Lesson 3: Adding and Subtracting Mentally in Grade 2

Master mental math strategies: counting on/back, making tens, using doubles, and mental computation techniques through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Solve mentally: 24 + 5 = ?
Definition:

Counting On: Starting with the larger number and counting up by the smaller number

Counting On Strategy:
  1. Start with the larger number (24)
  2. Count up by the smaller number (5)
  3. Count: 25, 26, 27, 28, 29
  4. The answer is 29
Start
24
Count
+5
Result
29
Step 1: Identify the larger number

Start with 24 (the larger number)

Step 2: Count up by 5

24 → 25 → 26 → 27 → 28 → 29

Step 3: Stop when you've counted 5 numbers

After counting 5 steps from 24, we reach 29

Step 4: State the answer

24 + 5 = 29

29
Final answer:

24 + 5 = 29

Applied rules:

• Counting On: Start with larger number and count up

• Mental Math: Keep track in your head

• Small Addends: Best for adding small numbers

2 Counting Back Strategy
Exercise 2
Solve mentally: 37 - 4 = ?
Definition:

Counting Back: Starting with the larger number and counting down by the smaller number

Start
37
Count Back
-4
Result
33
Step 1: Start with the larger number

Begin with 37

Step 2: Count back by 4

37 → 36 → 35 → 34 → 33

Step 3: Stop when you've counted back 4 numbers

After counting back 4 steps from 37, we reach 33

Step 4: State the answer

37 - 4 = 33

33
Final answer:

37 - 4 = 33

Applied rules:

• Counting Back: Start with larger number and count down

• Mental Math: Keep track in your head

• Small Subtrahends: Best for subtracting small numbers

3 Making Tens Strategy
Exercise 3
Solve mentally: 8 + 5 = ?
Definition:

Making Tens: Breaking apart numbers to create a sum of 10, then adding the remainder

8 + 5
8 + 2 + 3
Make 10
10 + 3
Result
13
Step 1: See how many more needed to make 10

From 8, we need 2 more to make 10

Step 2: Break apart the second number

5 = 2 + 3

Step 3: Add to make 10 first

8 + 2 = 10

Step 4: Add the remaining part

10 + 3 = 13

Step 5: State the answer

8 + 5 = 13

13
Final answer:

8 + 5 = 13

Applied rules:

• Making Tens: Use 10 as a benchmark number

• Breaking Apart: Split the second number strategically

• Sequential Addition: Add to make 10 first, then add remaining

Mental Math Strategies
Start + Count = Result
Counting Strategy
Count On
Larger + Smaller
Add by counting up
Count Back
Larger - Smaller
Subtract by counting down
Make Tens
a + b = (a + x) + (b - x)
Use 10 as benchmark
Key definitions:

Mental Math: Calculating in your head without writing anything down

Counting On: Starting with a number and counting forward

Counting Back: Starting with a number and counting backward

Making Tens: Using 10 as a benchmark to simplify addition

Mental Math Strategy:
  1. Look at the numbers: Decide which strategy to use
  2. Choose the best method: Counting on, counting back, or making tens
  3. Visualize in your mind: Picture the numbers and operations
  4. Keep track: Remember where you are in the process
  5. State the answer: Confidently say or write the result
Tip 1: Start with the larger number when adding.
Tip 2: Use your fingers if needed to keep track.
Tip 3: Practice with small numbers first.

Mental Math Strategy Guide

  • Counting On: For adding small numbers (like +1, +2, +3)
  • Counting Back: For subtracting small numbers (like -1, -2, -3)
  • Making Tens: For numbers that combine to make 10 easily
  • Doubles Plus One: For problems like 6+7 (think 6+6+1)
Solution: Exercises 4 to 5
4 Doubles Plus One Strategy
Exercise 4
Solve mentally: 7 + 8 = ?
Definition:

Doubles Plus One: Using a known double fact and adding one more

7 + 8
7 + 7 + 1
Double
14 + 1
Result
15
Step 1: Recognize the relationship

7 and 8 are consecutive numbers (one apart)

Step 2: Use the double fact

7 + 7 = 14 (known double fact)

Step 3: Add the extra one

Since 8 is one more than 7, add 1 to the double

Step 4: Calculate

14 + 1 = 15

Step 5: State the answer

7 + 8 = 15

15
Final answer:

7 + 8 = 15

Applied rules:

• Doubles Plus One: n + (n+1) = double n + 1

• Known Facts: Use memorized doubles to solve nearby problems

• Mental Math: Connect new problems to known facts

5 Compensation Strategy
Exercise 5
Solve mentally: 46 + 9 = ?
Definition:

Compensation: Adjusting one number to make the calculation easier, then adjusting the answer

46 + 9
46 + 10 - 1
Easy Calc
56 - 1
Result
55
Step 1: Adjust to make an easier problem

Add 10 instead of 9 (since 10 is easier to work with)

Step 2: Calculate the easier problem

46 + 10 = 56

Step 3: Adjust for the difference

We added 1 too many, so subtract 1 from the result

Step 4: Calculate the final answer

56 - 1 = 55

Step 5: State the answer

46 + 9 = 55

55
Final answer:

46 + 9 = 55

Applied rules:

• Compensation: Adjust one number to make calculation easier

• Balance: Whatever you add to one number, subtract from the result

• Mental Math: Use friendly numbers (like multiples of 10)

Mental Math Techniques and Strategies
Mental Math = Strategy + Practice
Success Formula
Key definitions:

Mental Math: Performing calculations in your head without writing anything down

Counting On: Starting with a number and counting forward

Counting Back: Starting with a number and counting backward

Making Tens: Using 10 as a benchmark to simplify addition

Comprehensive Mental Math Approach:
  1. Look at the problem: Identify which strategy might work best
  2. Choose your approach: Counting, making tens, doubles, or compensation
  3. Visualize the steps: Picture the numbers in your mind
  4. Execute mentally: Perform the calculation in your head
  5. Verify: Check if your answer seems reasonable
Tip 1: Practice with small numbers first, then work up to larger ones.
Tip 2: Use your knowledge of doubles facts to solve nearby problems.
Tip 3: Round numbers to make calculations easier, then adjust.
Tip 4: Memorize basic facts to build a foundation for mental math.
Common errors: Losing track while counting, misremembering facts, rushing through steps.
Practice recommendations: Daily practice, timed challenges, gradual progression.
Essential Mental Math Rules:

• Start with Larger: Begin counting from the larger number

• Use Known Facts: Connect new problems to facts you already know

• Make It Friendly: Adjust numbers to make calculations easier

• Check Reasonableness: Verify that your answer makes sense

Exercise with Visualization: Mental Math Progression
Exercise 6: Mental Math Fluency
Track mental math speed: Week 1: 10 problems/minute, Week 2: 12/minute, Week 3: 15/minute

Analysis: Regular practice improves mental math speed and accuracy.

  • Week 1: 10 problems per minute
  • Week 2: 12 problems per minute
  • Week 3: 15 problems per minute

Questions & Answers

Question: How can I get better at mental math? It's hard for me to do in my head.

Answer: Here are strategies to improve your mental math skills:

  • Start small: Practice with simple problems like 5+3 or 8-2
  • Use your fingers: It's okay to use fingers when starting out
  • Practice daily: Even 5-10 minutes each day helps
  • Learn number patterns: Notice how numbers relate to each other
  • Memorize basics: Know doubles facts (2+2, 3+3, etc.)

Remember, everyone learns at their own pace. Mental math gets easier with practice!

Start with one strategy at a time and master it before moving to the next.

Question: When should I use counting on versus making tens? I get confused.

Answer: Here's how to choose the right strategy:

  • Counting On: Use when adding a small number (like +1, +2, +3, +4)
  • Making Tens: Use when the numbers combine to make 10 easily
  • Example for counting on: 15 + 3 → count 16, 17, 18
  • Example for making tens: 8 + 5 → think 8 + 2 = 10, then 10 + 3 = 13

The key is to look at the numbers and ask yourself: "Which strategy will be faster and easier?"

With practice, you'll develop intuition for which strategy works best!

Question: How can I help my child practice mental math at home?

Answer: Here are effective ways to practice mental math at home:

  • Daily practice: Just 10-15 minutes each day is beneficial
  • Real-life situations: "We need 8 apples and already have 3, how many more?"
  • Games and apps: Use math games to make practice fun
  • Flashcards: For building automatic recall of basic facts
  • Encourage thinking aloud: Ask your child to explain their mental process

Focus on accuracy first, then gradually increase speed.

Celebrate progress and be patient - mental math skills develop over time!