Grade 6 - Number (Number Operations)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will apply arithmetic operations on whole numbers and decimal fractions in solving problems.

It is expected that students will:

estimate the solutions to calculations involving whole numbers and decimal fractions

To view the prescribed learning outcomes for Number (Number Operations) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Students' number sense and estimation skills complement their abilities to compute accurately using appropriate strategies and tools such as mental computation, paper-and-pencil calculations, calculators, and computers. Allowing students the freedom to create and solve their own problems by using strategies that are intuitively obvious to them helps them feel more comfortable with the problem-solving process.

Have students play the Maze game. Give each student a copy of the maze and a calculator. Each student begins by keying in 100 on the calculator. The goal is to choose a path that will give the player the largest value at the finish. Movement is unidirectional: players may not retrace a path or move upwards in the maze. For each segment moved along the maze, students key in the operation.

Reproduced with permission from Curriculum and Evaluation Standards for School Mathematics: Addenda Series, Grades 5-8: Developing Number Sense in the Middle Grades, copyright 1994 by the National Council of Teachers of Mathematics.
Ask students to figure out a quick way to compute an answer mentally and to explain why their shortcut works.

SUGGESTED ASSESSMENT STRATEGIES

Students need to be able to perform arithmetic operations relatively quickly and accurately, and to estimate solutions in a variety of situations. In some cases, you can assess their facility with calculations as part of problem-solving activities; in others, you may wish to devise specific activities or prompts to check on their development.

Observe and Question

After students have played the Maze game, ask them to write in their learning logs using prompts such as:
- I was surprised when ____________.
- My strategy for winning ____________.
Bring students together as a class or in small groups to talk about what they noticed and wrote about. For example, you might probe to determine whether they have generalized concepts such as:
- Dividing by a decimal fraction smaller than 1.0 results in a larger quotient.
- The product resulting when one of the factors is less than 10 is smaller than the largest factor. During their discussions, note:
- which students verbalize their strategies
- to what degree the strategies are comprehensible, sophisticated, and effective
Students who hesitate to share their ideas in a whole-group setting can be assessed by having them explain ideas to a partner or to the teacher in an interview.