Two Numbers Together: Compose and Decompose Numbers Up to 10
Item
Title
Two Numbers Together: Compose and Decompose Numbers Up to 10
Abstract/Description
In this unit, students will further extend the idea of seeing a number from multiple perspectives, specifically understanding simultaneously that “two and five is seven” (a composition view) and “seven is two and five” (a decomposition view). Although students have learned the order of numbers up to 10, counting the number of objects up to 10, and reading and writing numerals 1-9, it is also important for students to understand the quantitative relationships among the numbers. For example, if students only know the sequential order of the numbers, they may need to rely heavily upon counting strategies when adding and subtracting numbers. In order for students to be ready for learning basic addition and subtraction, developing a rich number sense based on the understanding of quantitative relationships among the numbers is crucial. More over, this foundation will also be important when students calculate 8+6. For example, students can use the relationships between numbers, 10=8+2 and 6=2+4 when calculating 8+6 e.g. 8+6=8+2+4=10+4=14. This is called, “the making-ten strategy” (1.OA.6) that students should be able to use in Grade 1.
In this unit, students will also learn how the decomposition of numbers can be expressed using equations. For example, students will understand that the decomposition of 8 can be expressed as 8 = 3 + 5 and read it as 8 is 3 and 5. However, the more formal way of reading and writing these equations will be introduced in Unit 5.
In the course of learning numbers and the structure of numbers, it is important for students to think about and visualize numbers through their own “lens” and, by doing so, will enrich their number sense. Teachers need to be careful to not rush into using numerals and doing calculations. By considering the students’ level of understanding, make sure they make connections and transitions smoothly between semi-concrete objects, such as counters, dice, and counting blocks, and more abstract representations, such as ten-frame cards, and numeral cards. Even if the textbook asks, “Five is made up of what numbers?” which prompts students to use a decomposition view, the teacher should consider asking, “ What numbers do we use to make five?” to prompt for the composition view. Decomposition and composition are opposites and their doing-undoing relationship means that asking students to engage in both ways of thinking will ultimately enhance their over-all understanding
In this unit, students will also learn how the decomposition of numbers can be expressed using equations. For example, students will understand that the decomposition of 8 can be expressed as 8 = 3 + 5 and read it as 8 is 3 and 5. However, the more formal way of reading and writing these equations will be introduced in Unit 5.
In the course of learning numbers and the structure of numbers, it is important for students to think about and visualize numbers through their own “lens” and, by doing so, will enrich their number sense. Teachers need to be careful to not rush into using numerals and doing calculations. By considering the students’ level of understanding, make sure they make connections and transitions smoothly between semi-concrete objects, such as counters, dice, and counting blocks, and more abstract representations, such as ten-frame cards, and numeral cards. Even if the textbook asks, “Five is made up of what numbers?” which prompts students to use a decomposition view, the teacher should consider asking, “ What numbers do we use to make five?” to prompt for the composition view. Decomposition and composition are opposites and their doing-undoing relationship means that asking students to engage in both ways of thinking will ultimately enhance their over-all understanding
Author/creator
Date
Resource type
Education/Pedagogical Resource
Pedagogical resource type
en
Lesson Plan/Sequence
Area/Discipline
Math
Intended audience level/student group
P-12
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