Grade 7 - 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 decimal fractions and integers and illustrate their use in solving problems.

It is expected that students will:

use patterns, manipulatives, and diagrams to demonstrate the concepts of multiplication and division by decimal fractions
use estimation strategies to predict or assess the reasonableness of their calculations
add, subtract, multiply, and divide decimal fractions (using technology for more than two-digit divisors or multipliers)
demonstrate an understanding of the order of operations, using paper and pencil and a calculator
add, subtract, multiply, and divide integers concretely, pictorially, and symbolically

It is expected that students will illustrate the use of ratios, rates, percentages, and decimal numbers in solving problems.

It is expected that students will:

estimate and calculate percentages
distinguish between rate and ratio
explain and demonstrate the use of proportion in solving problems
mentally convert proper fractions, decimal fractions, and percentages from one to another to facilitate the solution of problems

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

SUGGESTED INSTRUCTIONAL STRATEGIES

Students with a number sense will choose or invent methods for solving problems that reflect their own understanding of the relationships between numbers and operations, and will seek the most efficient ways to represent the problems and possible solutions. Using technology can help students deal with the complexity of the numbers they may encounter in problem situations. Yet concrete computations are still important when dealing with concepts such as integers, ratios, and percentages .

Using base-ten blocks with a flat representing 1, teach students to understand how 0.2 x 0.3 = 0.06. Students need to see that a part of a part is smaller than both beginning parts. Have students show simple multiplication using the base-ten blocks.
Model the use of positive and negative charges to calculate with integers. Provide students with two colour chips. For example: To calculate +4 - -2 = _____, students place four "plus" chips in front of them (e.g., ++++). Because there are no "negative" chips present, they cannot remove negative 2. Therefore they must insert two neutral (represented by two "plus" chips and two "negative" chips) (++++ --++). Now students can take away two "negative"chips, leaving a value of +6 (e.g., ++++++), therefore +4 - -2 = 16. Have students draw models to solve this problem.
Have students practise calculating percentages mentally. For example, if 1 percent of 200 is 2, what else can you determine? Extend the concept to include: 100 percent of 124 is 124. Extend the oral exercise to look at combinations of 1 percent, 10 percent, and 100 percent. For example, knowing that 10 percent of 400 is 40 and 1 percent of 400 is 4, how much is 23 percent of 400?

SUGGESTED ASSESSMENT STRATEGIES

Monitor students' skills and application of arithmetic operations involving decimal fractions and integers by collecting and analysing a variety of problem-solving activities as well as by asking students to explain the processes they use. In addition to assessing their accuracy of computation, watch for their use of logic, a systematic approach to problem solving, and their ability to make connections.

Observe

Observe students as they use models to do multiplication. Can students develop a generalization from the patterns to solve decimal placement in multiplication?
Analyse students' representations of integers with electrical charges and other formats. Do they accurately represent the process?

Collect

Collect patterns and statements written by students:
- Are they making simple connections from 1 percent to 10 percent?
- Have they followed and extended patterns?
- Have they given examples?
Collect student-generated transformation pathways. Are the procedures systematic and the rules clear?