Solved Exercises on Counting Inmates in Grade 1

Master counting inmates: addition and subtraction strategies with visual methods through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Counting inmates
Exercise 1
There are 4 inmates in cell A and 3 inmates in cell B. How many inmates are there in total?
Definition:

Counting inmates: Finding the total number of people in custody by adding groups together

Counting method:
  1. Count the inmates in each cell separately
  2. Add the cells together
  3. Find the total count
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7
Cell A
4
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Cell B
3
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Total
7
Step 1: Count inmates in Cell A

There are 4 inmates in Cell A

Step 2: Count inmates in Cell B

There are 3 inmates in Cell B

Step 3: Add both cells

4 inmates + 3 inmates = 7 inmates total

4 + 3 = 7
Final answer:

There are 7 inmates in total.

Applied rules:

• Grouping: Separate inmates by location

• Addition: Combine quantities to find totals

• Counting: Count each inmate once

2 Inmates transferred
Exercise 2
There were 8 inmates in the facility. 2 inmates were transferred to another prison. How many inmates are left?
Definition:

Subtraction: Taking away part of a group to find what remains

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6
8
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6
6
Step 1: Start with the total

There were 8 inmates in the facility

Step 2: Subtract the ones transferred

2 inmates were transferred

Step 3: Calculate what remains

8 - 2 = 6 inmates remaining

8 - 2 = 6
Final answer:

There are 6 inmates left in the facility.

Applied rules:

• Subtraction: Remove part of a group

• Counting backwards: Move left on the number line

• Remaining: What is left after taking away

3 New inmates arriving
Exercise 3
There are 5 inmates in the facility. 3 more inmates arrive today. How many inmates are there now?
Definition:

Addition: Combining groups to make a larger group

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8
5
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6
7
8
8
Step 1: Count the original inmates

There were 5 inmates in the facility

Step 2: Add the new arrivals

3 more inmates arrived

Step 3: Find the new total

5 + 3 = 8 inmates altogether

5 + 3 = 8
Final answer:

There are 8 inmates in the facility now.

Applied rules:

• Addition: Combining groups to make a larger group

• Counting forward: Move right on the number line

• Total: The final amount after combining

Detailed Summary: Counting Inmates

Definitions of Key Concepts

Counting Inmates: A mathematical strategy for finding the total number of people in custody by using addition and subtraction methods. This helps determine population changes in correctional facilities.

Addition: Combining groups to find a larger total (when new inmates arrive)

Subtraction: Removing part of a group to find what remains (when inmates leave)

Total: The final count after adding or subtracting.

Core Rules and Principles

Rule 1: Each inmate is counted exactly once in the total.

Rule 2: When inmates arrive, use addition to increase the count.

Rule 3: When inmates leave, use subtraction to decrease the count.

Step-by-Step Methods

  1. Identify the situation: Determine if inmates are arriving (add) or leaving (subtract)
  2. Count the starting number: How many inmates were there initially?
  3. Count the change: How many arrived or left?
  4. Perform the operation: Add or subtract accordingly
  5. Verify the result: Does the answer make sense?

Examples - Simple to Advanced

Simple Example: 3 inmates + 2 new inmates

Starting: 3 inmates

Arriving: 2 inmates

Total: 3 + 2 = 5 inmates

Medium Example: 8 inmates - 3 transferred

Starting: 8 inmates

Leaving: 3 inmates

Remaining: 8 - 3 = 5 inmates

Advanced Example: 10 inmates, 4 arrive, 2 leave

Starting: 10 inmates

After arrivals: 10 + 4 = 14 inmates

After departures: 14 - 2 = 12 inmates

Tips, Tricks, and Common Pitfalls

Tip 1: Use your fingers to help count when adding or subtracting.
Tip 2: Draw circles or dots to represent inmates when counting.
Tip 3: Use a number line to visualize adding (move right) or subtracting (move left).
Pitfall 1: Don't confuse addition with subtraction - arriving means add, leaving means subtract.
Pitfall 2: Make sure to count the starting number correctly before adding or subtracting.

Key Notes for Memorization

  • Arriving inmates = ADD to the total
  • Leaving inmates = SUBTRACT from the total
  • Each inmate is counted once in the total
  • Always start with the current number before adding or subtracting
  • The final number must be logical given the situation
  • Check your work by performing the opposite operation
Visual Counting Strategies
Counting Inmates
Addition and Subtraction Methods
Arrival Strategy
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Original: 3 inmates

Arrivals: 2 inmates

Total: 3 + 2 = 5 inmates

Departure Strategy
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Original: 5 inmates

Departures: 2 inmates

Remaining: 5 - 2 = 3 inmates

Net Change Strategy
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Original: 4 inmates

Arrivals: 2 inmates

Departures: 1 inmate

Total: 4 + 2 - 1 = 5 inmates

Verification Method
Checking Your Work
Double Check

If you calculated 7 inmates but started with 5 and 3 arrived, check: 5 + 3 = 8

You made an error - the correct answer is 8 inmates.

Always verify your calculations!

Counting Laws, Methods, Rules, and Definitions
Counting Inmates
Fundamental Counting Principles
Key definitions:

Population: The total number of inmates in a facility

Arrival: When a new inmate enters the facility (requires addition)

Departure: When an inmate leaves the facility (requires subtraction)

Complete counting methodology:
  1. Observe: Look at the current situation carefully
  2. Identify: Determine if inmates are arriving or leaving
  3. Starting number: Count the initial population
  4. Change: Count how many are arriving or leaving
  5. Calculate: Add or subtract accordingly
Tip 1: Keep a record of changes to track population over time.
Tip 2: Use different symbols for arrivals and departures to stay organized.
Tip 3: Practice with different scenarios to build confidence.
Tip 4: Use visual aids like drawings to help understand the problem.
Counting laws: Each inmate is counted once in the total, addition increases the count, subtraction decreases the count.
Best practices: Record each change, verify calculations, use visual aids for complex problems.
Counting principles to remember:

• One-to-one correspondence: Each inmate gets one count

• Stable order: Numbers always come in the same sequence

• Cardinality: The last number tells how many in total

• Addition principle: Arrivals increase the population

• Subtraction principle: Departures decrease the population

• Verification: Always check if the answer makes sense

Questions & Answers

Question: My child is confused about when to add and when to subtract when counting inmates. How can I help them understand the difference?

Answer: This is a common challenge for first graders! Here are helpful strategies:

  • Keywords: Teach them to listen for "arrive" (add) and "leave" or "go away" (subtract)
  • Actions: Use hand motions - thumbs up for adding, thumbs down for subtracting
  • Visual cues: Draw arrows pointing in for arrivals and out for departures
  • Memory phrase: "More coming in, add to the bin" and "Some go away, take away"

Example: "3 inmates arrive" → 3 more coming in → ADD 3

"2 inmates leave" → 2 going away → SUBTRACT 2

Practice with simple scenarios until the pattern becomes clear!

Question: When there are multiple changes, like some inmates arrive and some leave, how do I solve it?

Answer: Tackle multiple changes step by step:

  • Start with the beginning number of inmates
  • Handle each change one at a time in order
  • Follow the rule: Arrivals = ADD, Departures = SUBTRACT

Example: Start with 5 inmates

Step 1: 2 arrive → 5 + 2 = 7 inmates

Step 2: 1 leaves → 7 - 1 = 6 inmates

Final answer: 6 inmates

Work through each change in the order it happens!

Question: How can I help my students visualize the concept of counting inmates?

Answer: Use concrete visual aids to make the concept tangible:

  • Manipulatives: Use small figures or counters to represent inmates
  • Drawings: Have students sketch stick figures for inmates
  • Number lines: Show movement for adding (right) and subtracting (left)
  • Storytelling: Create narratives about inmates arriving and departing
  • Role play: Students can act out scenarios

For example: Give students 5 counters representing inmates. Add 2 more (arrivals) to show 5 + 2 = 7. Then remove 1 counter (departure) to show 7 - 1 = 6.

These visual tools help students understand the mathematical operations behind the scenarios.