## What to Do with Leftovers

### Monica Napier

#### Description

Students use unifix cubes to explore division with remainders to solve real world story problems.

#### Objectives

The student explains and demonstrates the meaning of division and of remainders (for the repeated subtraction and partitive models) using manipulatives, drawings, number sentences, and story problems.

#### Materials

- Copy of the book A REMAINDER OF ONE by: Elinor J. Pinczes, 1987, New York, Scholastic
- 24 bags of Unifix Cubes with 50 cubes in each bag
-Work Mat ( 12X18 sheets of construction paper - one for each student) Students will write problems and draw on this work mat after solving problems with cubes.
-Pencils
-Copy of Dare To Divide Division Word Problems Transparency and Key (associated file)
-Copy of the worksheet But I Have Some Left Over and Key (associated file)
-Copy of the Rubric (associated file) See Web Links Site Teach-nology for Rubric Maker

#### Preparations

1. Prepare the Dare To Divide Division Word Problems transparency for the overhead.

2. Place 50 unifix cubes into each recloseable plastic bag. Prepare enough bags so that each student will have a bag.

3. Download the Rubric from the associated file and make one copy for each student.

4. Download the activity sheet, But I Have Some Left Over from the associated file and make one copy for each student.

5. Download the Dare To Divide Division Word Problems sheet and make a transparency.

7. Count out sheets of 12X18 construction paper, one for each student that will be used as work mats.

#### Procedures

1. Review previous concepts:
Fact Families
Divison as Sharing
Division As Subtraction
Parts of a Division Problem (divisor,dividend, quotient)

2. Read the book titled A REMAINDER OF ONE by: Elinor J. Pinczes

3. Discuss the story and the concept of division with remainders.

4. Encourage the students to share a time when they tried to divide into equal groups for an activity or a game. Ask students what happened and discuss answers as students respond.

5. Explain that today the class will use unifix cubes to show how to divide to solve real world story problems.

6. Use Dare To Divide Division Word Problems transparency (see associated file) on overhead. Call on a student volunteer to read the first problem aloud. Use the unifix cubes on the overhead projector to model how to divide the total number of cubes (dividend) into groups to get the correct quotient. Discuss that sometimes when you divide you have leftovers or remainders. Discuss what you should do with the leftovers or remainders. Explain how the students will be assessed . Show the transparency of the Rubric.

7. Model the second problem using the unifix cubes. Model how to write the division problem correctly with the division sign, dividend, divisor, and quotient. Model how to write this vertically (long division). Call on a student to reread the problem and ask the student to tell in his/her own words the answer to the question in the problem. Model how to write in words the answer to the problem. Model how to draw a picture of the groups of unifix cubes that were used to show the answer to the second problem. Model how I will use the Rubric with the students. (see associated file for the Rubric)

8. Call on a student to tell in his/her own words how the unifix cubes were used to solve the second word problem. Call on a student to tell in his/her own words why the total did not divide equally and what was left over. Ask the class what you could do with what was left over.(Remainder).

9. Distribute activity materials (unifix cubes, work mat, But I Have Some Left Over activity sheet.)

10. Instruct students to solve problems #3,#4 and #5 from the transparency on their work mat using their unifix cubes. After solving the problem using the cubes, they should then write the problem down on their work mat correctly using the division sign, dividend, quotient, and divisor. Each student will model, draw, write the problems and an explanation of the answer on the work mat. Circulate and use the rubric to assess mastery of the skills.

11. After each student has completed mastery of problems #3,#4 and #5 they should complete the activity sheet titled “But I Have Some Left Over.” Students should use the unifix cubes to help them solve the problems. Problems should be completed on the activity sheet. Students do not need to draw the model. They do need to show the correct way to write the division problem with all the parts and write the answer to the question in own words. (Continue to circulate and complete a rubric on each student to assess mastery of skills on the problems from the transparency during the student work time)

12. Check the activity sheet “But I Have Some Left Over” as a whole class. (Key found in associated file) Discuss any problems the students may have encountered. Review the term “Remainder” during this time.

13. Collect the papers and the work mats to check for mastery of skills.

#### Assessments

Observe the students' performance while solving simple division problems with cubes to determine the students' ability to correctly divide the total number of cubes into the correct number of groups with the correct number of cubes left over as the remainder.

Use completed chart to formatively assess the student’s ability to:
-use unifix cubes to solve real world problems.
-write the correct answer to the question in words.
-draw a picture of the model of cubes used to solve problem.
-write the division problem correctly with the dividend, divisor, quotient, and remainder (vertically long division.)

#### Extensions

1. The ESE or ESOL student may only be required to show how to divide with the cubes and draw the model.

2. Ask students to explain the answers to the word problems to a partner.

3. Students may work with a partner in a cooperative manner to solve word problems and complete activity sheet.

4. Students may write their own word problems, exchange with another student and solve each other’s word problems.

5. Students may make up word problems to act out in front of the class.