Introduction
This unit plan will introduce your homeschooler to the world of addition and subtraction. They will recognize part-whole relationships, understand the symbols for addition, subtraction, and equality, and learn strategies for adding and subtracting within 10.
Building a Strong Foundation
Before we jump into the lessons, let's discuss why adding and subtracting within 10 is so important for your child's mathematical development.
It's natural for kids to think in terms of 10's due to the familiarity of their own hands. With 10 fingers, children easily visualize and understand groups of 5 and 10, making concepts like addition, subtraction, and even multiplication within 10 more intuitive.
These foundational skills form the building blocks for more complex mathematical concepts, laying the groundwork for future success in math. By mastering how to add and subtract within 10, your child will develop:
- Number Sense: Addition and subtraction help children develop a deep understanding of numbers and their relationships. They learn to recognize patterns, make connections, and develop mental math strategies.
- Problem-Solving Skills: Addition and subtraction provide children with problem-solving tools that they can apply in real-life situations. They learn to analyze problems, think critically, and find solutions using mathematical operations.
- Mathematical Fluency: By practicing addition and subtraction within 10, children become more fluent in their computation skills. Fluency enables them to perform calculations quickly and accurately, leading to increased confidence and efficiency in math.
- Mathematical Communication: Addition and subtraction involve verbal and written expression of mathematical ideas. Teaching your child to communicate their thinking helps them develop their language skills and effectively convey their mathematical reasoning.
Learning Goals for Adding and Subtracting Within 10
The activities in this unit will help your learner develop the following skills:
- Recognize and describe part-whole relationships for numbers up to 10.
- Understand and use the symbols for addition (+), subtraction (-), and equality (=).
- Add and subtract by counting on and counting back within 10.
- Apply the "make 10" strategy to add and subtract.
- Understand and use fact families to solve addition and subtraction problems.
Before beginning the lessons, your learner should be able to recognize, write, and count numbers up to 10.
Teaching Strategies for Adding and Subtracting Within 10
There are several strategies that can be used for teaching your homeschooler how to add and subtract within 10. Start the school year with part-whole relationships and introduce the addition, subtraction, and equal signs. Throughout the school year, allow your learner to explore more strategies, giving them time to develop fluency and become more confident with the skills.
Part-Whole Relationships
Part-whole relationships refer to understanding how numbers can be broken down into smaller parts or combined to form a whole. By recognizing these relationships, your child will develop a deeper understanding of adding and subtracting.
Here are a few ways to support part-whole fluency:
- Number Talks: Engage your child in number talks using manipulatives like Rekenreks or other visual aids. Ask questions such as, "How can we break the number 8 into two parts?" Encourage your child to explore different configurations and explain their thought process.
- Daily Routines and Calendar Activities: Incorporate part-whole fluency into your daily routines and calendar activities. For example, during calendar time, ask your child to identify how many days are left until the end of the week or how many days have passed since the beginning of the month.
- Assess Progress: Assess your child's progress of each strategy throughout the school year. That way, you can adjust the difficulty of their practice problems and know when they are ready to try other strategies.
Counting On and Counting Back
Once your child has developed fluency with part-whole relationships, it's time to introduce basic fact strategies. Basic fact strategies are mental strategies that help children add and subtract within 10 more efficiently. Two fundamental strategies are counting on and counting back.
Here are some examples of each strategy:
- Counting On: The counting on strategy involves starting with a number and counting forward to find the sum. For example, to solve 3 + 2, your child would start with 3 and count forward two more numbers: 4, 5. This strategy is effective when adding 1, 2, or 3.
- Counting Back: The counting back strategy is the inverse of counting on. It involves starting with a number and counting backward to find the difference. For example, to solve 5 - 2, your child would start with 5 and count backward two numbers: 4, 3. This strategy is effective when subtracting 1, 2, or 3.
Doubles and Near Doubles Strategies
Another effective strategy for adding and subtracting within 10 involves finding doubles and near doubles. These strategies will help your child solve problems involving numbers close to each other.
Here are some examples of each strategy:
- Doubles: The doubles strategy involves recognizing that when you add a number to itself, the result is double that number. For example, to solve 3 + 3, your child can recognize that it's the same as doubling 3, which is 6. This strategy is particularly useful for facts like 2 + 2, 3 + 3, and so on.
- Near Doubles: The near doubles strategy is an extension of the doubles strategy, involving adding or subtracting one from a double to find the sum or difference. For example, to solve 3 + 4, your child can recognize that it's the same as 3 + 3 + 1, which is 7. This strategy helps your child build fluency with addition and subtraction facts that are close to doubles.
Make Ten Strategy
Next, you can introduce your learner to the make ten strategy. This strategy involves using number combinations that add up to ten. By recognizing the combinations that make ten, your child can break down larger problems into smaller, more manageable parts.
Try these activities to reinforce the make ten strategy:
- Ten Frame Exploration: Use ten frames to help your child visualize and explore the combinations that make ten. Fill the ten frames with counters and ask your child to identify different ways to arrange the counters to make ten.
- Game-Based Practice: Engage your child in fun games that reinforce the make ten strategy. For example, play "Fill" on an interactive ten frame, where your child fills in the missing spaces to make a total of ten.
- Problem-Solving Scenarios: Present your child with real-life problem-solving scenarios that involve making ten. For example, ask them to determine how many more objects are needed to make a group of ten.
Fact Families
Addition and subtraction fact families consist of related math facts that involve the same set of numbers. For example, we can form a fact family for the numbers 3, 4, and 7 using the following facts: 3 + 4 = 7, 4 + 3 = 7, 7 - 3 = 4, and 7 - 4 = 3.
Fact families help children understand the relationships between addition and subtraction. They are especially helpful when students are first learning to solve subtraction problems by relating the problem to familiar addition facts. For example, to solve 9 - 5, your child can think about the addition fact 5 + _ = 9 and fill in the missing part, which is 4.
Sample Unit Plan for Adding and Subtracting Within 10
Now that we have discussed goals and strategies for adding and subtracting within 10, let’s explore a sample unit plan. The lessons are most effective when incorporated into a daily routine throughout the school year.
1. Introduction to Adding and Subtracting
- Review the concept of part-whole relationships for numbers up to 10.
- Provide students with hands-on materials such as counting blocks or manipulatives.
- Introduce the symbols for addition (+), subtraction (-), and equality (=).
2. Counting On and Back
- Teach your learner how to add by counting on and subtract by counting back.
- Provide problems and activities for your learner to practice these strategies.
3. Using Doubles and Near Doubles
- Teach your learner how to identify doubles and near doubles.
- Demonstrate examples of using doubles and near doubles to add and subtract within 10.
- Provide problems and activities for independent practice.
4. Make 10 Strategy
- Explain the "make 10" strategy for addition and subtraction.
- Show your learner different combinations of numbers that make 10.
- Practice addition and subtraction problems using the "make 10" strategy.
5. Fact Family Relationships
- Introduce the concept of fact families, which are groups of related addition and subtraction facts.
- Practice identifying fact families and solving problems using fact family relationships.
6. Review and Reflection
- Review the key concepts covered during the lessons, allowing your learner to share their experiences and insights.
- Reflect on the strategies learned and discuss when each strategy might be most useful.
Conclusion
Teaching addition and subtraction within 10 is an important milestone in your child's mathematical journey. By focusing on part-whole relationships, basic fact strategies, and problem-solving skills, you can help your child develop a solid foundation in math. Remember to make learning fun and engaging by incorporating games, manipulatives, and real-life scenarios. With your guidance and support, your homeschooler will become a confident and proficient mathematician.
