Problem
Check multiple relation to find correspondence rule
A table pairs each value of ♡ with a value of △. As ♡ goes 1, 2, 3, 4, 5, 6, the matching △ goes 2, 5, 8, 11, 14, 17. I need the value of △ that matches ♡ = 25.
Operations
Your answer
How to solve
Strategy Look for a Pattern — The △ row grows by a steady 3 each step, so the headline hint applies: first check whether △ is related to a multiple of ♡. Comparing △ with 3 × ♡ reveals a fixed rule, which we test on the small known pairs before stretching it to ♡ = 25.
1STEP 1
Notice the steady jump
The row reads 2, 5, 8, 11, 14, 17, and a steady jump of 3 points straight at the 3 times table.
5-2=3, 8-5=3, 11-8=3
Spotting a repeating 'add 3' is exactly the skip-counting/pattern skill a fourth grader uses to extend a sequence.
4.OA.C.5Look For A Pattern2STEP 2
Compare △ with 3 times ♡
Set against 3 times the top row, the bottom row sits 1 lower every time: 3 x top - 1.
△ = 3 × ♥ - 1
Matching the △ row to a familiar multiplication row, then noticing it sits a constant amount below, turns a list into one tidy rule.
5.OA.B.3Solve An Easier Related ProblemThe rule tying the two rows together is △ = 3 x ♡ - 1.
Why?
The △ row climbs by a steady 3 every time ♡ climbs by 1, so △ moves in step with 3 groups of ♡.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
At every position 3 x ♡ is the value of △ together with a fixed leftover of 1, and because both sides climb at the same steady rate that leftover never changes.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Check the rule on a known pair
Testing the top row at 6 gives 3 x 6 - 1 = 17, which matches the table.
3 × 6 - 1 = 17 ✓
Verifying the rule on a pair you can already see builds confidence before trusting it for ♡ = 25.
5.OA.A.2Guess And Check4STEP 4
Apply the rule to ♡ = 25
Substitute ♡ = 25 into the rule. Multiply 3 × 25 = 75, then subtract 1 to get 74.
△ = 3 × 25 - 1 = 75 - 1 = 74
Once the rule is trusted, finding any term is just a quick multiply-then-subtract.
5.OA.A.2Look For A PatternAnswer
74
♡ jumped from 6 to 25, an increase of 19 steps, so △ should rise by 19 × 3 = 57 from its value of 17 at ♡ = 6: 17 + 57 = 74. This matches, and 74 is sensibly close to 3 × 25 = 75, so the size is right.
Takeaway
When numbers climb by the same step, peek at the times table first: here △ is just 3 × ♡ minus 1.
- Notice the steady jump
- Compare △ with 3 times ♡
- Check the rule on a known pair
- Apply the rule to ♡ = 25
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested