Identify and Explain Arithmetic Patterns - 3rd Grade Math
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What property states that $(a\times b)\times c=a\times(b\times c)$ for any $a,b,c$?
What property states that $(a\times b)\times c=a\times(b\times c)$ for any $a,b,c$?
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Associative property of multiplication. Grouping doesn't change the product.
Associative property of multiplication. Grouping doesn't change the product.
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Identify the symmetry pattern in a multiplication table that shows $a\times b$ matches $b\times a$.
Identify the symmetry pattern in a multiplication table that shows $a\times b$ matches $b\times a$.
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Mirror symmetry across the diagonal. Shows commutative property: $a\times b=b\times a$.
Mirror symmetry across the diagonal. Shows commutative property: $a\times b=b\times a$.
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What pattern describes the $0$ row or $0$ column in a multiplication table?
What pattern describes the $0$ row or $0$ column in a multiplication table?
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All products are $0$. Zero times any number equals zero.
All products are $0$. Zero times any number equals zero.
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What pattern describes the $1$ row or $1$ column in a multiplication table?
What pattern describes the $1$ row or $1$ column in a multiplication table?
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Products equal the other factor. One times any number equals that number.
Products equal the other factor. One times any number equals that number.
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What is always true about $2\times n$ for a whole number $n$?
What is always true about $2\times n$ for a whole number $n$?
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$2\times n$ is always even. Multiplying by $2$ gives an even result.
$2\times n$ is always even. Multiplying by $2$ gives an even result.
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What is always true about $4\times n$ for a whole number $n$?
What is always true about $4\times n$ for a whole number $n$?
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$4\times n$ is always even. Since $4=2\times 2$, the result is even.
$4\times n$ is always even. Since $4=2\times 2$, the result is even.
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What expression shows $4\times n$ as two equal addends (two equal parts) using multiplication?
What expression shows $4\times n$ as two equal addends (two equal parts) using multiplication?
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$4\times n=(2\times n)+(2\times n)$. Shows $4$ groups split into two equal groups of $2$.
$4\times n=(2\times n)+(2\times n)$. Shows $4$ groups split into two equal groups of $2$.
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What property states that $a+b=b+a$ for any numbers $a$ and $b$?
What property states that $a+b=b+a$ for any numbers $a$ and $b$?
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Commutative property of addition. Order doesn't matter when adding numbers.
Commutative property of addition. Order doesn't matter when adding numbers.
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What property states that $a\times b=b\times a$ for any numbers $a$ and $b$?
What property states that $a\times b=b\times a$ for any numbers $a$ and $b$?
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Commutative property of multiplication. Order doesn't matter when multiplying numbers.
Commutative property of multiplication. Order doesn't matter when multiplying numbers.
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What property states that $(a+b)+c=a+(b+c)$ for any numbers $a,b,c$?
What property states that $(a+b)+c=a+(b+c)$ for any numbers $a,b,c$?
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Associative property of addition. Grouping doesn't change the sum.
Associative property of addition. Grouping doesn't change the sum.
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What property states that $a\times(b+c)=(a\times b)+(a\times c)$?
What property states that $a\times(b+c)=(a\times b)+(a\times c)$?
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Distributive property. Multiply each addend separately, then add.
Distributive property. Multiply each addend separately, then add.
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What is the identity property of addition written with a number $a$?
What is the identity property of addition written with a number $a$?
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$a+0=a$. Adding zero doesn't change the number.
$a+0=a$. Adding zero doesn't change the number.
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Identify the pattern in an addition table: as you move right $1$ column, what happens to the sum?
Identify the pattern in an addition table: as you move right $1$ column, what happens to the sum?
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The sum increases by $1$. Each column adds $1$ more to the first addend.
The sum increases by $1$. Each column adds $1$ more to the first addend.
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Identify the pattern in an addition table: as you move down $1$ row, what happens to the sum?
Identify the pattern in an addition table: as you move down $1$ row, what happens to the sum?
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The sum increases by $1$. Each row adds $1$ more to the second addend.
The sum increases by $1$. Each row adds $1$ more to the second addend.
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What pattern do you see on the main diagonal of an addition table (like $3+3$, $4+4$)?
What pattern do you see on the main diagonal of an addition table (like $3+3$, $4+4$)?
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Doubles: $n+n=2\times n$. Adding a number to itself equals multiplying by $2$.
Doubles: $n+n=2\times n$. Adding a number to itself equals multiplying by $2$.
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