Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (64 page)

Activity 2: Modeling Division

Students will use virtual manipulatives and rectangular arrays on a Web site to model division.

Materials

Computers with Internet access for students; computer with Internet access and digital projector for the teacher.

Procedure

1.
Instruct your students to go to
http://nlvm.usu.edu/
. They should click in the grades “3–5” column on the “Numbers and Operations” row and then scroll down to and click on “Rectangle Division.” They will see a division array and information on the right side of the screen explaining a division problem.

2.
Demonstrate how this Web site works. Start by working with the 10-by-10 grid and click on “Show Me.” Explain that students can change the divisor to model a division problem by moving the button on the left up or down. They can change the dividend on the lower right by clicking on either the up button or the down button. Note that the array adjusts to model the problem. Information is provided on the right side of the screen.

3.
Choose a problem to discuss as a class, such as
. Students should already know that the quotient is 7. Explain that the rectangular array shows that there are 7 groups of 5 in 35, with nothing left over. This division problem is linked to multiplication by showing that
.

4.
Instruct your students to create another problem, such as
, which is asking how many groups of 9 are in 35. Tell your students to move the button on the left side of the screen to 9 and make sure that the dividend is 35. This creates a 9 by 3 rectangular array. Explain that this array represents 3 groups of 9 within 35. Note that there are also 8 squares shaded in a different color. These 8 squares represent the remainder. Relate this division problem to its multiplication problem:
.

5.
Explain to your students that they are to complete at least 10 problems. They should click on “Test Me” on the bottom of the screen and the computer will generate a new problem. (
Note:
Depending on the problem, the array and grid will automatically change. Clicking on a different grid will change the problem.) Students are to change the dimensions of the array by changing the divisor according to the problem. Then they should consider the array, and complete the problem on the right by filling in the empty boxes. When they click on “Check,” the computer will check their answer. They can move on to another problem by clicking on “New Problem.” As students work, they should record their problems and answers for the discussion during Closure.

Closure

Discuss the activity. Ask students what problems they found to be difficult. Have a few students share their hardest problems.

Finding Dividends, Divisors, and Quotients

Number and Operations in Base Ten: 5.NBT.7

“Perform operations with multi-digit whole numbers and with decimals to hundredths.”

7. “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.”

Background

The procedures for adding, subtracting, multiplying, and dividing decimals are similar to the procedures for performing the basic operations with whole numbers, with the exception of placement of the decimal point. To master these operations, an understanding of place value is essential.

Activity 1: Place Value, Addition, and Subtraction of Decimals

Working in pairs or groups of three, students will write addition and subtraction problems involving decimals, based on specific instructions and place values.

Materials

Scissors; glue sticks; unlined paper; reproducibles, “Build a Problem” and “Number Cards,” for each pair or group of students.

Procedure

1.
If necessary, review the procedures for adding and subtracting decimals. Also, your students might find a review of place value helpful.

2.
Hand out copies of the reproducibles. Explain that “Build a Problem” contains instructions for building six problems: three decimal addition problems and three decimal subtraction problems. The instructions are based on place value. Cards containing numbers are on the reproducible, “Number Cards.” These cards contain the numbers students will use to create the problems, as well as the answers to the problems. Note that each problem requires three cards: two cards for the problem and one card for the answer.

3.
Explain that students are to cut out the cards. After cutting out the cards, they should match the cards to create problems and answers that satisfy the instructions. Caution them to start with the first problem and work in order. After they have created a problem, they should place the numbers that make up the problem, including its answer, on their unlined paper. They should include +, −, and = signs as necessary. After they have “built” all of the problems, they should glue the numbers and answers that make up each problem on their paper. (Gluing after they have built all of the problems allows them to adjust numbers if they make a mistake.) Note that some cards will not be used.

Closure

Check students' problems and answers. Instruct them to write an explanation of the strategies they used to build their problems.

Answers

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