Counting on: Starting with the larger number and counting up
- Start with the larger number (6)
- Count up 3 more: 7, 8, 9
- The answer is 9
We start with 6 (the larger number)
Count 3 more: 7, 8, 9
The last number counted is the answer
6 + 3 = 9
• Counting on strategy: Start with the larger number
• Sequential counting: Count each number in sequence
• One-to-one correspondence: Each count represents one added
Making ten: Breaking apart one number to make 10 with the other
8 is close to 10, needing 2 more
5 = 2 + 3 (so we can make 10 with 8)
(8 + 2) + 3 = 10 + 3 = 13
10 + 3 = 13
8 + 5 = 13
• Making ten strategy: Use 10 as a benchmark
• Decomposition: Break apart numbers strategically
• Associative property: Group numbers differently
Doubles plus one: Using a doubles fact and adding one more
4 + 5 is close to 4 + 4
4 + 4 = 8
Since 5 is one more than 4, add 1 to the double
8 + 1 = 9
4 + 5 = 9
• Doubles plus one strategy: Use known doubles facts
• Near doubles: Numbers that differ by 1
• Pattern recognition: See relationships between numbers
Commutative property: Order of addends doesn't change the sum
3 + 7 = 7 + 3 (start with the larger number)
Start at 7 and count 3 more: 8, 9, 10
The last number counted is the answer
3 + 7 = 10
3 + 7 = 10
• Commutative property: a + b = b + a
• Efficiency: Start with the larger number
• Counting on: Sequential counting strategy
Decomposition: Breaking numbers into parts to make addition easier
8 needs 2 more to make 10
6 = 2 + 4 (so we can make 10 with 8)
(8 + 2) + 4 = 10 + 4 = 14
10 + 4 = 14
6 + 8 = 14
• Decomposition strategy: Break numbers into helpful parts
• Make 10 strategy: Use 10 as a benchmark number
• Associative property: Group numbers differently
Number line: Visual tool to represent addition as movement
Begin at 5 on the number line
Move 9 places to the right
The number where you land is the answer
5 + 9 = 14
5 + 9 = 14
• Number line strategy: Visual representation of addition
• Forward movement: Addition moves right on number line
• Sequential counting: Each jump represents one added
Adding Strategies
Practice Makes Perfect
Counting On: Start at 6, count 3 more
Making 10: 8 + 2 = 10, then 10 + 3 = 13
Practice Makes Perfect!
This section provides a comprehensive overview of adding practice problems, including definitions, methods, strategies, and key concepts for 1st grade students.
Addition: Combining numbers to find a total or sum.
Counting On: Starting with the larger number and counting up.
Making Ten: Breaking apart numbers to make 10 with one addend.
Doubles Facts: Addition facts where both addends are the same.
• Always start with the larger number when counting on
• Use 10 as a benchmark number for easier addition
• The sum of two numbers within 20 will never exceed 20
• Order doesn't matter (commutative property)
Counting On: Start with the larger number and count up
Making Ten: Break apart numbers to make 10 first
Doubles Plus One: Use known doubles facts
Number Line: Visual representation of addition
Counting On: 6 + 3 = start at 6, count 3: 7, 8, 9
Making Ten: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13
Doubles Plus One: 4 + 5 = 4 + 4 + 1 = 8 + 1 = 9
Commutative: 3 + 7 = 7 + 3 = 10
• Start with the larger number to minimize counting
• Practice doubles facts regularly (they help with near doubles)
• Use fingers or drawings if needed initially
• Look for numbers that are close to 10
• Starting to count from 1 instead of the larger number
• Miscounting when counting on
• Not recognizing opportunities to make 10
• Forgetting that order doesn't matter
Questions & Answers
Question: I keep getting confused about which number to start counting from. How do I know which number is bigger?
Answer: Great question! Here's how to figure out which number is bigger:
When comparing two numbers:
- Look at single-digit numbers: 9 is bigger than 8, 8 is bigger than 7, etc.
- With double-digit numbers, look at the tens place first: 12 is bigger than 8
- If both numbers have the same tens digit, look at the ones place: 15 is bigger than 13
For addition, always start counting from the larger number. For example, in 4 + 7, start counting from 7 because it's larger than 4. Then count 4 more: 8, 9, 10, 11.
Practice with number lines to see which number comes later - that's the bigger one!
Question: My child seems to struggle with the "making ten" strategy. How can I help them understand this concept better?
Answer: The "making ten" strategy can be challenging at first! Here are ways to help:
- Use concrete objects: Show with counters, blocks, or fingers
- Focus on partners of 10: Practice 1+9, 2+8, 3+7, 4+6, 5+5 until automatic
- Visual aids: Use ten frames or number bonds to show the relationship
- Start simple: Begin with problems like 9 + 2, then progress to 8 + 3, 7 + 4
- Verbalize: Say "9 needs 1 more to make 10" and "I have 2, so 1 goes to make 10, leaving 1"
Emphasize that making 10 creates an easier problem. With consistent practice, children will recognize these patterns automatically. The strategy becomes very powerful once mastered!
Be patient - this concept typically takes several weeks to fully grasp.
Question: What are doubles facts? And why do we need to learn them?
Answer: Doubles facts are addition problems where both numbers are the same! Here are some examples:
Doubles facts: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20
We learn them because they're super helpful! Once you know 5+5=10, you can easily figure out 5+6 (that's just one more, so 11) or 5+4 (that's one less, so 9).
They're like a foundation that helps with other addition problems. When you see 7+8, you might think "I know 7+7=14, and 8 is one more than 7, so the answer is 14+1=15".
Doubles facts are like secret shortcuts that make addition faster and easier!