Do the rule to each number in. To find a rule, look at how the outs change as the ins go up by one: up by 3 each time means × 3, then fix it with + or −.
inputthe number that goes in
outputthe number that comes out
rulewhat is done to every input
positiona term's place in a pattern: 1st, 2nd, 3rd
Watch for: Finding a rule from the first pair only (+ 4 fits 1 → 5, but not 2 → 9). Doing × 3 + 1 as 3 + 1 first, then multiplying. Counting on from the last value instead of using the position.
At home: Make a 'machine': your child says a number, you say the out, and they guess your rule. Then swap.
Sample sheet and answer key
Luna's Space Adventure
Grade 4 · Input-output tables · 4.5B
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Follow the rule
Each row's rule is on the left. Do it to each number in.
In
1
4
7
9
10
+ 6
7
× 8
8
× 6 − 2
22
Find the rule
Which rule makes every out from its in?
In 1, 3, 6, 8 → Out 8, 24, 48, 64+ 12× 8× 9
In 1, 3, 7, 10 → Out 2, 8, 20, 29× 3 − 1× 8+ 7
In 2, 3, 6, 7 → Out 12, 17, 32, 37+ 11× 5 + 2+ 12
In 2, 3, 4, 8 → Out 12, 13, 14, 18× 2 − 1+ 10+ 15
Position and value
Each value comes from its position. Find the rule, then the missing values.
Position
1
2
3
4
5
12
Value
9
18
27
Rule?
Value at position 24?
Write the rule
Write each rule with n for the number in: n × 3 + 1.
In 2, 7, 9 → Out 3, 13, 17
In 2, 3, 4 → Out 4, 7, 10
In 1, 3, 6 → Out 6, 12, 21
In 2, 6, 9 → Out 16, 40, 58
Grade 4 · Sheet
Luna's Space Adventure
Grade 4 · Input-output tables · 4.5B
Answer key
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Follow the rule
Each row's rule is on the left. Do it to each number in.
In
1
4
7
9
10
+ 6
7
10
13
15
16
× 8
8
32
56
72
80
× 6 − 2
4
22
40
52
58
Find the rule
Which rule makes every out from its in?
In 1, 3, 6, 8 → Out 8, 24, 48, 64+ 12× 8× 9
In 1, 3, 7, 10 → Out 2, 8, 20, 29× 3 − 1× 8+ 7
In 2, 3, 6, 7 → Out 12, 17, 32, 37+ 11× 5 + 2+ 12
In 2, 3, 4, 8 → Out 12, 13, 14, 18× 2 − 1+ 10+ 15
Position and value
Each value comes from its position. Find the rule, then the missing values.
Position
1
2
3
4
5
12
Value
9
18
27
36
45
108
Rule?position × 9
Value at position 24?216
Write the rule
Write each rule with n for the number in: n × 3 + 1.
In 2, 7, 9 → Out 3, 13, 17n × 2 − 1
In 2, 3, 4 → Out 4, 7, 10n × 3 − 2
In 1, 3, 6 → Out 6, 12, 21n × 3 + 3
In 2, 6, 9 → Out 16, 40, 58n × 6 + 4
Answer key
Something wrong with this sheet? A wrong answer, a hard-to-read picture? Report it
New problems every time, three levels (gentle, core and stretch), themes to pick from, a second page if you want one. Each sheet comes with an answer key and a one-page guide for grown-ups.
