Grade 6 - 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 develop a number sense for common fractions and explore number sense for whole numbers.

It is expected that students will:

read and write numerals greater than a million
use estimation strategies for quantities up to a million
distinguish relationships among multiples, factors, composites, and primes
represent positive powers of numbers concretely, pictorially, and symbolically
use power, base, and exponent to represent repeated multiplication
explain the meaning of integers by extending their counting to numbers less than 0
identify practical applications of integers
read and write numbers to thousandths
demonstrate and explain the meaning of improper fractions and mixed numbers (positive) concretely and pictorially
demonstrate and describe equivalent mixed numbers and improper fractions concretely and pictorially
compare and order improper fractions, mixed numbers, and decimal fractions to thousandths
demonstrate and explain the meaning of ratio concretely and pictorially
demonstrate and explain the meaning of percentage concretely and pictorially

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

SUGGESTED INSTRUCTIONAL STRATEGIES

Students who have a number sense pay attention to the meaning of numbers and number operations and make realistic estimates for the results of computation. Students need many opportunities to estimate and check their solutions. Having to justify their mathematical thinking can help them develop their ability to communicate mathematically. The integration of mathematics with social studies topics (e.g., mapping, population distribution) provides students with real data for their work.

Read students the story The King's Chessboard by David Birch. Have students explore pattern by predicting the amounts that will result if one used a doubling pattern to cover the chessboard with grains of rice: one grain in the first square, two grains in the second square, four grains in the third square, and so on. Have them estimate the total number of grains and then find a way to calculate the result.
For this activity use pattern blocks. Ask students: If the shaded area is 1/3 cm³, what is the value of the whole design? Have students make a design with a value of eleven-thirds and have them explain how they determined the value of each piece.
Give pairs of students maps of the world and select five countries for the class to study. Have each pair of students estimate the area of each country using the map's scale and a centimetre grid. When they have finished, have them collect the class data and calculate an average area for each country. Have students consult the social studies text or another reference to check whether the average determined by the class or an estimate determined by one of the pairs is closest to the actual area of each country. Encourage students to express the area in various ways (3 400 000 km² or 3.4İmillion km² ).

SUGGESTED ASSESSMENT STRATEGIES

Students reveal their number sense as they engage in increasingly complex mathematical situations. In order to assess their thinking and the strategies they are using, present situations that require them to estimate and explain the reasonableness of their answers. Their ability to communicate their thinking will reveal how well they understand why various kinds of numbers occur and the relationships among the different ways to represent numbers.

Observe

Are students confident when using large numbers?
What different methods do they use when calculating?
How do they react when comparing their initial estimates to the results they get from calculating?

Question

Observe and note students' responses during conversations. Ask:
- How did you arrive at your estimate?
- Did anyone use a different strategy?
- How would you go about finding a country about the same size as ____________?

Collect

To what degree is the student able to represent fractions concretely and pictorially? Does the rationale given for her/his presentation make sense?
Use a worksheet to check students' ability to convert between decimal numbers and equivalent fractions.