fraction of the original strip do you see? Let s divide this half sheet into equal parts. (Fold so the X is showing. Put a star on one of the sides after you fold. Now open the sheet.) How many sections do you see? How many of the sections have a star? There is a star on one of the four sections. What part of the paper does that represent? 0. Write on the board: Help the students to connect the equation to the visual representation.

5 The teacher says or does. Jack and his friends travelled ½ mile and they stopped and rested times, including their final destination. How far did they travel before their first rest stop? (Assume that they travelled the same distance between stops.) (Use the number line with quarters to show divided into equal groups.). Write on the board: 8 8 We are now splitting the ½ into equal groups. We are looking for how many parts are in each group. Help the students to connect the equation to the visual representation. Teacher Notes:. Teachers should take the time to provide such explanations and to emphasize how fraction computation procedures transform the fractions in meaningful ways. In other words, they should focus on both conceptual understanding and procedural fluency and should emphasize the connections between them. The panel recommends several practices for developing understanding of computational procedures, including use of visual representations and estimation to reinforce conceptual understanding. Addressing students misconceptions and setting problems in real-world contexts also can contribute to improved understanding. (IES, 00). If using Step 9, move slowly and deliberately to ensure that students recognize the whole and of the whole.

6 Formative Assessment Find the following quotients: Answers: 8,, 8 Reference Mathematics Preparation for Algebra. (n.d.). Retrieved August, 0, from Doing What Works.