Understanding Near Doubles In Mathematics
The near doubles strategy helps students solve addition problems by using doubles facts as a foundation. Instead of starting from scratch, students adjust a familiar doubles fact by adding or subtracting 1. This approach promotes efficient mental math, deepens number sense, and encourages recognition of patterns and relationships between numbers.
For example, to solve 6 + 7, students can think of the near doubles fact 6 + 6 = 12 and then add 1 more to get 13.
Similarly, to solve 8 + 7, students can think of the near doubles fact 8 + 8 = 16 and then subtract 1 to get 15.
This strategy is particularly helpful for problems where the numbers are close in value, making adjustments intuitive.
Why Are Near Doubles Important?
Using Near Doubles To Build Fluency
Near doubles provide a stepping stone from basic addition strategies, such as counting all or counting on, to more advanced mental math. Anchoring their thinking in doubles facts allows students to:
- Solve problems more quickly and confidently.
- Reduce cognitive load, leaving more capacity for solving complex tasks.
Using Near Doubles To Strengthen Number Sense
Near doubles deepen number sense by helping students see numbers as flexible and interconnected. This strategy highlights that numbers close in value are often just 1 apart, making adjustments easier, and patterns in addition can be leveraged to simplify problem-solving.
When students use near doubles, they must think critically about how to adjust doubles facts to fit a new problem. This reasoning process strengthens their ability to justify their approach to solving problems, explain their thinking in terms of patterns and relationships, and build a foundation for more complex strategies, such as compensation and regrouping.
Teaching Strategies For Near Doubles
Introducing the near doubles strategy begins with building a strong foundation in doubles facts. Once students are confident in these, you can guide them to see how near doubles extend this understanding, providing a powerful tool for efficient problem-solving. Effective teaching strategies include using visual models, and highlighting patterns.
Building a Foundation with Doubles Facts
Begin by ensuring students have fluency with doubles facts (e.g., 2 + 2, 3 + 3,…). These facts form the anchor for near doubles. Once students are fluent with doubles, introduce the idea that many addition problems are just “one more” or “one less” than a doubles fact. When they connect near doubles to what they already know, students begin to approach these problems with confidence.
Using Visual Models to Bridge to Near Doubles
Visual models can spark student discovery of the near doubles strategy. Begin by modeling a doubles fact using tools like counters or ten frames. Then, pose an open-ended question to guide students toward making connections. For example:
- Model a Double: Show 6 + 6 = 12 using counters or fill a double ten frame to represent the two groups of 6. Then ask, “What do you notice about these two groups?” Students might identify that the groups are equal or that adding the two groups gives a total of 12.
- Introduce a Near Double: Add one more counter to one group to create 6 + 7. Then ask, “How can we use what we know about 6 + 6 to solve 6 + 7?” Encourage students to explore the relationship and share their reasoning.
- Support Reflection: After students share their thinking, highlight key ideas by saying things like, “So you’re saying that 6 + 7 is just 1 more than 6 + 6! Let’s record that!”
Guiding students to notice and verbalize the connection between doubles and near doubles enables them to actively construct their understanding of the strategy.
Highlighting Patterns in Near Doubles
Patterns provide a natural entry point for students to discover relationships between doubles and near doubles. Instead of explaining the patterns, use examples and prompts to let students uncover them on their own:
- Present examples by writing pairs of problems on the board, such as:
- 6 + 6 = 12 and 6 + 7 = ?
- 7 + 7 = 14 and 7 + 8 = ?
- Pose open-ended questions like, “What do you notice about these problems?” and “How are the doubles and near doubles connected?”
Give students time to discuss and share observations, encouraging them to articulate the pattern.
- Encourage Reasoning: Ask students to explain why the total for a near double is always 1 more (or 1 less) than the double. This step deepens their understanding and strengthens mathematical communication skills.
