Solved Exercises on Addition/Subtraction Charts in Grade 2

Master addition and subtraction within 100: number bonds, fact families, mental math strategies, place value, and visual representations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition Chart Practice
Exercise 1
Use the addition chart to find:
7 + 8 = ? and 9 + 6 = ?
Definition:

Addition Chart: A table showing all possible sums of numbers within a range (typically 0-10 or 0-9)

Addition Chart Method:
  1. Find the first number in the leftmost column
  2. Find the second number in the top row
  3. Follow the row and column until they intersect
  4. The intersection shows the sum
Problem
7 + 8
Result
15
Step 1: Locate 7 in the left column

Find the row starting with 7

Step 2: Locate 8 in the top row

Find the column starting with 8

Step 3: Find the intersection

The cell where row 7 and column 8 meet contains 15

7 + 8 = 15
Final answer:

7 + 8 = 15 and 9 + 6 = 15

Applied rules:

• Commutative Property: 7 + 8 = 8 + 7

• Chart Navigation: Row and column intersection

• Number Bonds: Understanding parts that make up a whole

+
0
1
2
3
4
5
6
7
8
9
0
0
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
10
2
2
3
4
5
6
7
8
9
10
11
3
3
4
5
6
7
8
9
10
11
12
4
4
5
6
7
8
9
10
11
12
13
5
5
6
7
8
9
10
11
12
13
14
6
6
7
8
9
10
11
12
13
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15
7
7
8
9
10
11
12
13
14
15
16
8
8
9
10
11
12
13
14
15
16
17
9
9
10
11
12
13
14
15
16
17
18
2 Subtraction Chart Practice
Exercise 2
Use the subtraction chart to find:
15 - 7 = ? and 12 - 5 = ?
Definition:

Subtraction Chart: A table showing all possible differences within a range (finding the missing addend)

Problem
15 - 7
Result
8
Step 1: Think of subtraction as finding the missing part

15 - 7 = ? means 7 + ? = 15

Step 2: Use addition facts

We know 7 + 8 = 15, so 15 - 7 = 8

Step 3: Verify the answer

Check: 8 + 7 = 15 ✓

15 - 7 = 8
Final answer:

15 - 7 = 8 and 12 - 5 = 7

Applied rules:

• Fact Families: Addition and subtraction are inverse operations

• Missing Addend: Subtraction finds the unknown addend

• Verification: Always check by adding back

7 + 8 = 15
8 + 7 = 15
15 - 7 = 8
15 - 8 = 7
3 Fact Family Relationships
Exercise 3
Complete the fact family for numbers 6, 9, and 15:
? + ? = ?, ? + ? = ?, ? - ? = ?, ? - ? = ?
Definition:

Fact Family: A group of related addition and subtraction facts using the same three numbers

Numbers
6, 9, 15
Family
4 facts
Step 1: Identify the largest number

15 is the largest number, so it's the sum in addition facts

Step 2: Write the two addition facts

6 + 9 = 15 and 9 + 6 = 15 (commutative property)

Step 3: Write the two subtraction facts

15 - 6 = 9 and 15 - 9 = 6

Step 4: Verify all facts

All four facts use only the numbers 6, 9, and 15

6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, 15 - 9 = 6
Final answer:

Fact family: 6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, 15 - 9 = 6

Applied rules:

• Fact Family Rule: 3 numbers make 4 related facts

• Commutative Property: Order doesn't matter in addition

• Inverse Operations: Addition and subtraction undo each other

6 + 9 = 15
9 + 6 = 15
15 - 6 = 9
15 - 9 = 6
Rules and methods, laws,...
a + b = c → c - a = b
Inverse Operations
Commutative
a + b = b + a
Order doesn't matter
Associative
(a + b) + c = a + (b + c)
Grouping doesn't matter
Identity
a + 0 = a
Adding zero doesn't change
Key definitions:

Addition: Combining two or more numbers to get a total

Subtraction: Taking away one number from another

Fact Family: Related addition and subtraction facts using the same numbers

Mental Math Strategies:
  1. Counting On: Start with larger number and count up
  2. Make Ten: Use ten as a benchmark (7 + 5 = 7 + 3 + 2 = 10 + 2 = 12)
  3. Decompose: Break numbers apart (15 - 7 = 15 - 5 - 2 = 8)
  4. Fact Families: Use known addition facts for subtraction
Tip 1: Use doubles facts (6 + 6 = 12) to help with near-doubles (6 + 7 = 13).
Tip 2: Always check subtraction by adding back (15 - 7 = 8, so 8 + 7 = 15).
Tip 3: Look for patterns in addition charts to memorize facts faster.
Solution: Exercises 4 to 5
4 Place Value Strategy
Exercise 4
Solve using place value:
24 + 35 = ? and 56 - 23 = ?
Definition:

Place Value: Each digit has a value based on its position (tens, ones)

Problem
24 + 35
Break Down
20+4+30+5
Result
59
Step 1: Separate tens and ones

24 = 20 + 4 and 35 = 30 + 5

Step 2: Add tens together

20 + 30 = 50

Step 3: Add ones together

4 + 5 = 9

Step 4: Combine results

50 + 9 = 59

24 + 35 = 59
Final answer:

24 + 35 = 59 and 56 - 23 = 33

Applied rules:

• Place Value: Tens added to tens, ones to ones

• Regrouping: When ones exceed 9, regroup to tens

• Subtraction: Same principle but with borrowing if needed

5 Number Bonds and Compensation
Exercise 5
Use compensation strategy:
38 + 27 = ? and 63 - 19 = ?
Definition:

Compensation: Adjust one number to make calculations easier, then adjust the answer

Problem
38 + 27
Compensate
40 + 25
Result
65
Step 1: Round one number to make it easier

Round 38 up to 40 (added 2), so subtract 2 from 27 to get 25

Step 2: Add the rounded numbers

40 + 25 = 65

Step 3: Verify the result

38 + 27 = 65 ✓

Step 4: For subtraction, add to make it easier

63 - 19: Think of it as 63 - 20 + 1 = 43 + 1 = 44

38 + 27 = 65
Final answer:

38 + 27 = 65 and 63 - 19 = 44

Applied rules:

• Compensation: Keep the equation balanced by adjusting both sides

• Rounding: Make numbers friendlier for mental math

• Verification: Always check by using another method

Add list of laws, methods, rules, definitions, expressions,.... Generate well SEO title for this section
a + b = b + a
Commutative Property
Key definitions:

Addition: Combining quantities to find a total

Subtraction: Finding the difference or missing part

Fact Family: Four related addition/subtraction facts using the same numbers

Complete methodology:
  1. Identify the operation: Determine if adding or subtracting
  2. Choose a strategy: Counting on, making ten, place value, or compensation
  3. Apply the method: Follow the steps of the chosen technique
  4. Verify the result: Check by using inverse operation
Tip 1: Practice number bonds to 10 (pairs that add to 10) to make calculations faster.
Tip 2: Use a hundreds chart to visualize addition and subtraction patterns.
Tip 3: Always check subtraction by adding your answer to the smaller number.
Tip 4: Look for doubles and near-doubles to speed up mental math.
Common errors: Forgetting to carry/borrow, misreading charts, mixing up addition/subtraction.
Exam preparation: Memorize addition facts to 20, practice fact families, work with place value.
Properties to know by heart:

• Commutative: a + b = b + a

• Identity: a + 0 = a

• Inverse: a + b = c means c - a = b

• Associative: (a + b) + c = a + (b + c)

Exercise with Visualization: Number Patterns
Exercise 6: Pattern Recognition
Observe patterns in addition:
Adding 10: 5, 15, 25, 35...
Adding 9: 5, 14, 23, 32...
Adding 11: 5, 16, 27, 38...

Analysis: Recognizing patterns helps with mental math and understanding number relationships.

  • Adding 10: Only tens place changes
  • Adding 9: Like adding 10 then subtracting 1
  • Adding 11: Like adding 10 then adding 1

Questions & Answers

Question: I don't understand why 7 + 8 = 15 and 8 + 7 = 15 are the same. Why does the order matter?

Answer: Great observation! Actually, the order doesn't matter in addition because of something called the commutative property. Let me explain:

  • Think of having 7 apples and getting 8 more. You now have 15 apples.
  • If you had 8 apples and got 7 more, you still have 15 apples.
  • The total amount doesn't change based on which number you start with.

This is different from subtraction where 8 - 7 ≠ 7 - 8. With addition, you're just combining amounts, so it doesn't matter which number comes first.

Example: 5 + 3 = 8 and 3 + 5 = 8. Both give you 8!

Question: When I do 15 - 7, I sometimes forget how to find the answer. How can I remember?

Answer: Here are several helpful strategies for subtraction like 15 - 7:

  • Think of addition: Ask yourself "7 + ? = 15". Since 7 + 8 = 15, then 15 - 7 = 8.
  • Count up: Start at 7 and count up to 15: 8, 9, 10, 11, 12, 13, 14, 15. That's 8 counts.
  • Use fact families: Remember that 7, 8, and 15 form a fact family: 7 + 8 = 15, 8 + 7 = 15, 15 - 7 = 8, 15 - 8 = 7.

Practice with smaller numbers first, then work up to larger ones. The more you practice, the more automatic it becomes!

Tip: Always check by adding back: 8 + 7 = 15 ✓

Question: I see patterns in the addition chart but I'm not sure how to use them. What patterns should I look for?

Answer: Great question! There are many useful patterns in addition charts:

  • Diagonal pattern: Numbers along the diagonal (0+0, 1+1, 2+2...) are doubles (0, 2, 4, 6, 8...).
  • Row/column symmetry: Each row and column is symmetrical due to the commutative property.
  • Increasing pattern: Moving right or down increases by 1 each step.
  • Adding 10 pattern: When adding 10, only the tens digit changes.

These patterns help you memorize facts faster. For example, if you know 6 + 4 = 10, you automatically know 4 + 6 = 10 too!

Practice finding these patterns in the chart - they'll make mental math much easier!