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Identify Number Patterns (In Arithmetic and the Multiplication Table)
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 That patterns aren't just found in shapes, they're also found in numbers.
 That we can see patterns in equations and in the multiplication table.
 That we can use number patterns to check our math and share things with friends.

Discussion Questions

Before VideoIs 91,934 even or odd? Explain.ANSWER

Even. I only look at the last digit, 4, which is even.

Odd. I only look at the last digit, 1, which is odd.
ANSWER
Even. Zero in the ones place means that the number is a multiple of 10, so it must be even.

Yes. Even numbers can be shared equally among two people.

No. Odd numbers cannot be shared equally among two people.


After VideoIf I have 4 socks and you have 8 socks, can we pair them all up if we put them together?ANSWER

Yes! 4 can be put into pairs, and 8 can be put into pairs, so if we put them together, we are just adding pairs.

Yes. All my socks can be put into pairs except one. All your socks can be put into pairs except one. Together, we have several pairs of socks and two unpaired socks. Those unpaired socks become a pair together!
ANSWER
I started with an even number of socks that can be put into pairs. Then I took away an odd number of socks, which means that I take away some pairs and also break up a pair to take one sock. That means that I have an unpaired sock left over, so the amount of leftover socks is an odd number. The rule is: even – odd = odd.

I get an even number! I can think of it as an odd number of groups of even numbers (which can be paired).

I get an odd number. For example, if I have 3 groups that each contain 5 socks, the socks in each group make 2 pairs with 1 sock unpaired. When I combine the groups, there are 3 unpaired socks, which still leaves 1 unpaired.



Vocabulary

Pattern
DEFINE
Something that follows a rule.

Combined
DEFINE
Added together.

Pair
DEFINE
Two of the same thing.

Sequence
DEFINE
When one thing follows another according to a rule.

Equation
DEFINE
Mathematical expressions that are equal to the same number.

Multiplication table
DEFINE
A tool that helps us quickly see the product of two numbers.

Even
DEFINE
Can be put into two equal groups, or into groups of two.

Odd
DEFINE
Cannot be put into two equal groups, or into groups of two.

Pattern
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT IS IDENTIFYING NUMBER PATTERNS (IN ARITHMETIC AND THE MULTIPLICATION TABLE)Having explored patterns with shapes, you will now discover that patterns can be found in numbers as well! Specifically, you will explore outcomes when even and odd numbers are added, subtracted, and multiplied.
To better understand identifying number patterns…
WHAT IS IDENTIFYING NUMBER PATTERNS (IN ARITHMETIC AND THE MULTIPLICATION TABLE). Having explored patterns with shapes, you will now discover that patterns can be found in numbers as well! Specifically, you will explore outcomes when even and odd numbers are added, subtracted, and multiplied. To better understand identifying number patterns…LET’S BREAK IT DOWN!
Odd and Even Socks
Adesina, April, and Marcos are folding laundry. Each person has several socks, and they want to know how they can tell if it’s an even or odd number. If we can put all the socks into pairs, then there is an even number. April has 6 socks, and they can be put into 3 pairs, so 6 is even. Marcos has 8 socks, and they can all be paired up as well, so 8 is even. Combined, they have 14 pairs of socks, and 14 socks can all be paired up as well, so that number is even. They have just discovered a pattern: Even + even = even, since there are no left overs. Next, they fold socks that are a different color. This time, Marcos has 5 socks and April has 9 socks. 5 is an odd number because one of the socks is not paired. 9 is also an odd number because one of the socks is unpaired. But, if Marcos and Adesina put their socks together, now their unpaired socks make a pair together! Therefore, odd + odd = even. Next, they work on a new pile of socks. This time, Marcos has 6 socks and April has 5 socks. 6 is even, since Marcos' socks can all be paired. 5 is odd, since April has one sock left unpaired. If they combine their socks, one sock is still unpaired, and the answer is still odd. Therefore, odd + even = odd! Now you try: Without calculating, can you tell if 7 + 12 is odd or even?
Odd and Even Socks Adesina, April, and Marcos are folding laundry. Each person has several socks, and they want to know how they can tell if it’s an even or odd number. If we can put all the socks into pairs, then there is an even number. April has 6 socks, and they can be put into 3 pairs, so 6 is even. Marcos has 8 socks, and they can all be paired up as well, so 8 is even. Combined, they have 14 pairs of socks, and 14 socks can all be paired up as well, so that number is even. They have just discovered a pattern: Even + even = even, since there are no left overs. Next, they fold socks that are a different color. This time, Marcos has 5 socks and April has 9 socks. 5 is an odd number because one of the socks is not paired. 9 is also an odd number because one of the socks is unpaired. But, if Marcos and Adesina put their socks together, now their unpaired socks make a pair together! Therefore, odd + odd = even. Next, they work on a new pile of socks. This time, Marcos has 6 socks and April has 5 socks. 6 is even, since Marcos' socks can all be paired. 5 is odd, since April has one sock left unpaired. If they combine their socks, one sock is still unpaired, and the answer is still odd. Therefore, odd + even = odd! Now you try: Without calculating, can you tell if 7 + 12 is odd or even?Googly Eyes
Adesina starts by putting 12 googly eyes into pairs. 12 can be put into 6 pairs, so 12 is even. If we subtract 4, which is an even number, then we have 8 googly eyes left, which is also even. Subtracting an even number from an even number doesn't leave any googly eyes unpaired. Even – even = even. If we try subtracting an odd number from an odd number, like 11 – 5 = 6, we end up with an even number! The unpaired googly eye in 11 is taken away by the unpaired eye in 5. Odd – odd = even. If we subtract an odd number from an even number, like 14 – 3 = 11, we get an odd number. Likewise, if we subtract an even number from an odd number, like 13 – 4 = 9, we also get an odd number. Then, even – odd = odd, and odd – even = odd. Now you try: Without calculating, can you tell if 21 – 9 is even or odd?
Googly Eyes Adesina starts by putting 12 googly eyes into pairs. 12 can be put into 6 pairs, so 12 is even. If we subtract 4, which is an even number, then we have 8 googly eyes left, which is also even. Subtracting an even number from an even number doesn't leave any googly eyes unpaired. Even – even = even. If we try subtracting an odd number from an odd number, like 11 – 5 = 6, we end up with an even number! The unpaired googly eye in 11 is taken away by the unpaired eye in 5. Odd – odd = even. If we subtract an odd number from an even number, like 14 – 3 = 11, we get an odd number. Likewise, if we subtract an even number from an odd number, like 13 – 4 = 9, we also get an odd number. Then, even – odd = odd, and odd – even = odd. Now you try: Without calculating, can you tell if 21 – 9 is even or odd?Multiplication Table
Adesina, Marcos, and April are looking at a multiplication table. They notice some interesting number patterns: The row showing multiples of 2 contains all even numbers. All multiples of 2 are even! Looking at the row with multiples of 5, they notice that you add 5 each time you move along the row. All multiples of 5 end in 5 or 0. This is how you know you cannot divide 23 by 5: it doesn’t end in 5 or 0. Looking at the row with multiples of 10, we can see that all multiples of 10 end in 0. Discovering these patterns can help us check our work. Now you try: Is 73 divisible by 5? Is 90 divisible by 10? Is 43 divisible by 2?
Multiplication Table Adesina, Marcos, and April are looking at a multiplication table. They notice some interesting number patterns: The row showing multiples of 2 contains all even numbers. All multiples of 2 are even! Looking at the row with multiples of 5, they notice that you add 5 each time you move along the row. All multiples of 5 end in 5 or 0. This is how you know you cannot divide 23 by 5: it doesn’t end in 5 or 0. Looking at the row with multiples of 10, we can see that all multiples of 10 end in 0. Discovering these patterns can help us check our work. Now you try: Is 73 divisible by 5? Is 90 divisible by 10? Is 43 divisible by 2?Multiplying Evens and Odds
Let’s see what happens when we multiply using even and odd numbers. To find the product of two numbers, we can look up the two numbers on the multiplication table to see what they multiply to. 2 and 4 are even, and when we multiply them, we get 8, which is also an even number. Then, even × even = even. 1 and 3 are odd, and if we multiply them, we get 3, an odd number. Same with 5 × 7 = 35. Then, odd × odd = odd. 2 is even and 3 is odd, and if we multiply them, we get 6, an even number. Same with 6 × 9 = 54. Then, even × odd = even. Also, odd × even = even. Now you try: Without calculating, can you tell if 11 × 16 is odd or even?
Multiplying Evens and Odds Let’s see what happens when we multiply using even and odd numbers. To find the product of two numbers, we can look up the two numbers on the multiplication table to see what they multiply to. 2 and 4 are even, and when we multiply them, we get 8, which is also an even number. Then, even × even = even. 1 and 3 are odd, and if we multiply them, we get 3, an odd number. Same with 5 × 7 = 35. Then, odd × odd = odd. 2 is even and 3 is odd, and if we multiply them, we get 6, an even number. Same with 6 × 9 = 54. Then, even × odd = even. Also, odd × even = even. Now you try: Without calculating, can you tell if 11 × 16 is odd or even? 
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Science & Math$_{/yr}

Science Only$_{/yr}
Does adding an even number to an even number make an even or odd number? Give an example.
Circle the numbers that are divisible by 2 and underline the numbers that are divisible by 5. 88, 95, 100, 314, 360, 225
Is the product of 5 and 8 even or odd?
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