As students share their thinking and write the equations, they begin to learn new facts. In the examples that follow, students work with either cubes or number cards to make 10 with one part given. Centers afford students opportunities to practice by recalling facts, computing mentally, and writing true equations. The centers within our materials play an important role in developing fluency. As displayed below, by Unit 2, students are noticing and using relationships between facts to mentally find differences. Here are some examples of how students continue to practice sums within 10 during warm-up routines throughout Units 1 and 2. To develop fluency within 10, students start with activities where they add or subtract 1 or 2, which not only encourages students to use strategies such as counting on or counting back, but also helps them relate addition and subtraction to counting. The work in this unit allows teachers to assess students’ understanding of addition and subtraction, as well as their fluency with facts within 5, a kindergarten goal. Unit 1 of our Grade 1 course begins with activities and centers focused on addition and subtraction within 10. ![]() ![]() With a foundational understanding of addition and subtraction, students begin to know a few facts. As they hear other students sharing their strategies, they may learn a strategy that is more efficient, and add that strategy to their repertoire. This important step supports students’ development of flexibility. Students are encouraged to use their fingers, counters, or 10-frames to help them determine the parts needed to make 10.ĭuring the synthesis of this activity, it is suggested that teachers highlight the different strategies used based on the given number. They then write an equation for each 10 they make using the frame 10 = _ + _. For example, in Lesson 13, Activity 2, students are given a number less than 10, and work with a partner to determine the part needed to make 10. In Unit 5 of our Kindergarten course, students compose numbers to 10 in ways that make sense to them. The fluency focus of kindergarten is to learn to accurately and efficiently add and subtract within 5, which supports the grade 1 work of composing and decomposing numbers within 10. The foundation for fluently adding and subtracting within 10 is built in kindergarten, when students first learn about the meaning of addition and subtraction through story problems. ![]() Students learn the meaning of the operations and the relationships between them. Let’s look at how students come to know their facts within 10. To better understand the intentional design of the curriculum, we will share how we thought about fluency development in grade 1. This progression develops within and across grade levels.įluency with Addition and Subtraction within 10 ” ( Adding It Up: Helping Children Learn Mathematics from the National Research Council, 2001) In the IM K–5 Math™ curriculum, the representations, strategies, and algorithms that are used are purposefully designed to build a coherent progression where conceptual understanding and procedural fluency develop in parallel. We define procedural fluency as “ using procedures flexibly, accurately, efficiently, and appropriately. ![]() Also included are ways for teachers track and assess students’ math fluency development over the course of the school year. We hope that this series of blog posts serves to bring to light the intentional design that supports students’ progress toward fluency over time, both within and across the grades. The final 2 posts will show the progression of fluency development in multiplication and division. The next post will highlight the development of procedural fluency with addition and subtraction algorithms. This first post is a deep dive into our Grade 1 course to show how students develop addition and subtraction fluency within 10. To outline how the IM K–5 Math™ curriculum focuses on fluency, we have a four-part series of blog posts. We appreciate these questions for a couple of reasons: 1) We took great care in thinking through fluency development in the design of the curriculum, and we are eager to share how we did it, and 2) We realize that the way we have incorporated fluency development is different from most curricula, and it may be difficult to recognize.
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