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Grade 5 · lesson 4 of 4

Generate Paired Patterns and Explain a Relationship

Build a table containing step number and both generated values.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: Pattern A starts at zero and adds four; B starts at zero and adds twelve.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Two rules can create paired values when applied the same number of times. Begin with the stated starting values, then match terms by step number. A relationship such as double depends on both the step sizes and starting values. It should be explained from the rules, not assumed from one matching pair.

Build a table containing step number and both generated values. Pair entries from the same row. Explain the ratio relationship when both start at zero and one repeated step is an exact multiple of the other.

Pair values from the same step row. A different starting value can change a simple multiplier relationship. Make a table with rows for step 0 through the requested step.

  1. Make a table with rows for step 0 through the requested step.
  2. Follow the worked example. Point to each number or shape feature and say what it tells you.
  3. Build a table containing step number and both generated values.
  4. Try the question and then the three practice questions. Check your answers and explain any change you make.
Worked example

See the method in action

Pattern A starts at zero and adds four; B starts at zero and adds twelve. At steps 1,2,3, pairs are (4,12),(8,24),(12,36). B is three times A because both start at zero and every step in B adds three times the amount in A. Pair values from the same step row. A different starting value can change a simple multiplier relationship. Make a table with rows for step 0 through the requested step.

Your turn

Check your reasoning

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Helpful tips
  • Pair values from the same step row.
  • A different starting value can change a simple multiplier relationship.
Patterns start at zero. A adds 2 each step and B adds 6. At step 2, what is B’s value?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

12

The second pattern repeats a six-unit step the stated number of times. The result is 12.

Take it further

A starts at zero adding five; B starts at zero adding ten. At step four: pair (20,40), with B twice A.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Patterns start at zero. A adds 2 each step and B adds 6. At step 3, what is B’s value?
Need a hint?
  • Pair values from the same step row.
  • A different starting value can change a simple multiplier relationship.
2. Patterns start at zero. A adds 2 each step and B adds 6. At step 4, what is B’s value?
Need a hint?
  • Pair values from the same step row.
  • A different starting value can change a simple multiplier relationship.
3. Patterns start at zero. A adds 2 each step and B adds 6. At step 5, what is B’s value?
Need a hint?
  • Pair values from the same step row.
  • A different starting value can change a simple multiplier relationship.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.