Problem Solving

Grade Level: 8

Materials: Calculator, paper, pencil

Objectives: Students' understanding of division and multiplication will be tested through:
(1) explorations using a calculator;
(2) problems that require a strategy before they can be solved;
(3) discussion topics that allow students to communicate their understanding with each other.
Mathematical Concepts: Multiplication, division, square, square root, word problems.

NCTM Standards:
Standard 1: Mathematics as problem solving
Standard 2: Communication
Standard 7: Computation and Estimation.

Procedure: Review with students problem solving strategies (Polya's).

Students will complete "Calculator Explorations", "Problem -solving", and the "Discussion topic" as outlined in the worksheet from Lola May's "Teaching Math - Extending the meaning of multiplication and division".

Answers: 1. (a) 13, (b) 32; 2. 1, 2, 5; 3. $1023.00; 4. (a) 431x52, (b) 135x24, 5. 48 x ? = 288;

6. Answers will vary. Students are expected to explain that the top number,. Called the 'dividend' is divided by the bottom number called the 'divisor'. The number of times the divisor divides the dividend called the 'quotient' is recorded after the equal sign.

Assessment: Students will share their method of computing the answers for the problems given.

References: Curriculum and Evaluation Standards for School Mathematics, NCTM, 1989;

Barry University reference librarians.

May, Lola (1994). "Teaching Math - Extending the meaning of multiplication and division", Teaching K-8, 25(3), 14-15.

Contributors: Major: Kimberley Collie
Minor: Carol Marinas

Worksheet

Answer the following questions. Show all you working for each question.

Calculator Explorations:

Using your calculators, find the answers to the following:

1. (a) What number times itself has a product of 169? (b) What number times itself has a product 1,024?

2. Which one-digit numbers, when divided into 1,2290, produce a quotient that is a whole number?

3. If you are given an allowance of $1 the first week, $2 the second week, $4 the third week and continue doubling the dollars for each week until the tenth week, how much money would you have after 10 weeks?

Problem Solving:

4. Using only the numbers 1,2,3,4 and 5 on your calculator, find (a) the largest possible product and (b) the smallest possible product of a three digit number. Each number an be used only once.

5. The division key on you calculator doesn't work. How would you solve this problem on the calculator without it? 288 divided by 48.

Discussion topic:

6. A student who has never seen a division problem enter your class. How would you explain to her why a division problem is written the way it is? Record the steps you use.