Arithmetic Sequences and Linear Growth

SubstitutePlans.com
Mathematics · Algebra I
SP-ALG1-012  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 2
Arithmetic Sequences and Linear Growth
Mathematics · Algebra I · Grades 9-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the sequence formula and one worked
example on the board.
Technology
None. Calculators are optional for arithmetic only.
Student
independence
High. Students work alone, then compare with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard
Goal for today: Students will find the common difference of an arithmetic sequence, write and use the rule aₙ = a₁ +
(n − 1)d, and solve linear growth word problems.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: An arithmetic sequence adds the SAME number each time (the common difference, d).
Formula: aₙ = a₁ + (n − 1)d.
☐ Write the example on the board: 3, 7, 11, 15, … has d = 4. The 10th term is 3 + (10 − 1)(4) = 3 + 36 = 39.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today is about patterns of numbers that go up or down by the same amount each time. These are
called arithmetic sequences. For example, 3, 7, 11, 15 goes up by 4 every step. You will find the pattern, jump ahead
to far-away terms using a formula, and use the idea to solve real-life growth problems. The formula and an example
are on the board.


SubstitutePlans.com
Mathematics · Algebra I
SP-ALG1-012  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 3
Run of show
Minutes
What you do
What students do
0–5
Take attendance the way the school requires. Hand out the
worksheet face down and ask students to wait.
Settle in and take out a pencil.
5–12
Read the board aloud. Explain: “To find d, subtract any
term from the next one. To find the 10th term, start at the
first term and add d nine times, which is a₁ + 9d.” Work
through the board example.
Follow along and copy the formula and
example.
12–28
Tell students to complete Part A (problems 1–8). Walk the
room. If a student is stuck, ask, “What number is added
each time? How many times do you add it to reach term
n?”
Find differences, extend sequences, and
use the formula.
28–40
Tell students to complete Part B (problems 9–10), the
table, question 11 and question 12. Partners may compare
quietly.
Solve the word problems, complete the
table, and write the rule.
40–46
Read the answers from the key. Students mark each right
or wrong and fix mistakes.
Check their work and correct errors in a
different color if possible.
46–50
Have students write the exit ticket sentence, then collect
all worksheets and stack them for the teacher.
Write one sentence. Hand in the worksheet.
If things go wrong
• If students use n instead of n − 1, tell them to check with the first term: the first term should equal a₁ when n
= 1, so (n − 1) = 0.
• If a student gets a negative common difference wrong, remind them to subtract in the same direction: next
term minus the term before.
• If a student is stuck on problem 8 (which term is 53), tell them to put 53 in for aₙ and solve the equation for n.
• If the class is noisy, remind them this is individual practice time. Partners may whisper during Part B.
Early finishers
• Write your own arithmetic sequence with a common difference of −5 and find its 12th term.
• Explain in two sentences why an arithmetic sequence looks like a linear equation.
Support and challenge
• Support: Have students complete problems 1, 2, 3, 4 and 9, and write out the first few terms when they need
to.
• Challenge: Ask students to find a₁ and d for an arithmetic sequence where a₃ = 11 and a₇ = 27.


SubstitutePlans.com
Mathematics · Algebra I
SP-ALG1-012  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 4
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: