Using Recursion in Models and Decision Making - Grade 1 Math

Learn how to use recursive thinking in models and decision making with visual exercises and step-by-step solutions.

Recursion Exercises 1 to 3
1 Plant Growth Model
Problem 1
A plant grows 2 inches each day. If it starts at 3 inches tall, how tall will it be after 4 days?
Definition:

Recursion: Repeating the same rule over and over. Each day, add 2 inches to yesterday's height.

Recursive method:
  1. Start with the beginning value
  2. Apply the same rule repeatedly
  3. Keep track of each step
  4. Continue until reaching the end
Day 0
3 inches
Day 1
3+2=5
Day 2
5+2=7
Day 3
7+2=9
Day 4
9+2=11
Step 1: Start with Day 0

Plant starts at 3 inches tall

Step 2: Apply the rule for Day 1

Add 2 inches: 3 + 2 = 5 inches

Step 3: Apply the rule for Day 2

Add 2 inches: 5 + 2 = 7 inches

Step 4: Apply the rule for Day 3

Add 2 inches: 7 + 2 = 9 inches

Step 5: Apply the rule for Day 4

Add 2 inches: 9 + 2 = 11 inches

After 4 days, the plant will be 11 inches tall
Final answer:

After 4 days, the plant will be 11 inches tall

Applied rules:

• Recursive pattern: Same rule applied repeatedly

• Starting value: Know where to begin

• Consistent rule: Add 2 inches each day

3
→
5
→
7
→
9
→
11
2 Savings Model
Problem 2
Emma saves $1 on Monday, $2 on Tuesday, $3 on Wednesday, and continues this pattern. How much will she save on Friday?
Definition:

Pattern recursion: Each day, save $1 more than the previous day.

Monday
$1
Tuesday
$2
Wednesday
$3
Thursday
$4
Friday
$5
Step 1: Identify the pattern

Each day, save $1 more than the previous day

Step 2: Apply the pattern for Thursday

Wednesday was $3, so Thursday is $3 + $1 = $4

Step 3: Apply the pattern for Friday

Thursday was $4, so Friday is $4 + $1 = $5

Emma will save $5 on Friday
Final answer:

Emma will save $5 on Friday

Applied rules:

• Pattern recognition: Identify the repeating rule

• Sequential addition: Add the same amount each time

• Continuation: Apply the rule to reach the target

3 Block Tower Model
Problem 3
A tower starts with 1 block. Each level adds 1 more block than the previous level. How many blocks are in the first 4 levels?
Definition:

Recursive building: Each level builds on the previous level following the same rule.

Level 1
1 block
Level 2
2 blocks
Level 3
3 blocks
Level 4
4 blocks
Total
10 blocks
Step 1: Level 1 has 1 block

First level starts the pattern

Step 2: Level 2 has 2 blocks

Each level adds 1 more than the previous level

Step 3: Level 3 has 3 blocks

Following the same pattern

Step 4: Level 4 has 4 blocks

Total blocks: 1 + 2 + 3 + 4 = 10

The first 4 levels have 10 blocks total
Final answer:

The first 4 levels have 10 blocks total

Applied rules:

• Recursive pattern: Each step follows the same rule

• Incremental addition: Add 1 more each time

• Accumulation: Add all values together

Recursion Concepts and Models
Next = Previous + Rule
Recursive Formula
Start Value
Initial Condition
Where to begin
Rule
Repeating Operation
What to do next
Repeat
Apply Rule Again
Continue pattern
Start
→ Rule →
Result 1
→ Rule →
Result 2
→ Rule →
Result 3
Continue...
Repetition: The same rule is applied multiple times in sequence.
Sequence: Each step depends on the result of the previous step.
Order: Steps must be followed in the correct sequence.
Detailed Summary and Key Concepts
4 Recursion Fundamentals
Key Definitions:

Recursion: A process where each step is defined in terms of previous steps

Recursive Pattern: A sequence where each term is created using the same rule

Base Case: The starting point or initial value

Base Case
Start Value
Rule
Operation
Iteration
Repeat
Step 1: Identify the starting point

Determine the initial value or base case

Step 2: Define the recursive rule

Specify what operation to perform on each step

Step 3: Apply the rule repeatedly

Use the result of each step as input for the next

Recursion builds complexity from simple rules
Key concept:

Recursion uses simple, repeated operations to create complex patterns

5 Common Mistakes
Common errors:

Mistake 1: Forgetting the starting value

Mistake 2: Changing the rule partway through

Mistake 3: Not tracking steps properly

Correct Process
Start → Rule → Result → Rule → Result...
Wrong Process
Start → Rule → Change Rule → Wrong Result
Step 1: Keep the same rule throughout

Don't change the operation partway through

Step 2: Track each step carefully

Write down each result to avoid mistakes

Step 3: Verify your final answer

Check that each step follows logically from the previous

Always verify: Does each step follow the same rule?
Remember:

Consistency is key - apply the same rule to each step!

Recursion Laws, Methods, and Definitions
f(n) = f(n-1) + Rule
Recursive Function
Key definitions:

Recursion: A process where each step is defined in terms of previous steps

Recursive Pattern: A sequence where each term is generated using the same rule

Base Case: The initial value that starts the recursive process

Recursive problem solving method:
  1. Identify the base case: What is the starting value?
  2. Determine the recursive rule: What operation is performed?
  3. Apply the rule: Use the previous result to generate the next
  4. Continue: Repeat the process for the required number of steps
  5. Track progress: Keep record of each step
  6. Verify: Check that each step follows the same rule
Tip 1: Always identify the starting value first.
Tip 2: Write down each step to avoid confusion.
Tip 3: The rule must be consistent throughout the process.
Tip 4: Draw diagrams to visualize the recursive process.
Common errors: Changing rules mid-process, forgetting base case, not tracking steps.
Exam preparation: Practice identifying recursive patterns in sequences.
Recursion rules to remember:

• Each step depends on the previous step(s)

• The recursive rule remains constant throughout

• Base case provides the starting point

• Recursive processes build complexity from simplicity

• Always verify that each step follows the rule

Questions & Answers

Question: I don't understand what recursion means. Can you explain it in simple words?

Answer: Recursion is like doing the same thing over and over again, but each time you build on what you did before!

  • It's like climbing stairs: each step depends on the step below it
  • You start with something (the first step)
  • Then you follow the same rule to get to the next step
  • And you keep doing the same thing until you reach your goal

For example: If you start with $1 and add $2 each day, you get $1, $3, $5, $7, etc.

Each number comes from the previous number using the same rule!

Question: How can I help my child understand recursive thinking in real life?

Answer: Use everyday examples that involve repeating patterns:

  • Building with blocks: each layer depends on the one below it
  • Stacking cups: each cup goes on top of the previous stack
  • Saving money: each day's savings depend on previous days
  • Plant growth: each day's height depends on the previous day's height

Encourage your child to notice patterns that repeat in daily life.

Ask questions like "What comes next?" and "How do you know?"

Question: How do I know if I'm doing recursion correctly?

Answer: Check these things to make sure you're doing recursion correctly:

  • Did you start with the right beginning number?
  • Are you using the same rule for each step?
  • Does each number come from the one before it?
  • Does your pattern make sense?

For example, if you start with 2 and add 3 each time, you should get: 2, 5, 8, 11, 14...

Each number is 3 more than the one before it!