Grade 7 - Number (Number Concepts)

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 demonstrate a number sense for decimal fractions and integers (including whole numbers).

It is expected that students will:

recognize, model, identify, and describe common multiples, common factors, least common multiples, greatest common factors, and prime factorization
write whole numbers as expanded numerals using powers of 10 and in scientific notation
use divisibility rules to determine whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11
read and write numbers to any number of decimal places
recognize and illustrate that all fractions and mixed numbers can be represented in decimal form (including terminating and repeating decimal fractions)
convert from terminating decimal fractions to common fractions and from single-digit repeating decimal numbers to common fractions using patterns
demonstrate concretely and pictorially that the sum of opposite integers is 0
represent integers in a variety of concrete, pictorial, and symbolic ways
compare and order integers

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

SUGGESTED INSTRUCTIONAL STRATEGIES

Personal encounters with meaningful number situations help students recognize the use of rational numbers to describe quantities. Rational numbers and proportions are an important focus in the Grade 7 curriculum. Instruction that builds on students' natural language and their informal notions of fractions, ratios, decimals, percents, and proportions enables them to become quantitatively literate.

Give pairs of students two calculators each and review how to use the addition constant feature to skip count by tens. Point out that the numbers that appear in the display are multiples of ten. Then have one student use a calculator to skip count by fours, while the other uses her/his calculator to skip count by fives. Invite predictions by asking: Would the two calculators ever show the same number? If so, which numbers? Have the pairs use the calculators to check their predictions. Encourage them to look for a number pattern. Ask why this pattern occurs. (The common multiples of 4, 5, and 10 are 20, 40, and 60.) Have students record repeated addition and multiples on a number line. Extend the investigation to the common multiples of other pairs of numbers. Encourage students to look for patterns.
Simulation: the stock market. Choose ten stocks that students are familiar with from the Toronto Stock Exchange. Give students a fictional amount of money to invest and have them track the movement of the stocks each day. Then, by converting to decimal fractions, have them calculate how much money they have made or lost.

SUGGESTED ASSESSMENT STRATEGIES

Students demonstrate their growing number sense through the ways that they use and interpret numbers, their growing sense of accuracy when computing, their ability to detect errors, and their common-sense approach to using numbers. Assess students' facility with using decimal fractions and integers by observing and questioning them as they work, as well as by collecting written evidence.

Observe

When students are explaining their predictions about common multiples, note which students:
- guess that some numbers will be the same without giving reasons
- predict that the product of the two numbers will be a common multiple
- predict that multiples of this product will also be common multiples

Question

Discuss with small groups or individuals:
- the strategies they used to convert information on common fractions to decimal numbers
- whether they noticed any patterns or developed any shortcuts
- the decisions they made regarding repeating decimals

Collect