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recognize, model, identify, and describe common multiples, common factors, least common multiples, greatest common factors, and prime factorization
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Josie and Pierre work part-time at a local store. Josie works one day every four days and Pierre works one day every six days. If they both start today and the store is open every day of the week, when will they work together again?
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write whole numbers as expanded numerals using powers of 10 and in scientific notation
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The sun has a diameter of about 1 382 400 km and
is about 148 640 000 km from earth. Using kilometres as the unit of length, write these numbers in the following two forms:
- using expanded notation with powers of 10
- using scientific notation
How would the numbers be affected if metres were used as units of length? What kinds of numbers are best expressed using scientific notation?
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use divisibility rules to determine whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11
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Baseball teams have nine players. If 365 people showed up for a tournament, would there be anyone left over after the teams were made up? Use a divisibility rule to decide without dividing.
Represent the 365 people with base-ten blocks and explain why the rule for 9 works. (Hint: how many groups of 9 are there in 100 and 10?)
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read and write numbers to any number of decimal places
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Carl saved his money and bought a mountain bike. His dad had given him $179.49, which was half the cost of the bike. Carl wrote a cheque for the full cost. Show in words and in numbers the amount on the cheque.
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recognize and illustrate that all fractions and mixed numbers can be represented in decimal form (including terminating and repeating decimal fractions)
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Juan was recording the results from probability experiments. The data were gathered as common fractions, but he wanted to write the numbers in decimal form to make it easier to compare results. Whenever possible, he did it mentally, by finding an equivalent common fraction with a denominator that is a power of 10. Finish his work, replacing the question marks with your answers. For which examples does his mental method not work? Explain.
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convert from terminating decimal fractions to common fractions and from single-digit repeating decimal numbers to common fractions using patterns
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Sometimes it is useful to write decimals in common fraction form. For example, it may be easier to visualize  of a box of candy than 0.25 of a box. Show how you could write the following decimals as fractions in their lowest terms.
0.245
1.62
Bart used his calculator to express these fractions as decimals.
 = 0.111......
 = 0.222......
 = 0.333......
Predict the decimals for  and  . Predict what fraction will have 0.88.... as a decimal. Check your predictions on your calculator. Can you explain the pattern in words?
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demonstrate concretely and pictorially that the sum of opposite integers is 0
represent integers in a variety of concrete, pictorial, and symbolic ways
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Play a game by tossing a red die and a green die together. For each toss, the red die shows how many points you win and the green die shows how many points you lose. Represent the points you win with red chips and the points you lose with green chips. If each point lost (green chip) can cancel a point won (red chip), show how you would find your score for each toss. How many ways could you get a score of zero (0)?
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compare and order integers
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The following temperatures were recorded for a variety of places across Canada at 3:00 p.m. on a certain day: +8イ, -3イ, -7イ, 0イ, +3イ, -12イ, +10イ. Arrange the temperatures from lowest to highest.
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Number (Number Concepts)
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