Number Sense Unit 1
Learning Goal:
- generate multiples and factors, using a variety of tools and strategies (Gr 7)
- determine common factors and common multiples using prime factorization of numbers (Gr 8)
Minds On...
List all of the multiples of 4. List all factors of 4.
Gr 7 Action....
Gr 8 Action ...
Consolidation
Grade 8: Nelson Math page 15 #14, 16, 17, 18
Note: Grade 7
Note: Grade 8
A prime number has exactly two distinct factors: itself and 1. A composite number has more than two distinct factors: itself, at least one number other than itself, and 1. Any composite number can be written as a product of prime numbers. This process is called the prime factorization of the original number.
10 x 2 is not a prime factorization of 20 because the number 10 is composite.
5 x 2 x 2 is a prime factorization of 20
A factor tree is a special diagram where you find the factors of a number, then the factors of those numbers, etc until you can't factor any more. The ends are all the prime factors of the original number.
Divisibility Rules
Minds On...
Action...
Option 1: Discover a rule that can be used to check if a number is divisible by 3. Use examples to show your work!
Option 2: Discover a rule that can be used to check if a number is divisible by 4. Use examples to show your work!
Option 3: Discover a rule that can be used to check if a number is divisible by 6. Use examples to show your work!
Option 4: Discover a rule that can be used to check if a number is divisible by 8. Use examples to show your work!
Option 5: Discover a rule that can be used to check if a number is divisible by 9. Use examples to show your work!
Consolidate...
1. Explain how you know that 123 123 123 900 is divisible by 2, 3, 5, 9 and 10. How do you know that it is also divisible by 6?
2. Determine 4 four-digit numbers that are divisible by 2, 3, and 5. Explain your reasoning.
Minds On...
Gr 7: Write each power as repeated multiplication.
Gr 8: What happens when you multiply a number by 10?
What happens when you divide a number by 10?
Action...
Gr 7: Powers can be used to express some numbers in several ways. For example 64 can be expressed as:
Gr 8: Rewrite any six digit number expressed as a power of 10?
Consolidate
Note 7: A power is a numerical expression that shows repeated multiplication. Example:
Note 8: Scientific Notation is a way of writing a number as a decimal between 1 and 10, multiplied by a power, for example 70 120 is written as 7.012 x 10
Expanded form is a way of writing a number that shows the value of each digit as a power of 10; for example, 1209 in expanded form is 1 x 10 + 2 x 10 + 9 x 1
Homework
Grade 7: pg. 19 #s 14, 15, 17, 20
Grade 8: pg. 22 #10, pg. 23#12, 16, 19
Order of Operations
Minds On...
Skill Testing Questions...The Best Part of all Canadian Contests
In order for my to claim my free prize at Tim Horton’s, I have to answer an addition, multiplication, and division question? Take a look at the skill testing question below.
Would everyone get the same answer? Let's see what we come up with!!!
2 x 18-4 + 4 = ?
Action...
Grade 7
Write an expression that matches the instruction. Add 5 to 8, square this number and multiply it by 6. Solve your expression. Show your work.
Consolidation...
Homework:
Grade 7: pages 28 -29 # 12, 14, 18, 19
Grade 8: page 37 #11, 12, 15, 17
Minds On...
Show how you could get two different answers if there were no rules for order of operations.
a) 125 - 5 - 5 b) 12 - 9 -2
Action..
Using order of operations design your very own skill-testing question for a lottery.
a) Where could you place brackets to make sure that the lottery winner gets the correct answer?
b) What other possible answers might people come up with if they did not use the correct order of operations?
Consolidate...
Exit Ticket
Minds on...
Action:
Grade 7: What are the smallest 3 different numbers with a greatest common factor of 45?
OR
Two ferry boats sail between Merryland and Dream Island. One boat takes 4 h for the round trip. The other takes 5 h. They both leave Merryland at 6:00 on October 8. when will they next dock at Merryland together? Explain your solution.
Grade 8: Three grade 8 classes decided to raise money for 2 charities by selling boxes of greeting cards. A box of cards cost $3.80 from the supplier and sold for $6.00. One class sold 150 boxes, the second 175, and the third 225. If the proceeds were divided equally between 2 charities, how much did each receive?