Visual Guide to Addition and Subtraction Strategies

Master addition and subtraction through visual representations, counting strategies, and number sense building activities.

Strategy Exercises & Solutions
1 Counting On Strategy
Exercise 1
Solve: 5 + 3 using the counting on strategy
Definition:

Counting On: Start with the larger number and count forward

Method:
  1. Start with the larger number (5)
  2. Count on the smaller number (3 more)
  3. 5, 6, 7, 8
5
+
3
=
8
Step 1: Identify the larger number

Start with 5 because it's larger than 3

Step 2: Count on from the larger number

Count 3 more: 6, 7, 8

Step 3: State the final answer

5 + 3 = 8

5 + 3 = 8
Final answer:

5 + 3 = 8

Applied rules:

• Counting On: Start with the larger addend

• Sequential Counting: Count forward by the amount of the smaller number

• Number Recognition: Understand that numbers represent quantities

2 Counting Back Strategy
Exercise 2
Solve: 8 - 3 using the counting back strategy
Definition:

Counting Back: Start with the first number and count backward

8
-
3
=
5
Step 1: Start with the first number

Begin with 8

Step 2: Count back by the subtracted number

Count back 3: 7, 6, 5

Step 3: State the final answer

8 - 3 = 5

8 - 3 = 5
Final answer:

8 - 3 = 5

Applied rules:

• Counting Back: Start with the minuend (first number)

• Sequential Counting: Count backward by the subtrahend (second number)

• Subtraction Concept: Removing a quantity from another quantity

3 Number Line Strategy
Exercise 3
Solve: 4 + 2 using the number line strategy
Definition:

Number Line: Visual representation showing numbers in order

0
1
2
3
4
5
6
7
8
4
+
2
=
6
Step 1: Start at the first number

Place finger on 4

Step 2: Move forward by the second number

Move 2 spaces to the right: 5, 6

Step 3: Land on the answer

We land on 6

4 + 2 = 6
Final answer:

4 + 2 = 6

Applied rules:

• Number Line Direction: Right for addition, left for subtraction

• Sequential Movement: Move one space for each unit

• Position Recognition: Identify where you land after movement

Visual Strategy Infographics
👆
Counting On
Start with the larger number and count up by the smaller number
👇
Counting Back
Start with the first number and count down by the second number
📏
Number Line
Move forward for addition, backward for subtraction
🤝
Part-Part-Whole
Understand how parts combine to make a whole
Addition Strategies
  • • Counting On: Start with the larger number
  • • Doubles: Adding the same number (5+5)
  • • Near Doubles: One number is one more than the other (5+6)
  • • Making Ten: Break apart numbers to make 10 (8+5 = 8+2+3)
Subtraction Strategies
  • • Counting Back: Start with the first number
  • • Think Addition: Use known addition facts (8-3: think 3+?=8)
  • • Part-Part-Whole: Understanding that subtraction finds a missing part
Core Concepts & Strategies
Counting On: 5 + 3 = 5, 6, 7, 8
Addition Strategy
Strategy 1
Count On
Start with larger number
Strategy 2
Count Back
Start with first number
Strategy 3
Number Line
Move right for +, left for -
Key definitions:

Addition: Combining two or more quantities

Subtraction: Taking away or finding the difference

Strategy: A plan to solve a math problem

Problem Solving Steps:
  1. Read the problem: Understand what's being asked
  2. Choose a strategy: Counting on, counting back, number line
  3. Apply the strategy: Follow the steps of your chosen method
  4. Check your answer: Does it make sense?
Tip 1: Always start counting on from the larger number.
Tip 2: Use your fingers to help visualize counting.
Tip 3: Draw dots or circles to represent numbers.
Tip 4: Practice with small numbers first.
Common errors: Counting the starting number when counting on, mixing up addition and subtraction strategies.
Success strategies: Using manipulatives, drawing pictures, practicing with number lines.
Additional Practice Problems
6 + 2 = ?
Practice Addition
Problem Set A

7 + 2 = ?

4 + 5 = ?

3 + 6 = ?

8 + 1 = ?

Problem Set B

9 - 3 = ?

7 - 2 = ?

8 - 4 = ?

6 - 1 = ?

Problem Solving Hints
  • • Read the problem slowly
  • • Identify if it's addition (+) or subtraction (-)
  • • Choose the best strategy for you
  • • Check your answer by counting again
Memory Helper: Addition makes numbers bigger, subtraction makes them smaller.
Visual Aid: Draw pictures to represent the numbers.
Important Reminders:

• In addition, the answer is called the sum

• In subtraction, the answer is called the difference

• The number being added to is called the addend

• The number being subtracted is called the subtrahend

Questions & Answers

Question: I get confused when doing 4 + 5. Should I count on from 4 or from 5? How do I know which number is bigger?

Answer: Great question! When using the counting on strategy, always start with the larger number. In 4 + 5, the larger number is 5, so you would start counting from 5.

To identify which number is larger, you can:

  • Think about which number comes later when counting: 1, 2, 3, 4, 5 - since 5 comes after 4, it's larger
  • Use your fingers - hold up 5 fingers and 4 fingers to compare
  • Draw dots - draw 5 dots and 4 dots to see which group has more

So for 4 + 5, you would count: 5, 6, 7, 8, 9. The answer is 9!

Starting with the larger number means fewer counts, which is faster and less likely to cause mistakes.

Question: When I do 7 - 3, I sometimes forget whether to count forward or backward. How can I remember?

Answer: Here's a helpful way to remember:

  • Subtraction means taking away - when you take something away, you have less
  • Think of it like eating cookies: if you have 7 cookies and eat 3, you end up with fewer cookies
  • On a number line, subtraction moves you backward (to the left) toward smaller numbers

So for 7 - 3, you start at 7 and count backward: 6, 5, 4. You end up with 4!

Another trick: subtraction is the opposite of addition, just like going backward is the opposite of going forward.

Question: My child seems to struggle with understanding when to add versus subtract in word problems. Any suggestions?

Answer: This is very common! Here are strategies to help identify operations in word problems:

  • Look for key words: Words like "more," "altogether," "total," "combined" often mean addition. Words like "less," "left," "take away," "difference" often mean subtraction.
  • Act out the problem: Use physical objects to demonstrate what's happening in the story.
  • Draw a picture: Visualizing helps children see if things are coming together or going apart.
  • Ask: "Are we putting together or taking away?"

Example: "Sara had 5 apples. She got 3 more." → Getting more means combining → Addition

"Tom had 8 cookies. He ate 3." → Eating takes away → Subtraction