Numerical Patterns and Ordered Pairs

5th Grade MathOrder of Operations4 pages

About this worksheet

A 5th grade math worksheet on generating and graphing numerical patterns (Common Core 5.OA.3). Two rules, add 2 and add 4, both start at 0. Students fill a table with the first five terms of each pattern, form ordered pairs, and plot them on a printed first-quadrant grid, where the points line up from (0, 0) through (8, 16). Analysis questions draw out that every y-value doubles its x-value and demand a reason grounded in the two rules. A partner challenge closes the sheet: from Maya's pairs (0, 0), (3, 9) and (6, 18), recover her two rules.

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Curriculum objectives covered

5.OA.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

The sheet is this standard in one arc: two given rules generate patterns, corresponding terms form ordered pairs, the pairs get graphed, and questions 4 to 7 identify and explain the times-2 and times-3 relationships, exactly as the standard's add-3 add-6 example describes.

What's inside this worksheet

Pattern Investigation: Follow the Rules

Students generate both sequences from 0 in a table, pairing corresponding terms into (2, 4), (4, 8), (6, 12) and (8, 16).

Graph on the Coordinate Plane

Each ordered pair gets plotted and labeled on the printed 0-to-16 grid. Students describe the straight line through the origin and extend the pattern to the sixth pair, (10, 20).

Analyze the Relationship

Questions 4 and 5 name the doubling relationship y = 2 × x and explain its cause: adding 4 each step accumulates twice as fast as adding 2.

Partner Challenge: Mystery Rule

Maya's pairs (0, 0), (3, 9), (6, 18) hide the rules add 3 and add 9. Students recover both and state that each y-value is 3 times its x-value.

Answer key

The key completes the table, lists all five plotted points, and gives the full doubling explanation plus Maya's rules.

How teachers use it

Bridging patterns to graphing

This sheet is where the OA and G strands shake hands. Insist the table is complete before any plotting; students who graph while generating tend to invent points.

Explaining why, not what

Most classes spot y = 2x fast. Question 5 is the graded one: the explanation must mention that 4 is twice 2, or it is pattern-spotting rather than reasoning.

Mystery rules as a game

After the partner challenge, have each student invent two rules of their own, write three pairs, and swap. Recovering a classmate's rule from (3, 9)-style evidence is the fastest reteach available.

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