Decomposing (splitting) a number is a foundational skill in number sense. The mastery of this skill helps students understand that a quantity can be composed of two smaller quantities in different ways. Further, these sets can be arranged in a variety of ways and the sum total is always the same; for example, we can reorder addends and the sum will be the same (4 + 2 = 2 + 4). Students will begin to develop the ability to record the results of compositions and decompositions of sets using equations. This skill lays a firm foundation for understanding of operations and algebraic thinking.
Understanding the Standard:
- Teach the concept of fact families to help students become familiar with common addition and subtraction equations.
- When adding, students can begin to develop the skill of decomposing numbers to find strategic ways to add numbers. For example, they can look for ways to “make 10” in order to make computing sums and differences easier ( if a student wants to add 8 + 6, he can first recognize that 6 = 2 + 4, add 2 to 8 to get 10, and then add 4 to get 14). This can be recorded in drawings or written equations.
- Activities that allow for number exploration are critical. One such way to do this is to give students a set of objects that total no more than 10. Have students find multiple ways to separate those objects into two sets and then ask students repeatedly what the total number of objects is. Students should understand that the total number of objects does not change and should be able to answer the question quickly without having to count all the objects again. From here, they can make addition sentences to represent their findings in writing.
- The use of manipulatives and technologies has a strong influence on their understanding of this skill. Being able to visualize numbers of objects by using coins, blocks, counters, or drawings will help students understand the concept.
- Teachers should also give students a numeral (like 7) and ask students to write the number as a sum of two numbers in different ways. Students can use their own diagrams or manipulatives to solve the problem.
Questions to Focus Instruction:
- When given a set of objects, can students separate that set into two groups and reason that they still have the same amount they originally started with?
- Can students find multiple ways to express a number through 10 as the sum of the quantities in two separate sets?
- Can students express their findings with manipulatives, drawings and number sentences?
Students can count fluently to 10. Given a specific number, they can create a set containing that number of objects. They can add on to a set and explain how the sum total changed or combine two individual sets and see that the total number of objects does not change.
At Grade Level:
Students understand that, for a given number, there are multiple ways to write the number as a sum of two numbers. Students can record these sums in different ways, including pictures and equations.
Students will add and subtract fluently, showing a variety of methods and strategies in computing the sums or differences. Students will work with fact families in subtraction to demonstrate the connection: if 7 + 3 = 10 and 3 + 7 = 10, then 10 - 3 = 7 and 10 - 7 = 3.