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.
Before beginning the activities, your learner should be able to count and write to 20.
Note: The color-coded blocks in this image show addition facts that can be solved using similar strategies.
The Importance of Adding and Subtracting Within 10
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.
Developing Fluency in Adding and Subtracting Within 10
Developing fluency in adding and subtracting involves more than just memorization of facts; it encompasses a deeper understanding of numbers and the relationships between them. Mathematically fluent students not only provide correct answers quickly but also use their knowledge of facts and computation strategies to efficiently solve problems, even those they have not encountered before.
Fluency vs. Memorization: Developing fluency in adding and subtracting is different from rote memorization of arithmetic facts. Fluency implies flexibility and efficiency in calculations. Mathematically fluent students can apply strategies based on their understanding of number relationships.
Extension of Counting: Adding and subtracting within 10 should be introduced as an extension of counting. Students can use strategies like counting on to add and counting back to subtract. However, the ultimate goal is for learners to move beyond these strategies to develop a deeper number sense.
Variety of Tools and Visual Aids: To help learners develop number sense, it's essential to introduce and encourage the use of various tools and visual aids. These may include ten frames, dot cards, strings of beads, connecting cubes, part-part-whole diagrams, number lines, and more.
Exploring Number Relationships: Through the use of these tools and visual aids, students can explore number relationships and understand how numbers can be composed and decomposed. This exploration builds a foundation for fluency in adding and subtracting.
Efficient Calculation Strategies: Fluency involves the ability to choose efficient strategies based on the problem at hand. Some of these strategies include: one more and one less, make ten, doubles and near doubles, applying the commutative property, using the inverse relationship of addition and subtraction.
Build on Finger-Counting: 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.
Key Concepts for Adding and Subtracting Within 10
When teaching this unit, it will be helpful to know the properties of addition and the parts of addition and subtraction equations.
Parts of Addition Equations: Addends are the numbers that are being added together and the sum is the result of adding them. In the equation 5 + 4 = 9, the addends are 5 and 4, while 9 is the sum.
Parts of Subtraction Equations: The minuend is the quantity from which another quantity is to be subtracted. The subtrahend is the quantity that is to be subtracted from the minuend and the difference is the result of subtracting the numbers. In the equation 8 - 2 = 6, the minuend is 8, the subtrahend is 2, and the difference is 6.
Commutative Property of Addition: The commutative property of addition states that the order of the addends can be changed without changing the sum. In other words, when we add two numbers, the result is the same regardless of the order in which we add them. For example, 3 + 2 is equivalent to 2 + 3 because they both have a sum of five.
The Identity Property: The identity property shows that adding 0 to another number or subtracting 0 from another number results in the same number. For example, 5 + 0 = 5 and 5 = 0 = 5.
Structure of Equations: Since both sides of an equation are equal, the equation can be written more than one way. For example, the equation 3 + 2 = 5 has the addends on the left and the sum on the right side. We can also write the same equation as 5 = 3 + 2 with the sum on the left and the addends on the right.
Unit Plan 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.
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 a variety of strategies such as make 10, doubles, and fact families to fluently add and subtract within 10.
Begin by exploring part-whole relationships and exploring properties of numbers. Part-whole relationships refer to understanding how numbers can be broken down into smaller parts or combined to form a whole. By recognizing part-whole relationships, your child will develop a deeper understanding of numbers and their properties.
Here are a few ways to explore number relationships and properties:
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.
Use part-part-whole diagrams (cherry or bar models) to facilitate discussions about number properties. For example, the commutative property shows that changing the order of the addends results in the same sum. The identity property shows that adding 0 to a number results in the same number. Similarly, subtracting 0 from a number results in the same number.
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.
2. Counting On/Back and One More/Less
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. A few fundamental strategies include counting on, counting back, one more, and one less.
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.
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.
4. 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.
5. Addition and Subtraction 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.
Here are a few ways to teach your learner about fact families:
Start by using counters, toys, or story problems to show that addition and subtraction are inverse (opposite) operations. Write equations to demonstrate the relationship between the numbers.
For example: There were 8 crayons in a box. Sally took 2 crayons out, now there are 6 left in the box (8 - 2 = 6). Then, Sally put 2 crayons back in the box with the other 6 crayons (6 + 2 = 8).
Use a number line to visually represent addition and subtraction as moving in opposite directions. Show how adding moves to the right on the number line, while subtracting moves to the left. You can also use part-part-whole diagrams to illustrate addition and subtraction relationships.
Once your learner is comfortable understanding the connection between addition and subtraction, encourage them to use addition facts to solve subtraction equations. 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.
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.
With over 12 years of experience as a classroom teacher, tutor, and homeschool parent, my specialty is easing math anxiety for students of all ages. I'm committed to empowering parents to confidently support their children in math!
