Number Patterns 1
Patterns are all around us and occur in a wide range of forms. Being able to identify patterns is extremely important. Through the investigation of patterns, possible connections can be examined and predictions made. Sometimes we are given a series of numbers and asked to identify a pattern. These numbers may be increasing or decreasing in regular amounts. A pattern could be arithmetic, which is adding or subtracting a regular amount to a number, or the pattern might be geometric, which is multiplying or dividing by a regular amount.
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Content Focus: Number Patterns
Learning Intention: Explore and describe number patterns resulting from performing multiplication/repeated addition. |
Moderate
On line Calculator
You can find and create number patterns by using a calculator or by shading in values in rectangular grids up to a value of 100.
Ask a friend to enter 2, +, 2, =, =, =, = into the online calculator and to describe what he or she sees on the calculator display. Describe what happened on the online hundred chart. |
You can create printable charts that start at whatever number you specify and count by whatever interval you like. You could make an even numbers chart, or a multiples of 3 chart, or . . . the possibilities are endless!
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Difficult
Prime and Composite Numbers
A prime number has only two factors: 1 and itself.
A composite number has more than two factors.
The number 1 is neither prime nor composite.
A composite number has more than two factors.
The number 1 is neither prime nor composite.
Make the Sieve of Eratosthenes to find prime numbers. On a printed 100's chart, blacken the box for the number 1, which is neither prime nor composite. Circle the next unmarked number (2), and then cross out all of its multiples—that is, count by 2’s and cross out every number you land on, except for 2 itself. Circle the next unmarked number (3), and then cross out all of its multiples. Keep going until every number is either circled (prime) or crossed out (composite).
TASK:
Find all the prime numbers up to 400. You could do this by crossing out multiples in a 2-400 number grid. Which multiples will you choose to cross out? How can you be sure that you are left with the primes? Games
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ChallengeImagine you want to find all the prime numbers up to 1000 by crossing out multiples in a 2-1000 number grid.
Which number will you cross out last? |
Factors and Multiples Solitaire
Try to find the longest possible chain of factors and multiples. Keep track of the order in which you mark the numbers. Can you find a way to mark 50 or more without breaking the chain?
Arrow Directions
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Starting at the number given, each arrow means to move one square in the direction shown. What number is “45 ← ← ↑ → ↑”? How would you use arrows to say, “Start and 27 and move to 59”? Make up your own arrow code for someone to follow.
Race 100Odd-Even-Prime RacePlay “Odd-Even-Prime Race.″ Roll two dice. If your token is starting on an odd number, move that many spaces forward. From an even number (except 2), move backward — but never lower than the first square. If you are starting on a prime number (including 2), you may choose to either add or multiply the dice and move that many spaces forward. The first person to reach or pass 100 wins the game.
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Play “Race to 100.″ Take turns rolling one or two dice and moving that many spaces on the hundreds chart. If you correctly predict your landing place before you move (without counting squares!), then you can go one extra space as a bonus. The first person to reach or pass 100 wins the game.
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