Analyze and Graph Number Patterns - 5th Grade Math
Card 1 of 20
Identify the rule: ordered pairs $(1,4),(2,7),(3,10)$ follow what equation?
Identify the rule: ordered pairs $(1,4),(2,7),(3,10)$ follow what equation?
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$y=3x+1$. Each $y$ increases by $3$ as $x$ increases by $1$, with $y$-intercept $1$.
$y=3x+1$. Each $y$ increases by $3$ as $x$ increases by $1$, with $y$-intercept $1$.
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Identify the missing value: Pattern A "Start $0$, add $4$" gives $0,4,8,12$; if $B=3A$, what is $B$ at term $3$?
Identify the missing value: Pattern A "Start $0$, add $4$" gives $0,4,8,12$; if $B=3A$, what is $B$ at term $3$?
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$24$. Term 3 of A is $8$, so $B=3×8=24$.
$24$. Term 3 of A is $8$, so $B=3×8=24$.
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What do the $x$-coordinate and $y$-coordinate represent when graphing two patterns?
What do the $x$-coordinate and $y$-coordinate represent when graphing two patterns?
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$x$ is the term from pattern 1; $y$ is the corresponding term from pattern 2. Standard convention: first pattern on $x$-axis, second on $y$-axis.
$x$ is the term from pattern 1; $y$ is the corresponding term from pattern 2. Standard convention: first pattern on $x$-axis, second on $y$-axis.
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What does the term "corresponding terms" mean for two patterns listed by term number?
What does the term "corresponding terms" mean for two patterns listed by term number?
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Terms in the same position (same term number) in each pattern. Terms at the same position number in both sequences match up.
Terms in the same position (same term number) in each pattern. Terms at the same position number in both sequences match up.
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What is an ordered pair made from two patterns, using corresponding terms?
What is an ordered pair made from two patterns, using corresponding terms?
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A pair $(x,y)$ where $x$ is from pattern 1 and $y$ is the matching term from pattern 2. First pattern gives $x$, second pattern gives $y$ at same position.
A pair $(x,y)$ where $x$ is from pattern 1 and $y$ is the matching term from pattern 2. First pattern gives $x$, second pattern gives $y$ at same position.
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Identify the first five terms for the rule "Start $0$, add $3$".
Identify the first five terms for the rule "Start $0$, add $3$".
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$0,3,6,9,12$. Starting at $0$, add $3$ repeatedly: $0+3=3$, $3+3=6$, etc.
$0,3,6,9,12$. Starting at $0$, add $3$ repeatedly: $0+3=3$, $3+3=6$, etc.
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Identify the first five terms for the rule "Start $0$, add $6$".
Identify the first five terms for the rule "Start $0$, add $6$".
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$0,6,12,18,24$. Starting at $0$, add $6$ repeatedly: $0+6=6$, $6+6=12$, etc.
$0,6,12,18,24$. Starting at $0$, add $6$ repeatedly: $0+6=6$, $6+6=12$, etc.
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What is the relationship between corresponding terms if one pattern is "Start $0$, add $3$" and the other is "Start $0$, add $6$"?
What is the relationship between corresponding terms if one pattern is "Start $0$, add $3$" and the other is "Start $0$, add $6$"?
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Each term in the second pattern is $2$ times the corresponding term in the first. Since $6=2×3$, each "add $6$" term equals $2×$ the "add $3$" term.
Each term in the second pattern is $2$ times the corresponding term in the first. Since $6=2×3$, each "add $6$" term equals $2×$ the "add $3$" term.
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What are the first three ordered pairs for patterns "Start $0$, add $3$" and "Start $0$, add $6$"?
What are the first three ordered pairs for patterns "Start $0$, add $3$" and "Start $0$, add $6$"?
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$(0,0),(3,6),(6,12)$. Pairs corresponding terms: $(0,0)$, $(3,6)$, $(6,12)$.
$(0,0),(3,6),(6,12)$. Pairs corresponding terms: $(0,0)$, $(3,6)$, $(6,12)$.
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Which equation matches the ordered pairs from "Start $0$, add $3$" and "Start $0$, add $6$": $y=2x$ or $y=x+3$?
Which equation matches the ordered pairs from "Start $0$, add $3$" and "Start $0$, add $6$": $y=2x$ or $y=x+3$?
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$y=2x$. Each $y$-value is twice its $x$-value: $0=2×0$, $6=2×3$, $12=2×6$.
$y=2x$. Each $y$-value is twice its $x$-value: $0=2×0$, $6=2×3$, $12=2×6$.
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Identify the first four terms for pattern A: "Start $2$, add $4$".
Identify the first four terms for pattern A: "Start $2$, add $4$".
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$2,6,10,14$. Start at $2$, add $4$ repeatedly: $2+4=6$, $6+4=10$, $10+4=14$.
$2,6,10,14$. Start at $2$, add $4$ repeatedly: $2+4=6$, $6+4=10$, $10+4=14$.
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Identify the first four terms for pattern B: "Start $1$, add $2$".
Identify the first four terms for pattern B: "Start $1$, add $2$".
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$1,3,5,7$. Start at $1$, add $2$ repeatedly: $1+2=3$, $3+2=5$, $5+2=7$.
$1,3,5,7$. Start at $1$, add $2$ repeatedly: $1+2=3$, $3+2=5$, $5+2=7$.
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What is the relationship between patterns A "Start $2$, add $4$" and B "Start $1$, add $2$" for corresponding terms?
What is the relationship between patterns A "Start $2$, add $4$" and B "Start $1$, add $2$" for corresponding terms?
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Each term in A is $2$ times the corresponding term in B. Check: $2=2×1$, $6=2×3$, $10=2×5$, $14=2×7$ confirms the pattern.
Each term in A is $2$ times the corresponding term in B. Check: $2=2×1$, $6=2×3$, $10=2×5$, $14=2×7$ confirms the pattern.
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What are the first three ordered pairs $(A,B)$ for A "Start $2$, add $4$" and B "Start $1$, add $2$"?
What are the first three ordered pairs $(A,B)$ for A "Start $2$, add $4$" and B "Start $1$, add $2$"?
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$(2,1),(6,3),(10,5)$. Pairs corresponding terms from A and B in order.
$(2,1),(6,3),(10,5)$. Pairs corresponding terms from A and B in order.
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Identify the first four terms for pattern B: "Start $1$, add $4$".
Identify the first four terms for pattern B: "Start $1$, add $4$".
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$1,5,9,13$. Start at $1$, add $4$ repeatedly: $1+4=5$, $5+4=9$, $9+4=13$.
$1,5,9,13$. Start at $1$, add $4$ repeatedly: $1+4=5$, $5+4=9$, $9+4=13$.
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Which equation matches the relationship if $B-A=-4$ for all corresponding terms?
Which equation matches the relationship if $B-A=-4$ for all corresponding terms?
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$B=A-4$. Rearranging $B-A=-4$ gives $B=A-4$.
$B=A-4$. Rearranging $B-A=-4$ gives $B=A-4$.
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Choose the ordered pair that correctly matches term $4$ for patterns: A "Start $3$, add $5$" and B "Start $10$, add $5$".
Choose the ordered pair that correctly matches term $4$ for patterns: A "Start $3$, add $5$" and B "Start $10$, add $5$".
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$(18,25)$. Term 4: A is $3+5×3=18$, B is $10+5×3=25$.
$(18,25)$. Term 4: A is $3+5×3=18$, B is $10+5×3=25$.
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What is the relationship between corresponding terms if both patterns increase by $5$ each step, but starts are $3$ and $10$?
What is the relationship between corresponding terms if both patterns increase by $5$ each step, but starts are $3$ and $10$?
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Pattern B is always $7$ greater than pattern A. Same rate of change, but B starts $7$ higher: $10-3=7$.
Pattern B is always $7$ greater than pattern A. Same rate of change, but B starts $7$ higher: $10-3=7$.
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Identify the missing term: start $2$, rule “add $5$”; sequence $2,7,12,\underline{\ \ },22$.
Identify the missing term: start $2$, rule “add $5$”; sequence $2,7,12,\underline{\ \ },22$.
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$17$. Each term adds $5$ to the previous: $12+5=17$.
$17$. Each term adds $5$ to the previous: $12+5=17$.
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What is the meaning of “corresponding terms” in two patterns?
What is the meaning of “corresponding terms” in two patterns?
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Terms in the same position, such as $1$st with $1$st, $2$nd with $2$nd. Pairs terms by position in each sequence.
Terms in the same position, such as $1$st with $1$st, $2$nd with $2$nd. Pairs terms by position in each sequence.
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