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 need to make 10? It seems like extra steps. Can't I just count up from the first number?
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 struggles 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: When should I introduce the making ten strategy versus other addition strategies? How do I sequence these skills?
Answer: The sequencing of addition strategies is important for building mathematical understanding:
- Counting All: Initially, students count all objects to find sums
- Counting On: Then they learn to start with one number and count on
- Number Bonds: Develop understanding of how numbers break apart
- Making Ten: Finally, apply this knowledge to make 10 strategically
Introduce making ten after students are comfortable with:
- Basic addition facts to 10
- Understanding that numbers can be broken apart
- Knowing number combinations that make 10
Students should have multiple strategies available and choose the most efficient one for each problem. Making ten is most effective for problems like 8 + 4, 7 + 5, etc., where one number is close to 10.