Making Ten: Break apart one number to complete the other to 10, then add the remainder
- Start with the larger number (8)
- Determine how much more is needed to make 10 (2 more)
- Break apart the second number (5 = 2 + 3)
- Add to make 10, then add the remainder
8 needs 2 more to make 10
5 = 2 + 3
8 + 2 = 10
10 + 3 = 13
8 + 5 = 13
• Decomposition: Breaking apart numbers to make 10
• Associative Property: Grouping numbers differently doesn't change the sum
• Place Value: Understanding tens and ones
Making Ten: Decompose one addend to complete the other to 10
7 needs 3 more to make 10
6 = 3 + 3
7 + 3 = 10
10 + 3 = 13
7 + 6 = 13
• Number Bonds: Understanding part-part-whole relationships
• Decomposition: Breaking numbers into friendly parts
• Regrouping: Reorganizing numbers for easier computation
Making Ten: Use the near ten strategy for efficient addition
9 needs 1 more to make 10
4 = 1 + 3
9 + 1 = 10
10 + 3 = 13
9 + 4 = 13
• Near Ten Strategy: 9 is close to 10, so make it 10
• Compensation: Adjust one number to make computation easier
• Place Value: Understanding tens and ones
Making Ten: Breaking apart one number to complete the other to 10
Number Bonds: Pairs of numbers that add up to a specific total
Decomposition: Breaking numbers into smaller parts
- Identify the larger number: Which addend is closer to 10?
- Determine how much more to make 10: What's needed to reach 10?
- Break apart the other number: Split to provide what's needed
- Add to make 10: Complete the first step
- Add the remainder: Complete the calculation
- Making Ten Strategy: A mental math technique that breaks apart one addend to create a sum of 10 with the other addend, then adds the remaining amount. This strategy leverages the fact that 10 is a "friendly number" that makes calculations easier.
- Number Bonds: Pairs of numbers that add up to a specific total, especially pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5). These are fundamental building blocks for the making ten strategy.
- Decomposition: Breaking apart numbers into smaller, more manageable parts. In making ten, this involves splitting one number into two parts: one that completes the other number to 10, and a remainder.
- Ten Frame: A visual tool with 10 spaces used to represent numbers and show how they relate to 10. This provides a concrete representation of the making ten process.
- Rule 1: Always make one of the numbers equal to 10 by borrowing from the other. This creates a simpler calculation involving 10.
- Rule 2: The total sum remains the same regardless of how numbers are grouped (Associative Property). This allows us to rearrange the numbers for easier computation.
- Rule 3: Use number bonds to 10 as a foundation for the strategy. Knowing these automatically speeds up the process.
- Rule 4: The number 10 is considered a "friendly number" that makes calculations easier due to our base-10 number system.
- Step 1: Look at both numbers in the addition problem and identify them clearly.
- Step 2: Identify which number is closer to 10 (usually the larger number). This will be the number you make into 10.
- Step 3: Determine how many more are needed to make 10 from that number. This requires knowledge of number bonds.
- Step 4: Break apart the second number into two parts: the amount needed to make 10 and the remainder.
- Step 5: Add the first number to the amount needed to make 10, resulting in 10.
- Step 6: Add the remainder to 10 to get the final answer.
- Simple: 9 + 2 → 9 needs 1 more to make 10, so break 2 into 1 + 1 → 9 + 1 = 10, 10 + 1 = 11
- Intermediate: 8 + 5 → 8 needs 2 more to make 10, so break 5 into 2 + 3 → 8 + 2 = 10, 10 + 3 = 13
- Advanced: 7 + 6 → 7 needs 3 more to make 10, so break 6 into 3 + 3 → 7 + 3 = 10, 10 + 3 = 13
- Expert: 6 + 7 → 6 needs 4 more to make 10, so break 7 into 4 + 3 → 6 + 4 = 10, 10 + 3 = 13
- Tip: Practice number bonds to 10 until they become automatic. This is crucial for quick execution.
- Trick: Start with the larger number when possible, as it typically requires less adjustment.
- Pitfall: Forgetting to add the remainder after making 10. This is the most common error.
- Warning: Don't break apart the number incorrectly. Always ensure the two parts add up to the original number.
- Memory Aid: "Make 10 first, then add the rest!" or "What does the first number need to make 10?"
- Takeaway 1: Making 10 simplifies addition problems by creating friendlier numbers to work with.
- Takeaway 2: This strategy builds number sense and mental math skills that transfer to other operations.
- Takeaway 3: It's a foundational strategy that leads to more complex mental math techniques.
• Number Recognition: Identifying which number is closer to 10 and how much more is needed
• Decomposition Skills: Breaking numbers into appropriate parts that serve the strategy
• Regrouping: Reorganizing numbers for easier computation while maintaining the same sum
• Visualization: Using mental or physical models to represent the process and understand the concept
Questions & Answers
Question: Why do we have to make 10? It seems like extra work. Can't I just count all the numbers together?
Answer: Great question! Making 10 is actually a shortcut that becomes more helpful as math gets harder. Here's why it's valuable:
- 10 is a "benchmark" number that's easy to work with mentally
- Once you know how to make 10, you can do addition quickly in your head
- It builds strong number sense and understanding of how numbers work together
- Counting works for now, but making 10 is more efficient as numbers get bigger
For example, with 8 + 5: Instead of counting 8, 9, 10, 11, 12, 13, you can think "8 needs 2 more to make 10, so I take 2 from the 5, leaving 3, then 10 + 3 = 13." Once you practice, this is faster!
This strategy also prepares you for more advanced math in future grades.
Question: My child is struggling with breaking numbers apart. How can I help them develop this decomposition skill?
Answer: Decomposition is a critical skill that takes time to develop! Try these approaches:
- Use manipulatives: Give your child 5 small toys and ask them to split into two groups (2 and 3, 1 and 4, etc.)
- Draw circles: Draw 5 circles and cross out different amounts to show how 5 can be broken into parts
- Real-world examples: "I have 5 cookies, I eat 2, how many are left?" (5 = 2 + 3)
- Number bond diagrams: Show the whole number at the top, parts below in a circle diagram
Start with smaller numbers (up to 5), then gradually work up to 10. Practice number bonds daily: "What goes with 7 to make 10?" (Answer: 3).
Once your child masters decomposing numbers, the making ten strategy will become much clearer. This is foundational work that builds important mathematical reasoning skills.
Question: How do I know when to use the making ten strategy versus other addition strategies? When is it most effective?
Answer: The making ten strategy is most effective for problems where one number is close to 10. Look for these patterns:
- Best cases: 9 + ?, 8 + ?, 7 + ? (where the second number isn't too large)
- Good cases: 6 + ?, 5 + ? (when the other number is large enough to make 10)
- Less effective: 3 + 4, 2 + 5 (both numbers far from 10)
Students should have multiple strategies available and choose the most efficient one for each problem. Making ten is most effective when one addend is 7, 8, or 9, and the other addend is large enough to make 10.
For example: 9 + 4 is perfect for making ten (9 + 1 + 3), but 3 + 4 is better solved by counting on or knowing the fact.