LESSON PLAN

Pattern Rules Using Words and Numbers

Apothem Team

Grade 3 · Algebra & Patterning

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

I have a pattern rule: start at 6, add 4 each time. What are the first 5 terms? (6, 10, 14, 18, 22.) What is the 10th term? Without listing all 10: add 4 nine times from 6. 6 + 9x4 = 42. Check by listing: does this work?

Explore

Students receive a table with position filled in (1 through 8) and must complete the values using a given rule. Then reverse: given values, find the rule. Then: given the rule and two terms, fill in a gap in the sequence. Each reversal requires deeper rule understanding.

Consolidate

Practice

Students complete 4 tables of values from given rules and find rules from 4 given tables. Predict the 12th term for each. Exit ticket: write the rule in words for the pattern 2, 5, 8, 11, 14.

Exit ticket

Students complete 4 tables of values from given rules and find rules from 4 given tables. Predict the 12th term for each. Exit ticket: write the rule in words for the pattern 2, 5, 8, 11, 14.

TIP Tables of values are the most algebraically powerful tool in Grade 3. Build the habit of recording patterns as tables from the very first lesson on this topic.

WORKED EXAMPLES

The pattern 7, 11, 15, 19 has rule: start at 7, add 4. What is the 15th term?

Term 1 = 7. Each step adds 4. Term 15 = 7 + (15-1)x4 = 7 + 56 = 63. Build the table to verify: the 5th term is 7+4x4=23, the 10th is 7+9x4=43, the 15th is 7+14x4=63.

A pattern has rule: start at 100, subtract 8. Which term is the first to be less than 20?

We need 100 - 8n < 20, so 8n > 80, n > 10. Term 11 is the first term less than 20. Check: term 10 = 100 - 8x10 = 20 (exactly 20, not less). Term 11 = 100 - 8x11 = 12. Yes, 12 < 20.

MATERIALS

•Table of values recording sheets

•Pattern strips

•Hundred charts

•Drum or rhythm instrument for song patterns

•Pattern cards with start and rule given

WATCH FOR

!Students may list all terms to find a distant term, even when the rule is given. Accept this initially, then ask: is there a faster way? Guide toward applying the rule directly.

!Students who confuse term number and term value will make errors when using rules. Always use a two-column table to keep position and value separate.