LESSON PLAN

Patterns with Words, Numbers, Symbols, and Variables

Apothem Team

Grade 5 · 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

Show the pattern 3, 7, 11, 15. Rule in words: start at 3, add 4. Can I write this shorter? Term n = 4n - 1. Check: n=1: 4-1=3. n=2: 8-1=7. n=3: 12-1=11. Yes! Now: what is term 25? 4x25-1=99. Immediate, no listing required.

Explore

Pattern rule challenge: each group receives a table of values with 5 rows. They must: (1) identify the constant difference, (2) find the variable rule (term = ?n + ?), (3) verify with 3 term numbers, (4) find term 15, (5) find which term has value 100 (set up and solve the equation).

Consolidate

Practice

Students find rules for 4 tables of values, use each rule to find term 10, and solve for the term number that gives a specified value. Exit ticket: what is term 12 in the pattern with rule 4n + 5?

Exit ticket

Students find rules for 4 tables of values, use each rule to find term 10, and solve for the term number that gives a specified value. Exit ticket: what is term 12 in the pattern with rule 4n + 5?

TIP Always verify a rule by substituting at least two term numbers. If both check out, the rule is likely correct. If one fails, the rule needs adjustment.

WORKED EXAMPLES

Find the variable rule for: n=1,2,3,4; values=6,9,12,15.

Constant difference: 3. Rule: 3n + b. Substituting n=1: 3(1)+b=6, b=3. Rule: term n = 3n+3 = 3(n+1). Verify: n=2: 3x2+3=9. n=4: 3x4+3=15. Correct.

Using rule term n = 3n+3, which term equals 21?

3n+3=21. 3n=18. n=6. The 6th term is 21. Check: 3x6+3=21. Correct.

MATERIALS

•Table of values sheets

•Pattern cards

•Hundred chart

•Algebraic pattern-rule recording sheets

WATCH FOR

!Students may confuse the constant difference with the constant term in the rule. The constant difference is the coefficient of n; the constant term is found by solving for when n=1.

!Students may not verify their rules. Two checks are the minimum: if both pass, the rule is almost certainly correct.